Federal Funds Target Rate Surprise and Equity Duration/67531/metadc... · Tee, Kienpin. Federal...
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APPROVED: Naranjan Tripathy, Major Professor Ian Liu, Committee Member Robert Pavur, Committee Member Mazhar Siddiqi, Committee Member Marcia Staff, Chair of the Department of Finance, Insurance, Real Estate, and Law O. Finley Graves, Dean of the College of Business Mark Wardell, Dean of the Toulouse Graduate School FEDERAL FUNDS TARGET RATE SURPRISE AND EQUITY DURATION Kienpin Tee, BIT, MS Dissertation Prepared for the Degree of DOCTOR OF PHILOSOPHY UNIVERSITY OF NORTH TEXAS May 2013
Transcript of Federal Funds Target Rate Surprise and Equity Duration/67531/metadc... · Tee, Kienpin. Federal...
APPROVED: Naranjan Tripathy, Major Professor Ian Liu, Committee Member Robert Pavur, Committee Member Mazhar Siddiqi, Committee Member Marcia Staff, Chair of the Department of Finance, Insurance, Real Estate, and Law O. Finley Graves, Dean of the College of
Business Mark Wardell, Dean of the Toulouse
Graduate School
FEDERAL FUNDS TARGET RATE SURPRISE AND EQUITY DURATION
Kienpin Tee, BIT, MS
Dissertation Prepared for the Degree of
DOCTOR OF PHILOSOPHY
UNIVERSITY OF NORTH TEXAS
May 2013
Tee, Kienpin. Federal Funds Target Rate Surprise and Equity Duration. Doctor of
Philosophy (Finance), May 2013, 100 pp., 30 tables, 1 figure, references, 51 titles.
In this paper I use an equity duration framework to develop and empirically test the
hypothesis that returns on growth stock portfolios react more strongly to Federal Funds target
rate change announcements, as compared to value stock portfolios. When I decompose the
Federal Funds rate change, I find that portfolio returns are only sensitive to rate shocks, as
opposed to the predictable component of rate change.
Since growth stocks are expected to have higher duration than value stocks, I further
explore the well documented polarity between value and growth stocks, by examining the
interest rate sensitivities of portfolios that diverge along four fundamental-to-prices ratios:
dividend yield, book-to-market value, earnings-to-price and cashflows-to-price. In each case, I
find that price reactions are more pronounced for portfolios with high growth characteristics. I
also document that portfolio returns react asymmetrically to positive and negative target rate
surprises, and that this reaction is conditional on the state of business cycles - periods of
economic expansions and recessions.
To improve the robustness of my results, several statistical applications have been
applied. First, I include Newey-west estimators to examine significant levels of regression
estimates. Second, I check if there is any contemporaneous correlation across target rate shocks
by applying ARIMA tests, and to overcome the problem resulted from serial correlation of target
rate shocks, I substitute white noise residuals from the regressions on the rate shocks for target
rate shocks to be new exogenous variables.
ii
Copyright 2013
by
Kienpin Tee
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ACKNOWLEDGEMENTS
Many people deserve my unyielding gratitude for making possible this dissertation and
the ultimate completion of my doctorate degree.
First I must thank my dissertation chair, Dr Naranjan Tripathy, for his remarkable support
and careful supervision to guide me through the dissertation process. I sincerely appreciate Dr
Tripathy for being a dedicated mentor during my time at the doctoral program. I also would like
to thank my committee members, Dr Steve Cole, Dr Ian Liu, Dr Robert Pavur, and Dr Mazhar
Siddiqi, for their insightful feedbacks and inspiring discussions.
I must also thank my colleagues and other staffs in FIREL department. Thank for your
friendship, encouragement and support.
Lastly, I would like to express my gratitude to my family members. In particular, I would
like to thank my wife, Xiaoshu Li, for her limitless understanding, sacrifice and love. I am
thankful to my lovely nine-month old boy for always cheering me up with his sunny smiles.
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TABLE OF CONTENTS
Page ACKNOWLEDGEMENTS ……………………………………………………………….. ........ iii
LIST OF TABLES ………………………………………………………………………… ....... vii
LIST OF FIGURES ………………………………………………………………………... ..... viii
CHAPTER 1 INTRODUCTION …………………………………………………………... .........1
1.1 Background …………………………………………………………………….. .........1
1.2 Purpose of Study ……………………………………………………………..… .........2
CHAPTER 2 LITERATURE REVIEW …………………………………………………… .........5
2.2 Shock in Federal Funds Target Rate …………………………………………… .........5
2.3 Equity Duration …………………… …………………………………………... .........6
2.4 Equity Duration using Dividend Discount Model ……………………………… ........8
CHAPTER 3 DATA AND METHODOLOGY …………………………………………… ......13
CHAPTER 4 EMPIRICAL RESULTS ……………………………………………………. .......21
4.1 Federal Funds Rate Surprises and Stock Returns ……………………………… .......21
4.2 Equity Duration based on Federal Funds Rate Surprises ………………………........22
4.3 Asymmetric Effects of Surprise Signs …………………………………..…….. ........31
4.4 Equity Duration of Surprise Signs based on Federal Funds Rate Surprises ……. ......34
4.5 Asymmetric Reaction of Surprise Signs and Business Cycles ………….……… ......44
4.6 Equity Duration of Surprise Signs and Business Cycles based on Federal Funds Rate
Surprises ………………...……………… .......…………………………………..49
4.7 Robustness Test: White Noise Residuals of Target Shock ………………….….. ......62
4.8 Robustness Test: Federal Funds Rate Surprises based on White Noise Residuals. ....65
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4.9 Robustness Test: Equity Duration of Federal Funds Rate Surprises based on White
Noise Residuals …………………………………...………………………… ......67
4.10 Robustness Test: Asymmetric Effects of Surprise Signs based on White Noise
Residuals …………………………………………………………………..... ......72
4.11 Robustness Test: Equity Duration of Different Surprise Signs based on White
Noise Residuals ………………………………………………………....….. .......74
4.12 Robustness Test: Asymmetric Effects of Surprise Signs and Business Cycles
based on White Noise Residuals ………………………………………....… .......80
4.13 Robustness Test: Equity Duration of Surprise Signs and Business Cycles based
on White Noise Residuals …………………………………………………. ........82
CHAPTER 5 DISCUSSIONS AND CONCLUSIONS …………………………………… ........94
REFERENCES ……………………………………………………………………………… .....97
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LIST OF TABLES
Page Table 3.1 Distributions of Sample Firms and 171 Observations of Fed Funds Target
Announcements..................................................................................................................14
Table 4.1: The Response of Equity Prices to Federal Funds Rate Changes, by Industry Portfolios and by Market Indexes ......................................................................................................23
Table 4.2: The Response of Equity Prices to Federal Funds Rate Changes, by Portfolios based on Fundamental-to-Price Ratios ............................................................................................24
Table 4.3: Wald Test - Sensitivity of Stock Prices to Target Changes Surprises, by Portfolios based on Fundamental-to-Price Ratios .............................................................................27
Table 4.4: Paired Difference Test - Response of Stock Prices to Target Changes Surprises, by Portfolios based on Fundamental-to-Price Ratios .............................................................30
Table 4.5: Asymmetric Response of Equity Prices to Positive and Negative Surprises, by Industry Portfolios and by Market Indexes .......................................................................33
Table 4.6: Asymmetric Response of Equity Prices to Positive and Negative Surprises, by Portfolios based on Fundamental-to-Price Ratios .............................................................35
Table 4.7: Wald Test - Sensitivity of Stock Prices to Negative & Positive Target Changes Surprises, by Portfolios based on Fundamental-to-Price Ratios .......................................38
Table 4.8: Paired Difference Test - Sensitivity of Stock Prices to Negative & Positive Target Changes Surprises, by Portfolios based on Fundamental-to-Price Ratios ........................42
Table 4.9: Asymmetric Response of Equity Prices to Different Business Cycles, by Industry Portfolios and by Market Indexes .....................................................................................46
Table 4.10: Asymmetric Response of Equity Prices to Different Business Cycles, by Portfolios based on Fundamental-to-Price Ratios .............................................................................51
Table 4.11.1 & 4.11.2: Wald Test - Sensitivity of Stock Prices to Negative & Positive Target Changes Surprises during different business cycles, by Portfolios based on Fundamental-to-Price Ratios. ..................................................................................................................53
Table 4.12.1 & 4.12.2: Paired Difference Test - Sensitivity of Stock Prices to Negative & Positive Target Changes Surprises during different business cycles, by Portfolios based on Fundamental-to-Price Ratios. ......................................................................................58
Table 4.13: ARIMA Procedure of White Noise Residuals Derivation .........................................63
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Table 4.14: The Response of Equity Prices to White-Noise Residuals of Surprises and Expected components of the target rate changes, by Industry Portfolios and by Market Indexes ...66
Table 4.15: The Response of Equity Prices to White-Noise Residuals of Surprises and Expected components of the target rate changes, by Portfolios based on Fundamental-to-Price Ratios ................................................................................................................................68
Table 4.16: Wald Test - Sensitivity of Stock Prices to White-Noise Residuals of Surprises, by Portfolios based on Fundamental-to-Price Ratios .............................................................70
Table 4.17: Paired Difference Test - Response of Stock Prices to White-Noise Residuals of Surprises, by Portfolios based on Fundamental-to-Price Ratios .......................................71
Table 4.18: Asymmetric Response of Equity Prices to Positive and Negative Surprises, by Industry Portfolios and by Market Indexes .......................................................................73
Table 4.19: Asymmetric Response of Equity Prices to Positive and Negative White-Noise Residuals of Surprises of the target rate changes, by Portfolios based on Fundamental-to-Price Ratios .......................................................................................................................75
Table 4.20: Wald Test - Sensitivity of Stock Prices to Negative & Positive White-Noise Residuals of Surprises, by Portfolios based on Fundamental-to-Price Ratios ..................76
Table 4.21: Paired Difference Test - Sensitivity of Stock Prices to Negative & Positive White-Noise Residuals of Surprises, by Portfolios based on Fundamental-to-Price Ratios . 78-79
Table 4.22: Asymmetric Response of Equity Prices to Different Business Cycles, by Dividend Yield Portfolios .................................................................................................................81
Table 4.23: Asymmetric Response of Equity Prices to White-Noise Residuals of Surprises during Different Business Cycles, by Market Indexes and by Portfolios based on Fundamental-to-Price Ratios ...................................................................................................................84
Table 4.24.1 & 4.24.2: Wald Test - Sensitivity of Stock Prices to Negative & Positive White-Noise Residuals of Surprises during different business cycles, by Portfolios based on Fundamental-to-Price Ratios ............................................................................................86
Table 4.25.1 & 4.25.2: Paired Difference Test - Sensitivity of Stock Prices to Negative & Positive White-Noise Residuals of Surprises during different business cycles, by Portfolios based on Fundamental-to-Price Ratios .............................................................90
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LIST OF FIGURES
Page
Figure 3.1: Graphical Distribution of the Actual Changes in Federal Funds Target Rates & the Corresponding Unanticipated Changes of Target Rates ....................................................17
1
CHAPTER 1
INTRODUCTION
1.1 Background
This paper presents evidence that changes in Federal Funds rate have effects on equity
returns, and that these effects are more pronounced on growth stocks as compared to value
stocks. This is part of a broader concern that has a long history in academic literature: the impact
of the Federal Reserve’s monetary policy on financial markets. The chairman of the Federal
Reserve, Ben Bernanke, said “the most direct and immediate effects of monetary policy actions,
such as changes in the Federal Funds target rate, are on the financial markets”. This paper does
discover that an increase (decrease) in the Federal Funds target rate results in negative (positive)
portfolio returns.
This study recognizes that if Federal Funds target rate change can be anticipated, then it
should have no impact on assets prices. When I decompose the Federal Funds rate change to its
predictable and unpredictable components, I find that portfolio returns are more sensitive to rate
change shocks than they are to unadjusted rate change. The predictable component of rate
change has no effect on portfolio returns. My results are consistent with Bernanke and Kuttner
(2005) who also report the effects of unanticipated monetary policy actions of stock prices.
However, Bernanke and Kuttner (2005) only focus on the price reactions of broad based equity
portfolios. I use an equity duration framework to extend the analysis of stock price reaction to
Federal fund rate shocks by segmenting portfolios, based on their inherent levels of interest
sensitivity.
According to discounted cash flow models employed by several studies of equity
duration, firms with cash flows weighted more toward the future have high fundamental-to-price
2
ratios (growth firms), while firms with cash flows weighted more the present have low
fundamental-to-price ratios (value firms) 1. Similar to the characteristics of long-term bonds,
growth firms are high duration assets while value firms are low duration assets. Dechow, Sloan
and Soliman (2004) provide analytical proof that growth stocks have higher duration than value
stocks. Further, Campbell and Mei (1993) and Cornell (1999) show that growth companies have
high betas because of their higher cash flow risks and higher duration of these cash flows.
Following Cochrane (1999) and Lettau and Watcher (2007), who also study interest sensitivity of
stock prices, I differentiate equity portfolios along the growth-value axis through four
fundamental-to-prices ratio: dividend yield, book-to-market value, earnings-to-price, and
cashflows-to-price. In each case, I find that price reactions are more pronounced for portfolios
with low fundamental-to-prices characteristics (growth stocks). I also find strong evidence of
asymmetric price reaction to the signs (positive or negative) of the target rate shocks, and this
reaction is conditional to business cycles.
1.2 Purpose of Study
While previous studies have examined the equity duration effects in response to Federal
Funds rate change, my paper makes the following contributions. First, compared to other studies
that use unadjusted changes in interest rate, this paper uses the unanticipated changes in Federal
Funds target rates and applies an event study approach to examine the impact of monetary policy
on stock prices 2. In doing so, this paper provides a better understanding of the effects monetary
policy change on equity duration in the context of an informationally efficient market.
1 See Casabona, Fabozzi, and Francis (1984), Leibowitz et al (1989), Blitzer and Dash (2004), and Dechow, Sloan and Soliman (2004). 2 Smirlock and Yawitz (1985) find that stock prices respond only to unexpected changes in monetary policy, therefore using raw target changes might bias the impact of target rate change on asset pricing.
3
Second, those studies that do analyze equity price sensitivity to Federal Funds or interest
rate shocks, either ignore the variation in duration-type risk across portfolios, or report
conflicting results in support of it. Using sensitivity tests, Bernanke and Kuttner (2005) and Garg
(2008) find little evidence in support of the impact of unexpected monetary policy actions across
industry-based portfolios. While Thorbecke (1997) finds that small firms stocks are more
sensitive to monetary shocks than stocks of large firms, Guo (2004) shows that the size effect is
mostly concentrated during adverse business conditions. As noted earlier, my paper employs the
shocks in Federal Funds target rates to examine interest rate sensitivity across portfolios with
varying ratios of fundamental-to-prices, including ratios of dividend-to-price, book-to-market,
earnings-to-price, and cashflows-to-price 3.
Third, this paper examines whether portfolio returns react asymmetrically to positive and
negative target rate surprises, and whether this reaction is conditional on the state of business
cycles. There is some evidence to suggest that stock prices react differently to bad and good
news (Koutmos (1998, 1999)). Lobo (2000) found that stock market participants tend to discount
bad news more vigorously and more quickly, thereby reducing the observed impact of the news
when it does arrive. Chulia, Martens and Dijk (2010) use high-frequency intraday data and find
that the response of positive surprise (bad news for the stocks) is larger and that in case of bad
news the mere occurrence of a surprise matters most. My results show that asymmetric equity
price response to positive and negative rate surprises is dependent on whether the economy is in
a recession or expansion. Specifically, I find that during economic contraction, only positive rate
3 Stattman (1980), Rosenberg, Reid and Lanstein (1985), and Fama and French (1992) document a positive relation between average return and book-to-market ratio. Basu (1983) finds a positive relation between average return and E/P. Rozeff (1984), Shiller (1984), Flood, Hodrick, and Kaplan (1986), Campbell and Shiller (1987), and Fama and French (1988) also find evidence supporting D/P forecasts returns. Basu (19770, Jaffe, Keim, and Westerfield (1989), and Davis (1994) find evidence of the relation between cash flow yield and subsequent returns. They provide some evidences of growth stock characteristics on stocks with lower ratio of price-to-cash flows
4
surprises have significant price reaction, while during economic expansion, only negative rate
surprises have significant price reaction. The evidence of cyclical variation in the response of
stocks to rate increase or decrease should be useful to guide to Federal policymakers in setting or
signaling target rates.
Fourth, to improve the robustness of statistical results, several innovative statistical
methods have been applied to the study of equity duration. Newey-west estimators were added,
in addition to the common t-statistics, to examine the significant level of regression estimates in
the change of target rates. The measure reduces the possibility of type 1 error, especially in time
series regression estimates. To check if there is any contemporaneous correlation across target
rate shocks, ARIMA tests were applied to the time series of interest rate shocks. Besides that, to
overcome the problems resulted from serial correlation on target rate shocks, white noise
residuals from the regressions on the rate shocks were substituted for the target rate shocks.
These white noise residuals become new exogenous variables.
5
CHAPTER 2
LITERATURE REVIEW
2.1 Shock in Federal Funds Target Rate
Given that an increase in the Federal Funds target rate signals an immediate increase in
market interest rates, then, based on discounted cash flow model one would expect a fall in asset
prices. Yet evidence supporting this view is inconclusive.4 Cook and Hahn (1989) find a strong
response in the 1970s, but regressions using data from the 1980s and 1990s show little, if any,
impact of Federal policy on interest rates. Roley and Sellon (1995), for example, conclude that
‘‘although casual observation suggests a close connection, the relationship between Federal
actions and long-term interest rates appears much looser and more variable’’. Theories such as
the present value of future cash flows [Presented by Crowder (2006)] about stock price valuation
also suggest that contractionary monetary policy will lower stock prices and vice versa.
However, this posited negative relationship may be offset by changes in the money demand,
since lower company earnings are associated with lower money demand and correspondingly, a
lower interest rate, positing a positive relationship.
These studies, however, did not distinguish between anticipated and unanticipated
announcements. In fact based on the findings of this paper, the results turn out to be more
interesting, once the two are differentiated. Smirlock and Yawitz (1985) find that stock prices
respond only to unexpected changes in monetary policy, therefore using raw target changes
might bias the impact of target rate change on asset pricing.
Also, according to some studies, unanticipated policy changes affect the stock market
more than anticipated ones due to the market's "forward looking" nature. These studies
decompose the target change into an unanticipated component (shock) and an anticipated 4 See evidence presented in Kuttner (2001).
6
component. The anticipated component is estimated using the price of Federal Funds futures
contracts, which is assumed to embody expectations of the effective Federal Funds rate,
averaged over the settlement months. Krueger and Kuttner (1996) found that the Federal Funds
futures rates yielded efficient forecasts of Funds rate changes. Kuttner (2001) subsequently used
these futures data to estimate the response of the term structure to monetary policy. He separates
changes in Funds target rate into anticipated and unanticipated components and finds that interest
rates’ response to anticipated target rate changes is small, while their response to unanticipated
changes is large and highly significant.
Bernanke and Kuttner (2005) later performed an extensive analysis of the impact of
Federal Fund rate changes on equity prices. They found that the effects of unanticipated
monetary policy actions on expected excess returns account for the largest part of the response of
stock prices, and that a hypothetical unanticipated 25-basis-point cut in the Federal Funds rate
target is associated with about a 1% increase in broad stock indexes.
2.2 Equity Duration
Several earlier researchers also examine equity duration by using the various proxies for
the discount rates. Chance (1982) uses different interest rate series to examine equity duration
and finds inconsistent results across different series. Campbell and Shiller (1989) apply two
nominal discount rates (the annualized 30-day Treasury bills rate and the growth rate in
aggregate per capita consumption of nondurables and services) and one real discount rate (the
squared ex post annual real return of US stock index). Lobo (2002) applies interest rate surprises
constructed from survey data and changes in the 3-month T-bill yield to examine stock market
reactions. These studies on equity duration, however, do not use target changes of the Federal
7
Funds rates 5 , as a proxy for the changes in discount rates. This paper, on the other hand,
proposes to extend the equity duration framework to studying the impact of monetary-policy-
induced interest rate shocks on stock price. To this end, the anticipated and unanticipated
components of Federal Funds rates changes are to be incorporated as proxies for interest rates.
Further, some studies do examine the shock effect in Federal Funds target rates using
methods other than gauging market expectation from Federal Funds future contracts but
consistently experience difficulty in drawing accurate shocks in Federal Funds rates changes.
Bernanke and Blinder (1992), Campbell and Ammer (1993), and Gao (2004) employ VAR
(vector autoregression) models that could potentially produce biased results6. More specifically,
VAR models always involve non-practical assumptions have been identified by many
literatures.7 Using the futures contract approach followed by Kuttner (2001) avoids the problems
associated with the VAR approach.8 Some other papers apply survey-based methods to estimate
the market expectation on the fund target rates. This measure of target rate surprises, again, is
theoretically less robust than the approach suggested by Kuttner (2001). The survey target
represents only a subset of the entire market participants and the survey results do not actually
reflect the market expectation as a whole. Meanwhile the expected component of the release is
5 Bernanke and Blinder (1992) show that the funds rate is a good indicator of monetary policy action. 6 Conventional VAR specifications often produce some empirical puzzles. These puzzles can be grouped into four categories. In the liquidity puzzle positive monetary policy shocks, the innovations in monetary aggregates (such as M1, M2 ...), are associated with increases rather than decreases in nominal interest rates. In the price puzzle, the monetary policy shocks, the innovations in interest rates, are linked with increases rather than decreases in the price level. In the exchange rate puzzle, positive monetary policy shocks, the innovations in interest rates, are associated with an effect of depreciation rather than appreciation of the exchange rate. 7 See Kim and Roubini (2000) and Parrado (2001) 8 Some early authors also analyzed stock market reactions to the innovation in aggregate money (M1). However, as pointed out by Cornell (1983), I cannot draw any conclusive inference from those results because they are consistent with a host of hypotheses. In contrast, the unexpected change in the Federal Funds rate target has a natural interpretation as an innovation in monetary policy. There is a caveat though: Stock prices fall after a monetary tightening may also reflect the fact that investors interpret the money tightening as a rise in future inflation (Romer and Romer [2000]). However, many papers find that a monetary tightening strengthened the U.S. dollar in the foreign exchange markets during both periods, which is inconsistent with the anticipated inflation hypothesis. Also, it is not clear why inflation has asymmetric effects on stocks of different sizes.
8
incorporated in the Federal Funds futures prices available immediately before the
announcement.9
In summary, this research aims to estimate the effect of changes in Federal Reserve
policy on a spectrum of equity prices, using the Federal Funds futures data to distinguish the
anticipated from the unanticipated changes in the fund rate target. In particular, an equity
duration model is used to examine interest rate sensitivity of cross-sectional portfolios with
varying ratios of prices to fundamentals, including ratios of book-to-market value, price-to-
earning, price-to-dividends, and cash flows-to-price. The study assumes that changes in the
Federal Funds target rate is the unique factor that impacts equity duration. Changes are that other
contemporaneous factors could be associated with the Federal Funds rate announcement, and
these could confound my analysis. To mitigate such problem, a short (one-day) window event
study is applied throughout the entire paper.
2.3 Equity Duration using Dividend Discount Model
According to the cash flow discounted model, firms with cash flows weighted more
toward the future (growth firms) endogenously low high fundamental-to-price ratios, while firms
with cash flows weighted more toward the present (value firms) have high fundamental-to-price
ratios. Similar to the characteristics of long-term bonds, growth firms are high duration assets
while value firms are low duration assets.
The central idea of this argument is that the effect of interest rate changes on growth
stocks would appear to operate through the discounted cash flow mechanism. Since the greater
portion of the growth stock’s return is in the distant future, its present value will experience
9 Chun (2006) shows that the forecasts of the Federal Funds rate extracted from the Federal Funds futures prices are more accurate than survey forecasts.
9
greater absolute fluctuations with changes in the discount rate, which is presumed to be
influenced by interest rates. On the other hand, value stocks would be less volatile with respect to
interest rate movements. The sensitivity of stock price to interest rate change has fortunately
been recognized as the duration effect.10
The essential concept of duration, which was developed by Macaulay in 1938, is defined
as the weighted average of the times of receipts from an investment where the weights are equal
to the present values of the payments. Duration effectively measures the sensitivity of an
investment value to changes in the discount rate in the perfect-certainty cash flow (DCF) model.
While most of the early works on duration applied the concept to the analysis of fixed-interest
bonds, some researchers have attempted to apply duration to equity. This effort has, for the first
time, been completed by Casabona et al (1984) using a single constant growth rate for dividends
in the DCF model (the Gordon-Shapiro model). The application of equity duration in the real
world, however, is far from widespread. The reasons for this are: first, unlike plain bonds, the
terminal value of equities is not fixed; and second, interest payments of plain bonds are
predetermined and known in advance. Dividend payments of equities are not as certain.
The earliest literature on this topic was Gordon’s dividend discount model, which values
a stock based on its estimated dividend, the equity discount rate (k), and the dividend growth rate
(g). Casabona, Fabozzi, and Francis (1984) derive equity duration from first principles as simply
1/(k-g). The solution is intuitive — this is the average age of a perpetuity whose payout grows at
a rate of g per year, and is discounted at a rate of k.
Following Gordon’s dividend discount model and the framework of Casabona, Fabozzi,
and Francis (1984), Blitzer and Dash (2004) propose a simple model to describe the relationship
between asset values and a discount rate shock. Like Gordon’s model, dividends are assumed to 10 See Casabona, Fabozzi, and Francis (1984), and Blitzer and Dash (2004).
10
be paid consistently over an infinite period and taxation is ignored. This research applies the
model of Blitzer and Dash (2004) and extends the analysis based on the ratios of fundamental-to-
prices while using the shocks of Federal Funds target rate changes as proxies for discount rate
changes.
Let us review the model of Blitzer and Dash (2004) by looking at the equity valuation
embodied in Gordon’s dividend discount model.
𝑉 = 𝐷𝑘−𝑔
(1)
where V is the value of the stock, D is the next period dividend payment (a known constant), k is
the equity discount rate, and g is the dividend growth rate.
From (1), take the first derivative of V with respect to k,
𝜕𝑉𝜕𝑘
=−𝐷
(𝑘 − 𝑔)2
From (1), take the first derivative of V with respect to g,
𝜕𝑉𝜕𝑔
=𝐷
(𝑘 − 𝑔)2
From (1), take log on both sides,
ln(𝑉) = ln(𝐷) − ln (𝑘 − 𝑔)11
Then taking the derivative with respect to the discount rate, k,
1𝑉�𝜕𝑉𝜕𝑘� = −1
(𝑘−𝑔) (1 − 𝜕𝑔𝜕𝑘
) (2)12
According to the definition of duration, discount rate sensitivity of an equity share
investment is defined as:
𝐷𝑈𝑅𝐴𝑇𝐼𝑂𝑁𝑒 =−𝜕𝑉𝜕𝑘
∗1𝑉
11 This equation follows Equation #9 in Blitzer & Dash (2004) 12 Equation (2) follows Equation #10 in Blitzer & Dash (2004)
11
Since the left-hand term of Equation (2) follows the definition of duration, the right-hand
term must also represent equity duration.
In this research, because an instantaneous change in stock return (one-day window) is
being used, a change of dividend growth rate in response to a change of discount rate within such
a short window is extremely minimal. If I assume that the sensitivity of g with respect to k, 𝜕𝑔𝜕𝑘
, is
zero, then the equity duration model is:
𝐷𝑈𝑅𝐴𝑇𝐼𝑂𝑁𝑒 =1
(𝑘 − 𝑔)
The equation implies that equity duration is equal to the Price-Dividend ratio because
𝑉𝐷
=1
(𝑘 − 𝑔)
So 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑌𝑖𝑒𝑙𝑑 = 𝑘 − 𝑔 = 1/𝐷𝑈𝑅𝐴𝑇𝐼𝑂𝑁𝑒 (3)
According to this Equation (3), I would expect low dividend yield (growth) stock to be
more sensitive to a change in the discount rate than high dividend yield (value) stock. Past
studies have extended the concept of duration and employ other measures to differentiate the
cross section of stock returns between value and growth stocks.
Berk, Green, and Naik (1999) decompose the value of an asset into an asset in place and
a growth option and show that acquiring an asset with low systematic risk shrinks the firm’s
book-to-market ratio and lowers its future returns. Berk and Green (2004) value a firm with large
research and development expenses and show how the discount rate and cash flow risk interact
to produce risk premia that change over the project life cycle. Their model endogenously
generates a long duration for growth stocks. Leibowitz and Kogelman (1993) employ the
sensitivity of the value of long-run cash flows to discount rates and reconcile various measures
of equity duration. Bernanke and Gertler (1989, 1994) prove that the amplification effect of the
12
premium on external Funds is negatively related to firms’ net worth. Dechow, Sloan, and
Soliman (2004) measure cash flow duration of both value and growth stocks and find that growth
stocks have higher duration than value stocks, resulting in higher betas of the growth stocks.
Santos and Veronesi (2004) propose a model that connects time variation in betas to time
variation in expected returns through the method of duration, and show that beta variation exist
across industry portfolios. Campbell and Vuolteenaho (2004) decompose the market risk into
news about cash flows and news about discount rates. They find that growth stocks have higher
beta with respect to discount rate news than do value stocks, consistent with the view that growth
stocks have higher duration.
Collectively, the above cited prior research shows that discount rate risk is crucial in asset
pricing models, and that growth stocks, which are considered high-duration assets, react more
strongly to such discount rate risk. The current research extends the work on previous literature
by employing the shocks in Federal fund target rates to examine interest rate sensitivity across
portfolios with varying ratios of prices to fundamentals. In particular, this research will extend
Equation (3) to apply to other measures of cash flow fundamentals, namely earning yield (E/P),
the ratio of cash flow to prices (C/P), and the book-to-market ratio (B/M).
13
CHAPTER 3
DATA AND METHODOLOGY
The data set for this research consists of the meeting dates and subsequent monetary
policy announcements from the Federal Open Market Committee (FOMC) website. For the
purpose of this study, I include a meeting date regardless of whether or not the FOMC meeting
actually resulted in a rate change announcement. The fact that the FOMC decides not to change
the target rate can surprise the money market and may cause the movement in asset prices.
Federal Funds futures rates are obtained from Bloomberg, daily stock returns of NYSE, AMEX,
and Nasdaq from CRSP, and financial data such as annual dividends, cash flows, earnings, and
book values from COMPUSTAT. As the operators in utility industries are regulated by Public
Utility Commission in such a way that the rates they could charge their customers are regulated
and adjusted according to the operators’ accounting costs and cost of capital, this industry is thus
somehow immune to or little affected by changes in monetary policy13. Firms of the utility
industry (SIC code 4900-4949)14 are excluded from the sample firms.
In Table 3.1, panel A shows the distribution of sample firms from year 1990 to 2008.
Throughout the 19-year sample periods, the ratio of the number of non-utility firms to that of
utility firms increases gradually from approximately 21-to-1 in year 1990 to the peak of 43.67-
to-1 in year 2001, primarily due to reducing number of utility firms. The ratio then consistently
ranges between 41-to-1 and 43-to-1 throughout the period of 2002 till 2008.
13 See Sanyal and Bulan (2010), Jamison (2008), and Lazar (2011). 14 The sic codes are based on industry portfolios constructed from CRSP returns as in Fama and French (1988) and the data are available from French’s web page.
14
Table 3.1: Distributions of Sample Firms and 171 Observations of Fed Funds Target Announcements
Tables below document the distributions of sample firms and the 171 observations of Fed Funds Target Announcements. Panel A records the distribution of utility and non-utility firms from year 1990 to 2008. Panel B records the distribution of 171 observations of Fed Funds target announcements, by raw target rate change (2nd column), by rate change shock (3rd column), by rate change shock during expansions (4th column), and by rate change shock during recessions (5th column). Panel C records the distributions of the events in rate change surprise for both expansion (table on the left) and recession (table on the right) periods. In both tables under Panel C, there are 13 distinct events and the surprise sign of each event is recorded in 4th column.
Panel A Year 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
Non-Utility 1813 1818 1820 1815 1816 1813 1817 1815 1825 1835 1848 1870 1871 1873 1877 1875 1874 1874 1875 Utility 177 173 172 178 178 182 179 182 173 164 152 131 131 130 127 130 132 133 133
Total Firms 3941 4089 4352 4806 5362 5691 5806 6133 6152 6022 5978 5852 5613 5559 5538 5593 5618 5601 5601
Panel B
Event Number of Target Rate Change
Number of Rate Change Shock
Number of Rate Change Shock During Expansion
Number of Rate Change Shock During Recession
Positive 31 46 40 6 Negative 45 73 56 17 No Change 95 52 47 5 Total 171 171 143 28
Panel C
Expansion Periods
Recession Periods Event Sign Frequency Probability
Event Sign Frequency Probability
Rate Up < Exp Up
Neg
ativ
e
7 4.90%
Rate Up < Exp Up
Neg
ativ
e
0 0.00% Rate Down > Exp Down 19 13.29%
Rate Down > Exp Down 14 50.00%
Rate Down < Exp Up 0 0.00%
Rate Down < Exp Up 1 3.57% Rate Down < Exp Unchg 0 0.00%
Rate Down < Exp Unchg 0 0.00%
Rate Unchg < Exp Up 30 20.98%
Rate Unchg < Exp Up 2 7.14% Rate Up > Exp Up
Posi
tive
13 9.09%
Rate Up > Exp Up
Posi
tive
0 0.00% Rate Up > Exp Down 0 0.00%
Rate Up > Exp Down 0 0.00%
Rate Up > Exp Unchg 0 0.00%
Rate Up > Exp Unchg 0 0.00% Rate Down < Exp Down 4 2.80%
Rate Down < Exp Down 5 17.86%
Rate Unchg > Exp Down 23 16.08%
Rate Unchg > Exp Down 1 3.57% Rate Up = Exp Up
NIL
11 7.69%
Rate Up = Exp Up
NIL
0 0.00% Rate Down = Exp Down 1 0.70%
Rate Down = Exp Down 1 3.57%
Rate Unchg = Exp Unchg 35 24.48%
Rate Unchg = Exp Unchg 4 14.29%
Total 143 100.00%
Total 28 100%
• “Rate” represents the actual target rate movement. “Exp” represents the market expectation.
15
Following Kuttner (2001), Federal Funds futures prices are used to gauge Federal Funds
target rate shocks. Because the Federal fund futures market was not operational till 1989, the
dataset covers only post-1989 period. On 12 December 2008, FOMC decided to establish a target
range for the Federal Funds rate of 25 basis points to 0 – 0.25 percent. Since such a narrow target
range is not appropriate for the estimation of the unanticipated component of the Federal Funds
target, my sample period is Jan 1990 to Oct 2008.
Ten portfolios are constructed and sorted by four ratios of fundamental-to-price at the end
of the previous year. The ratios are: dividend yield (D/P), book-to-market ratio (B/M), earning
yield (E/P), and cashflows-to-price (C/P).
For each monetary policy announcement, the surprise component of the change in the
Federal Funds target rate is measured using Federal Funds futures. Kuttner (2001) and Guo
(2004) show that expected changes in policy should have little or no effect on asset prices. In
order to measure of the impact of monetary policy surprises, most studies such as Cook and
Hahn (1989), Bernanke and Kuttner (2005), Bredin, Gavin and O’Reilly (2003) employ event-
study approach and the FOMC meeting dates as event windows.
Following Bernanke and Kuttner (2005), Kuttner (2001) and Poole and Rasche (2000), I
use changes in the Federal Funds futures rate are used as estimates of the Federal Funds target
rate shocks. The Federal Funds futures rate is defined as 100 minus the price of a futures
contract. As suggested by Kuttner (2001), the anticipated and unanticipated components of a
FOMC decision on the Federal Funds target is derived from the change in the futures contract’s
price relative to the day prior to the policy action. For an event taking place on day t of month n,
the unexpected, or “surprise” target rate change is calculated as the change in the “spot-month”
16
(the month in which the target is changed) futures contract rate on the day of the rate change,
which is then multiplied by the number of the days in the month affected by the change:
∆�̃�𝑢 =𝑚
𝑚− 𝑡(𝑓𝑛,𝑡
0 − 𝑓𝑛,𝑡−10 )
where ∆�̃�𝑢 is the unanticipated target rate change, 𝑓𝑛,𝑡0 is the spot-month futures rate on day t of
month n, and m is the number of days in the month. In the case where the rate change occurs on
the first day of the month, 𝑓𝑛,𝑡−10 becomes 𝑓𝑛−1,𝑚
1 , the latter denotes the one-month futures rate
from the last day of the previous month.
After the unexpected target rate change is computed, the expected component of the rate
change ∆�̃�𝑡𝑒 is derived by subtracting the unanticipated change from the actual ∆�̃�:
∆�̃�𝑡𝑒 = ∆�̃� − ∆�̃�𝑡𝑢
Figure 3.1 plots the graph of both the actual changes in target rates and the corresponding
unanticipated changes of target rates from 1990 to 2008. Triangle symbols represent the actual
target changes and plus symbols represent the corresponding shocks. From the graph, it is
observed that most shocks fall between the ranges of (-20 bp, +20 bp). From year 2004 to 2006,
the shocks are close to zero, however, showing that the market is better able to anticipate
monetary policy changes during this period.
17
Figure 3.1: Graphical Distribution of the Actual Changes in Fed Funds Target Rates & the Corresponding Unanticipated Changes of Target Rates
-100.0
-80.0
-60.0
-40.0
-20.0
0.0
20.0
40.0
60.0
80.0
100.0
8/30/1989 5/26/1992 2/20/1995 11/16/1997 8/12/2000 5/9/2003 2/2/2006 10/29/2008Rate
(bp)
Actual Target Rate vs Target Rate Shock (in Basis Point)
Target Surprise Actual Change
18
Setting the timing right is critical for event-study analysis. Before 1994, the FOMC did
not explicitly announce changes in its target Federal Funds rates. When the Federal established
its current policy of announcing changes in the target rate, market participants generally became
aware of policy actions on the day after the FOMC’s decision. That is, the decisions of FOMC
were implicitly transferred to money markets via the size and type of open market operation.
Following Rudebusch (1995), most pre-1994 rate changes were assigned to the date of the
Desk’s implementation, which are typically those of the next open market operation following
the FOMC decision.
The policy of announcing target rate changes, which began in February 1994, the Federal
Reserve started to announce its intention to change the Funds rate target on the day of its
decision. Such change eliminates virtually all of the timing ambiguity associated with rate
changes in the earlier part of the sample. Moreover, because the change in the target rate is
usually announced prior to the close of the futures market, the closing futures price generally
incorporates the day’s news about monetary policy. The only exception is October 15, 1998,
when a 25-basis-point rate cut was announced after the close of the futures markets. In this case,
the difference between the opening rate on the 16th and the closing rate on the 15th is used to
calculate the surprise. For the purpose of this paper, the relevant sample of events is defined as
those days when the Funds target rate was changed, and days corresponding to FOMC meetings.
The 17 September 2001 observation is excluded from the analysis, as that day’s rate cut occurred
on the first day of trading following the September 11 terrorist attacks. There are also 20
unscheduled FOMC meetings that usually produce larger impacts on stock market, and 7
simultaneous unemployment report releases that occurred prior to year 2004. While several
previous papers exclude the sample of unscheduled meetings and of simultaneous factors, I
19
conduct my tests with and without these events, and found that excluding these subsample from
does not significantly change my estimate results15. The final sample contains 171 observations.
Panel B of Table 3.1 shows that throughout the 19-year sample period, FOMC increased
the target rates 31 times, decreased it 45 times, and left it unchanged 95 times. However, when I
collectively decompose the target rate change announcements, I obtain 46 positive target rate
surprises, 73 negative target rate surprises, and 52 no surprises. Since a relatively larger part of
my sample period covered economic expansion, I do have a higher number of the rate change
announcements occurring during economic expansion (143) compared to economic contractions
(28). However, when I compare the distribution of positive, negative, and no interest rate
surprise across the two business cycles, I find that recessionary period contain a relatively higher
frequency of negative rate surprise – suggesting that the Federal takes more aggressive rate
reduction measures during recessions. The possibility the Federal takes a more interventionist
stance during recessions, may also be inferred by the lower relative frequency of no surprises (5
out of 28) during such periods.
In Panel C of Table 3.1, I further breakdown my events frequencies to see if I can
determine whether the market validates or contradicts the Federal’s intent, and compare these
distributions across the two business cycles. If the rate shock is in the same direction as the rate
change announcement, I interpret it as a validation, and if it is otherwise, I interpret it is a
contradiction of the Federal’s intent. While the sample sizes for such scenarios within each
business cycle are too small to make valid statistical comparisons, it appears that there is a
tendency for the market to validate the Federal’s move to decrease rates during recessions, and to
some extent, contradict such a move during expansion. Another interesting observation is that
during expansions, a relatively high percentage (32.87%) of the target rate changes is completely 15 The subsample test is not shown in the paper. The results could be obtained from the author upon request.
20
anticipated (no shock) by the market, while such event only happens 17.86% of the times during
recessions. This again could underscore the Federal’s intent to take more aggressive recovery
measures during recessions.
21
CHAPTER 4
EMPIRICAL RESULTS
4.1 Federal Funds Rate Surprises and Stock Returns
Table 4.1 and Table 4.2 present the following two OLS regression results of equity stock
prices reaction to the 171 observations of the changes in Federal Funds target rates:
𝑅𝑡 = 𝛼 + 𝛽𝑟𝑎𝑤∆𝑟𝑡𝑟𝑎𝑤 + 𝜀𝑡 (4)
where 𝑅𝑡 is the one-day stock return on the announcement day of Federal Funds target change
and ∆𝑟𝑡𝑟𝑎𝑤 is the raw change in Federal Funds target rates; and:
𝑅𝑡 = 𝛼 + 𝛽𝑒∆�̃�𝑡𝑒 + 𝛽𝑢∆�̃�𝑡𝑢 + 𝜀𝑡 (5)
where ∆�̃�𝑡𝑒 is the expected change in Federal Funds target rates and ∆�̃�𝑡𝑢 is the unexpected
change in Federal Funds target rates.
The responses of ten industry portfolios16 and three market portfolios, including the value
weighted (VW), equally weighted (EW), and S&P500 (SP) indices, are reported in Table 4.1.
From Model A, the industries that display the strongest response to the raw changes in Federal
Funds rates are “Durable” and “Wholesale/Retail”. Among the three market indexes, only EW
responds significantly to the raw changes (𝛽𝑟𝑎𝑤) in Eq. (4). All coefficients indicate that a
negative relation exists between stock return and change in Federal Funds rate but the low R-
squares across all regressions (way below five percent level) give little evidence to support such
relation. Further examination shows that the stock price reactions are small and insignificant
across all industries and market indexes. Plus, the zero R-square on portfolio “Utilities” seems to
support my reason of excluding utility industry from my stock sample in the following tests. That
16 10 industry portfolios are constructed from CRSP returns as in Fama and French (1988).
22
is, utility industry is immune to a change in Federal funds target rate. Newey-west statistics,
which represent more conservative estimates, confirm the above results.
When the target rate change is broken down into its expected and surprise components
(Model B), a significant negative relation appears between stock return and unanticipated change
in Federal Funds rate. All portfolios confirm that only unanticipated components (𝛽𝑢 ) in the
target rate decisions matter while the expected target rate (𝛽𝑒) changes do not. Not only the
estimators, 𝛽𝑢s, are also greater in magnitudes and more significant than the estimators, 𝛽𝑟𝑎𝑤s,
reported in Model A, the R-squares from Eq. (5) are almost twice as large compared to those
from Eq. (4).
4.2 Equity Duration based on Federal Funds Rate Surprises
I run the same two regressions on ten portfolios constructed and ranked on the basis of
selected fundamental-to-price characteristics. Estimates associated with portfolios ranked on the
basis of dividend-to-price (DP), book-to-market (BM), earnings-to-price (EP), and cashflows-to-
price (CP) ratios are presented in panels A, B, C, and D of Table 4.2, respectively. In each panel,
portfolio ranking are ordered from the smallest (P1) to the largest (P10) ratios. The purpose of
this design is to differentiate each set of portfolios along the growth-value polarity, such that
portfolios with lower fundamental-to-price ratios (P1, P2) would capture the characteristics of
growth stocks, while portfolios with higher fundamental-to-price ratios (P10, P9) would capture
the characteristics of value stocks. Based on my hypotheses, I expect growth stock portfolios
(P1,P2), or portfolios with higher duration will exhibit greater price sensitivity to Federal Funds
rate shocks, relative to those exhibited by the value stock portfolios (P10, P9).
23
Table 4.1: The Response of Equity Prices to Federal Funds Rate Changes, by Industry Portfolios and by Market Indexes The following table shows the results of 1-day equity return of 10 industry portfolios on changes in the Federal funds rate (Model A), and on the surprises and expected components of the target rate changes (Model B). The 10 industry portfolios are constructed based on SIC code as in Fama & French (1988). The last three categories record the price response of three market indexes: VW and EW are the value-weighted and equal-weighted market portfolios, respectively, and S&P500 is the index portfolio of S&P 500. The models are estimated for individual stocks in AMEX, NYSE, and Nasdaq following 171 FOMC meetings between Jan 1990 and Oct 2008. Average coefficient estimates and R-square values are shown across all portfolios. The asterisks of ***, **, and * represent t-statistical significance at the 1%, 5%, and 10% level, respectively, based on the standard errors given in parentheses. The plus signs of +++, ++, and + represent Newey-West statistical significant at the 1%, 5%, and 10% level, respectively, based on Newey-West standard errors. Model A 𝑅𝑡 = 𝛼 + 𝛽𝑟𝑎𝑤∆𝑟𝑡𝑟𝑎𝑤 + 𝜀𝑡
Model B 𝑅𝑡 = 𝛼 + 𝛽𝑒∆�̃�𝑡𝑒 + 𝛽𝑢∆�̃�𝑡𝑢 + 𝜀𝑡
Model A: Raw funds rate changes Model B: Anticipated and unanticipated components Portfolio α βraw R2 α βe βu R2 Non-Durable 0.1730 *** +++ -0.3463
0.0122 0.1618 *** +++ -0.2114
-0.7247
0.0161
(0.0574)
(0.2395) (0.0591)
(0.2918)
(0.5247)
Durable 0.2355 *** +++ -0.9239 *** +++ 0.0472 0.1874 ** +++ -0.3420
-2.5563 *** + 0.0861
(0.0765)
(0.3192) (0.0772)
(0.3817)
(0.6863)
Manufacturing 0.2507 *** +++ -0.5643 * ++ 0.0221 0.2286 *** +++ -0.2972
-1.3136 **
0.0324
(0.0692)
(0.2888) (0.0710)
(0.3507)
(0.6307)
Energy 0.1882 ** +++ -0.3237
0.0046 0.1859 ** +++ -0.2966
-0.3997
0.0046
(0.0881)
(0.3676) (0.0908)
(0.4488)
(0.8069)
High Tech 0.3131 *** +++ -0.8851 * 0.0204 0.2484 ** ++ -0.1032
-3.0787 ***
0.0534
(0.1131)
(0.4722) (0.1147)
(0.5666)
(1.0189)
Telecommunication 0.2126 ** ++ -0.8685 ** + 0.0232 0.1533
-0.1522 -2.8780 ***
0.0560
(0.1039)
(0.4336) (0.1053)
(0.5203)
(0.9356)
Wholesale/Retail 0.2623 *** +++ -0.8631 *** ++ 0.0417 0.2187 *** +++ -0.3367
-2.3398 *** + 0.0739
(0.0763)
(0.3184) (0.0773)
(0.3821)
(0.6871)
Healthcare 0.1961 ** +++ -0.3134
0.0054 0.1692 ** ++ 0.0121
-1.2265 *
0.0174
(0.0786)
(0.3281) (0.0806)
(0.3981)
(0.7159)
Utilities 0.1231 ** ++ 0.0015
0.0000 0.1473 ** ++ -0.2906
0.8210
0.0187
(0.0567)
(0.2367) (0.0579)
(0.2863)
(0.5147)
Others 0.2130 *** +++ -0.5324 ** +++ 0.0330 0.1896 *** +++ -0.2498
-1.3252 ***
0.0522
(0.0531) (0.2218) (0.0543) (0.2681) (0.4821) VW 0.2791 *** +++ -0.5469 + 0.01365 0.23783 *** ++ -0.0479 -1.9469 ** 0.03724
(0.0857)
(0.3576)
(0.0873)
(0.4314)
(0.7756)
EW 0.2122 *** +++ -0.6209 ** ++ 0.0294 0.17643 *** +++ -0.1889
-1.8327 *** 0.05896
(0.0657)
(0.2744)
(0.0668)
(0.3298)
(0.5931)
S&P500 0.2615 *** +++ -0.5182
0.01131 0.23125 ** ++ -0.1531
-1.5426 * 0.02296 (0.0893) (0.3728) (0.0916) (0.4524) (0.8135)
24
Table 4.2: The Response of Equity Prices to Federal Funds Rate Changes, by Portfolios based on Fundamental-to-Price Ratios The following table shows the results of 1-day equity return on changes in the Federal funds rate (Model A), and on the surprises and expected components of the target rate changes (Model B). The models are estimated for individual stocks in AMEX, NYSE, and Nasdaq following 171 FOMC meetings between Jan 1990 and Oct 2008. Average coefficient estimates and R-square values are shown across all portfolios. The asterisks of ***, **, and * represent t-statistical significance at the 1%, 5%, and 10% level, respectively. The plus signs of +++, ++, and + represent Newey-West statistical significant at the 1%, 5%, and 10% level, respectively, based on Newey-West standard errors. Panel A records the price response of three market indexes: VW and EW are the value-weighted and equal-weighted market portfolios, respectively, and S&P500 is the index portfolio of S&P 500. Panel B records the price response of 10 portfolios sorted by dividend yield (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). Panel C records the price response of 10 portfolios sorted by book-to-market ratio. Panel D records the price response of 10 portfolios sorted by earnings-to-price ratio. Panel E records the price response of 10 portfolios sorted by cashflows-to-price ratio. Model A 𝑅𝑡 = 𝛼 + 𝛽𝑟𝑎𝑤∆𝑟𝑡𝑟𝑎𝑤 + 𝜀𝑡 Model B 𝑅𝑡 = 𝛼 + 𝛽𝑒∆�̃�𝑡𝑒 + 𝛽𝑢∆�̃�𝑡𝑢 + 𝜀𝑡
Model A: Raw funds rate changes Model B: Anticipated and unanticipated components Portfolio α βraw R2 α βe βu R2
Pane
l A: D
ivid
end
Yie
ld P1 0.2946 *** +++ -0.8235 ** +++ 0.0351 0.2522 *** +++ -0.311
-2.2612 *** 0.0633
P2 0.2664 *** +++ -0.7371 ** +++ 0.0373 0.2428 *** +++ -0.4517
-1.5377 ** 0.0489 P3 0.2302 *** +++ -0.515 * + 0.0192 0.2165 *** +++ -0.3488
-0.9814
0.0233
P4 0.235 *** +++ -0.4568 * + 0.0189 0.2161 *** +++ -0.2283
-1.098 ** 0.0287 P5 0.2281 *** +++ -0.4532 * ++ 0.022 0.2115 *** +++ -0.2534
-1.0138 ** 0.0309
P6 0.2076 *** +++ -0.4433 * ++ 0.02 0.1956 *** +++ -0.2977
-0.852
0.0245 P7 0.208 *** +++ -0.3059
0.0115 0.1892 *** +++ -0.0794
-0.9416 ** 0.0246
P8 0.1363 *** +++ -0.212
0.0082 0.1232 *** +++ -0.0547
-0.6533 * 0.0176 P9 0.1243 *** +++ -0.4271 ** ++ 0.0305 0.1116 ** +++ -0.2741
-0.8562 ** 0.0386
P10 0.1081 * ++ -0.4845 ** + 0.0225 0.0942 + -0.3164 -0.9563 * 0.0282
Pane
l B: B
ook-
to-m
arke
t P1 0.2766 *** +++ -0.6834
0.0145 0.2099 ** + 0.1217
-2.9421 *** 0.0561 P2 0.2646 *** +++ -0.8231 ** ++ 0.0271 0.21 ** ++ -0.1643
-2.6714 *** 0.0631
P3 0.252 *** +++ -0.6546 * + 0.0213 0.2122 ** ++ -0.1733
-2.0047 *** 0.0453 P4 0.2711 *** +++ -0.6851 ** ++ 0.0256 0.2345 *** +++ -0.243
-1.9254 *** 0.0478
P5 0.2579 *** +++ -0.7323 ** ++ 0.0347 0.2277 *** +++ -0.3676
-1.7553 *** 0.0526 P6 0.2309 *** +++ -0.6468 ** ++ 0.032 0.2039 *** +++ -0.3206
-1.562 *** 0.0488
P7 0.222 *** +++ -0.5752 ** ++ 0.0263 0.192 *** +++ -0.2133
-1.5907 *** 0.0479 P8 0.2165 *** +++ -0.4856 * + 0.0219 0.1917 *** +++ -0.1861
-1.3261 ** 0.0392
P9 0.2081 *** +++ -0.3942
+ 0.0147 0.196 *** +++ -0.2479
-0.8045
0.0189 P10 0.2763 *** +++ -0.7928 *** +++ 0.0489 0.2377 *** +++ -0.3256 -2.1035 *** + 0.0842
25
Pa
nel C
: Ear
ning
s-to
-pric
e
P1 0.2802 *** +++ -0.6449 *
0.0174 0.2149 ** ++ 0.1434
-2.8566 *** 0.0715 P2 0.2497 *** +++ -0.6559 * + 0.022 0.2077 ** ++ -0.1487
-2.0791 *** 0.0492
P3 0.2618 *** +++ -0.528 * + 0.0162 0.2306 *** +++ -0.1504
-1.5874 ** 0.0334 P4 0.263 *** +++ -0.5244 * ++ 0.0186 0.2413 *** +++ -0.2625
-1.259 ** 0.0283
P5 0.251 *** +++ -0.569 ** ++ 0.0256 0.2306 *** +++ -0.3227
-1.2599 ** 0.0356 P6 0.2223 *** +++ -0.5368 ** ++ 0.0227 0.1972 *** +++ -0.2336
-1.3877 ** 0.0377
P7 0.2301 *** +++ -0.5529 ** ++ 0.0281 0.2112 *** +++ -0.3253
-1.1915 ** 0.038 P8 0.2406 *** +++ -0.5747 ** ++ 0.0298 0.2166 *** +++ -0.2847
-1.3884 ** 0.0455
P9 0.2515 *** +++ -0.6426 ** +++ 0.0374 0.2276 *** +++ -0.3536
-1.4533 *** 0.053 P10 0.2458 *** +++ -0.6016 ** ++ 0.0272 0.2235 *** +++ -0.3322 -1.3573 ** 0.0385
Pane
l D: C
ashf
low
s-to
-pric
e P1 0.2106 *** +++ -0.668 ** ++ 0.0319 0.1713 ** +++ -0.1931
-2.0005 *** 0.0654 P2 0.2106 *** +++ -0.5793 ** ++ 0.0282 0.179 *** +++ -0.1971
-1.6518 *** 0.0538
P3 0.223 *** +++ -0.5439 ** ++ 0.0251 0.1949 *** +++ -0.2047
-1.4956 *** 0.0453 P4 0.2577 *** +++ -0.4358
+ 0.015 0.227 *** +++ -0.0653
-1.4753 ** 0.0376
P5 0.2412 *** +++ -0.5619 * ++ 0.0199 0.2141 *** +++ -0.2339
-1.4821 ** 0.034 P6 0.2975 *** +++ -0.6344 ** ++ 0.0243 0.2644 *** +++ -0.2354
-1.7537 *** 0.0442
P7 0.2594 *** +++ -0.6798 ** ++ 0.0267 0.2218 *** +++ -0.2249
-1.9561 *** 0.0516 P8 0.275 *** +++ -0.5974 * ++ 0.0217 0.2458 *** +++ -0.2452
-1.5854 ** 0.0374
P9 0.2737 *** +++ -0.7292 ** ++ 0.0329 0.2438 *** +++ -0.3676
-1.7435 *** 0.0497 P10 0.232 *** +++ -0.6866 ** +++ 0.0327 0.206 *** +++ -0.3728 -1.5669 ** 0.0469
26
(6)
Taken as a whole, results in panels A, B, C, and D are qualitatively similar to the full
sample results in the ten industry portfolios and the three market portfolios (Table 4.1) in the
following ways. (1) when target rate change is decomposed into an expected and surprise
component, only the surprise component (𝛽𝑢 ) has a significant and negative effect on portfolio
returns, (2) expected component (𝛽𝑒) has no effect on portfolio returns, (3) 𝛽𝑢 estimates are
predominantly greater in magnitudes and significance compared to the 𝛽𝑟𝑎𝑤 estimates, and (4)
R-squares from Eq. (5) are always larger compared to those from Eq. (4).
A unique finding from panels A, B, C, and D is that the sensitivity of stock price
reactions decreases gradually from growth stocks (P1) to value stocks (P10). This pattern is more
pronounced when portfolio returns are regressed on the Federal Funds rate shocks (𝛽𝑢 ). I further
investigate if growth stocks, which are considered high-duration assets, react more strongly to
such discount rate risk. These results are presented in Table 4.3 and Table 4.4.
Following Guo (2004) who applies Wald test to examine the difference in stock reaction
to target changes between small and big stocks, I estimate an equation system of two portfolios
using seemingly unrelated regression (SUR) to investigate whether the reaction to target rate
changes by growth stocks portfolios (P1, P2) and value stocks portfolios (P10, P9) are
statistically different. The model is shown as follows:
∆𝑃𝑡,𝑖 = 𝛼𝑖 + 𝛽1𝑖 ∗ ∆�̃�𝑡𝑒 + 𝛽2𝑖 ∗ ∆�̃�𝑡𝑢 + 𝜀𝑡,𝑖
∆𝑃𝑡,𝑗 = 𝛼𝑗 + 𝛽1𝑗 ∗ ∆�̃�𝑡𝑒 + 𝛽2𝑗 ∗ ∆�̃�𝑡𝑢 + 𝜀𝑡,𝑗
where ∆𝑃𝑡,𝑖 ( ∆𝑃𝑡,𝑗) is the return on the ith (jth) decile portfolios. Table 4.3 reports the White’s
(1980) heteroskedastic-consistent F statistics of the null hypothesis 𝛽2𝑖 = 𝛽2𝑗, where bold face
denotes significance at the 5 percent level.
27
Table 4.3: Wald Test - Sensitivity of Stock Prices to Target Changes Surprises, by Portfolios based on Fundamental-to-Price Ratios Table shows the results of the following SUR regression for the price changes of ith and jth decile portfolios, ΔPt,i and ΔPt,j, on the shocks in changes of the Federal Funds rate target from Jan 1990 through Oct 2008, with a total of 171 observations. P1 through P10 are 10 portfolios sorted by respective ratio of fundamental-to-price. All portfolios are constructed using stocks listed on NYSE, AMEX, and Nasdaq, and are obtained from CRSP. Panel A records the price response of 10 portfolios sorted by dividend yield (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). Panel B records the price response of 10 portfolios sorted by book-to-market ratio. Panel C records the price response of 10 portfolios sorted by earnings-to-price ratio. Panel D records the price response of 10 portfolios sorted by cashflows-to-price ratio. The table reports the heteroskedastic-consistent Wald statistics of the null hypothesis 𝛽2𝑖 = 𝛽2𝑗 . Bold denotes significance at the 5 percent level.
∆𝑃𝑡,𝑖 = 𝛼𝑖 + 𝛽1𝑖 ∗ ∆�̃�𝑡𝑒 + 𝛽2𝑖 ∗ ∆�̃�𝑡𝑢 + 𝜀𝑡,𝑖 ∆𝑃𝑡,𝑗 = 𝛼𝑗 + 𝛽1𝑗 ∗ ∆�̃�𝑡𝑒 + 𝛽2𝑗 ∗ ∆�̃�𝑡𝑢 + 𝜀𝑡,𝑗
P1 P2 P3 P4 P5 P6 P7 P8 P9
Pane
l A: D
ivid
end
Yie
ld P2 9.6200
P3 20.3600 7.7000
P4 13.9500 4.0900 0.4700
P5 13.0200 4.6800 0.0300 0.2400
P6 17.1000 7.6100 0.4000 2.1400 0.7400
P7 10.1100 3.6500 0.0200 0.3700 0.1000 0.1500
P8 9.3100 4.4000 0.7300 1.6000 1.3200 0.3800 1.3100
P9 6.5600 2.2600 0.0900 0.4000 0.2000 0.0000 0.0900 1.0200 P10 5.0000 1.3600 0.0000 0.1000 0.0200 0.0600 0.0000 0.9700 0.1600
Pane
l B: B
ook-
to-m
arke
t P2 1.1000
P3 6.2300 9.0400
P4 6.4400 8.6200 0.1700
P5 6.6200 8.9500 1.5300 0.6800
P6 6.3300 8.3800 2.8400 1.9400 0.9900
P7 6.3500 8.2600 2.3400 1.7700 0.8000 0.0300
P8 7.8700 9.9400 5.0600 4.0000 3.5700 1.6100 1.9100
P9 12.6700 16.8700 11.7100 10.2500 12.3100 11.1300 12.1100 6.5900 P10 1.7300 1.2000 0.0500 0.1700 0.9300 2.3500 2.5200 6.3600 18.4800
28
Pa
nel C
: Ear
ning
s-to
-pri
ce
P2 9.9900
P3 18.7500 5.3500
P4 22.4800 12.4200 3.2900
P5 17.5800 9.3500 2.1600 0.0000
P6 13.7500 5.0200 0.6600 0.5300 0.5800
P7 13.5700 6.4600 1.7000 0.0900 0.1100 1.1600
P8 10.6600 3.9300 0.4300 0.3200 0.3600 0.0000 1.2900
P9 9.7600 3.2900 0.1900 0.7200 0.8900 0.1100 1.9800 0.1200 P10 11.6800 4.3800 0.5500 0.1600 0.1700 0.0200 0.5100 0.0200 0.2500
Pane
l D: C
ashf
low
s-to
-pr
ice
P2 2.3500
P3 4.0200 0.5400
P4 3.7600 0.6300 0.0100
P5 2.7000 0.4700 0.0000 0.0000
P6 0.8000 0.1700 1.1800 2.0100 2.0400
P7 0.0200 1.3700 3.6500 5.1600 5.4600 1.3800
P8 1.8300 0.0600 0.1300 0.2700 0.2800 0.8900 4.5200
P9 0.6000 0.1100 0.8800 1.4400 1.4000 0.0000 1.3800 0.7700 P10 1.7000 0.0900 0.0700 0.1300 0.1100 0.6700 2.7000 0.0100 0.7800
29
F-statistics on each pairs of portfolios price reactions are separately reported for
dividend-to-price (DP), book-to-market (BM), earnings-to-price (EP), and cashflows-to-price
(CP) ratios, as presented in panels A, B, C, and D respectively. In each panel, I expect to find
significant F-ratios (1) under columns labeled P1 and P2, and (2) along rows labeled P10 and P9.
What I do find, however, is a preponderance of significant F-ratios under columns labeled P1
and P2 in the first three panels out of the four. I can thus infer that price sensitivity to interest
rate shocks are the strongest for the highest growth stocks in my sample (first and second
deciles), and they are significantly more sensitive to target changes than most of the other deciles
(second through tenth deciles).
Apart from the Wald Test, this paper runs regression on the return difference between a
pair of portfolios with the same independent variables in Equation (5), and then uses a T-test to
determine if regression estimates from their respective regressions are significant different from
one another. Table 4.4 reports the results on model:
∆𝑃𝑡,𝑖 − ∆𝑃𝑡,𝑗 = 𝛼 + 𝛽1 ∗ ∆�̃�𝑡𝑒 + 𝛽2 ∗ ∆�̃�𝑡𝑢 + 𝜀𝑡 (7)
The results further confirm the conclusions made from the Wald tests. That is, the T-tests
are significant under columns labeled P1 and P2 in the first three panels.
30
Table 4.4: Paired Difference Test - Response of Stock Prices to Target Changes Surprises, by Portfolios based on Fundamental-to-Price Ratios Table shows results of regression of the mean difference of one-day price changes between ith and jth decile portfolios, (∆𝑃𝑡,𝑖 −∆𝑃𝑡,𝑗), where i ≠ j, on shocks in the federal funds rate target from Jan 1990 through Oct 2008 with a total of 171 observations. P1 through P10 are 10 portfolios sorted by respective ratio of fundamental-to-price. All portfolios are constructed using stocks listed on NYSE, AMEX, and Nasdaq, and are obtained from CRSP. Panel A records the price response of 10 portfolios sorted by dividend yield (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). Panel B records the price response of 10 portfolios sorted by book-to-market ratio. Panel C records the price response of 10 portfolios sorted by earnings-to-price ratio. Panel D records the price response of 10 portfolios sorted by cashflows-to-price ratio. The table reports the t test of the null hypothesis 𝛽2 = 0. Bold denotes significance at the 5 percent level.
∆𝑃𝑡,𝑖 − ∆𝑃𝑡,𝑗 = 𝛼 + 𝛽1 ∗ ∆�̃�𝑡𝑒 + 𝛽2 ∗ ∆�̃�𝑡𝑢 + 𝜀𝑡
P1 P2 P3 P4 P5 P6 P7 P8 P9
Pane
l A: D
ivid
end
Yie
ld P2 -0.7235
P3 -1.2798 -0.5563 P4 -1.1631 -0.4396 0.1167 P5 -1.2474 -0.5239 0.0324 -0.0842 P6 -1.4092 -0.6857 -0.1294 -0.2461 -0.1618 P7 -1.3196 -0.5960 -0.0398 -0.1564 -0.0722 0.0896 P8 -1.6079 -0.8844 -0.3281 -0.4448 -0.3605 -0.1987 -0.2884 P9 -1.4050 -0.6815 -0.1252 -0.2419 -0.1576 0.0042 -0.0854 0.2029 P10 -1.3049 -0.5814 -0.0251 -0.1418 -0.0575 0.1043 0.0147 0.3030 0.1001
Pane
l B: B
ook-
to-m
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t P2 -0.2707 P3 -0.9374 -0.6668 P4 -1.0167 -0.7460 -0.0793 P5 -1.1868 -0.9161 -0.2494 -0.1701 P6 -1.3801 -1.1094 -0.4427 -0.3634 -0.1933 P7 -1.3514 -1.0807 -0.4140 -0.3347 -0.1646 0.0287 P8 -1.6160 -1.3453 -0.6786 -0.5993 -0.4292 -0.2359 -0.2646 P9 -2.1376 -1.8669 -1.2002 -1.1209 -0.9508 -0.7575 -0.7862 -0.5216 P10 -0.8385 -0.5679 0.0989 0.1782 0.3483 0.5415 0.5128 0.7775 1.2991
Pane
l C: E
arni
ngs-
to-
pric
e
P2 -0.7775 P3 -1.2692 -0.4917 P4 -1.5976 -0.8201 -0.3284 P5 -1.5967 -0.8192 -0.3275 0.0009 P6 -1.4690 -0.6914 -0.1998 0.1287 0.1277 P7 -1.6651 -0.8876 -0.3959 -0.0675 -0.0684 -0.1962 P8 -1.4682 -0.6907 -0.1990 0.1294 0.1285 0.0008 0.1969 P9 -1.4033 -0.6258 -0.1341 0.1943 0.1934 0.0657 0.2618 0.0649 P10 -1.4993 -0.7217 -0.2301 0.0984 0.0974 -0.0303 0.1659 -0.0311 -0.0960
Pane
l D: C
ashf
low
s-to
-pr
ice
P2 -0.3487 P3 -0.5050 -0.1562 P4 -0.5252 -0.1765 -0.0203 P5 -0.5184 -0.1697 -0.0135 0.0068 P6 -0.2468 0.1019 0.2582 0.2784 0.2716 P7 -0.0445 0.3043 0.4605 0.4808 0.4740 0.2023 P8 -0.4151 -0.0664 0.0898 0.1101 0.1033 -0.1683 -0.3707 P9 -0.2570 0.0918 0.2480 0.2682 0.2614 -0.0102 -0.2125 0.1582 P10 -0.4336 -0.0848 0.0714 0.0916 0.0848 -0.1868 -0.3891 -0.0184 -0.1766
31
4.3 Asymmetric Effects of Surprise Signs
As discovered by several researchers17, asymmetries may exist depending on the sign of
the surprise (bad news vs. good news). To examine whether there is a significant difference of
post-announcement return between positive and negative shocks in Federal Funds rate changes, I
run asymmetric tests based on the following OLS model:
𝑅𝑡 = 𝛼 + (𝛽1 + 𝛽2 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 < 0) + (𝛽3 + 𝛽4 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 > 0) + 𝜀𝑡 (8)
, where D(A) is a dummy variable taking the value 1 if the event A is true and 0 otherwise. Note
that for the convenience of interpreting and comparing the shock impacts, I take absolute values
on all the surprise values.
Table 4.5 shows the results from Equation (8) on stock returns of ten different industries
and of three market portfolios. Intercept coefficients (𝛽1and 𝛽3) indicate whether the presence of
surprise matters. Slope coefficients (𝛽2 and 𝛽4) measure the impact of surprise on stock returns.
The R-squares of the regression across portfolios in Table 4.5 are generally showing more
convincing results than those in Table 4.1 and Table 4.2. Several R-squares are well above 10
percent level, proving to be better fitted models. It seems to be the case that breaking the shocks
into negative and positive components is important in studying impact of Federal Funds rate
changes.
In term of intercept coefficients, the existence of positive surprises gives negative impact
on stock returns across all portfolios but the estimates, 𝛽3s, are significant at five percent level
towards only three industries (Non-durable, Manufacturing, and Wholesale/Retail), while
negative surprises positively impact stock returns but the estimates, 𝛽1s, are only important for
Utility industry at five percent level. The Equality test at the second last column statistically
17 See Lobo (2000) and Chulia, Martens, & Djik (2010).
32
rejects the null 𝛽1= 𝛽3 in seven out of ten industries. For the market indexes, none of the three
indexes present sufficient evidence to support the statement that the presence of negative or
positive surprises is important at five percent significant level although the equality test results
prove that the intercept coefficients are significantly different.
In term of slope coefficients, both negative and positive shocks are positively correlated
with stock returns across all market indexes and most industry portfolios. Utility is the only
industry portfolio that reacts significantly negatively with the negative shocks. One percent
increases in negative shock shrinkages the stock return of Utility by 1.676%. Among the ten
industries, Durable and Wholesale/Retail response most substantially (at 1% significant level) to
the negative shocks, while Non-durable, Manufacturing, Wholesale/Retail, and Utility response
to the positive shocks at 5% significant level. The Equality test statistically reject null 𝛽2= 𝛽4
only for portfolio Non-durable and Utility. This result implies that the impact difference between
negative and positive shocks in most industries does not vary statically. Surprising, the Newey-
west estimates suggest that shocks do not affect price movement when the shocks are broken
down into positive and negative components.
33
Table 4.5: Asymmetric Response of Equity Prices to Positive and Negative Surprises, by Industry Portfolios and by Market Indexes The following table shows the results of 1-day equity return of 10 industry portfolios on the negative and positive white-noise residuals of surprises of the target rate changes. The 10 industry portfolios are constructed based on SIC code as in Fama & French (1988). The last three categories record the price response of three market indexes: VW and EW are the value-weighted and equal-weighted market portfolios, respectively, and S&P500 is the index portfolio of S&P 500.
𝑅𝑡 = 𝛼 + (𝛽1 + 𝛽2 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 < 0) + (𝛽3 + 𝛽4 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 > 0) + 𝜀𝑡
where D(A) is a dummy variable taking the value 1 if the event A is true and 0 otherwise. Negative and positive surprises occur 73 and 46 cases respectively. The models are estimated for individual stocks in AMEX, NYSE, and Nasdaq based on 163 white-noise residuals of target rate change shocks following 171 FOMC meetings between Jan 1990 and Oct 2008. Average coefficient estimates and R-square values are shown across all portfolios. The asterisks of ***, **, and * represent t-statistical significance at the 1%, 5%, and 10% level, respectively, based on the standard errors given in parentheses.Columns headed "Equality Test" contain p-values of F-test statistics for testing the indicated restrictions for the average coefficients. The p-values of “Equality Test” in bold denotes significance at 5% level.
Negative Surprise Positive Surprise Equality Test
Portfolio α β1 β2 β3 β4 R2 Ho: β1=β3
Ho: β2=β4
Non-Durable 0.16389
++ 0.08646 0.58153
-0.4412 ** + 5.84559 ** 0.06215 0.0087 0.0449
(0.1009)
(0.1501) (0.6701)
(0.1931) (2.5168)
Durable 0.15786
++ 0.0942 2.67395 *** -0.4924 * + 6.34523 * 0.12461 0.0257 0.2839
(0.1323)
(0.1968) (0.8786)
(0.2533) (3.3001)
Manufacturing 0.22857 * ++ 0.03669 1.5233 * -0.5293 ** + 7.62303 ** 0.08131 0.0187 0.0526
(0.1210)
(0.1800) (0.8038)
(0.2317) (3.0191)
Energy 0.13142 0.11182
0.36396 -0.1116
2.64025
0.00724 0.4758 0.5793
(0.1587)
(0.2361) (1.0541)
(0.3038) (3.9593)
High Tech 0.21627 0.07005
3.33412 ** -0.5676
+ 7.70324
0.08136 0.1033 0.3931
(0.1977)
(0.2941) (1.3129)
(0.3784) (4.9312)
Telecommunication 0.13177
0.05335
3.10334 **
-0.4895
6.19871
0.07918 0.1318 0.5109
(0.1820)
(0.2707)
(1.2087)
(0.3484)
(4.5400)
Wholesale/Retail 0.2253 * +++ 0.00763
2.66716 *** + -0.5379 ** ++ 6.82779 ** 0.11398 0.0379 0.2251
(0.1324)
(0.1969)
(0.8791)
(0.2534)
(3.3018)
Healthcare 0.14453
0.12805
0.99858
-0.4165
5.68102
0.04591 0.0482 0.1935
(0.1389)
(0.2067)
(0.9227)
(0.2660)
(3.4657)
Utilities 0.06536
0.32807 ** ++ -1.676 **
-0.2892
5.36221 ** 0.07523 0.0017 0.0062
(0.0984)
(0.1464)
(0.6536)
(0.1884)
(2.4550)
Others 0.14762
++ 0.08264
1.46638 **
-0.3173 *
5.22424 ** 0.09571 0.0299 0.1184 (0.0927) (0.1380) (0.6160) (0.1776) (2.3137) VW 0.14166 0.23311 1.74226 * -0.4493 7.57427 ** 0.0817 0.0214 0.1319
(0.1492)
(0.2219)
(0.9909)
(0.2856)
(3.7218)
EW 0.15325
++ 0.05998
2.00284 ***
-0.4231 * + 6.02945 ** 0.10176 0.033 0.1735
(0.1141)
(0.1698)
(0.7579)
(0.2185)
(2.8469)
S&P500 0.12245
0.05998
1.24596
-0.4587
8.15744 ** 0.06742 0.0185 0.089 (0.1565) (0.1698) (1.0396) (0.2996) (3.9046)
34
4.4 Equity Duration of Surprise Signs based on Federal Funds Rate Surprises
To study equity duration based on asymmetric effect of the Federal Funds rate shocks, I
run Equation (8) across ten decile portfolios based on different ratios of fundamental-to-price.
That is, similar to the tests on the raw change and the shock of target rate change (Table 4.2),
estimates associated with portfolios ranked on the basis of dividend-to-price (DP), book-to-
market (BM), earnings-to-price (EP), and cashflows-to-price (CP) ratios are presented in panels
A, B, C, and D of Table 4.6, respectively. The test results from these four panels are generally
close the ones in Table 4.5: R-squares, ranging between 5% and 15%, indicate better fitted
regressions than the models regressing on pure surprises; intercept coefficients are positively
correlated with negative surprises but are negatively correlated with positive surprises; slope
coefficients are positively correlated with both negative and positive surprises; F-tests reject
intercept equality (null 𝛽1= 𝛽3) in most portfolios while reject slope equality (null 𝛽2= 𝛽4) only
in three portfolios in Panel B and one portfolio in Panel D.
Perhaps something unique about these four panels is some hesitant evidences of equity
durations. Across portfolios sorted by dividend yield (Panel A of Table 4.6), for example, the
magnitudes of 𝛽2 (negative shock slope coefficient) decreases gradually from 2.3520 of the first
decile to 1.3602 of the tenth decile, and the magnitudes of 𝛽4 (positive shock slope coefficient)
decreases from 8.1560 of the first decile to 5.9132 of the tenth decile. Some similar evidences
could be found in Panel C, D, and E.
35
Table 4.6: Asymmetric Response of Equity Prices to Positive and Negative Surprises, by Portfolios based on Fundamental-to-Price Ratios The table shows the results for the impact of the presence and the magnitude of surprises in Fed Funds rate changes on 1-day stock returns, allowing for different effects of positive and negative surprises.
Model: 𝑅𝑡 = 𝛼 + (𝛽1 + 𝛽2 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 < 0) + (𝛽3 + 𝛽4 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 > 0) + 𝜀𝑡
where D(A) is a dummy variable taking the value 1 if the event A is true and 0 otherwise. Negative and positive surprises occur 73 and 46 cases respectively. The models are estimated for individual stocks in AMEX, NYSE, and Nasdaq following 171 FOMC meetings between Jan 1990 and Oct 2008. Average coefficient estimates and R-square values are shown across all portfolios. The asterisks of ***, **, and * represent statistical significance at the 1%, 5%, and 10% level, respectively. The plus signs of +++, ++, and + represent Newey-West statistical significant at the 1%, 5%, and 10% level, respectively, based on Newey-West standard errors. Columns headed "Equality Test" contain p-values of F-test statistics for testing the indicated restrictions for the average coefficients. The p-values of “Equality Test” in bold denotes significance at 5% level. Panel A records the price response of three market indexes: VW and EW are the value-weighted and equal-weighted market portfolios, respectively, and S&P500 is the index portfolio of S&P 500. Panel B records the price response of 10 portfolios sorted by dividend yield (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). Panel C records the price response of 10 portfolios sorted by book-to-market ratio. Panel D records the price response of 10 portfolios sorted by earnings-to-price ratio. Panel E records the price response of 10 portfolios sorted by cashflows-to-price ratio.
Negative Surprise Positive Surprise Equality Test
Portfolio α β1 β2 β3 β4 R2 Ho:
β1=β3 Ho:
β2=β4
Pane
l A D
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end
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P1 0.2088 ++ 0.1264 2.3520 ** -0.5634 ** 8.1560 ** 0.1149 0.0118 0.1041 P2 0.2135 * ++ 0.1130 1.5872 ** -0.5032 ** + 7.2537 ** 0.0932 0.0105 0.0712 P3 0.1918 ++ 0.0796 1.1465 -0.5015 ** 8.0506 *** 0.0745 0.0141 0.0258 P4 0.2029 * ++ 0.0796 1.1087 -0.4383 ** 6.2628 ** 0.0748 0.0144 0.0623 P5 0.1937 ** ++ 0.0769 0.9984 -0.3090 4.2805 * 0.0575 0.0485 0.1990 P6 0.1493 + 0.1083 0.9397 -0.3776 ** 6.6191 *** 0.0748 0.0148 0.0294 P7 0.1422 ++ 0.0693 1.1096 * + -0.2509 4.8923 ** 0.0640 0.0786 0.1126 P8 0.0927 ++ 0.0376 0.8380 * ++ -0.2212 + 4.2839 ** 0.0588 0.0839 0.0791 P9 0.0425 0.0920 1.1041 ** + -0.2299 5.3149 *** 0.0945 0.0362 0.0366 P10 0.0019 0.0949 1.3602 ** -0.2084 5.9132 ** 0.0699 0.1388 0.0903
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P1 0.1251 0.2187 2.7423 ** -0.5370 + 7.8426 * 0.0928 0.0345 0.2741 P2 0.1897 + 0.0827 2.7860 *** -0.5679 * + 7.3458 * 0.1009 0.0377 0.2644 P3 0.1964 + 0.0943 2.0138 ** -0.5487 ** + 7.2769 ** 0.0868 0.0232 0.1543 P4 0.1982 ++ 0.1539 1.7255 * -0.4413 * 5.5767 0.0800 0.0281 0.2759 P5 0.2338 * +++ 0.0639 1.8158 ** -0.5664 ** ++ 7.1505 ** 0.0989 0.0107 0.0975 P6 0.2173 * +++ 0.0036 1.7835 ** -0.4243 * 5.2849 * 0.0781 0.0617 0.2420 P7 0.1819 ++ 0.0236 1.8690 ** -0.4384 ** + 6.4136 ** 0.0930 0.0383 0.1190 P8 0.1764 * ++ 0.0496 1.4790 ** -0.4046 ** + 5.9645 ** 0.0838 0.0287 0.0983 P9 0.2089 ** +++ -0.0042 1.0479 -0.4149 ** + 6.0257 ** 0.0570 0.0487 0.0681 P10 0.2172 ** +++ -0.0459 2.8310 *** + -0.4057 * ++ 6.7700 ** 0.1377 0.1006 0.1698
36
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P1 0.1810 + 0.1215 2.7460 *** -0.4854 * 5.8746 0.1024 0.0470 0.4323 P2 0.1975 ++ 0.0647 2.1968 ** -0.5497 ** + 7.3704 ** 0.0922 0.0275 0.1550 P3 0.2063 ++ 0.1004 1.5797 * -0.4786 * + 6.7714 ** 0.0729 0.0283 0.1320 P4 0.2091 * ++ 0.1292 1.2169 -0.5279 ** + 7.9433 *** 0.0836 0.0070 0.0346 P5 0.2106 * ++ 0.1138 1.1900 -0.4795 ** + 6.6718 ** 0.0826 0.0085 0.0624 P6 0.2012 * ++ 0.0520 1.4896 ** -0.5586 *** ++ 7.6773 *** 0.0982 0.0066 0.0348 P7 0.2244 ** +++ 0.0357 1.2943 * -0.4994 ** + 6.5654 ** 0.0870 0.0104 0.0531 P8 0.2190 ** +++ 0.0242 1.6047 ** -0.4690 ** + 6.5230 ** 0.0945 0.0186 0.0724 P9 0.2157 ** +++ 0.0600 1.5928 ** -0.4484 ** + 6.2703 ** 0.0981 0.0150 0.0863 P10 0.1911 * ++ 0.0834 1.5240 ** -0.4492 ** + 7.0622 ** 0.0843 0.0210 0.0664
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e P1 0.1768 ++ 0.0194 2.1746 *** -0.4331 * + 5.2049 * 0.0991 0.0532 0.3214 P2 0.1693 ++ 0.0153 1.9440 *** -0.4033 * + 5.8163 ** 0.0951 0.0530 0.1709 P3 0.1778 ++ 0.0651 1.6134 ** -0.4502 ** + 6.4791 ** 0.0948 0.0171 0.0847 P4 0.2481 ** +++ 0.0023 1.6475 ** -0.5222 ** ++ 6.8410 ** 0.0899 0.0193 0.0761 P5 0.2066 ++ 0.0827 1.5053 * -0.5508 ** + 7.5784 ** 0.0834 0.0121 0.0653 P6 0.2460 * +++ 0.0757 1.8642 ** -0.4991 ** + 7.0124 ** 0.0869 0.0254 0.1252 P7 0.2127 +++ 0.0748 2.0449 ** -0.5744 ** ++ 7.7181 ** 0.1024 0.0128 0.0954 P8 0.2439 * +++ 0.0704 1.6375 * -0.5570 ** ++ 7.4834 ** 0.0848 0.0145 0.0808 P9 0.1984 ++ 0.1380 1.7536 ** -0.4870 ** + 7.2185 ** 0.0946 0.0136 0.0980 P10 -0.1199 + + 0.1214 1.6501 ** -0.4949 ** + 7.6360 ** 0.0986 0.0099 0.0548
37
(9)
The evidence of equity duration as presented in Table 4.6 is less robust without a
statistical comparison of shock impacts across the ten quintile portfolios. Similar to the
methodology applied previously, I use Wald test to examine whether there is a statistically
difference in stock price reaction to each direction of the shocks between growth stocks (low
ratio of fundamental-to-price) and value stocks (high ratio of fundamental-to-price). I modify the
SUR Equation System (6) for testing asymmetric impact on the sign of the surprises. The model
is shown as below:
∆𝑃𝑡,𝑖 = 𝛼𝑖 + (𝛽1𝑖 + 𝛽2𝑖 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 < 0) + (𝛽3𝑖 + 𝛽4𝑖 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 > 0) + 𝜀𝑡,𝑖
∆𝑃𝑡,𝑗 = 𝛼𝑗 + �𝛽1𝑗 + 𝛽2𝑗 ∗ ∆�̃�𝑡𝑢�𝐷(∆�̃�𝑡𝑢 < 0) + �𝛽3𝑗 + 𝛽4𝑗 ∗ ∆�̃�𝑡𝑢�𝐷(∆�̃�𝑡𝑢 > 0) + 𝜀𝑡,𝑗
Table 4.7 reports the Wald statistics of the null hypothesis 𝛽2𝑖 = 𝛽2𝑗 , and of the null
hypothesis 𝛽4𝑖 = 𝛽4𝑗 , based on portfolios by dividend-to-price (DP), book-to-market (BM),
earnings-to-price (EP), and cashflows-to-price (CP), respectively. The p-values are recorded in
parentheses and bold denotes significance at the five percent level.
38
Table 4.7: Wald Test - Sensitivity of Stock Prices to Negative & Positive Target Changes Surprises, by Portfolios based on Fundamental-to-Price Ratios Table shows the results of the following SUR regression for the price changes of ith and jth decile portfolios, ΔPt,i and ΔPt,j, on the NEGATIVE shocks (Table on the left) and on the POSITIVE shocks (Table on the right), allowing for different effects of positive and negative surprises, from Jan 1990 through Oct 2008 with a total of 171 observations. P1 through P10 are 10 portfolios sorted by respective ratio of fundamental-to-price. All portfolios are constructed using stocks listed on NYSE, AMEX, and Nasdaq, and are obtained from CRSP. Panel A records the price response of 10 portfolios sorted by dividend yield (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). Panel B records the price response of 10 portfolios sorted by book-to-market ratio. Panel C records the price response of 10 portfolios sorted by earnings-to-price ratio. Panel D records the price response of 10 portfolios sorted by cashflows-to-price ratio. The table reports the heteroskedastic-consistent Wald statistics of the null hypothesis 𝛽2𝑖 = 𝛽2𝑗 and of the null hypothesis 𝛽4𝑖 = 𝛽4𝑗 . Bold denotes significance at the 5 percent level.
∆𝑃𝑡,𝑖 = 𝛼𝑖 + (𝛽1𝑖 + 𝛽2𝑖 ∗ ∆�̃�𝑡𝑢) ∗ 𝐷(∆�̃�𝑡𝑢 < 0) + (𝛽3𝑖 + 𝛽4𝑖 ∗ ∆�̃�𝑡𝑢) ∗ 𝐷(∆�̃�𝑡𝑢 > 0) + 𝜀𝑡,𝑖 ∆𝑃𝑡,𝑗 = 𝛼𝑗 + (𝛽1𝑗 + 𝛽2𝑗 ∗ ∆�̃�𝑡𝑢) ∗ 𝐷(∆�̃�𝑡𝑢 < 0) + (𝛽3𝑗 + 𝛽4𝑗 ∗ ∆�̃�𝑡𝑢) ∗ 𝐷(∆�̃�𝑡𝑢 > 0) + 𝜀𝑡,𝑗
Impact from Negative Shocks (H0: 𝛽2𝑖 = 𝛽2𝑗) Impact from Positive Shocks (H0: 𝛽4𝑖 = 𝛽4𝑗)
P1 P2 P3 P4 P5 P6 P7 P8 P9 P1 P2 P3 P4 P5 P6 P7 P8 P9
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P2 6.39
0.63
P3 10.77 2.86
0.01 0.66
P4 9.67 2.85 0.03
1.59 0.87 4.71
P5 9.62 3.66 0.34 0.25
5.59 6.61 15.58 5.81
P6 10.38 4.04 0.61 0.60 0.06
0.87 0.27 2.07 0.19 6.75
P7 5.48 1.40 0.01 0.00 0.15 0.31
2.68 2.43 5.27 1.22 0.31 2.28
P8 5.03 1.90 0.39 0.36 0.15 0.06 0.69
2.33 2.11 4.11 1.35 0.00 2.22 0.25
P9 3.13 0.68 0.01 0.00 0.05 0.12 0.00 1.04 1.15 0.78 1.91 0.26 0.36 0.56 0.09 1.10 P10 1.74 0.12 0.13 0.19 0.41 0.54 0.31 1.72 0.62 0.63 0.31 0.91 0.03 0.59 0.11 0.36 1.19 0.24
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0.15
P3 2.22 7.20
0.10 0.00
P4 3.82 10.62 1.35
1.35 2.09 3.32
P5 2.37 5.92 0.56 0.12
0.09 0.02 0.02 2.49
P6 1.83 4.12 0.47 0.03 0.02
0.92 1.23 2.47 0.05 4.03
P7 1.58 3.56 0.17 0.20 0.05 0.15
0.30 0.26 0.43 0.48 0.69 1.81
P8 2.87 5.61 1.89 0.41 1.32 1.58 2.46
0.45 0.44 0.81 0.07 1.16 0.56 0.23
P9 4.77 8.78 4.57 2.26 4.86 6.20 7.88 2.67 0.39 0.36 0.54 0.07 0.74 0.45 0.12 0.00 P10 0.01 0.00 2.08 4.00 4.84 5.34 5.33 11.68 21.26 0.12 0.05 0.06 0.33 0.05 0.76 0.05 0.29 0.26
39
Pane
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1.52
P3 9.20 5.02
0.39 0.34
P4 11.87 10.51 2.38
1.54 0.25 1.76
P5 9.61 8.38 1.79 0.01
0.18 0.29 0.01 2.17
P6 5.87 3.10 0.08 1.41 1.93
0.86 0.04 0.58 0.10 1.54
P7 6.00 3.95 0.52 0.07 0.16 0.68
0.10 0.22 0.02 1.66 0.01 1.57
P8 3.76 1.71 0.00 1.73 2.24 0.22 1.90
0.09 0.25 0.03 1.64 0.02 1.56 0.00
P9 3.82 1.81 0.00 1.61 2.31 0.15 1.53 0.00 0.03 0.43 0.11 2.26 0.16 2.04 0.11 0.08 P10 4.50 2.25 0.02 0.95 1.17 0.01 0.58 0.08 0.08 0.30 0.03 0.04 0.55 0.11 0.27 0.19 0.24 0.72
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e P2 0.61 0.30 P3 2.95 1.45
1.08 0.41
P4 2.24 1.05 0.01
1.53 0.89 0.12
P5 2.70 1.93 0.14 0.37
2.40 2.21 1.02 0.70
P6 0.76 0.06 0.66 0.72 2.12
1.83 1.02 0.21 0.03 0.37
P7 0.12 0.09 1.93 2.10 4.20 0.66
3.09 2.32 1.13 0.73 0.02 0.71
P8 1.83 0.83 0.01 0.00 0.27 0.96 3.24
2.34 1.74 0.67 0.39 0.01 0.30 0.08
P9 0.97 0.28 0.17 0.13 0.75 0.21 1.54 0.25 1.57 1.09 0.33 0.12 0.11 0.05 0.32 0.09 P10 1.49 0.68 0.01 0.00 0.19 0.52 1.64 0.00 0.16 2.26 1.83 0.77 0.40 0.00 0.31 0.01 0.02 0.18
40
First, let’s look at the sensitivity of stock price towards the negative surprises. Based on
portfolios by dividend yield (Panel A), only the extreme high growth stocks (P1) reacts
statistically greater than the remaining portfolios. Surprisingly, even though the returns of P1 is
significantly different from those of P2 through P8, I cannot reject the null 𝛽2𝑖 = 𝛽2𝑗 between
this portfolio and the extreme high value stocks, which are confirmed by pairs (P1, P9) and (P1,
P10). The Wald test based on portfolios by book-to-market ratio (Panel B) leads us to a different
conclusion. For the growth stocks portfolios, only some pairs across P2 shows significant results
against other portfolios while for the value stock portfolios, P9 and P10 together present some
evidences to reject the null 𝛽4𝑖 = 𝛽4𝑗 against all other portfolios. The Wald test results based on
portfolios by earnings price ratio (Panel C) shows that most of the bold values are the ones that
involve P1 and P2, which represent the extreme high growth stocks. As for the portfolios sorted
by cashflows price ratio (Panel D), none of the pairs between any two portfolios shows a
significant result.
Second, let’s proceed to the sensitivity of stock price towards the positive surprises. Out
of the four panels that run the sensitivity tests, none of them provides conclusive results that
present significant difference in stock price reaction between growth stocks and value stocks.
Only the Wald test based on portfolios by dividend yield (Panel A) presents some significant
pairs across P3 and P5. However since these two portfolios represent merely mid-growth stocks,
I have no sufficient evidence to conclude that the growth stocks react significant differently from
the value stocks towards the positive shocks.
Overall, equity duration can be noticed only when the shocks are negative, and applies
only on a few portfolios sorted by certain ratios of fundamental-to-price. Portfolios by dividend
yield and earnings price ratio show that only first decile (P1) portfolio performs significantly
41
better than the remaining stocks on negative surprises. Portfolios by book-to-market ratio show
some evidences of asymmetric effect on negative surprises in second decile (P2), ninth decile
(P9), and tenth decile (P10) portfolios. Meanwhile portfolios by cashflows-to-price ratio do not
provide any proof of equity duration either on negative or positive shocks.
In sum, the Wald test results reflect that significant asymmetric results exist only on
negative surprises and only across a few particular portfolios. These findings do not really
support the sensitivity theory proposed by cash flow discounted model. The Wald test results are
further validated by Paired Difference Test. Table 4.8 shows the paired difference T-test results
on model:
∆𝑃𝑡,𝑖 − ∆𝑃𝑡,𝑗 = 𝛼 + (𝛽1 + 𝛽2 ∗ ∆�̃�𝑡𝑢) ∗ 𝐷(∆�̃�𝑡𝑢 < 0) + (𝛽3 + 𝛽4 ∗ ∆�̃�𝑡𝑢) ∗ 𝐷(∆�̃�𝑡𝑢 > 0) + 𝜀𝑡 (10)
Most of the “pairs” that show significant relation in Table 4.8 display the same
significant level in Table 4.7 as well. It is possible that conducting an asymmetric test based on
simply whether the surprise is positive or negative is not sufficient enough to explain the
sensitivity of stock price across growth-value portfolio classification. Other simultaneous
asymmetric factors, such as the direction of the target rate decision (loosening vs. tightening
monetary policy) and the macroeconomic environment (expansions vs. recessions) should also
be taken into consideration. In the following session, I conduct a comprehensive analysis of
simultaneous asymmetric effects based on the signs of the target rate surprises and the business
cycles.
42
Table 4.8: Paired Difference Test - Sensitivity of Stock Prices to Negative & Positive Target Changes Surprises, by Portfolios based on Fundamental-to-Price Ratios Table shows results of regression of the mean difference of one-day price changes between ith and jth decile portfolios, (∆𝑃𝑡,𝑖 − ∆𝑃𝑡,𝑗), where i ≠ j, on the NEGATIVE shocks (Table on the left) and on the POSITIVE shocks (Table on the right), allowing for different effects of positive and negative surprises, from Jan 1990 through Oct 2008 with a total of 171 observations. P1 through P10 are 10 portfolios sorted by respective ratio of fundamental-to-price. All portfolios are constructed using stocks listed on NYSE, AMEX, and Nasdaq, and are obtained from CRSP. Panel A records the price response of 10 portfolios sorted by dividend yield (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). Panel B records the price response of 10 portfolios sorted by book-to-market ratio. Panel C records the price response of 10 portfolios sorted by earnings-to-price ratio. Panel D records the price response of 10 portfolios sorted by cashflows-to-price ratio. The table reports the t statistics of the null hypothesis 𝛽2 = 0 and 𝛽4 = 0. The t-statistics is in parentheses and bold denotes significance at the 5 percent level.
∆𝑃𝑡,𝑖 − ∆𝑃𝑡,𝑗 = 𝛼 + (𝛽1 + 𝛽2 ∗ ∆�̃�𝑡𝑢) ∗ 𝐷(∆�̃�𝑡𝑢 < 0) + (𝛽3 + 𝛽4 ∗ ∆�̃�𝑡𝑢) ∗ 𝐷(∆�̃�𝑡𝑢 > 0) + 𝜀𝑡
Impact from Negative Shocks (H0: 𝛽2 = 0) Impact from Positive Shocks (H0: 𝛽4 = 0)
P1 P2 P3 P4 P5 P6 P7 P8 P9 P1 P2 P3 P4 P5 P6 P7 P8 P9
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P2 0.76 0.01 P3 1.21 0.44
0.06 0.06
P4 1.24 0.48 0.04
0.05 0.04 -0.01
P5 1.35 0.59 0.15 0.11
0.06 0.06 0.00 0.01
P6 1.41 0.65 0.21 0.17 0.06
0.08 0.07 0.01 0.02 0.01
P7 1.24 0.48 0.04 0.00 -0.11 -0.17
0.12 0.12 0.06 0.07 0.06 0.05
P8 1.51 0.75 0.31 0.27 0.16 0.10 0.27
0.20 0.20 0.14 0.15 0.14 0.13 0.08
P9 1.25 0.48 0.04 0.00 -0.11 -0.16 0.01 -0.27
0.20 0.19 0.14 0.15 0.14 0.12 0.08 0.00
P10 0.99 0.23 -0.21 -0.25 -0.36 -0.42 -0.25 -0.52 -0.26 0.24 0.23 0.17 0.19 0.17 0.16 0.11 0.03 0.04
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t P2 -0.04
0.07
P3 0.73 0.77
0.05 -0.02
P4 1.02 1.06 0.29
-0.01 -0.08 -0.06
P5 0.93 0.97 0.20 -0.09
0.05 -0.03 -0.01 0.05
P6 0.96 1.00 0.23 -0.06 0.03
0.12 0.05 0.07 0.13 0.08
P7 0.87 0.92 0.14 -0.14 -0.05 -0.09
0.14 0.07 0.09 0.15 0.09 0.02
P8 1.26 1.31 0.53 0.25 0.34 0.30 0.39
0.12 0.05 0.06 0.13 0.07 -0.01 -0.02
P9 1.69 1.74 0.97 0.68 0.77 0.74 0.82 0.43
0.14 0.07 0.09 0.15 0.09 0.02 0.00 0.02
P10 -0.09 -0.05 -0.82 -1.11 -1.02 -1.05 -0.96 -1.35 -1.78 0.17 0.10 0.12 0.18 0.13 0.05 0.03 0.05 0.03
43
Pane
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P3 1.17 0.62
0.00 -0.04
P4 1.53 0.98 0.36
-0.04 -0.08 -0.03
P5 1.56 1.01 0.39 0.03
-0.02 -0.06 -0.02 0.01
P6 1.26 0.71 0.09 -0.27 -0.30
0.05 0.01 0.05 0.09 0.07
P7 1.45 0.90 0.29 -0.08 -0.10 0.20
0.04 0.00 0.05 0.08 0.06 -0.01
P8 1.14 0.59 -0.02 -0.39 -0.41 -0.12 -0.31
0.06 0.02 0.06 0.10 0.08 0.01 0.02
P9 1.15 0.60 -0.01 -0.38 -0.40 -0.10 -0.30 0.01
0.03 -0.01 0.03 0.06 0.05 -0.02 -0.02 -0.03 P10 1.22 0.67 0.06 -0.31 -0.33 -0.03 -0.23 0.08 0.07 0.03 -0.01 0.03 0.06 0.05 -0.02 -0.01 -0.03 0.00
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e P2 0.23
0.01
P3 0.56 0.33
-0.05 -0.06
P4 0.53 0.30 -0.03
-0.05 -0.07 -0.01
P5 0.67 0.44 0.11 0.14
-0.09 -0.10 -0.05 -0.04
P6 0.31 0.08 -0.25 -0.22 -0.36
-0.13 -0.14 -0.08 -0.07 -0.03
P7 0.13 -0.10 -0.43 -0.40 -0.54 -0.18
-0.09 -0.10 -0.04 -0.04 0.00 0.03
P8 0.54 0.31 -0.02 0.01 -0.13 0.23 0.41
-0.12 -0.13 -0.07 -0.06 -0.03 0.01 -0.03
P9 0.42 0.19 -0.14 -0.11 -0.25 0.11 0.29 -0.12
-0.14 -0.15 -0.09 -0.09 -0.05 -0.01 -0.05 -0.02
P10 0.52 0.29 -0.04 0.00 -0.14 0.21 0.39 -0.01 0.10 -0.09 -0.10 -0.04 -0.03 0.00 0.04 0.00 0.03 0.05
44
4.5 Asymmetric Reaction of Surprise Signs and Business Cycles
As reported in previous studies18, asymmetric price reaction to interest rate surprise may
exist depending on the direction of the surprise (bad news vs. good news). From a pure DFC
perspective, a negative (positive) target rate surprise is considered to be good news (bad news),
as an unanticipated cut (raise) in target rate leads to a forecast of (1) a lower (higher) borrowing
rate available to a firm, and (2) a lower (higher) discount rate required by an investor. However,
it would be unrealistic to expect the Federal Reserve to announce rate changes that are
independent of the prevailing business conditions. An intended (or unintended) consequence of a
rate change (or surprise) in a given direction during an economic expansion may be the opposite
of what is expected during an economic recession. For example, during an expansion period, if
inflation is expected to rise, the Federal Reserve will tend to respond by increasing the Federal
Funds target rates to preempt the rising inflation. A positive surprise in target rate during
expansion periods could happen when target rate increase is greater than what market had
anticipated. This may signal a higher inflation rate, and drop in stock price. On the other hand,
during a recession the Federal Reserve tends to cut target rate to boost business activity. If,
during bad times, investors tend to expect something worse, a negative surprise (actual rate cut
less than expected rate cut) is usually a norm and may not really be a “surprise”. A positive
surprise, however, may signal a reversal of the business cycles and forecast a prosperous future
outlook. Instead of being a bad news as suggested by the DCF approach, a positive Federal
Funds rate surprise during contraction periods may actually result in a stock price increase. I
therefore propose the hypothesis that asymmetric price reaction to positive or negative interest
rate shocks is conditional on the prevailing business cycle.
18 See Lobo (2000) and Chulia, Martens, & Djik (2010).
45
(11)
I design the following test to examine the interaction between the direction of the Federal
Funds rate surprise (positive and negative shocks) and business cycle (periods of economic
contraction and expansion):
𝑅𝑡 = 𝛼 + {(𝛽1 + 𝛽2 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 < 0) + (𝛽3 + 𝛽4 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 > 0)} ∗ 𝐷(𝐶𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛) +
{(𝛽5 + 𝛽6 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 < 0) + (𝛽7 + 𝛽8 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 > 0)} ∗ 𝐷(𝐸𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛) + 𝜀𝑡
where D(A) is a dummy variable taking the value 1 if the event A is true and 0 otherwise. Like
Equation (8), all surprises in Equation (11) are in absolute values.
I first estimate Equation (11) on different industries and on the market portfolios. Results
on the ten different industries and the three market portfolios are reported in Table 4.9.
𝛽1 (𝛽3 ) and 𝛽2 (𝛽4 ) represent intercept and slope coefficients of negative (positive)
surprise during contraction periods, while 𝛽5 (𝛽7) and 𝛽6 (𝛽8 ) represent intercept and slope
coefficients of negative (positive) surprise during expansion periods. Something interesting
about Table 4.9 is that the regressions across all portfolios have greater R-squares than the
simple model regression tests on Equation (5) and the sign-asymmetric model regression tests on
Equation (8). Across industry portfolios, R-squares range from 4.39% to 21.7%. Also, all three
market indexes have R-squares greater than 20%. Such a tremendous increase in R-square values
implies that isolating the shocks into negative and positive as well as into different sub-periods
based on business cycles is crucial in applying the shocks in Federal Funds target rate changes
into empirical studies. And such separation has, unfortunately, been overlooked by previous
literatures.
46
Table 4.9: Asymmetric Response of Equity Prices to Different Business Cycles, by Industry Portfolios and by Market Indexes The following table shows the results on the impact of the presence and magnitude of surprises in Federal funds rate changes on 1-day stock returns of 10 industry portfolios, allowing for different effects of positive and negative surprises and for different economic cycles. Here is the regression equation:
𝑅𝑡 = 𝛼 + {(𝛽1 + 𝛽2 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 < 0) + (𝛽3 + 𝛽4 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 > 0)} ∗ 𝐷(𝐶𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛) + {(𝛽5 + 𝛽6 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 < 0) + (𝛽7 + 𝛽8 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 > 0)} ∗ 𝐷(𝐸𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛) + 𝜀𝑡 where D(A) is a dummy variable taking the value 1 if the event A is true and 0 otherwise. The 10 industry portfolios are constructed based on SIC code as in Fama & French (1988). Negative and positive surprises occur 17 and 6 cases during contraction periods and 56 and 40 cases during expansion periods, respectively. The models are estimated for individual stocks in AMEX, NYSE, and Nasdaq following 171 FOMC meetings between Jan 1990 and Oct 2008. Average coefficient estimates and R-square values are shown across all portfolios. The asterisks of ***, **, and * represent statistical significance at the 1%, 5%, and 10% level , respectively, based on the standard errors given in parentheses. The plus signs of +++, ++, and + represent Newey-West statistical significant at the 1%, 5%, and 10% level, respectively, based on Newey-West standard errors. Columns headed "Cross Period Equality Test" contain p-values of F-test statistics for testing the indicated restrictions for the average coefficients. The p-values of “Cross Period Equality Test” in bold denotes significance at 5% level. Contraction Expansion Cross Period
Negative Surprise Positive Surprise Negative Surprise Positive Surprise Equality Test
Portfolio β1 β2 β3 β4 β5 β6 β7 β8 R2 Ho: β2=β6
Ho: β4=β8
Non-Durable 0.2007 -0.8426
-0.9491 *** ++ 21.0543 *** +++ -0.075 3.19966 *** + -0.2091 0.40108 0.19873 0.0037 0.0003
(0.2582)
(0.8989) (0.3383)
(4.6574)
(0.1543) (1.0349) (0.1907) (2.6768)
Durable 0.25852 1.84706
-1.1116 ** ++ 22.3762 *** +++ 0.01803 3.80838 *** -0.1728 0.10938 0.17808 0.2995 0.0044
(0.3549)
(1.2356) (0.4650)
(6.4022)
(0.2122) (1.4226) (0.2622) (3.6796)
Manufacturing -0.0036 0.59382
-1.232 *** ++ 25.3103 *** +++ -0.0734 3.75993 *** -0.2248 1.19904 0.1848 0.0606 0.0006
(0.3157)
(1.0989) (0.4136)
(5.6939)
(0.1887) (1.2652) (0.2332) (3.2725)
Energy -0.2095 0.90743
-1.075 * ++ 18.0716 ** + 0.15841 0.62484 0.18522 -2.472 0.04387 0.9019 0.0297
(0.4313)
(1.5014) (0.5651)
(7.7792)
(0.2578) (1.7285) (0.3186) (4.4710)
High Tech 0.32887 0.74472
-1.5219 ** +++ 25.5749 *** +++ -0.2027 7.94935 *** -0.1478 0.69227 0.1489 0.0109 0.0311
(0.5268)
(1.8341) (0.6903)
(9.5029)
(0.3149) (2.1115) (0.3892) (5.4616)
Telecommunication 0.26193
0.42164
-1.4154 ** +++ 26.5276 *** +++ -0.2345
8.14237 *** + -0.0745
-1.4883
0.17609 0.0027 0.0075
(0.4767)
(1.6594)
(0.6245)
(8.5979)
(0.2849)
(1.9104)
(0.3521)
(4.9415)
Wholesale/Retail 0.26941
1.40053
-1.0972 ** ++ 22.3263 *** +++ -0.1166
4.32012 ***
-0.2381
0.78611
0.17369 0.1222 0.0057
(0.3539)
(1.2321)
(0.4637)
(6.3838)
(0.2116)
(1.4185)
(0.2614)
(3.6690)
Healthcare 0.34099
-0.6586
-1.0643 ** +++ 17.6587 *** +++ -0.0553
3.68315 ** ++ -0.1823
1.3938
0.10338 0.0297 0.0462
(0.3729)
(1.2982)
(0.4886)
(6.7264)
(0.2229)
(1.4946)
(0.2755)
(3.8659)
Utilities 0.46901 *
-3.0331 *** ++ -1.2017 *** +++ 20.1434 *** +++ 0.16432
0.61759
-0.0514
0.79209
0.19422 0.0076 0.0006
(0.2544)
(0.8855)
(0.3333)
(4.5881)
(0.1521)
(1.0195)
(0.1879)
(2.6369)
Others 0.01711
0.68685
-0.9759 *** ++ 20.0064 *** +++ -0.0154
3.46739 *** ++ -0.0801
0.17481
0.21701 0.0298 0.0002 (0.2390) (0.8319) (0.3131) (4.3103) (0.1428) (0.9577) (0.1765) (2.4773) VW 0.38294 -0.3554 -1.9822 *** +++ 30.0072 *** +++ 0.00337 5.72563 *** + 0.05873 -0.3571 0.21427 0.0031 0.0003
(0.3821)
(1.3303)
(0.5006)
(6.8926)
(0.2284)
(1.5315)
(0.2823)
(3.9614)
EW 0.12917
0.55022
-1.1453 *** +++ 21.12 *** +++ -0.1023
4.91203 *** + -0.1308
0.50662
0.20742 0.0063 0.0017
(0.2968)
(1.0333)
(0.3889)
(5.3539)
(0.1774)
(1.1896)
(0.2192)
(3.0771)
S&P500 0.47188
-1.158
-2.0368 *** +++ 31.169 *** +++ 0.01597
5.71071 *** + 0.08092
-0.1262
0.2056 0.0015 0.0004 (0.4000) (1.3925) (0.5241) (7.2151) (0.2391) (1.6032) (0.2955) (4.1467)
47
Under “Contraction” panel, Utilities is the only industry, among all industry and market
portfolios, showing significantly negative (also proved by Newey-west statistics) reaction to the
negative shocks. A 1% rise in the negative shock drops the stock price of Utilities by 3.03%. A
possible explanation on such uniqueness on Utilities is that under normal conditions, Utility
industry is regulated and is immune to most macroeconomic factors. For example, the
participators may be subsidized by local government should there be a rise in capital cost.
However, during contraction periods, the industry may lose its special treatment due to the heavy
burden sustained by the government. A negative surprise during contraction periods may even
signal a worse future outlook on the industry. The fact that all portfolios, except Utilities, show
insignificant relation between negative shocks and stock returns validates my previous argument
that a negative surprise during recessions is not something extraordinary and may not really be a
“surprise” to the money market.
For the impact of positive surprises under “Contraction” panel, the intercept
coefficients,𝛽3𝑠 , react significantly and negatively (in terms of T-statistics and Newey-west
statistics) to the positive shocks across all ten industry portfolios and all three market indexes.
The result indicates that the existence of positive surprise itself decreases the stock returns by at
most 1.52% in industry portfolios and at most 2.04% in market indexes. The slope coefficients,
𝛽4s, on the other hand, show significant and positive relations between the positive shocks and
the stock returns. Judging on the magnitudes of the slope coefficients alone, the negative effect
of the intercept coefficients would easily be cancelled out. The results indicate that for every 1%
increase in the shock, stock returns increase by at least 17.66% (at most 26.25%) in industry
portfolios and increase by at least 21.12% (at most 31.17%) in market indexes. The positive
relation between the positive shocks and the stock returns during contraction periods confirms
48
my previous signaling argument that a positive surprise implies a reverse in the cycle trends and
that the worst era is already over.
Under “Expansion” panel, none of the coefficients on positive surprise shows significant
relation between the positive shocks and the stock returns. My results appear to be puzzling from
a purely DCF model perspective. Consider the finding that during “Expansion”, none of the
coefficients on positive surprise is statistically significant. A positive surprise occurs either when
a rate increase is underestimated or a rate cut is overestimated. An underestimated rate increase
signals the perception of Federal Reserve that ongoing inflation has to be slowed down. An
overestimated rate cut signals the perception that current money market does not need as much
additional money supply as anticipated by the market. Both would unexpectedly raise the
borrowing cost for a firm and discount rate for an investor, and thus signal “bad news” for asset
prices. This lack of significant relation between the positive interest rate shocks and the stock
returns can be explained in terms of behavioral finance. According to the prospect theory
proposed by Kahneman and Tversky (1979), the value function for an individual is concave in
the gain domain and convex in the loss domain. During “good” times, investors harvest profit
more often from the money market and tend to be over-confident and optimistic.
On the other hand, in facing the bad news, investors have a tendency to discount bad
news less rigorously than good news. This argument is further validated from the negative
surprise during expansion periods. 𝛽6 is significantly and positively correlated with stock returns
during expansion periods across all portfolios, except Energy and Utilities. The insignificance of
Utility industry stock performance towards negative shocks during expansions confirms my
previous argument that this industry is immune to macroeconomic shocks during normal periods.
49
In the last two columns of Table 4.9, I run a cross-period equality test on all the slope
coefficients for both negative and positive shocks. The second last column shows the p-values of
F-test on the null 𝛽2= 𝛽6 while the last column shows the p-values of F-test on the null 𝛽4= 𝛽8.
Across the cross-period test for the negative surprise (second last column), all but three
portfolios show that the impact of negative surprise during contractions is significantly different
from that during expansions. Meanwhile across the last column, all portfolios show significant
different impact of positive shocks between contractions and expansions. The results confirm my
hypothesis on the simultaneous asymmetry that the asymmetric impact on stock returns are
jointly caused by both the signs of the target rate surprises and the business cycles.
4.6 Equity Duration of Surprise Signs and Business Cycles based on Federal Funds Rate
Surprises
Similar to the previous test, I also run Equation (11) on the ten-decile portfolios based on
the four fundamental-to-price ratios. The results of the ranked portfolios are presented in Table
4.10. Panel A presents the results for DP, panel B presents the results for BM, panel C presents
the results for EP, and panel D presents the results for CP. I find strong evidence of asymmetric
price reaction to positive and negative interest rate shocks. I also find that the asymmetries are
pronounced when I compare them across business cycles. I specifically find that portfolio returns
only respond to positive interest rate shocks during contractions and to negative interest rate
shocks during expansions. In contrast to the results from Equation (8), the slope coefficients of
negative and positive surprises in Equation (11) show positive relation between stock returns and
rate shocks. Also, regressions based on Equation (8) generate R-squares ranging from 1.76% to
8.42%, while regressions based on Equation (11) generate R-squares ranging from 11.63% to
23.39%. Higher R-square value from Equation (7) implies that separation of Federal Funds rate
50
shocks between business cycles is not only important in proving asymmetries but also important
in generating a more reliable relation between stock returns and monetary policy shocks.
I also consider the impact of equity duration as I compare the slope coefficients of 𝛽2 ,
𝛽4 ,𝛽6 and 𝛽8 of Equation (11). While the magnitudes of the surprise slope coefficients appear to
decrease gradually from the first decile (P1) portfolio to the tenth decile (P10), I apply the Wald
test to examine whether there is a statistically difference in the coefficients associated with the
positive (𝛽4) and negative ( 𝛽6 ) surprises across each portfolio deciles along the growth-value
axis. The Wald test results across the deciles portfolios are reported in Panels A through D of
Table 4.11.1 and Table 4.11.2, for portfolio deciles based on DP, BM, EP, and CP, respectively.
Table 4.11.1 reports the Wald test results associated with negative (𝛽2) and positive (𝛽4)
surprises during contractions periods, while Table 4.11.2 reports the Wald test results associated
with negative (𝛽6) and positive (𝛽8) surprises during expansion periods.
During contractions across the positive surprise [Table 4.11.1], only Panel A (DP)
demonstrates quite a number of significant pairs across growth stocks portfolios (P1, P2) and
across value stocks portfolios (P10, P9) that statistically reject the null hypothesis. Meanwhile,
across negative surprise during contractions, I barely find any consistent evidence of equity
duration in each of the four panels.
On the other hand, during expansions across the negative surprise [Table 4.11.2], Panel A
(DP), Panel B (BP), and Panel C (EP) demonstrate several bold pairs across growth stocks
portfolios (P1, P2). Meanwhile, across positive surprise during expansions, I barely find any
statistical evidence of equity duration in each of the four panels.
51
Table 4.10: Asymmetric Response of Equity Prices to Different Business Cycles, by Portfolios based on Fundamental-to-Price Ratios The following table shows the results on the impact of the presence and magnitude of surprises in Federal funds rate changes on 1-day stock returns, allowing for different effects of positive and negative surprises and for different economic cycles. Here is the regression equation:
𝑅𝑡 = 𝛼 + {(𝛽1 + 𝛽2 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 < 0) + (𝛽3 + 𝛽4 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 > 0)} ∗ 𝐷(𝐶𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛) + {(𝛽5 + 𝛽6 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 < 0) + (𝛽7 + 𝛽8 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 > 0)} ∗ 𝐷(𝐸𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛) + 𝜀𝑡
where D(A) is a dummy variable taking the value 1 if the event A is true and 0 otherwise. Negative and positive surprises occur 17 and 6 cases during contraction periods and 56 and 40 cases during expansion periods, respectively. The models are estimated for individual stocks in AMEX, NYSE, and Nasdaq following 171 FOMC meetings between Jan 1990 and Oct 2008. Average coefficient estimates and R-square values are shown across all portfolios. The asterisks of ***, **, and * represent statistical significance at the 1%, 5%, and 10% level, respectively. The plus signs of +++, ++, and + represent Newey-West statistical significant at the 1%, 5%, and 10% level, respectively, based on Newey-West standard errors. Columns headed "Cross Period Equality Test" contain p-values of F-test statistics for testing the indicated restrictions for the average coefficients. The p-values of “Cross Period Equality Test” in bold denotes significance at 5% level. Panel A records the price response of three market indexes: VW and EW are the value-weighted and equal-weighted market portfolios, respectively, and S&P500 is the index portfolio of S&P 500. Panel B records the price response of 10 portfolios sorted by dividend yield (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). Panel C records the price response of 10 portfolios sorted by book-to-market ratio. Panel D records the price response of 10 portfolios sorted by earnings-to-price ratio. Panel E records the price response of 10 portfolios sorted by cashflows-to-price ratio. Contraction Expansion Cross Period
Negative Surprise Positive Surprise Negative Surprise Positive Surprise Equality Test
Portfolio β1 β2 β3 β4 β5 β6 β7 β8 R2 Ho: β2=β6 Ho: β4=β8
Pane
l A: D
ivid
end
Yiel
d
P1 0.2078 1.1920 -1.8025 *** +++ 32.1447 *** +++ -0.0028 4.5516 *** + -0.1106 -0.3195 0.2307 0.0766 0.0000 P2 0.2135 0.3660 -1.2747 *** +++ 26.6524 *** +++ -0.0228 3.8327 *** + -0.1761 0.2918 0.2061 0.0386 0.0002 P3 0.0611 0.5180 -1.2412 *** ++ 28.0406 *** +++ 0.0111 2.6454 ** -0.1559 0.7039 0.1851 0.1965 0.0001 P4 0.1071 0.3330 -1.3059 *** ++ 24.9962 *** +++ -0.0135 2.6766 ** + -0.1271 -0.1766 0.1969 0.1096 0.0000 P5 0.1849 -0.0957 -0.8672 ** ++ 17.7801 *** +++ -0.0401 2.9466 *** + -0.0648 -0.6552 0.1504 0.0284 0.0013 P6 -0.0180 0.6600 -1.0680 *** + 23.2005 *** +++ 0.0609 2.0919 ** -0.1354 1.0637 0.1841 0.3019 0.0001 P7 -0.0687 0.5926 -0.9749 *** ++ 17.7170 *** +++ -0.0137 2.8040 *** + -0.0713 1.0300 0.1647 0.0849 0.0017 P8 -0.1924 0.9584 -0.4899 * +++ 11.6050 *** +++ 0.0454 1.6451 ** + -0.0705 1.3698 0.1163 0.5243 0.0213 P9 -0.0864 0.8905 -0.5240 ** 15.0414 *** +++ 0.0601 2.3977 *** +++ -0.0741 1.7282 0.1829 0.1650 0.0030 P10 -0.0620 0.8746 -0.5935 + 17.1259 *** +++ 0.0263 3.1272 *** ++ -0.0556 2.1126 0.1399 0.1257 0.0131
Pane
l B: B
ook-
to-m
arke
t
P1 0.3102 1.0796 -1.6987 *** +++ 26.7607 *** +++ 0.0405 6.0494 *** -0.0935 0.7313 0.1561 0.0532 0.0137 P2 0.2596 1.1423 -1.6218 *** +++ 26.3906 *** +++ -0.0908 5.6533 *** + -0.1510 0.2172 0.1740 0.0440 0.0045 P3 0.2184 0.4324 -1.4448 *** +++ 26.3346 *** +++ -0.0780 4.9675 *** + -0.1771 0.2460 0.1790 0.0237 0.0016 P4 0.3465 0.0388 -1.5424 *** +++ 26.6066 *** +++ -0.0265 4.6032 *** -0.0292 -1.9400 0.1895 0.0164 0.0003 P5 0.2799 0.2480 -1.1711 *** ++ 23.9031 *** +++ -0.1090 4.2884 *** -0.2950 1.0789 0.1954 0.0202 0.0015 P6 0.0257 0.4922 -1.1925 *** +++ 23.1911 *** +++ -0.1510 4.5088 *** ++ -0.1432 -0.8457 0.2033 0.0119 0.0003 P7 0.0763 0.9219 -1.1278 *** ++ 21.5744 *** +++ -0.0826 3.7272 *** -0.1593 0.9182 0.1754 0.0767 0.0016 P8 0.0895 0.4298 -0.9567 *** +++ 20.4292 *** +++ -0.0730 3.6031 *** + -0.1757 0.8494 0.1833 0.0301 0.0012 P9 -0.0177 0.0501 -0.9456 *** ++ 18.5977 *** +++ -0.1191 3.3220 *** + -0.1800 1.3461 0.1472 0.0272 0.0046 P10 -0.0240 1.4427 -0.9370 ** +++ 19.6216 *** +++ -0.2004 5.8260 *** + -0.1526 1.8593 0.2339 0.0048 0.0052
52
Pane
l C: E
arni
ngs-
to-p
rice
P1 0.1990 1.4278 -1.5895 *** +++ 25.8935 *** +++ -0.0260 5.3140 *** + -0.0901 -1.2221 0.1784 0.0746 0.0026 P2 0.2328 0.6239 -1.5294 *** +++ 27.7685 *** +++ -0.0959 4.9719 *** + -0.1178 -0.3994 0.1892 0.0270 0.0005 P3 0.1699 0.2384 -1.3125 *** +++ 24.3170 *** +++ -0.0464 4.2535 *** -0.1331 0.2942 0.1626 0.0320 0.0019 P4 0.2095 0.0713 -1.3839 *** +++ 27.2138 *** +++ 0.0096 3.4278 *** -0.1460 0.6943 0.1906 0.0486 0.0002 P5 0.2588 -0.4060 -1.0868 *** ++ 22.7609 *** +++ -0.0658 4.0491 *** -0.2183 0.9039 0.2024 0.0046 0.0007 P6 0.0588 0.5406 -1.2627 *** +++ 24.7137 *** +++ -0.0547 3.5713 *** -0.2415 1.3198 0.2041 0.0531 0.0003 P7 0.1440 0.3353 -1.1256 *** ++ 22.2816 *** +++ -0.0735 2.9043 *** + -0.2434 0.9768 0.1867 0.0792 0.0005 P8 -0.0074 0.7904 -1.1718 *** ++ 23.2575 *** +++ -0.0760 3.5287 *** + -0.1946 0.6434 0.2088 0.0604 0.0002 P9 0.1282 0.6172 -1.0758 *** ++ 20.3296 *** +++ -0.0434 3.4692 *** + -0.1636 0.9153 0.1820 0.0541 0.0015 P10 0.2011 0.2984 -1.3501 *** +++ 26.0626 *** +++ -0.0529 3.6964 *** + -0.1110 0.3747 0.1990 0.0347 0.0001
Pane
l D: C
ashf
low
s-to
-pric
e P1 -0.0036 1.0608 -1.1090 *** +++ 21.1355 *** +++ -0.1134 4.7299 *** -0.1646 -0.4384 0.1975 0.0264 0.0015 P2 0.0764 0.7222 -1.0418 *** +++ 21.5263 *** +++ -0.1206 4.3796 *** ++ -0.1256 0.0946 0.2013 0.0163 0.0006 P3 -0.0256 0.8090 -1.0476 *** ++ 21.4966 *** +++ -0.0340 3.7987 *** ++ -0.1943 1.0487 0.1959 0.0487 0.0011 P4 0.0719 0.5777 -1.3205 *** +++ 21.8795 *** +++ -0.1192 3.6912 *** -0.2228 1.3829 0.1794 0.0495 0.0017 P5 0.1977 0.4534 -1.4298 *** +++ 27.5359 *** +++ -0.0342 3.3034 ** -0.2025 0.4632 0.1840 0.1071 0.0002 P6 0.2797 0.3636 -1.2631 *** +++ 25.1401 *** +++ -0.0851 4.2664 *** -0.1745 0.4139 0.1792 0.0319 0.0010 P7 0.2590 0.3973 -1.4193 *** +++ 25.6536 *** +++ -0.0998 4.8830 *** -0.2078 0.9402 0.1993 0.0147 0.0011 P8 0.1754 0.1995 -1.5284 *** +++ 26.9339 *** +++ -0.0779 4.4014 *** -0.1311 0.0124 0.1941 0.0193 0.0003 P9 0.3882 0.1489 -1.3909 *** +++ 26.5095 *** +++ -0.0303 4.1868 *** -0.1210 0.2029 0.1970 0.0231 0.0004 P10 0.1582 0.4303 -1.3027 *** +++ 25.7638 *** +++ -0.0105 4.2159 *** + -0.1375 0.8392 0.2077 0.0233 0.0003
53
Table 4.11.1: Wald Test - Sensitivity of Stock Prices to Negative & Positive Target Changes Surprises during different business cycles, by Portfolios based on Fundamental-to-Price Ratios. Tables show the results of the following SUR regression for the price changes of ith and jth decile portfolios, ΔPt,i and ΔPt,j, on the negative and positive shocks during different business cycles. The tests on each type of shocks (POSITIVE or NEGATIVE) and during each business cycle (CONTRACTION or EXPANSION) are shown in each sub-table below. P1 through P10 are 10 portfolios sorted by respective ratio of fundamental-to-price. All portfolios are constructed using stocks listed on NYSE, AMEX, and Nasdaq, and are obtained from CRSP. Panel A records the price response of 10 portfolios sorted by dividend yield (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). Panel B records the price response of 10 portfolios sorted by book-to-market ratio. Panel C records the price response of 10 portfolios sorted by earnings-to-price ratio. Panel D records the price response of 10 portfolios sorted by cashflows-to-price ratio. The tables reports the heteroskedastic-consistent Wald statistics of the null hypothesis 𝛽2𝑖 =𝛽2𝑗 and of the null hypothesis 𝛽4𝑖 = 𝛽4𝑗 . Bold denotes significance at the 5 percent level.
∆𝑃𝑡,𝑖 = 𝛼𝑖 + {(𝛽1𝑖 + 𝛽2𝑖 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 < 0) + (𝛽3𝑖 + 𝛽4𝑖 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 > 0)} ∗ 𝐷(𝐶𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛)+ {(𝛽5𝑖 + 𝛽6𝑖 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 < 0) + (𝛽7𝑖 + 𝛽8𝑖 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 > 0)} ∗ 𝐷(𝐸𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛) + 𝜀𝑡,𝑖
∆𝑃𝑡,𝑗 = 𝛼𝑖 + ��𝛽1𝑗 + 𝛽2𝑗 ∗ ∆�̃�𝑡𝑢�𝐷(∆�̃�𝑡𝑢 < 0) + �𝛽3𝑗 + 𝛽4𝑗 ∗ ∆�̃�𝑡𝑢�𝐷(∆�̃�𝑡𝑢 > 0)� ∗ 𝐷(𝐶𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛)+ ��𝛽5𝑗 + 𝛽6𝑗 ∗ ∆�̃�𝑡𝑢�𝐷(∆�̃�𝑡𝑢 < 0) + �𝛽7𝑗 + 𝛽8𝑗 ∗ ∆�̃�𝑡𝑢�𝐷(∆�̃�𝑡𝑢 > 0)� ∗ 𝐷(𝐸𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛) + 𝜀𝑡,𝑗
Impact from NEGATIVE Shocks during CONTRACTIONs (H0: 𝛽2𝑖 =𝛽2𝑗) Impact from POSITIVE Shocks during CONTRACTIONs (H0: 𝛽4𝑖 = 𝛽4𝑗)
P1 P2 P3 P4 P5 P6 P7 P8 P9 P1 P2 P3 P4 P5 P6 P7 P8 P9
Pane
l A: D
ivid
end
Yiel
d
P2 3.86 6.35 P3 1.74 0.17
2.40 0.53
P4 2.34 0.01 0.36
6.03 0.64 3.61
P5 4.71 1.18 3.27 2.11
21.82 16.20 34.08 22.24
P6 0.77 0.43 0.14 1.15 5.37
8.16 2.21 6.26 1.30 10.29
P7 0.67 0.17 0.02 0.32 2.86 0.03
14.46 9.56 15.76 9.42 0.00 6.19
P8 0.07 0.65 0.44 1.06 3.55 0.27 0.66
18.97 15.66 22.70 18.04 4.53 15.27 6.85
P9 0.10 0.42 0.26 0.67 2.31 0.12 0.34 0.03 11.56 7.63 11.79 7.97 0.66 5.79 1.01 3.23 P10 0.09 0.32 0.18 0.43 1.46 0.07 0.19 0.02 0.00 7.66 4.13 6.27 3.42 0.02 2.09 0.03 3.61 0.75
Pane
l B: B
ook-
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arke
t P2 0.02 0.02 P3 0.87 3.01
0.01 0.00
P4 1.97 5.62 1.24
0.00 0.01 0.02
P5 0.97 2.56 0.25 0.33
0.42 0.74 1.62 2.07
P6 0.34 0.86 0.02 0.93 0.49
0.47 0.77 1.59 1.96 0.16
P7 0.03 0.10 1.01 4.00 4.26 1.96
1.04 1.84 3.57 4.84 1.89 1.03
P8 0.38 0.84 0.00 0.53 0.19 0.03 1.93
1.34 2.18 4.35 4.96 2.63 2.49 0.39
P9 0.88 1.74 0.36 0.00 0.17 1.15 4.42 1.02 2.06 3.30 5.54 6.10 4.45 4.62 1.92 0.89 P10 0.10 0.10 1.58 3.26 3.39 2.18 0.79 3.26 6.38 1.38 1.88 2.60 3.01 1.62 1.14 0.41 0.08 0.13
54
Pane
l C: E
arni
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rice P2 3.04 0.62
P3 4.71 0.97
0.31 2.91
P4 4.59 1.66 0.25
0.16 0.06 2.82
P5 6.66 4.41 2.44 2.24
0.72 3.89 0.53 7.26
P6 1.44 0.02 0.45 2.08 9.96
0.10 1.08 0.03 2.20 1.58
P7 1.70 0.21 0.03 0.44 4.18 0.38
0.69 2.77 0.50 5.68 0.07 1.99
P8 0.58 0.07 0.96 2.95 9.56 0.50 2.06
0.37 1.86 0.13 3.32 0.06 0.63 0.35
P9 0.94 0.00 0.45 1.74 7.79 0.04 0.68 0.26 1.65 5.21 1.87 10.31 1.64 5.24 1.22 2.76 P10 1.88 0.26 0.01 0.25 2.64 0.29 0.01 1.42 0.85 0.00 0.26 0.34 0.24 2.16 0.34 2.95 1.72 10.26
Pane
l D: C
ashf
low
s-to
-pric
e P2 0.65 0.52 P3 0.29 0.05
3.00 1.67
P4 0.94 0.13 0.35
3.28 2.17 0.06
P5 1.12 0.37 0.80 0.15
4.67 4.51 1.17 1.11
P6 1.92 0.64 1.07 0.36 0.07
0.64 0.05 0.89 1.98 5.79
P7 1.51 0.48 0.91 0.22 0.02 0.01
0.06 0.86 4.76 7.31 14.10 2.88
P8 2.34 1.21 1.81 0.99 0.52 0.26 0.38
0.26 0.00 1.33 2.62 7.28 0.13 1.69
P9 2.29 1.30 1.94 1.12 0.56 0.38 0.55 0.02 0.61 0.11 0.51 1.13 3.58 0.04 3.29 0.32 P10 1.05 0.33 0.58 0.10 0.00 0.03 0.01 0.27 0.60 0.53 0.08 0.53 0.93 2.84 0.01 1.74 0.13 0.00
55
Table 4.11.2 (continued from Table 4.11.1): Wald Test - Sensitivity of Stock Prices to Negative & Positive Target Changes Surprises during different business cycles, by Portfolios based on Fundamental-to-Price Ratios. Tables show the results of the following SUR regression for the price changes of ith and jth decile portfolios, ΔPt,i and ΔPt,j, on the negative and positive shocks during different business cycles. The tests on each type of shocks (POSITIVE or NEGATIVE) and during each business cycle (CONTRACTION or EXPANSION) are shown in each sub-table below. P1 through P10 are 10 portfolios sorted by respective ratio of fundamental-to-price. All portfolios are constructed using stocks listed on NYSE, AMEX, and Nasdaq, and are obtained from CRSP. Panel A records the price response of 10 portfolios sorted by dividend yield (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). Panel B records the price response of 10 portfolios sorted by book-to-market ratio. Panel C records the price response of 10 portfolios sorted by earnings-to-price ratio. Panel D records the price response of 10 portfolios sorted by cashflows-to-price ratio. The tables reports the heteroskedastic-consistent Wald statistics of the null hypothesis 𝛽6𝑖 =𝛽6𝑗 and of the null hypothesis 𝛽8𝑖 = 𝛽8𝑗 . Bold denotes significance at the 5 percent level.
∆𝑃𝑡,𝑖 = 𝛼𝑖 + {(𝛽1𝑖 + 𝛽2𝑖 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 < 0) + (𝛽3𝑖 + 𝛽4𝑖 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 > 0)} ∗ 𝐷(𝐶𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛)+ {(𝛽5𝑖 + 𝛽6𝑖 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 < 0) + (𝛽7𝑖 + 𝛽8𝑖 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 > 0)} ∗ 𝐷(𝐸𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛) + 𝜀𝑡,𝑖
∆𝑃𝑡,𝑗 = 𝛼𝑖 + ��𝛽1𝑗 + 𝛽2𝑗 ∗ ∆�̃�𝑡𝑢�𝐷(∆�̃�𝑡𝑢 < 0) + �𝛽3𝑗 + 𝛽4𝑗 ∗ ∆�̃�𝑡𝑢�𝐷(∆�̃�𝑡𝑢 > 0)� ∗ 𝐷(𝐶𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛)+ ��𝛽5𝑗 + 𝛽6𝑗 ∗ ∆�̃�𝑡𝑢�𝐷(∆�̃�𝑡𝑢 < 0) + �𝛽7𝑗 + 𝛽8𝑗 ∗ ∆�̃�𝑡𝑢�𝐷(∆�̃�𝑡𝑢 > 0)� ∗ 𝐷(𝐸𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛) + 𝜀𝑡,𝑗
Impact from NEGATIVE Shocks during EXPANSIONs (H0: 𝛽6𝑖 = 𝛽6𝑗) Impact from POSITIVE Shocks during EXPANSIONs (H0: 𝛽8𝑖 = 𝛽8𝑗)
P1 P2 P3 P4 P5 P6 P7 P8 P9 P1 P2 P3 P4 P5 P6 P7 P8 P9
Pane
l A: D
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Yiel
d
P2 2.20
0.24 P3 10.51 7.89
0.45 0.14
P4 8.40 6.27 0.01
0.01 0.15 0.91
P5 5.52 3.27 0.60 0.63
0.04 0.56 1.81 0.30
P6 12.49 11.40 1.66 2.78 5.18
0.59 0.33 0.10 1.87 3.13
P7 4.30 2.57 0.08 0.06 0.09 2.11
0.38 0.20 0.05 0.78 1.93 0.00
P8 7.69 6.70 1.70 2.17 4.08 0.46 4.99
0.39 0.24 0.11 0.73 1.48 0.03 0.06
P9 3.71 2.36 0.09 0.13 0.54 0.16 0.47 3.14 0.50 0.35 0.22 0.88 1.52 0.12 0.21 0.11 P10 1.39 0.46 0.25 0.23 0.04 1.23 0.19 5.27 1.86 0.61 0.46 0.32 0.88 1.34 0.19 0.32 0.20 0.08
Pane
l B: B
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t P2 0.52 0.13 P3 1.83 2.12
0.06 0.00
P4 2.87 3.84 0.80
1.47 2.42 4.32
P5 3.27 4.49 2.56 0.57
0.02 0.27 0.58 7.80
P6 1.76 2.00 0.68 0.03 0.30
0.27 0.26 0.58 0.61 3.47
P7 4.22 5.94 4.91 2.97 2.23 4.88
0.00 0.12 0.22 4.73 0.03 3.72
P8 4.07 5.23 4.71 2.64 2.07 5.42 0.09
0.00 0.07 0.14 3.06 0.03 2.84 0.00
P9 4.65 5.98 5.08 3.16 2.99 6.24 0.72 0.42 0.04 0.21 0.34 3.11 0.03 3.18 0.12 0.20 P10 0.03 0.02 0.86 1.87 4.23 3.16 9.64 11.86 15.57 0.10 0.34 0.46 2.69 0.16 1.99 0.29 0.37 0.10
56
Pane
l C: E
arni
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rice P2 0.41
0.36
P3 2.82 2.55
0.86 0.36
P4 6.69 9.75 4.63
1.03 0.73 0.16
P5 2.39 2.67 0.19 2.86
1.01 0.80 0.25 0.05
P6 4.20 4.59 1.72 0.15 1.91
1.34 1.03 0.58 0.42 0.22
P7 6.22 7.96 4.44 1.30 7.51 3.04
0.77 0.53 0.17 0.06 0.00 0.12
P8 3.43 3.85 1.25 0.04 1.36 0.01 2.93
0.56 0.30 0.04 0.00 0.05 0.41 0.12
P9 3.67 4.30 1.47 0.01 1.89 0.06 2.07 0.02 0.74 0.49 0.14 0.03 0.00 0.13 0.00 0.07 P10 2.91 2.98 0.70 0.27 0.50 0.06 2.62 0.12 0.33 0.42 0.16 0.00 0.06 0.17 0.51 0.23 0.05 0.28
Pane
l D: C
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low
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-pric
e P2 0.03 0.18 P3 0.02 0.00
1.14 0.67
P4 0.08 0.03 0.04
1.51 1.13 0.08
P5 4.64 6.95 8.56 11.67
0.28 0.08 0.24 0.93
P6 2.36 2.42 2.67 3.14 1.77
0.32 0.06 0.25 0.84 0.00
P7 2.60 2.87 3.45 3.62 0.99 0.10
0.73 0.36 0.01 0.15 0.19 0.31
P8 3.96 4.83 5.36 6.56 0.11 1.15 0.59
0.07 0.00 0.59 1.46 0.18 0.17 0.94
P9 2.96 3.65 4.17 4.85 0.24 0.58 0.25 0.06 0.13 0.01 0.36 0.95 0.05 0.04 0.55 0.04 P10 2.11 2.57 2.75 2.52 0.53 0.08 0.00 0.26 0.16 0.49 0.24 0.02 0.15 0.07 0.12 0.01 0.39 0.34
57
(12)
These evidences that price sensitivity varies between growth stocks and value stocks
suggest that existence of equity duration is conditional to both the direction of surprise and the
type of business cycles. The evidences also imply that the price sensitivity matters only when the
factors (signs of surprise and business cycles) of asset pricing become statistically significant.
This conclusion is further checked by using paired difference T-test. The model is tested on
Equation (12):
∆𝑃𝑡,𝑖 − ∆𝑃𝑡,𝑗 = 𝛼 + {(𝛽1 + 𝛽2 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 < 0) + (𝛽3 + 𝛽4 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 > 0)} ∗ 𝐷(𝐶𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛) +
{(𝛽5 + 𝛽6 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 < 0) + (𝛽7 + 𝛽8 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 > 0)} ∗ 𝐷(𝐸𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛) + 𝜀𝑡
The results of paired difference T-test are shown in Table 4.12.1 and Table 4.12.2. On the
positive surprise column during contractions [Table 4.12.1], only Panel A (DP) demonstrates
significant pairs across growth stocks portfolios (P1, P2) and across value stocks portfolios (P10,
P9) that statistically reject the null hypothesis. On the negative surprise column during
contractions, I cannot find sufficient evidence of equity duration.
On the other hand, during expansions across the negative surprise [Table 4.12.2], Panel A
(DP) demonstrates large number of significant pairs across growth stocks portfolios (P1, P2), and
Panel B (BP) demonstrates some scattered bold pairs across value stocks portfolios (P10, P9)
that statistically reject the null hypothesis.
The results of Table 4.12.1 and Table 4.12.2 validate the ones found in Table 4.11.1 and
Table 4.11.2, respectively. However, I find week support for the hypothesis the growth and value
stocks exhibit price sensitivity variance across value-growth stocks measurements. The statistics
results of equity duration are not consistent across ratios DP, BP, EP, and CP. Overall, only the
results from DP consistently support the existence of equity duration when the surprises are spilt
into different directions and into different business cycles.
58
Table 4.12.1: Paired Difference Test - Sensitivity of Stock Prices to Negative & Positive Target Changes Surprises during different business cycles, by Portfolios based on Fundamental-to-Price Ratios. Table shows results of regression of the mean difference of one-day price changes between ith and jth decile portfolios, (∆𝑃𝑡,𝑖 − ∆𝑃𝑡,𝑗), where i ≠ j, on the negative and positive shocks during different business cycles. The tests on each type of shocks (POSITIVE or NEGATIVE) and during each business cycle (CONTRACTION or EXPANSION) are shown in each sub-table below. P1 through P10 are 10 portfolios sorted by respective ratio of fundamental-to-price. All portfolios are constructed using stocks listed on NYSE, AMEX, and Nasdaq, and are obtained from CRSP. Panel A records the price response of 10 portfolios sorted by dividend yield (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). Panel B records the price response of 10 portfolios sorted by book-to-market ratio. Panel C records the price response of 10 portfolios sorted by earnings-to-price ratio. Panel D records the price response of 10 portfolios sorted by cashflows-to-price ratio. The table reports the t test of the null hypothesis 𝛽2 = 0 and the null hypothesis 𝛽4= 0. Bold denotes significance at the 5 percent level.
∆𝑃𝑡,𝑖 − ∆𝑃𝑡,𝑗 = 𝛼 + {(𝛽1 + 𝛽2 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 < 0) + (𝛽3 + 𝛽4 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 > 0)} ∗ 𝐷(𝐶𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛) + {(𝛽5 + 𝛽6 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 < 0) + (𝛽7 + 𝛽8 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 > 0)}∗ 𝐷(𝐸𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛) + 𝜀𝑡
Impact from NEGATIVE Shocks during CONTRACTIONs (H0: 𝛽2 = 0) Impact from POSITIVE Shocks during CONTRACTIONs (H0: 𝛽4= 0)
P1 P2 P3 P4 P5 P6 P7 P8 P9 P1 P2 P3 P4 P5 P6 P7 P8 P9
Pane
l A: D
ivid
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Yiel
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P2 0.83 5.47 P3 0.67 -0.15
4.19 -1.28
P4 0.86 0.03 0.19
7.15 1.68 2.96
P5 1.29 0.46 0.61 0.43
14.44 8.97 10.25 7.29
P6 0.53 -0.29 -0.14 -0.33 -0.76
9.15 3.68 4.96 2.00 -5.29
P7 0.60 -0.23 -0.07 -0.26 -0.69 0.07
14.63 9.16 10.44 7.48 0.19 5.48
P8 0.23 -0.59 -0.44 -0.63 -1.05 -0.30 -0.37
21.04 15.57 16.85 13.89 6.60 11.89 6.41
P9 0.30 -0.52 -0.37 -0.56 -0.99 -0.23 -0.30 0.07
17.79 12.32 13.60 10.65 3.35 8.65 3.16 -3.25
P10 0.32 -0.51 -0.36 -0.54 -0.97 -0.21 -0.28 0.08 0.02 15.85 10.38 11.66 8.70 1.41 6.70 1.22 -5.19 -1.94
Pane
l B: B
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t P2 -0.06 0.09 P3 0.65 0.71
0.11 0.01
P4 1.04 1.10 0.39
-0.17 -0.26 -0.28
P5 0.83 0.89 0.18 -0.21
2.35 2.26 2.25 2.52
P6 0.59 0.65 -0.06 -0.45 -0.24
3.12 3.03 3.01 3.29 0.77
P7 0.16 0.22 -0.49 -0.88 -0.67 -0.43
4.91 4.82 4.80 5.08 2.56 1.79
P8 0.65 0.71 0.00 -0.39 -0.18 0.06 0.49
6.06 5.97 5.95 6.23 3.71 2.94 1.15
P9 1.03 1.09 0.38 -0.01 0.20 0.44 0.87 0.38
7.78 7.69 7.67 7.95 5.43 4.66 2.87 1.72
P10 -0.36 -0.30 -1.01 -1.40 -1.19 -0.95 -0.52 -1.01 -1.39 6.74 6.65 6.63 6.91 4.39 3.62 1.83 0.68 -1.04
59
Pane
l C: E
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rice P2 0.80 -1.89
P3 1.19 0.39
1.49 3.38
P4 1.36 0.55 0.17
-1.40 0.49 -2.89
P5 1.83 1.03 0.64 0.48
3.00 4.89 1.51 4.40
P6 0.89 0.08 -0.30 -0.47 -0.95
1.10 3.00 -0.39 2.51 -1.89
P7 1.09 0.29 -0.10 -0.26 -0.74 0.21
3.41 5.30 1.92 4.81 0.41 2.31
P8 0.64 -0.17 -0.55 -0.72 -1.20 -0.25 -0.46
2.46 4.35 0.97 3.86 -0.54 1.35 -0.95
P9 0.81 0.01 -0.38 -0.55 -1.02 -0.08 -0.28 0.17
5.44 7.33 3.95 6.84 2.45 4.34 2.03 2.99 P10 1.13 0.33 -0.06 -0.23 -0.70 0.24 0.04 0.49 0.32 -0.22 1.67 -1.71 1.18 -3.21 -1.32 -3.63 -2.68 -5.66
Pane
l D: C
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e P2 0.34
-0.34
P3 0.25 -0.09
-0.36 -0.02
P4 0.48 0.14 0.23
-1.03 -0.69 -0.67
P5 0.61 0.27 0.36 0.12
-6.52 -6.18 -6.16 -5.49
P6 0.70 0.36 0.45 0.21 0.09
-4.27 -3.93 -3.91 -3.24 2.25
P7 0.66 0.32 0.41 0.18 0.06 -0.03
-4.63 -4.29 -4.27 -3.59 1.89 -0.36
P8 0.86 0.52 0.61 0.38 0.25 0.16 0.20
-6.01 -5.67 -5.65 -4.98 0.51 -1.74 -1.38
P9 0.91 0.57 0.66 0.43 0.30 0.21 0.25 0.05
-5.44 -5.10 -5.08 -4.40 1.08 -1.16 -0.81 0.57
P10 0.63 0.29 0.38 0.15 0.02 -0.07 -0.03 -0.23 -0.28 -4.53 -4.19 -4.17 -3.50 1.99 -0.26 0.10 1.48 0.91
60
Table 4.12.2 (continued from Table 4.12.1): Paired Difference Test - Sensitivity of Stock Prices to Negative & Positive Target Changes Surprises during different business cycles, by Portfolios based on Fundamental-to-Price Ratios. Table shows results of regression of the mean difference of one-day price changes between ith and jth decile portfolios, (∆𝑃𝑡,𝑖 − ∆𝑃𝑡,𝑗), where i ≠ j, on the negative and positive shocks during different business cycles. The tests on each type of shocks (POSITIVE or NEGATIVE) and during each business cycle (CONTRACTION or EXPANSION) are shown in each sub-table below. P1 through P10 are 10 portfolios sorted by respective ratio of fundamental-to-price. All portfolios are constructed using stocks listed on NYSE, AMEX, and Nasdaq, and are obtained from CRSP. Panel A records the price response of 10 portfolios sorted by dividend yield (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). Panel B records the price response of 10 portfolios sorted by book-to-market ratio. Panel C records the price response of 10 portfolios sorted by earnings-to-price ratio. Panel D records the price response of 10 portfolios sorted by cashflows-to-price ratio. The table reports the t statistics of the null hypothesis 𝛽6 = 0 and the null hypothesis 𝛽8= 0. Bold denotes significance at the 5 percent level.
∆𝑃𝑡,𝑖 − ∆𝑃𝑡,𝑗 = 𝛼 + {(𝛽1 + 𝛽2 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 < 0) + (𝛽3 + 𝛽4 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 > 0)} ∗ 𝐷(𝐶𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛) + {(𝛽5 + 𝛽6 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 < 0) + (𝛽7 + 𝛽8 ∗ ∆�̃�𝑡𝑢)𝐷(∆�̃�𝑡𝑢 > 0)}∗ 𝐷(𝐸𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛) + 𝜀𝑡
Impact from NEGATIVE Shocks during EXPANSIONs (H0: b6i = 0) Impact from POSITIVE Shocks during EXPANSIONs (H0: b8i =0)
P1 P2 P3 P4 P5 P6 P7 P8 P9 P1 P2 P3 P4 P5 P6 P7 P8 P9
Pane
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d P2 0.72
-0.62 P3 1.91 1.19
-1.01 -0.39
P4 1.88 1.16 -0.03
-0.14 0.47 0.87
P5 1.60 0.89 -0.30 -0.27
0.35 0.96 1.36 0.49
P6 2.46 1.74 0.55 0.58 0.85
-1.35 -0.73 -0.34 -1.21 -1.70
P7 1.75 1.03 -0.16 -0.13 0.14 -0.71
-1.31 -0.70 -0.31 -1.17 -1.66 0.03
P8 2.91 2.19 1.00 1.03 1.30 0.45 1.16
-1.60 -0.99 -0.60 -1.46 -1.95 -0.26 -0.29
P9 2.15 1.44 0.25 0.28 0.55 -0.31 0.41 -0.75
-1.93 -1.31 -0.92 -1.79 -2.28 -0.58 -0.61 -0.33
P10 1.42 0.71 -0.48 -0.45 -0.18 -1.04 -0.32 -1.48 -0.73 -2.29 -1.67 -1.28 -2.15 -2.64 -0.94 -0.98 -0.69 -0.36
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t P2 0.40 0.47 P3 1.08 0.69
0.43 -0.04
P4 1.45 1.05 0.36
2.62 2.15 2.19
P5 1.76 1.36 0.68 0.31
-0.43 -0.90 -0.86 -3.05
P6 1.54 1.14 0.46 0.09 -0.22
1.50 1.03 1.07 -1.12 1.93
P7 2.32 1.93 1.24 0.88 0.56 0.78
-0.23 -0.70 -0.66 -2.85 0.20 -1.73
P8 2.45 2.05 1.36 1.00 0.69 0.91 0.12
-0.16 -0.63 -0.59 -2.78 0.27 -1.66 0.07
P9 2.73 2.33 1.65 1.28 0.97 1.19 0.41 0.28
-0.68 -1.15 -1.11 -3.30 -0.25 -2.18 -0.45 -0.52
P10 0.22 -0.17 -0.86 -1.22 -1.54 -1.32 -2.10 -2.22 -2.50 -1.20 -1.66 -1.63 -3.81 -0.76 -2.70 -0.96 -1.03 -0.52
61
Pane
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-0.83
P3 1.06 0.72
-1.53 -0.71
P4 1.89 1.54 0.83
-1.93 -1.10 -0.40
P5 1.26 0.92 0.20 -0.62
-2.15 -1.32 -0.62 -0.22
P6 1.74 1.40 0.68 -0.14 0.48
-2.55 -1.73 -1.02 -0.62 -0.41
P7 2.41 2.07 1.35 0.52 1.14 0.67
-2.23 -1.41 -0.70 -0.30 -0.08 0.32
P8 1.79 1.44 0.72 -0.10 0.52 0.04 -0.62
-1.90 -1.07 -0.36 0.03 0.25 0.66 0.34
P9 1.84 1.50 0.78 -0.04 0.58 0.10 -0.56 0.06
-2.16 -1.33 -0.63 -0.23 -0.01 0.40 0.08 -0.26 P10 1.62 1.28 0.56 -0.27 0.35 -0.13 -0.79 -0.17 -0.23 -1.61 -0.78 -0.07 0.33 0.54 0.95 0.63 0.29 0.55
Pane
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e P2 0.35 -0.52 P3 0.93 0.58
-1.49 -0.96
P4 1.04 0.69 0.11
-1.87 -1.35 -0.38
P5 1.43 1.08 0.50 0.39
-0.92 -0.40 0.56 0.95
P6 0.46 0.11 -0.47 -0.58 -0.96
-0.90 -0.37 0.59 0.97 0.02
P7 -0.15 -0.50 -1.08 -1.19 -1.58 -0.62
-1.40 -0.87 0.09 0.47 -0.48 -0.50
P8 0.33 -0.02 -0.60 -0.71 -1.10 -0.13 0.48
-0.49 0.04 1.00 1.38 0.44 0.41 0.91
P9 0.54 0.19 -0.39 -0.50 -0.88 0.08 0.70 0.21 -0.65 -0.13 0.83 1.22 0.27 0.25 0.75 -0.17 P10 0.51 0.16 -0.42 -0.52 -0.91 0.05 0.67 0.19 -0.03 -1.26 -0.74 0.23 0.61 -0.34 -0.36 0.14 -0.77 -0.61
62
4.7 Robustness Test: White Noise Residuals of Target Shock
Ideally, there shall not be serial correlation across time series among the shocks. The
estimates of unexpected target rate change (shocks) should be a series of white noise. I run
ARIMA specification to check whether the shocks are white noise. The test results are shown in
Table 4.13. Panel A of Table 4.13 presents autocorrelation check on the shocks up to 24 lags. At
a brief glance, lag 3 and lag 8 spread beyond two standard errors and they seem to be highly
significantly reacting to the shocks. To verify whether the lag 3 and the lag 8 are statistically
significant in a numerical way, I run conditional least square estimation on the two lags. The
results are shown in Panel B of Table 4.13. From the result, both lag 3 and lag 8 of the shocks are
significant at five percent significant level.
Besides autocorrelation among the time series shocks, I also would like to check and
control for, if there is any contemporaneous correlation between the residuals in the shocks series
(residuals from the estimation in Panel B) and the announced FOMC rate changes. I run a
conditional least square estimation of residuals from Panel B on the full sample series lags of
target raw change. As shown in Panel C of Table 4.13, I find that only lag 2 of raw change
significantly affects the residuals with P-value of 0.0062.
63
Table 4.13: ARIMA Procedure of White Noise Residuals Derivation Tables below explain ARIMA procedure for deriving white noise residuals of shocks in target rate change. The tests are based on 171 observations of Federal Funds Target announcements from year 1990 to 2008. Panel A shows autocorrelation chart of shocks in target rate change, for time series lags 0-24. “.” marks two standard errors. The asterisks represent the autocorrelation statistics of each lag. Panel B shows conditional least squares estimation of the shocks on 3rd and 8th time series lags, which represent the significant lags as discovered in Panel A. Panel C shows conditional least squares estimation of the regression residuals in Panel B on time series lags of 1-9 for raw change in Federal funds target rates. Panel D shows conditional least squares estimation of the Federal funds target shocks on 3rd and 8th time series shock lag as well as 2nd time series raw change lag. Residuals from regression in Panel D are the White Noise Residuals of shocks in target rate change. Panel A
Panel B
Panel C
Panel D
64
Altogether, I discover that lag 3 and lag 8 of the target rate shocks, and lag 2 of target rate
raw change react significantly to the time series shocks. Statistically, I need to get rid of the three
significant components of serial correlation. Practically speaking, however, I could not come up
with an economic implication for the existence of such correlation. The Federal Reserve, on
average, had around eight meetings per year during the nineteen-year sample period. Having a
significant 8th lag in the target rate shocks, for example, implies that a Federal Reserve decision
could be affected by another decision made a year ago. A possible explanation for such statistical
discover is the numerous zero shocks in the observations. As indicated by the Panel B in Table
3.1, there are thirty percent or 52 zero shocks out of 171 observations. Given such a high
frequency of zero-shock observations, there is a high possibility of repeating a zero shock
followed by a sequence of seven non-zero observations. If the existence of significant serial
correlation as shown in Table 4.13 is caused by the fact of high frequency of zero-shock
observations, I attribute the significant results to “coincidence” and no further adjustment is
needed.
Nevertheless, in order to generate white noise estimates, I run a conditional least square
estimate of the shocks in target rate change on the above mentioned three factors. The results are
displayed in Panel D of Table 4.13. The residuals of this estimation represent the white noise
residuals I am looking for. Finally I apply the white noise residuals from this model as my new
estimates of target rate shocks.
65
4.8 Robustness Test: Federal Funds Rate Surprises based on White Noise Residuals
Table 4.14 presents an OLS regression results of one-day stock reaction of ten industry
portfolios and three market indexes, based on 163 white noise residuals of target rate shocks
following 171 FOMC meetings between Jan 1990 and Oct 2008. The regression model is:
𝑅𝑡 = 𝛼 + 𝛽𝑒∆�̃�𝑡𝑒 + 𝛽𝑢∆𝑊𝑁𝑡� + 𝜀𝑡 (13)
The model is similar to the one tested in Panel B of Table 4.1, except that I replace the
independent variable ∆�̃�𝑡𝑢 with ∆𝑊𝑁𝑡� , where ∆𝑊𝑁𝑡� is the white noise residuals of target rate
shocks. All thirteen portfolios display results that are quite similar to the ones tested with pure
shocks. Not only the level of R-squares and the magnitudes of estimates, these portfolios also
confirm that only unanticipated components in the target rate decisions matter while expected
target rate changes do not. The results also validate that the white noise residuals are negatively
correlated with stock returns.
66
Table 4.14: The Response of Equity Prices to White-Noise Residuals of Surprises and Expected components of the target rate changes, by Industry Portfolios and by Market Indexes The following table shows the results of 1-day equity return of 10 industry portfolios on the white-noise residuals of surprises and expected components of the target rate changes. The 10 industry portfolios are constructed based on SIC code as in Fama & French (1988). The models are estimated for individual stocks in AMEX, NYSE, and Nasdaq based on 163 white-noise residuals of target rate change shocks following 171 FOMC meetings between Jan 1990 and Oct 2008. Average coefficient estimates and R-square values are shown across all portfolios. The asterisks of ***, **, and * represent t-statistical significance at the 1%, 5%, and 10% level, respectively, based on the standard errors given in parentheses. Model 𝑅𝑡 = 𝛼 + 𝛽𝑒∆�̃�𝑡𝑒 + 𝛽𝑢∆𝑊𝑁𝑡� + 𝜀𝑡
Anticipated and unanticipated components
Portfolio α βe βu R2 Non-Durable 0.2093 *** -0.3159
-0.6669
0.0153
(0.0586)
(0.2935)
(0.5575)
Durable 0.3052 *** -0.6491 * -2.4411 *** 0.0799
(0.0759)
(0.3805)
(0.7227)
Manufacturing 0.3021 *** -0.4578
-1.2792 * 0.0316
(0.0698)
(0.3500)
(0.6648)
Energy 0.2013 ** -0.3519
-0.0892
0.0037
(0.0911)
(0.4564)
(0.8668)
High Tech 0.3840 *** -0.4456
-3.0810 *** 0.0501
(0.1145)
(0.5737)
(1.0897)
Telecommunication 0.2786 *** -0.4745
-2.7033 *** 0.0474
(0.1049)
(0.5259)
(0.9988)
Wholesale/Retail 0.3257 *** -0.6027
-2.3286 *** 0.0710
(0.0768)
(0.3849)
(0.7310)
Healthcare 0.2268 *** -0.1354
-1.0310
0.0119
(0.0799)
(0.4004)
(0.7604)
Utilities 0.1304 ** -0.2178
0.9312 * 0.0215
(0.0580)
(0.2907)
(0.5520)
Others 0.2551 *** -0.4005
-1.1956 ** 0.0442
(0.0538) (0.2695) (0.5119)
VW 0.3380 *** -0.2711
-2.0154 ** 0.0381
(0.0861)
(0.4312)
(0.8191)
EW 0.2580 *** -0.3916
-1.7045 *** 0.0497
(0.0667)
(0.3340)
(0.6344)
S&P500 0.3226 *** -0.3395
-1.6653 * 0.0259 (0.0899)
(0.4505)
(0.8557)
67
4.9 Robustness Test: Equity Duration of Federal Funds Rate Surprises based on White Noise
Residuals
Similar to equity duration tests on the pure shocks, I use white noise residuals of the
shocks to run a regression on ten portfolios constructed and ranked based on selected
fundamental-to-price characteristics. Estimates associated with portfolios ranked on the basis of
dividend-to-price (DP), book-to-market (BM), earnings-to-price (EP), and cashflows-to-price
(CP) ratios are presented in panels A, B, C, and D of Table 4.15, respectively. In each panel,
portfolio ranking are ordered from the smallest (P1) to the largest (P10) ratios. The purpose of
this design is to differentiate each set of portfolios along the growth-value polarity, such that
portfolios with lower fundamental-to-price ratios (P1, P2) would capture the characteristics of
growth stocks, while portfolios with higher fundamental-to-price ratios (P10, P9) would capture
the characteristics of value stocks.
Taken as a whole, results in panels A, B, C, and D of Table 4.15 are qualitatively similar
to the pure shock sample results in the respective panel of Table 4.2 in the following ways. (1)
when target rate change is decomposed into an expected and surprise component, only the
surprise white noise residuals (∆𝑊𝑁𝑡� ) has a significant and negative effect on portfolio returns,
(2) expected component (𝛽𝑒) has no effect on portfolio returns, (3) the sensitivity of stock price
reactions decreases gradually from growth stocks (P1) to value stocks (P10).
68
Table 4.15: The Response of Equity Prices to White-Noise Residuals of Surprises and Expected components of the target rate changes, by Portfolios based on Fundamental-to-Price Ratios The following table shows the regression results of 1-day equity return on the white-noise residuals of surprises and expected components of the target rate changes. P1 through P10 are 10 portfolios sorted by dividend ratio (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). The models are estimated for individual stocks in AMEX, NYSE, and Nasdaq based on 163 white-noise residuals of target rate change shocks following 171 FOMC meetings between Jan 1990 and Oct 2008. Average coefficient estimates and R-square values are shown across all portfolios. The asterisks of ***, **, and * represent t statistical significance at the 1%, 5%, and 10% level, respectively. Panel A records the price response of 10 portfolios sorted by dividend yield (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). Panel B records the price response of 10 portfolios sorted by book-to-market ratio. Panel C records the price response of 10 portfolios sorted by earnings-to-price ratio. Panel D records the price response of 10 portfolios sorted by cashflows-to-price ratio. Model 𝑅𝑡 = 𝛼 + 𝛽𝑒∆�̃�𝑡𝑒 + 𝛽𝑢∆𝑊𝑁𝑡� + 𝜀𝑡
Anticipated and unanticipated components Portfolio α βe βu R2
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d
P1 0.3588 *** -0.5736 -2.1848 *** 0.0587 P2 0.3202 *** -0.6301 * -1.4537 ** 0.0461 P3 0.2800 *** -0.4820
-0.8643 0.0219
P4 0.2830 *** -0.3726
-1.1012 * 0.0297 P5 0.2672 *** -0.3648
-1.0040 * 0.0301
P6 0.2569 *** -0.4286
-0.8879 0.0285 P7 0.2385 *** -0.1811
-0.7758 0.0168
P8 0.1661 *** -0.1435
-0.5563 0.0138 P9 0.1609 *** -0.3831 * -0.7227 * 0.0337 P10 0.1455 ** -0.4253
-0.6881 0.0200
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P1 0.3409 *** -0.2112 -2.8702 *** 0.0500 P2 0.3283 *** -0.4499
-2.6148 *** 0.0572
P3 0.3142 *** -0.4131
-1.9348 ** 0.0415 P4 0.3247 *** -0.4517
-1.8475 ** 0.0427
P5 0.3079 *** -0.5672
-1.6929 ** 0.0489 P6 0.2786 *** -0.5125
-1.5033 ** 0.0463
P7 0.2711 *** -0.3997
-1.4396 ** 0.0402 P8 0.2570 *** -0.3359
-1.2396 ** 0.0342
P9 0.2404 *** -0.3601
-0.6436 0.0157 P10 0.3286 *** -0.5727 * -1.9922 *** 0.0760
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P1 0.3318 *** -0.1579 -2.7676 *** 0.0621 P2 0.3016 *** -0.3873
-1.9968 ** 0.0438
P3 0.3150 *** -0.3543
-1.5296 ** 0.0311 P4 0.3139 *** -0.4420
-1.2025 * 0.0279
P5 0.2979 *** -0.4780
-1.1963 * 0.0339 P6 0.2664 *** -0.4088
-1.3590 ** 0.0365
P7 0.2719 *** -0.4713
-1.2021 ** 0.0386 P8 0.2846 *** -0.4524
-1.3703 ** 0.0445
P9 0.3033 *** -0.5250 * -1.3518 ** 0.0491 P10 0.3009 *** -0.4980
-1.1759 * 0.0328
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e P1 0.2536 *** -0.4238 -1.9448 *** 0.0594 P2 0.2579 *** -0.3942
-1.5491 *** 0.0475
P3 0.2629 *** -0.3838
-1.3983 ** 0.0396 P4 0.2974 *** -0.2453
-1.4509 ** 0.0355
P5 0.2919 *** -0.4201
-1.4281 ** 0.0324 P6 0.3473 *** -0.4385
-1.6123 ** 0.0374
P7 0.3128 *** -0.4329
-1.9387 *** 0.0482 P8 0.3321 *** -0.4562
-1.5948 ** 0.0386
P9 0.3288 *** -0.5545
-1.6606 ** 0.0452 P10 0.2876 *** -0.5601 -1.4603 ** 0.0432
69
(14)
I further investigate if growth stocks, which are considered high-duration assets, react
more strongly to white noise residuals as they do to the pure shocks. These results are presented
in Table 4.16 and Table 4.17. Under Table 4.16, I estimate an equation system of two portfolios
using seemingly unrelated regression (SUR) to investigate whether the reaction by growth stocks
portfolios (P1, P2) and value stocks portfolios (P10, P9) are statistically significant. The model is
shown as follows:
∆𝑃𝑡,𝑖 = 𝛼𝑖 + 𝛽1𝑖 ∗ ∆�̃�𝑡𝑒 + 𝛽2𝑖 ∗ ∆𝑊𝑁𝑡� + 𝜀𝑡,𝑖
∆𝑃𝑡,𝑗 = 𝛼𝑗 + 𝛽1𝑗 ∗ ∆�̃�𝑡𝑒 + 𝛽2𝑗 ∗ ∆𝑊𝑁𝑡� + 𝜀𝑡,𝑗
where ∆𝑃𝑡,𝑖 ( ∆𝑃𝑡,𝑗) is the return on the ith (jth) decile portfolios. Table 4.16 reports the White’s
(1980) heteroskedastic-consistent F statistics of the null hypothesis 𝛽2𝑖 = 𝛽2𝑗, where bold face
denotes significance at the 5 percent level.
Similar to the SUR results based on pure shocks, columns labeled P1 and P2 in the first
three panels display numerous significant F-statistics. I can thus infer that even with the
application of white noise residuals, price sensitivity to interest rate shocks are the strongest for
the highest growth stocks in my sample (first and second deciles), and they are significantly
more sensitive to target changes than most of the other deciles (second through tenth deciles).
The SUR results are further validated by paired difference test, as shown in Table 4.17.
The table reports T-test results based on model:
∆𝑃𝑡,𝑖 − ∆𝑃𝑡,𝑗 = 𝛼 + 𝛽1 ∗ ∆�̃�𝑡𝑒 + 𝛽2 ∗ ∆𝑊𝑁𝑡� + 𝜀𝑡 (15)
70
Table 4.16: Wald Test - Sensitivity of Stock Prices to White-Noise Residuals of Surprises, by Portfolios based on Fundamental-to-Price Ratios. Table shows the results of the following SUR regression on the price changes of ith and jth decile portfolios, ΔPt,i and ΔPt,j, on the white-noise residuals of surprises in changes of the Federal Funds rate target from Jan 1990 through Oct 2008, with a total of 171 observations. P1 through P10 are 10 portfolios sorted by respective ratio of fundamental-to-price. All portfolios are constructed using stocks listed on NYSE, AMEX, and Nasdaq, and are obtained from CRSP. Panel A records the price response of 10 portfolios sorted by dividend yield (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). Panel B records the price response of 10 portfolios sorted by book-to-market ratio. Panel C records the price response of 10 portfolios sorted by earnings-to-price ratio. The table reports the heteroskedastic-consistent Wald statistics of the null hypothesis 𝛽2𝑖 = 𝛽2𝑗 . Bold denotes significance at the 5 percent level.
∆𝑃𝑡,𝑖 = 𝛼𝑖 + 𝛽1𝑖 ∗ ∆�̃�𝑡𝑒 + 𝛽2𝑖 ∗ ∆𝑊𝑁𝑡� + 𝜀𝑡,𝑖 ∆𝑃𝑡,𝑗 = 𝛼𝑗 + 𝛽1𝑗 ∗ ∆�̃�𝑡𝑒 + 𝛽2𝑗 ∗ ∆𝑊𝑁𝑡� + 𝜀𝑡,𝑗
P1 P2 P3 P4 P5 P6 P7 P8 P9
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P2 9.0300 P3 19.7800 7.9700 P4 12.9500 3.8900 0.6700 P5 12.2000 4.3500 0.1000 0.1900 P6 15.8700 7.2300 0.2000 1.8600 0.7200 P7 9.5900 3.5100 0.0000 0.3600 0.1200 0.1200 P8 8.5200 3.9700 0.5300 1.4100 1.2100 0.3600 1.1900 P9 6.0100 2.0400 0.0400 0.3500 0.1800 0.0000 0.0700 0.9400 P10 4.3900 1.1100 0.0100 0.0500 0.0000 0.0900 0.0200 1.1300 0.2700
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t P2 1.2300 P3 6.1200 8.6600 P4 6.5000 8.4700 0.1900 P5 6.4400 8.4200 1.4500 0.5800 P6 6.3600 8.2600 3.0400 2.0100 1.1900 P7 6.3100 8.0200 2.4000 1.7800 0.9400 0.0400 P8 7.6000 9.2900 4.8000 3.6900 3.4100 1.3600 1.6900 P9 12.3400 16.1100 11.4900 9.8800 11.8700 10.3200 11.5800 6.7100 P10 1.6800 1.0900 0.0600 0.2000 0.9300 2.4800 2.6800 6.4300 18.0700
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P3 19.0100 5.2300 P4 22.5200 11.8600 3.1300 P5 17.5400 9.0300 2.1600 0.0000 P6 13.4100 4.6300 0.5600 0.5900 0.7600 P7 12.8000 5.6800 1.3800 0.0300 0.0200 0.9100 P8 10.2900 3.5400 0.3400 0.3800 0.5000 0.0000 1.0600 P9 10.1500 3.3200 0.2500 0.5400 0.7900 0.0300 1.3300 0.0200 P10 12.1400 4.4400 0.6600 0.0700 0.1000 0.0800 0.2100 0.1100 0.2800
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e P2 3.0000 P3 4.2300 0.3800 P4 4.4000 0.6100 0.0400 P5 3.4800 0.5600 0.0600 0.0000 P6 1.0500 0.1900 1.0000 2.0500 2.4500 P7 0.0500 1.5900 3.6900 5.9300 6.8400 1.7100 P8 2.3400 0.0600 0.0700 0.2800 0.3600 1.0100 5.7100 P9 0.8200 0.1200 0.7500 1.4600 1.6100 0.0100 1.6600 0.8400 P10 2.2600 0.1300 0.0100 0.0900 0.1100 0.8500 3.3100 0.0200 0.9700
71
Table 4.17: Paired Difference Test - Response of Stock Prices to White-Noise Residuals of Surprises, by Portfolios based on Fundamental-to-Price Ratios. Table shows results of regression of the mean difference of one-day price changes between ith and jth decile portfolios, (∆𝑃𝑡,𝑖 −∆𝑃𝑡,𝑗), where i ≠ j, on white-noise residuals of surprises in the federal funds rate target from Jan 1990 through Oct 2008 with a total of 171 observations. P1 through P10 are 10 portfolios sorted by respective ratio of fundamental-to-price. All portfolios are constructed using stocks listed on NYSE, AMEX, and Nasdaq, and are obtained from CRSP. Panel A records the price response of 10 portfolios sorted by dividend yield (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). Panel B records the price response of 10 portfolios sorted by book-to-market ratio. Panel C records the price response of 10 portfolios sorted by earnings-to-price ratio. Panel D records the price response of 10 portfolios sorted by cashflows-to-price ratio. The table reports the t test of the null hypothesis 𝛽2 = 0. Bold denotes significance at the 5 percent level.
∆𝑃𝑡,𝑖 − ∆𝑃𝑡,𝑗 = 𝛼 + 𝛽1 ∗ ∆�̃�𝑡𝑒 + 𝛽2 ∗ ∆𝑊𝑁𝑡� + 𝜀𝑡
P1 P2 P3 P4 P5 P6 P7 P8 P9
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P2 -0.7126 P3 -1.2872 -0.5746 P4 -1.1469 -0.4343 0.1402 P5 -1.2225 -0.5099 0.0647 -0.0756 P6 -1.3781 -0.6655 -0.0910 -0.2312 -0.1557 P7 -1.3006 -0.5880 -0.0134 -0.1537 -0.0781 0.0776 P8 -1.5719 -0.8593 -0.2847 -0.4250 -0.3494 -0.1938 -0.2713 P9 -1.3756 -0.6630 -0.0884 -0.2287 -0.1531 0.0025 -0.0750 0.1963 P10 -1.2460 -0.5334 0.0412 -0.0991 -0.0235 0.1321 0.0546 0.3259 0.1296
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t P2 -0.2880 P3 -0.9532 -0.6652 P4 -1.0359 -0.7479 -0.0827 P5 -1.1945 -0.9065 -0.2413 -0.1586 P6 -1.4074 -1.1194 -0.4542 -0.3714 -0.2129 P7 -1.3738 -1.0858 -0.4206 -0.3378 -0.1793 0.0336 P8 -1.6222 -1.3343 -0.6690 -0.5863 -0.4277 -0.2149 -0.2485 P9 -2.1479 -1.8599 -1.1947 -1.1120 -0.9534 -0.7405 -0.7741 -0.5257 P10 -0.8407 -0.5527 0.1125 0.1953 0.3538 0.5667 0.5331 0.7816 1.3072
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P3 -1.2999 -0.4881 P4 -1.6217 -0.8099 -0.3218 P5 -1.6332 -0.8214 -0.3333 -0.0115 P6 -1.4859 -0.6741 -0.1860 0.1357 0.1473 P7 -1.6610 -0.8492 -0.3611 -0.0393 -0.0278 -0.1751 P8 -1.4793 -0.6675 -0.1794 0.1424 0.1539 0.0066 0.1817 P9 -1.4531 -0.6412 -0.1532 0.1686 0.1802 0.0329 0.2079 0.0262 P10 -1.5553 -0.7435 -0.2554 0.0664 0.0779 -0.0693 0.1057 -0.0760 -0.1022
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e P2 -0.3932 P3 -0.5262 -0.1330 P4 -0.5697 -0.1765 -0.0435 P5 -0.5787 -0.1854 -0.0524 -0.0090 P6 -0.2844 0.1088 0.2418 0.2853 0.2943 P7 -0.0649 0.3283 0.4613 0.5048 0.5137 0.2195 P8 -0.4592 -0.0660 0.0670 0.1105 0.1194 -0.1748 -0.3943 P9 -0.2985 0.0948 0.2278 0.2712 0.2802 -0.0141 -0.2335 0.1608 P10 -0.4931 -0.0999 0.0331 0.0766 0.0855 -0.2087 -0.4282 -0.0339 -0.1946
72
From Table 4.17, T-statistics are significant under columns labeled P1 and P2 in the first
three panels. These results further confirm the findings of the Wald tests as recorded in Table
4.16.
4.10 Robustness Test: Asymmetric Effects of Surprise Signs based on White Noise Residuals
As discovered earlier, asymmetries exist when the target rate surprises are isolated into
negative sign and positive sign. I would like to examine whether such asymmetries still exist
when the stock returns are regressed with white noise residuals instead of pure shocks. I run
asymmetric tests based on the following OLS model:
𝑅𝑡 = 𝛼 + �𝛽1 + 𝛽2 ∗ ∆𝑊𝑁𝑡��𝐷(∆�̃�𝑡𝑢 < 0) + �𝛽3 + 𝛽4 ∗ ∆𝑊𝑁𝑡��𝐷(∆�̃�𝑡𝑢 > 0) + 𝜀𝑡 (16)
Again, for the convenience of interpreting and comparing the shock impacts, I take absolute
values on all white noise residuals.
Table 4.18 shows the results from Equation (16) for ten different industries and for three
market portfolios. Similar to the model in Table 4.5, intercept coefficients (𝛽1and 𝛽3) indicate
whether the presence of surprise matters and slope coefficients (𝛽2 and 𝛽4) measure the impact
of surprise on stock returns. In contrast to the results in Table 4.5, however, Table 4.18 shows
that stock returns react only to negative surprise. Among the portfolios that show at least five
percent significant level of reaction include Durable, Manufacturing, High Tech,
Telecommunication, Wholesale/Retail, Utilities, Others, VW, and EW.
Under the Equality test columns, none of the tests on the null hypotheses is rejected. This
result implies that the impact difference between negative and positive shocks in most industries
does not vary statistically.
73
Table 4.18: Asymmetric Response of Equity Prices to Positive and Negative Surprises, by Industry Portfolios and by Market Indexes The following table shows the results of 1-day equity return of 10 industry portfolios on the negative and positive white-noise residuals of surprises of the target rate changes. The 10 industry portfolios are constructed based on SIC code as in Fama & French (1988). The last three categories record the price response of three market indexes: VW and EW are the value-weighted and equal-weighted market portfolios, respectively, and S&P500 is the index portfolio of S&P 500. Model: 𝑅𝑡 = �𝛽1 + 𝛽2 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� < 0� + �𝛽3 + 𝛽4 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� > 0�+ 𝜀𝑡
where D(A) is a dummy variable taking the value 1 if the event A is true and 0 otherwise. Negative and positive surprises occur 73 and 46 cases respectively. The models are estimated for individual stocks in AMEX, NYSE, and Nasdaq based on 163 white-noise residuals of target rate change shocks following 171 FOMC meetings between Jan 1990 and Oct 2008. Average coefficient estimates and R-square values are shown across all portfolios. The asterisks of ***, **, and * represent t-statistical significance at the 1%, 5%, and 10% level, respectively, based on the standard errors given in parentheses. Columns headed "Equality Test" contain p-values of F-test statistics for testing the indicated restrictions for the average coefficients. The p-values of “Equality Test” in bold denotes significance at 5% level. Negative Surprise Positive Surprise Equality Test
Portfolio β1
β2
β3
β4
R2
Ho: β1=β3
Ho: β2=β4
Non-Durable 0.1880 * 1.0291
0.0858
1.4202
0.0915
0.5436 0.8358
(0.1122)
(0.8154)
(0.1248)
(1.6984)
Durable 0.2057
3.3406 *** 0.1642
0.4314
0.1580
0.8491 0.2367
(0.1459)
(1.0601)
(0.1622)
(2.2081)
Manufacturing 0.2368 * 1.9541 ** 0.1638
1.3165
0.1341
0.7161 0.7770
(0.1339)
(0.9727)
(0.1489)
(2.0263)
Energy 0.2937 * -0.2699
0.0630
1.5750
0.0350
0.3784 0.5302
(0.1747)
(1.2692)
(0.1942)
(2.6437)
High Tech 0.2365
4.2268 *** 0.2829
-0.5866
0.1140
0.8876 0.1930
(0.2193)
(1.5934)
(0.2438)
(3.3190)
Telecommunication 0.0758
4.0698 *** 0.2540
-1.0602
0.0919
0.5539 0.1301
(0.2008)
(1.4591)
(0.2233)
(3.0394)
Wholesale/Retail 0.1918
3.4567 *** 0.1844
0.7394
0.1649
0.9732 0.2727
(0.1470)
(1.0684)
(0.1635)
(2.2254)
Healthcare 0.3220 ** 0.6907
0.0714
0.8376
0.0657
0.2744 0.9544
(0.1528)
(1.1102)
(0.1699)
(2.3126)
Utilities 0.2901 *** -1.8565 ** 0.0604
1.1283
0.0648
0.1665 0.1097
(0.1105)
(0.8031)
(0.1229)
(1.6729)
Others 0.1768 * 1.9232 ** 0.1354
1.1786
0.1655
0.7884 0.6669
(0.1028) (0.7473) (0.1144) (1.5567)
VW 0.2567
2.7083 ** 0.2491
-0.1234
0.1237
0.9753 0.3078
(0.1649)
(1.1979)
(0.1833)
(2.4953)
EW 0.1890
2.4419 *** 0.0999
1.2048
0.1370
0.6403 0.5636
(0.1273)
(0.9251)
(0.1416)
(1.9270)
S&P500 0.2500
2.2769 * 0.2460
0.0013
0.0983
0.9876 0.4331 (0.1725) (1.2533) (0.1918) (2.6106)
74
4.11 Robustness Test: Equity Duration of Different Surprise Signs based on White Noise
Residuals
I continue to study equity duration of asymmetric effect based on white noise residuals of
the shocks. Table 4.19 shows the estimates associated with portfolios ranked on the basis of
dividend-to-price (DP), book-to-market (BM), earnings-to-price (EP), and cashflows-to-price
(CP) ratios, as presented in panels A, B, C, and D, respectively. The test results confirm the
regression results on the industry portfolios that only negative surprise matters in explaining
stock returns.
Compared to the results based on pure shocks, R-squares across all decide portfolios
based on white noise residuals increase by at least 20 percent. The better fitted models imply that
white noise residuals are probably better substitutions for the pure shocks. Something in common
between pure shocks and white noise residuals is the hesitant evidences of equity durations.
Across portfolios sorted by dividend yield (Panel A of Table 4.19), for example, the magnitudes
of 𝛽2 (negative shock slope coefficient) decreases gradually from 3.0563 of the first decile to
1.5763 of the tenth decile. Some similar evidences could be found in Panel C, D, and E.
As the tests with pure shocks, I also conduct Wald test (Table 4.20) and Paired
Difference test (Table 4.21) with white noise residuals. The tests from the two tables suggest that
equity duration can be noticed only when the shocks are negative, and applies only on portfolios
sorted by ratios of dividend yield and book-to-market. These results are similar to the ones
tested with pure shocks.
75
Table 4.19: Asymmetric Response of Equity Prices to Positive and Negative White-Noise Residuals of Surprises of the target rate changes, by Portfolios based on Fundamental-to-Price Ratios. The following table shows the regression results of 1-day equity return on changes on the white-noise residuals of surprises of the target rate changes, allowing for different effects of positive and negative surprises. Here is the regression equation:
Model 𝑅𝑡 = �𝛽1 + 𝛽2 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� < 0� + �𝛽3 + 𝛽4 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� > 0�+ 𝜀𝑡
where D(A) is a dummy variable taking the value 1 if the event A is true and 0 otherwise. Negative and positive WN residuals occur 68 and 95 cases respectively. The models are estimated for individual stocks in AMEX, NYSE, and Nasdaq following 171 FOMC meetings between Jan 1990 and Oct 2008. Average coefficient estimates and R-square values are shown across all portfolios. The asterisks of ***, **, and * represent t statistical significance at the 1%, 5%, and 10% level, respectively. Columns headed "Equality Test" contain p-values of F-test statistics for testing the indicated restrictions for the average coefficients. The p-values of “Equality Test” in bold denotes significance at 5% level. Panel A records the price response of 10 portfolios sorted by dividend yield (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). Panel B records the price response of 10 portfolios sorted by book-to-market ratio. Panel C records the price response of 10 portfolios sorted by earnings-to-price ratio. Panel D records the price response of 10 portfolios sorted by cashflows-to-price ratio.
Negative WN residuals Positive WN residuals Equality Test
Portfolio β1 β2 β3 β4 R2 Ho: β1=β3 Ho: β2=β4
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P1 0.2646 * 3.0563 *** 0.2153
0.6808 0.1608 0.8301 0.3580 P2 0.2353 * 2.2644 ** 0.1755
1.3866 0.1517 0.7662 0.6976
P3 0.1946
1.6701 * 0.1419
1.8495 0.1178 0.7888 0.9353 P4 0.1860
1.8277 ** 0.2303 * 0.3446 0.1443 0.8009 0.4518
P5 0.1668
1.7148 ** 0.2347 * 0.1465 0.1482 0.6757 0.3899 P6 0.1606
1.6432 ** 0.1850
0.8578 0.1364 0.8822 0.6711
P7 0.1190
1.7405 ** 0.1397
1.4719 0.1465 0.8912 0.8743 P8 0.0846
1.2051 ** 0.1034
0.9081 0.1122 0.8775 0.8286
P9 0.1105
1.2702 ** 0.0395
1.5121 0.1101 0.5807 0.8667 P10 0.0566 1.5763 * -0.0239 2.5159 0.0697 0.6412 0.6280
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P1 0.3430 * 3.1323 ** 0.1897
-0.5133 0.1097 0.6094 0.2797 P2 0.2540
3.3219 *** 0.2045
-0.1917 0.1255 0.8509 0.2360
P3 0.2509
2.5460 ** 0.2037
0.2130 0.1204 0.8417 0.3797 P4 0.2874 * 2.3319 ** 0.1898
0.5331 0.1319 0.6671 0.4805
P5 0.2348 * 2.3667 ** 0.1960
0.5612 0.1392 0.8523 0.4402 P6 0.1843
2.3147 ** 0.1684
0.8376 0.1391 0.9334 0.4905
P7 0.1492
2.4216 *** 0.1685
0.9227 0.1408 0.9174 0.4733 P8 0.1642
2.0781 ** 0.1295
1.3252 0.1411 0.8412 0.6986
P9 0.1779
1.2710
0.1191
1.6560 0.1089 0.7352 0.8436 P10 0.1643 3.3678 *** 0.1619 1.6357 0.2155 0.9897 0.4022
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P1 0.2646 * 3.0563 *** 0.2153
0.6808 0.1608 0.7763 0.1825 P2 0.2353 * 2.2644 ** 0.1755
1.3866 0.1517 0.8719 0.3740
P3 0.1946
1.6701 * 0.1419
1.8495 0.1178 0.7094 0.5836 P4 0.1860
1.8277 ** 0.2303 * 0.3446 0.1443 0.8893 0.6842
P5 0.1668
1.7148 ** 0.2347 * 0.1465 0.1482 0.4992 0.8751 P6 0.1606
1.6432 ** 0.1850
0.8578 0.1364 0.6300 0.7860
P7 0.1190
1.7405 ** 0.1397
1.4719 0.1465 0.8893 0.6242 P8 0.0846
1.2051 ** 0.1034
0.9081 0.1122 0.9908 0.5276
P9 0.1105
1.2702 ** 0.0395
1.5121 0.1101 0.9328 0.5164 P10 0.0566 1.5763 * -0.0239 2.5159 0.0697 0.6756 0.9205
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2.6956 *** 0.1386
0.3895 0.1336 0.8723 0.2979 P2 0.1594
2.4396 *** 0.1218
1.1924 0.1453 0.8348 0.5378
P3 0.1533
2.3000 *** 0.1599
0.8948 0.1382 0.9711 0.4913 P4 0.2173 * 2.1193 ** 0.2180
0.2835 0.1489 0.9970 0.3826
P5 0.2379 * 2.0012 ** 0.1689
0.8595 0.1199 0.7426 0.6283 P6 0.2898 ** 2.2719 ** 0.1898
1.2308 0.1521 0.6432 0.6677
P7 0.2200
2.7716 *** 0.1869
0.6204 0.1393 0.8802 0.3842 P8 0.2474 * 2.2625 ** 0.2663 * -0.0035 0.1417 0.9292 0.3442 P9 0.2607 * 2.3626 ** 0.1844
1.0630 0.1474 0.7196 0.5856
P10 0.2390 * 2.1153 ** 0.0996 1.8253 0.1373 0.4837 0.8967
76
Table 4.20: Wald Test - Sensitivity of Stock Prices to Negative & Positive White-Noise Residuals of Surprises, by Portfolios based on Fundamental-to-Price Ratios. Tables show results of the following SUR regression for the price changes of ith and jth decile portfolios, ΔPt,i and ΔPt,j, on the NEGATIVE (Table on the left) and on the POSITIVE (Table on the right) white-noise residuals of surprises, from Jan 1990 through Oct 2008 with a total of 171 observations. P1 through P10 are 10 portfolios sorted by respective ratio of fundamental-to-price. All portfolios are constructed using stocks listed on NYSE, AMEX, and Nasdaq, and are obtained from CRSP. Panel A records the price response of 10 portfolios sorted by dividend yield (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). Panel B records the price response of 10 portfolios sorted by book-to-market ratio. Panel C records the price response of 10 portfolios sorted by earnings-to-price ratio. The tables reports the heteroskedastic-consistent Wald statistics of the null hypothesis 𝛽2𝑖 = 𝛽2𝑗 and of the null hypothesis 𝛽4𝑖 = 𝛽4𝑗 . Bold denotes significance at the 5 percent level.
∆𝑃𝑡,𝑖 = (𝛽1𝑖 + 𝛽2𝑖 ∗ ∆𝑊𝑁𝑡�) ∗ 𝐷�∆𝑊𝑁𝑡� < 0� + (𝛽3𝑖 + 𝛽4𝑖 ∗ ∆𝑊𝑁𝑡�) ∗ 𝐷�∆𝑊𝑁𝑡� > 0� + 𝜀𝑡,𝑖 ∆𝑃𝑡,𝑗 = (𝛽1𝑗 + 𝛽2𝑗 ∗ ∆𝑊𝑁𝑡�) ∗ 𝐷�∆𝑊𝑁𝑡� < 0� + (𝛽3𝑗 + 𝛽4𝑗 ∗ ∆𝑊𝑁𝑡�) ∗ 𝐷�∆𝑊𝑁𝑡� > 0� + 𝜀𝑡,𝑗
Impact from Negative WN residuals (H0: b2i = b2j) Impact from Positive WN residuals (H0: b4i = b4j) P1 P2 P3 P4 P5 P6 P7 P8 P9 P1 P2 P3 P4 P5 P6 P7 P8 P9
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P2 4.74 0.87 P3 9.72 3.59 1.59 0.50 P4 6.28 1.66 0.38 0.11 2.18 7.92 P5 6.25 2.16 0.02 0.18 0.23 2.53 7.33 0.13 P6 7.01 2.65 0.01 0.51 0.07 0.03 0.44 2.34 0.90 1.48 P7 4.14 1.15 0.03 0.05 0.01 0.08 0.35 0.01 0.17 1.93 3.41 0.70 P8 5.00 2.53 0.59 1.29 1.09 0.77 2.00 0.02 0.12 0.56 0.24 0.56 0.00 0.51 P9 4.32 1.96 0.39 0.88 0.64 0.45 1.17 0.04 0.22 0.01 0.06 0.89 1.40 0.32 0.00 0.86 P10 2.66 0.79 0.02 0.13 0.04 0.01 0.09 0.62 0.64 0.94 0.49 0.20 2.21 2.81 1.36 0.86 2.70 1.59
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77
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P3 8.08 5.11 1.52 0.14 P4 7.23 5.55 0.17 1.83 0.56 0.29 P5 8.44 7.98 1.63 1.53 1.95 0.90 0.63 0.23 P6 4.09 2.07 0.02 0.36 3.68 2.37 1.16 1.09 0.84 0.22 P7 3.98 2.44 0.06 0.00 1.09 0.35 0.94 0.21 0.07 0.00 0.22 0.91 P8 2.12 0.71 0.35 1.26 4.89 0.61 2.17 1.13 0.32 0.16 0.01 0.08 0.51 0.04 P9 3.02 1.43 0.04 0.34 3.02 0.02 0.57 0.46 0.86 0.14 0.03 0.03 0.39 1.04 0.03 0.13 P10 4.14 2.31 0.03 0.01 0.97 0.12 0.01 1.12 0.35 2.45 1.35 1.11 0.90 0.39 0.09 1.13 0.88 2.04
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e P2 0.54 1.23 P3 1.02 0.18 0.38 0.19 P4 1.89 0.86 0.30 0.01 1.60 0.78 P5 2.13 1.34 0.78 0.18 0.22 0.18 0.00 1.00 P6 1.00 0.19 0.01 0.25 0.88 0.91 0.00 0.19 2.22 0.38 P7 0.03 0.70 1.66 4.18 6.59 3.87 0.06 0.48 0.13 0.26 0.15 1.33 P8 0.89 0.20 0.01 0.20 0.75 0.00 4.12 0.17 2.08 1.30 0.18 1.88 5.13 1.42 P9 0.44 0.03 0.02 0.49 1.14 0.10 2.16 0.14 0.41 0.02 0.04 1.15 0.08 0.08 0.58 3.72 P10 1.34 0.57 0.20 0.00 0.08 0.20 3.35 0.16 0.68 1.89 0.50 1.18 3.53 1.34 0.67 2.60 5.81 1.48
78
Table 4.21: Paired Difference Test - Sensitivity of Stock Prices to Negative & PositiveWhite-Noise Residuals of Surprises, by Portfolios based on Fundamental-to-Price Ratios. Table shows results of regression of the mean difference of one-day price changes between ith and jth decile portfolios, (∆𝑃𝑡,𝑖 − ∆𝑃𝑡,𝑗), where i ≠ j, on the NEGATIVE (Table on the left) and on the POSITIVE (Table on the right) white-noise residuals of surprises, from Jan 1990 through Oct 2008 with a total of 171 observations. P1 through P10 are 10 portfolios sorted by respective ratio of fundamental-to-price. All portfolios are constructed using stocks listed on NYSE, AMEX, and Nasdaq, and are obtained from CRSP. Panel A records the price response of 10 portfolios sorted by dividend yield (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). Panel B records the price response of 10 portfolios sorted by book-to-market ratio. Panel C records the price response of 10 portfolios sorted by earnings-to-price ratio. Panel D records the price response of 10 portfolios sorted by cashflows-to-price ratio. The table reports the t statistics of the null hypothesis 𝛽2 = 0 and 𝛽4 = 0. Bold denotes significance at the 5 percent level.
∆𝑃𝑡,𝑖 − ∆𝑃𝑡,𝑗 = (𝛽1 + 𝛽2 ∗ ∆𝑊𝑁𝑡�) ∗ 𝐷(∆�̃�𝑡𝑢 < 0) + (𝛽3 + 𝛽4 ∗ ∆𝑊𝑁𝑡�) ∗ 𝐷(∆�̃�𝑡𝑢 > 0) + 𝜀𝑡
Impact from Negative WN residuals (H0: 𝛽2 = 0) Impact from Positive WN residuals (H0: 𝛽4 = 0) P1 P2 P3 P4 P5 P6 P7 P8 P9 P1 P2 P3 P4 P5 P6 P7 P8 P9
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P2 0.79 0.03 P3 1.39 0.59 0.07 0.04 P4 1.23 0.44 -0.16 0.08 0.05 0.01 P5 1.34 0.55 -0.04 0.11 0.10 0.07 0.03 0.02 P6 1.41 0.62 0.03 0.18 0.07 0.10 0.07 0.03 0.03 0.01 P7 1.32 0.52 -0.07 0.09 -0.03 -0.10 0.15 0.12 0.08 0.07 0.05 0.04 P8 1.85 1.06 0.46 0.62 0.51 0.44 0.54 0.18 0.15 0.11 0.10 0.08 0.08 0.03 P9 1.79 0.99 0.40 0.56 0.44 0.37 0.47 -0.07 0.15 0.12 0.08 0.08 0.06 0.05 0.01 -0.03 P10 1.48 0.69 0.09 0.25 0.14 0.07 0.16 -0.37 -0.31 0.21 0.18 0.14 0.13 0.11 0.10 0.06 0.03 0.05
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t P2 -0.19 0.09 P3 0.59 0.78 0.09 0.00 P4 0.80 0.99 0.21 0.06 -0.03 -0.04 P5 0.77 0.96 0.18 -0.03 0.11 0.02 0.02 0.05 P6 0.82 1.01 0.23 0.02 0.05 0.16 0.07 0.07 0.10 0.05 P7 0.71 0.90 0.12 -0.09 -0.05 -0.11 0.19 0.10 0.10 0.14 0.09 0.04 P8 1.05 1.24 0.47 0.25 0.29 0.24 0.34 0.18 0.09 0.09 0.12 0.07 0.02 -0.01 P9 1.86 2.05 1.27 1.06 1.10 1.04 1.15 0.81 0.17 0.08 0.07 0.11 0.06 0.01 -0.03 -0.01 P10 -0.24 -0.05 -0.82 -1.04 -1.00 -1.05 -0.95 -1.29 -2.10 0.18 0.09 0.09 0.12 0.07 0.02 -0.02 0.00 0.01
79
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rice P2 0.58 0.06
P3 1.32 0.74 0.01 -0.06 P4 1.43 0.85 0.11 0.04 -0.02 0.04 P5 1.76 1.18 0.44 0.33 0.00 -0.06 -0.01 -0.04 P6 1.27 0.69 -0.05 -0.16 -0.49 0.08 0.02 0.07 0.03 0.08 P7 1.43 0.86 0.12 0.00 -0.33 0.16 0.09 0.03 0.08 0.04 0.09 0.01 P8 1.04 0.46 -0.28 -0.39 -0.72 -0.23 -0.40 0.11 0.05 0.10 0.06 0.11 0.03 0.02 P9 1.23 0.65 -0.09 -0.21 -0.53 -0.04 -0.21 0.19 0.07 0.00 0.06 0.02 0.06 -0.01 -0.02 -0.04 P10 1.40 0.82 0.08 -0.03 -0.36 0.13 -0.03 0.36 0.17 0.05 -0.01 0.05 0.01 0.05 -0.03 -0.03 -0.05 -0.01
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e P2 0.26 0.01 P3 0.40 0.14 0.02 0.01 P4 0.58 0.32 0.18 -0.05 -0.06 -0.06 P5 0.69 0.44 0.30 0.12 -0.07 -0.08 -0.08 -0.02 P6 0.42 0.17 0.03 -0.15 -0.27 -0.12 -0.13 -0.14 -0.07 -0.05 P7 -0.08 -0.33 -0.47 -0.65 -0.77 -0.50 -0.05 -0.06 -0.07 0.00 0.02 0.07 P8 0.43 0.18 0.04 -0.14 -0.26 0.01 0.51 -0.08 -0.09 -0.09 -0.03 -0.01 0.04 -0.03 P9 0.33 0.08 -0.06 -0.24 -0.36 -0.09 0.41 -0.10 -0.09 -0.10 -0.11 -0.04 -0.02 0.03 -0.04 -0.01 P10 0.58 0.32 0.18 0.00 -0.11 0.16 0.66 0.15 0.25 -0.07 -0.08 -0.09 -0.02 0.00 0.05 -0.02 0.01 0.02
80
(17)
4.12 Robustness Test: Asymmetric Effects of Surprise Signs and Business Cycles based on
White Noise Residuals
When tested with pure shocks, asymmetric tests of both surprise signs and business
cycles provide strong evidence in support of my hypothesis that asymmetric price reaction to
positive or negative interest rate shocks is conditional on the prevailing business cycle. I
specifically find positive interest rate surprises have effect on stock returns only during
recessions, but have no effect during an expansion. On the other hand, negative interest rate
surprises have effect on stock returns only during expansions, but have effect during a recession.
I would like to examine whether such asymmetries still exist when the stock returns are
regressed with white noise residuals instead of pure shocks. I run asymmetric tests based on the
following OLS model:
𝑅𝑡 = 𝛼 + ��𝛽1 + 𝛽2 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� < 0� + �𝛽3 + 𝛽4 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� > 0�� ∗ 𝐷(𝐶𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛) +
��𝛽5 + 𝛽6 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� < 0� + �𝛽7 + 𝛽8 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� > 0�� ∗ 𝐷(𝐸𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛) + 𝜀𝑡
where D(A) is a dummy variable taking the value 1 if the event A is true and 0 otherwise. Like
equations involving shocks with opposite directions, all surprises in Equation (17) are in absolute
values.
Similar to the previous sessions, I first estimate Equation (17) on different industries and
on the market portfolios. Results on those portfolios are reported in Table 4.22.
When I compare each portfolio of Table 4.22 against that of Table 4.9, every industry
portfolio and market index in Table 4.22 records a higher R-square, indicating a better fitted
model with the use of white noise residuals.
81
Table 4.22: Asymmetric Response of Equity Prices to Different Business Cycles, by Dividend Yield Portfolios The following table shows results on the impact of the presence and magnitude of surprises in Federal funds rate changes on 1-day stock returns, allowing for different effects of positive and negative white-noise residuals of surprises and for different economic cycles. Here is the regression equation: 𝑅𝑡 = ��𝛽1 + 𝛽2 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� < 0� + �𝛽3 + 𝛽4 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� > 0�� ∗ 𝐷(𝐶𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛) + ��𝛽5 + 𝛽6 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� < 0� + �𝛽7 + 𝛽8 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� > 0�� ∗ 𝐷(𝐸𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛) + 𝜀𝑡
where D(A) is a dummy variable taking the value 1 if the event A is true and 0 otherwise. P1 through P10 are 10 portfolios sorted by dividend yield ratio (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). Negative and positive residuals of white-noises occur 11 and 12 cases during contraction periods and 57 and 83 cases during expansion periods, respectively. The models are estimated for individual stocks in AMEX, NYSE, and Nasdaq based on 163 white-noise residuals of target rate change shocks following 171 FOMC meetings between Jan 1990 and Oct 2008. Average coefficient estimates and R-square values are shown across all portfolios. The asterisks of ***, **, and * represent statistical significance at the 1%, 5%, and 10% level, respectively, based on the standard errors given in parentheses. Columns headed "Cross Period Equality Test" contain p-values of F-test statistics for testing the indicated restrictions for the average coefficients. The p-values of “Cross Period Equality Test” in bold denotes significance at 5% level. Contraction Expansion Cross Period Portfolio Negative Surprise Positive Surprise Negative Surprise Positive Surprise Equality Test β1
β2
β3
β4
β5
β6
β7
β8 R2 Ho: β2=β6 Ho: β4=β8
Non-Durable 0.0943
-0.4298
0.1527
5.4716 * 0.0694
4.2979 *** 0.1944
-1.8044 0.2026 0.0063 0.0147
(0.3205)
(1.2161)
(0.3478)
(3.0967)
(0.1190)
(1.2407)
(0.1316)
(1.9944)
Durable 0.4073
1.7506
0.5850
2.2449
0.1001
5.5033 *** 0.2301
-2.4015 0.2052 0.1078 0.1932
(0.4320)
(1.6396)
(0.4689)
(4.1750)
(0.1604)
(1.6727)
(0.1774)
(2.6888)
Manufacturing 0.3953
-0.2805
-0.0350
7.3434 ** 0.0786
5.5686 *** 0.3122 ** -2.4200 0.2185 0.0054 0.0092
(0.3877)
(1.4712)
(0.4208)
(3.7464)
(0.1439)
(1.5010)
(0.1592)
(2.4127)
Energy 0.8987 * -2.8403
-0.7856
8.6779 * 0.1446
1.9393
0.2106
-0.6453 0.0700 0.0932 0.0807
(0.5227)
(1.9835)
(0.5673)
(5.0508)
(0.1940)
(2.0236)
(0.2146)
(3.2528)
High Tech 0.8241
-0.6964
0.2380
3.3109
-0.0935
11.0917 *** 0.3826
-3.3004 0.1885 0.0008 0.2247
(0.6397)
(2.4276)
(0.6943)
(6.1817)
(0.2375)
(2.4767)
(0.2627)
(3.9811)
Telecommunication 0.5185
-0.6437
-0.0800
6.6257
-0.2495
11.1951 *** 0.4396 * -5.5395 0.2024 0.0002 0.0349
(0.5737)
(2.1770)
(0.6226)
(5.5435)
(0.2130)
(2.2210)
(0.2356)
(3.5701)
Wholesale/Retail 0.3828
1.7026
0.5570
2.8753
0.0728
5.9872 *** 0.2566
-2.1598 0.2149 0.0697 0.2001
(0.4346)
(1.6491)
(0.4717)
(4.1993)
(0.1613)
(1.6825)
(0.1785)
(2.7044)
Healthcare 0.8559 * -2.5819
-0.0258
4.0722
0.1137
4.5934 *** 0.1514
-1.2014 0.1245 0.0036 0.1843
(0.4508)
(1.7109)
(0.4893)
(4.3566)
(0.1674)
(1.7455)
(0.1851)
(2.8057)
Utilities 0.4776
-3.9018 *** -0.1414
5.7159 * 0.1486
1.2565
0.1711
-1.5365 0.1496 0.0026 0.0094
(0.3213)
(1.2192)
(0.3487)
(3.1047)
(0.1193)
(1.2439)
(0.1319)
(1.9995)
Others 0.1268
0.4759
0.0605
5.4680 * 0.0625
4.9683 *** 0.2440 ** -1.7175 0.2614 0.0048 0.0097
(0.2949) (1.1193) (0.3201) (2.8501) (0.1095) (1.1419) (0.1211) (1.8355)
VW 0.4308
-0.4781
0.1350
4.0885
0.0271
8.1023 *** 0.3538 * -2.8233 0.2080 0.0009 0.0723
(0.4777)
(1.8130)
(0.5185)
(4.6166)
(0.1773)
(1.8496)
(0.1962)
(2.9732)
EW 0.4272
-0.3369
0.0098
5.1736
-0.0045
6.7475 *** 0.1994
-1.4010 0.2321 0.0004 0.0490
(0.3661)
(1.3893)
(0.3973)
(3.5376)
(0.1359)
(1.4174)
(0.1503)
(2.2783)
S&P500 0.3679
-0.9658
0.1864
3.8093
0.0117
8.0394 *** 0.3426 * -2.5942 0.1871 0.0009 0.1065 (0.4992) (1.8944) (0.5418) (4.8240) (0.1853) (1.9328) (0.2050) (3.1067)
82
Under “Contraction” panel of Table 4.22, similar to the result of pure shocks, Utilities is
the only industry showing significantly negative reaction to the negative residual. However when
I look at the "Positive Surprise" column, unlike the results of pure shocks where all portfolios
react significantly and positively to positive shocks, there is only one industry portfolio
(Manufacturing) demonstrating significant reaction at five percent level. The magnitude also
decreases from 25.31% (pure shocks) to 7.3434% (white noise residuals).
Under “Expansion” panel of Table 4.22, the slope coefficients on negative and positive
surprise display results consistent with those of pure shocks in Table 4.9. 𝛽6 is significantly and
positively correlated with stock returns during expansion periods across all portfolios, except
Energy and Utilities. And none of the slope coefficients on positive surprise 𝛽8 is statistically
significant. These findings further validate that investors have a tendency to discount bad news
(positive surprise) less rigorously than good news (negative surprise) during expansion periods.
4.13 Robustness Test: Equity Duration of Surprise Signs and Business Cycles based on White
Noise Residuals
Similar to the equity duration test with pure shocks, I also run Equation (17) on the ten-
decile portfolios based on the four fundamental-to-price ratios. The results of the ranked
portfolios are presented in Table 4.23. Panel A presents the results for DP, panel B presents the
results for BM, panel C presents the results for EP, and panel D presents the results for CP. In
contrast to the tests with pure shocks, I only find strong evidence of asymmetric price reaction to
positive and negative interest rate shocks during expansion periods. I specifically find that
portfolio returns only respond to negative interest rate shocks during expansions. The results are
consistent with those displayed by industry and market portfolios.
83
Next, I apply the Wald test to examine whether there is a statistically difference in the
coefficients associated with the positive (𝛽4) and negative (𝛽6 ) surprises across each portfolio
deciles along the growth-value axis. The Wald test results across the deciles portfolios are
reported in Panels A through D of Table 4.24.1 and Table 4.24.2, for portfolio deciles based on
DP, BM, EP, and CP, respectively. Table 4.24.1 reports the Wald test results associated with
negative (𝛽2) and positive (𝛽4) surprises during contractions periods, while Table 4.11.2 reports
the Wald test results associated with negative (𝛽6) and positive (𝛽8) surprises during expansion
periods.
During contractions [Table 4.24.1], I barely see any significant pair across growth stocks
portfolios (P1, P2) and across value stocks portfolios (P10, P9). This finding holds on both
negative and positive residuals. Meanwhile, during expansions [Table 4.11.2], Panel A (DP), and
Panel C (EP) demonstrate several significant pairs across growth stocks portfolios (P1, P2), and
Panel B (BM) displays significant pairs across value stocks portfolios (P9, P10).
Finally I use paired difference T-test to check for price sensitivity. The results of paired
difference T-test are shown in Table 4.12.1 and Table 4.12.2. During contractions [Table 4.25.1],
I barely see any significant pair across growth stocks portfolios (P1, P2) and across value stocks
portfolios (P10, P9). This finding holds on both negative and positive residuals. Meanwhile,
during expansions [Table 4.12.2], Panel A (DP) demonstrates several significant pairs across
growth stocks portfolios (P1, P2), and Panel B (BM) displays significant pairs across value
stocks portfolios (P9, P10).
84
Table 4.23: Asymmetric Response of Equity Prices to White-Noise Residuals of Surprises during Different Business Cycles, by Market Indexes and by Portfolios based on Fundamental-to-Price Ratios. The following table shows the regression results of 1-day stock returns on the white-noise residuals of surprises of the target rate changes, allowing for different effects of positive and negative surprises and for different economic cycles. Here is the regression equation:
𝑅𝑡 = ��𝛽1 + 𝛽2 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� < 0� + �𝛽3 + 𝛽4 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� > 0�� ∗ 𝐷(𝐶𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛) + ��𝛽5 + 𝛽6 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� < 0� + �𝛽7 + 𝛽8 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� > 0�� ∗ 𝐷(𝐸𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛) + 𝜀𝑡
where D(A) is a dummy variable taking the value 1 if the event A is true and 0 otherwise. Negative and positive residuals occur 57 and 83 cases during contraction periods and 11 and 12 cases during expansion periods, respectively. The models are estimated for individual stocks in AMEX, NYSE, and Nasdaq following 171 FOMC meetings between Jan 1990 and Oct 2008. Average coefficient estimates and R-square values are shown across all portfolios. The asterisks of ***, **, and * represent t statistical significance at the 1%, 5%, and 10% level, respectively. Columns headed "Equality Test" contain p-values of F-test statistics for testing the indicated restrictions for the average coefficients. The p-values of “Equality Test” in bold denotes significance at 5% level. Panel A records the price response of 10 portfolios sorted by dividend yield (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). Panel B records the price response of 10 portfolios sorted by book-to-market ratio. Panel C records the price response of 10 portfolios sorted by earnings-to-price ratio. Panel D records the price response of 10 portfolios sorted by cashflows-to-price ratio. Contraction Expansion Cross Period
Negative Surprise Positive Surprise Negative Surprise Positive Surprise Equality Test
Portfolio β1 β2 β3 β4 β5 β6 β7 β8 R2 Ho: β2=β6 Ho: β4=β8
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P1 0.7122
-0.0134
0.1184
6.5998 0.0652
6.9625 *** 0.3654 ** -3.3384 0.2368 0.0035 0.0114 P2 0.4075
0.0982
0.1298
7.0539 * 0.0834
5.6831 *** 0.3213 ** -2.6290 0.2382 0.0080 0.0108
P3 0.1054
0.6286
0.1837
7.3002 ** 0.1083
4.1071 *** 0.2859 * -2.3176 0.1984 0.0909 0.0103 P4 0.1376
0.6777
0.2458
5.1797 0.0945
4.2876 *** 0.3570 ** -3.2751 0.2249 0.0464 0.0068
P5 0.0755
0.5594
0.4061
2.8327 0.0716
4.3829 *** 0.3124 ** -2.4427 0.2273 0.0255 0.0800 P6 0.0721
0.8233
0.3467
4.4355 0.0912
3.6458 *** 0.2855 ** -2.3545 0.2130 0.0993 0.0198
P7 -0.1237
0.9761
0.1314
4.3045 0.0419
4.3461 *** 0.2132 * -0.5867 0.2206 0.0309 0.0387 P8 -0.2431
1.2736
0.0482
3.7098 0.0644
2.5831 *** 0.1740 * -0.9613 0.1748 0.3145 0.0592
P9 -0.1630
0.9557
-0.1648
5.9787 ** 0.0652
3.1424 *** 0.1469
-1.0546 0.1973 0.1030 0.0055 P10 -0.1688 0.7290 -0.5428 8.8139 *** -0.0255 4.2632 *** 0.1173 -0.2827 0.1462 0.0516 0.0064
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P1 0.9683
-1.0473
-0.0500
4.1793 0.0727
8.3773 *** 0.3015
-3.1208 0.1661 0.0034 0.1465 P2 0.8918 * -0.6038
-0.0245
5.1211 0.0040
8.0158 *** 0.3328
-3.2945 0.1906 0.0022 0.0727
P3 0.6707
-0.8301
0.1222
5.6351 0.0259
7.1759 *** 0.3414 * -3.4948 0.2067 0.0013 0.0312 P4 0.5766
-0.5903
0.2391
4.5296 0.0869
6.6818 *** 0.2962
-2.5886 0.2098 0.0024 0.0687
P5 0.7107 * -0.8042
0.2332
5.1859 0.0298
6.3391 *** 0.3183 * -2.9804 0.2303 0.0010 0.0256 P6 0.2617
0.0886
0.2100
5.0752 0.0205
6.2872 *** 0.2808 * -2.4343 0.2393 0.0017 0.0242
P7 0.2729
0.5531
0.3887
3.2782 0.0163
5.4851 *** 0.2397
-1.5962 0.2095 0.0122 0.1141 P8 0.1939
0.3033
0.2761
4.5566 0.0311
5.3928 *** 0.2203
-1.5781 0.2345 0.0048 0.0424
P9 0.0791
-0.0995
0.1649
4.7379 0.0656
4.3918 *** 0.2015
-0.7791 0.1867 0.0147 0.0859 P10 0.2965 0.8697 0.1448 4.9814 -0.0160 7.6166 *** 0.2484 * -0.7700 0.3050 0.0005 0.0829
85
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P1 0.7407
0.0212
-0.0434
5.2803
0.0632
7.6552 *** 0.3474 * -3.9054 0.2368 0.0053 0.0466 P2 0.6214
-0.4088
-0.1211
7.3220 * 0.0085
7.0545 *** 0.3476 * -3.6023 0.2382 0.0026 0.0144
P3 0.4837
-0.6049
0.1706
5.0145
0.0901
6.1534 *** 0.3046 * -2.4610 0.1984 0.0036 0.0544 P4 0.4887
-0.5621
0.0331
7.0747 * 0.0671
5.5338 *** 0.3586 ** -2.8985 0.2249 0.0042 0.0088
P5 0.4265
-0.8090
0.1417
5.9498 * 0.1092
5.5337 *** 0.2747 * -2.1892 0.2273 0.0011 0.0146 P6 0.2184
0.4451
0.2282
4.9130
0.0791
5.1376 *** 0.2052
-1.4468 0.2130 0.0175 0.0502
P7 0.3385
0.2762
0.2791
4.6661
0.0804
4.3885 *** 0.2708 * -2.2072 0.2206 0.0258 0.0306 P8 0.0539
1.1080
0.4967
3.8075
0.0729
5.1587 *** 0.2609 * -2.1215 0.1748 0.0251 0.0449
P9 0.2597
0.5422
0.3751
3.6087
0.0990
4.9519 *** 0.2804 ** -1.8159 0.1973 0.0164 0.0851 P10 0.5446 -0.6157 0.1757 6.1840 * 0.0570 5.4328 *** 0.2645 * -1.6722 0.1462 0.0026 0.0234
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e P1 0.3446
0.2610
0.1522
4.3571 -0.0020
6.6262 *** 0.2427
-2.5839 0.2197 0.0021 0.0482 P2 0.2700
0.3874
0.2617
4.6994 0.0114
5.9208 *** 0.2195
-1.8903 0.2392 0.0034 0.0460
P3 0.0462
0.8380
0.2555
4.1187 0.0335
5.6372 *** 0.2482 * -1.8218 0.2207 0.0117 0.0602 P4 0.3195
0.2625
0.3590
3.0282 0.0836
5.2590 *** 0.2958 ** -2.2412 0.2152 0.0112 0.0821
P5 0.4620
-0.0484
0.0799
7.0563 * 0.0989
4.9541 *** 0.3266 * -3.3925 0.1964 0.0231 0.0082 P6 0.7233 * -0.7090
0.1850
5.8523 0.0960
6.0704 *** 0.3101 * -2.1593 0.2270 0.0030 0.0413
P7 0.5108
-0.1496
0.0778
5.8622 0.0197
7.1121 *** 0.3187 * -2.8562 0.2237 0.0017 0.0281 P8 0.5032
-0.5131
0.1733
5.0820 0.0554
6.4808 *** 0.3948 ** -3.4221 0.2272 0.0018 0.0253
P9 0.6793 * -0.6092
0.1657
6.0168 0.0664
6.2117 *** 0.3128 * -2.5224 0.2296 0.0023 0.0278 P10 0.4502 -0.4292 -0.1013 7.4239 ** 0.0613 6.0898 *** 0.2366 -1.5883 0.2264 0.0018 0.0145
86
Table 4.24.1: Wald Test - Sensitivity of Stock Prices to Negative & Positive White-Noise Residuals of Surprises during different business cycles, by Portfolios based on Fundamental-to-Price Ratios. Tables show the results of the following SUR regression for the price changes of ith and jth decile portfolios, ΔPt,i and ΔPt,j, on the negative and positive white-noise residuals of surprises during different business cycles. The tests on the type of residual shocks (POSITIVE or NEGATIVE) and during the different business cycles (CONTRACTION or EXPANSION) are shows in the titles of each sub-table below. P1 through P10 are 10 portfolios sorted by respective ratio of fundamental-to-price. All portfolios are constructed using stocks listed on NYSE, AMEX, and Nasdaq, and are obtained from CRSP. Panel A records the price response of 10 portfolios sorted by dividend yield (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). Panel B records the price response of 10 portfolios sorted by book-to-market ratio. Panel C records the price response of 10 portfolios sorted by earnings-to-price ratio. Panel D records the price response of 10 portfolios sorted by cashflows-to-price ratio. Panel A records the price response of 10 portfolios sorted by dividend yield (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). Panel B records the price response of 10 portfolios sorted by book-to-market ratio. Panel C records the price response of 10 portfolios sorted by earnings-to-price ratio. The tables reports the heteroskedastic-consistent Wald statistics of the null hypothesis 𝛽2𝑖 =𝛽2𝑗 and of the null hypothesis 𝛽4𝑖 = 𝛽4𝑗 . Bold denotes significance at the 5 percent level.
∆𝑃𝑡,𝑖 = ��𝛽1𝑖 + 𝛽2𝑖 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� < 0� + �𝛽3𝑖 + 𝛽4𝑖 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� > 0�� ∗ 𝐷(𝐶𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛)+ ��𝛽5𝑖 + 𝛽6𝑖 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� < 0� + �𝛽7𝑖 + 𝛽8𝑖 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� > 0�� ∗ 𝐷(𝐸𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛) + 𝜀𝑡,𝑖
∆𝑃𝑡,𝑗 = ��𝛽1𝑗 + 𝛽2𝑗 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� < 0� + �𝛽3𝑗 + 𝛽4𝑗 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� > 0�� ∗ 𝐷(𝐶𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛)+ ��𝛽5𝑗 + 𝛽6𝑗 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� < 0� + �𝛽7𝑗 + 𝛽8𝑗 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� > 0�� ∗ 𝐷(𝐸𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛) + 𝜀𝑡,𝑗
Impact from NEGATIVE WN residuals during CONTRACTIONs (H0: 𝛽2𝑖 =𝛽2𝑗)
Impact from POSITIVE WN residuals during CONTRACTIONs (H0: 𝛽4𝑖 = 𝛽4𝑗)
P1 P2 P3 P4 P5 P6 P7 P8 P9 P1 P2 P3 P4 P5 P6 P7 P8 P9
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P2 0.04 0.26 P3 0.99 1.24 0.09 0.03 P4 0.88 1.25 0.02 1.43 1.35 2.95 P5 0.55 0.68 0.02 0.10 7.86 11.39 19.28 11.40 P6 1.14 1.59 0.16 0.13 0.39 2.70 3.09 5.15 1.04 4.26 P7 1.05 1.43 0.28 0.25 0.64 0.08 1.70 1.79 2.60 0.41 3.04 0.00 P8 1.14 1.41 0.51 0.54 0.92 0.37 0.29 2.82 3.13 4.11 2.00 0.03 0.98 1.94 P9 0.57 0.63 0.11 0.09 0.21 0.02 0.00 0.44 0.60 0.44 0.66 0.02 1.85 0.12 0.16 4.59 P10 0.29 0.28 0.01 0.00 0.03 0.01 0.09 0.60 0.15 0.05 0.24 0.22 1.22 5.63 2.35 3.53 11.11 5.05
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t P2 0.51 0.16 P3 0.06 0.18 0.21 0.11 P4 0.22 0.00 0.28 0.00 0.24 1.09 P5 0.05 0.07 0.00 0.19 0.04 0.00 0.20 0.27 P6 0.74 0.57 2.24 1.18 3.92 0.01 0.03 0.28 0.05 0.06 P7 1.58 1.72 5.10 3.86 10.83 1.34 0.29 1.11 3.26 1.20 4.70 3.78 P8 0.96 0.79 2.58 1.54 4.27 0.24 0.30 0.03 0.21 0.84 0.06 0.65 0.54 1.02 P9 0.44 0.22 0.83 0.36 1.29 0.13 1.50 0.72 0.05 0.28 0.86 0.11 0.74 0.63 0.46 0.04 P10 1.56 1.39 2.64 1.99 3.86 0.84 0.17 0.60 1.81 0.01 0.12 0.34 0.02 0.21 0.11 0.43 0.00 0.04
87
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P3 0.76 0.15 0.13 3.11 P4 0.50 0.07 0.01 0.38 0.04 3.21 P5 0.78 0.38 0.14 0.36 0.01 0.69 0.40 1.04 P6 0.19 1.38 3.25 6.23 10.41 0.13 1.77 0.02 4.44 1.21 P7 0.05 0.68 1.50 2.70 5.43 0.15 0.23 1.91 0.13 4.10 1.72 0.18 P8 1.01 3.50 5.74 10.51 15.46 2.10 4.21 0.54 3.07 0.56 6.42 3.28 0.99 0.45 P9 0.23 1.37 2.56 4.41 8.76 0.04 0.39 1.81 0.98 4.33 1.27 8.96 6.37 2.36 1.61 0.41 P10 0.35 0.06 0.00 0.01 0.11 3.44 2.68 11.38 6.84 0.01 0.36 0.26 0.43 0.00 0.66 1.40 3.24 7.21
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e P2 0.05 0.00 P3 0.91 0.77 0.04 0.06 P4 0.00 0.05 1.25 0.39 0.60 0.32 P5 0.18 0.57 3.15 0.58 2.53 4.06 6.58 14.87 P6 2.16 3.50 7.91 4.45 2.29 0.92 1.15 1.86 5.12 1.49 P7 0.34 0.78 3.23 0.75 0.05 2.06 1.01 1.34 2.25 5.46 1.06 0.04 P8 1.16 2.18 5.59 2.54 1.06 0.24 0.85 0.35 0.48 0.90 2.93 2.67 0.27 0.51 P9 1.23 2.28 5.69 2.72 1.16 0.05 1.14 0.06 0.80 1.13 1.84 4.44 0.78 0.03 0.00 0.47 P10 0.77 1.51 4.03 1.31 0.38 0.27 0.25 0.02 0.15 2.40 3.35 4.48 7.27 0.01 1.18 0.84 1.94 1.23
88
Table 4.24.2 (continued from Table 4.24.1): Wald Test - Sensitivity of Stock Prices to Negative & Positive White-Noise Residuals of Surprises during different business cycles, by Portfolios based on Fundamental-to-Price Ratios. Tables show the results of the following SUR regression for the price changes of ith and jth decile portfolios, ΔPt,i and ΔPt,j, on the negative and positive white-noise residuals of surprises during different business cycles. The tests on the type of residual shocks (POSITIVE or NEGATIVE) and during the different business cycles (CONTRACTION or EXPANSION) are shows in the titles of each sub-table below. P1 through P10 are 10 portfolios sorted by respective ratio of fundamental-to-price. All portfolios are constructed using stocks listed on NYSE, AMEX, and Nasdaq, and are obtained from CRSP. Panel A records the price response of 10 portfolios sorted by dividend yield (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). Panel B records the price response of 10 portfolios sorted by book-to-market ratio. Panel C records the price response of 10 portfolios sorted by earnings-to-price ratio. Panel D records the price response of 10 portfolios sorted by cashflows-to-price ratio. Panel A records the price response of 10 portfolios sorted by dividend yield (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). Panel B records the price response of 10 portfolios sorted by book-to-market ratio. Panel C records the price response of 10 portfolios sorted by earnings-to-price ratio. The tables reports the heteroskedastic-consistent Wald statistics of the null hypothesis 𝛽6𝑖 =𝛽6𝑗 and of the null hypothesis 𝛽8𝑖 = 𝛽8𝑗 . Bold denotes significance at the 5 percent level.
∆𝑃𝑡,𝑖 = ��𝛽1𝑖 + 𝛽2𝑖 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� < 0� + �𝛽3𝑖 + 𝛽4𝑖 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� > 0�� ∗ 𝐷(𝐶𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛)+ ��𝛽5𝑖 + 𝛽6𝑖 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� < 0� + �𝛽7𝑖 + 𝛽8𝑖 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� > 0�� ∗ 𝐷(𝐸𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛) + 𝜀𝑡,𝑖
∆𝑃𝑡,𝑗 = ��𝛽1𝑗 + 𝛽2𝑗 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� < 0� + �𝛽3𝑗 + 𝛽4𝑗 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� > 0�� ∗ 𝐷(𝐶𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛)+ ��𝛽5𝑗 + 𝛽6𝑗 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� < 0� + �𝛽7𝑗 + 𝛽8𝑗 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� > 0�� ∗ 𝐷(𝐸𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛) + 𝜀𝑡,𝑗
Impact from NEGATIVE WN residuals during EXPANSIONs (H0: 𝛽6𝑖 = 𝛽6𝑗)
Impact from POSITIVE WN residuals during EXPANSIONs (H0: 𝛽8𝑖 = 𝛽8𝑗)
P1 P2 P3 P4 P5 P6 P7 P8 P9 P1 P2 P3 P4 P5 P6 P7 P8 P9
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P2 5.37 0.66 P3 18.80 10.48 0.95 0.16 P4 12.73 6.96 0.20 0.00 0.58 2.17 P5 10.75 5.20 0.37 0.06 0.52 0.04 0.03 1.82 P6 17.16 12.03 0.88 2.46 2.91 0.60 0.08 0.00 1.97 0.01 P7 7.05 3.18 0.13 0.01 0.00 1.67 3.04 2.87 2.57 7.66 4.72 4.11 P8 12.68 9.45 2.75 4.25 5.63 1.96 9.84 1.47 1.07 0.85 3.06 1.49 1.32 0.16 P9 8.48 5.27 0.93 1.53 2.01 0.33 3.15 1.30 1.19 0.79 0.62 2.25 0.97 0.86 0.18 0.02 P10 3.67 1.37 0.02 0.00 0.01 0.34 0.01 5.52 3.56 1.84 1.45 1.28 2.88 1.59 1.47 0.05 0.34 0.65
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t P2 0.33 0.03 P3 1.65 2.38 0.06 0.05 P4 2.97 4.74 1.16 0.11 0.52 1.51 P5 3.18 4.91 2.93 0.47 0.01 0.07 0.43 0.24 P6 2.40 3.42 2.01 0.38 0.01 0.10 0.33 1.11 0.02 0.55 P7 4.95 7.91 7.31 4.06 4.12 3.83 0.54 1.39 3.58 1.09 4.21 1.63 P8 4.48 6.33 6.13 3.08 3.00 4.00 0.04 0.47 1.06 2.75 0.74 2.56 1.43 0.00 P9 7.47 11.02 11.57 7.43 9.49 12.31 4.05 4.25 1.01 2.07 4.28 1.81 4.73 3.66 0.88 1.06 P10 0.24 0.10 0.17 0.78 2.16 2.34 7.43 8.92 19.20 0.88 1.53 2.54 1.15 2.51 1.43 0.44 0.46 0.00
89
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rice P2 0.98 0.10
P3 4.20 3.11 1.51 1.93 P4 6.32 7.03 2.01 0.56 0.58 0.39 P5 4.88 5.32 1.24 0.00 1.24 1.78 0.09 1.10 P6 6.57 6.68 2.92 0.93 1.00 2.43 3.27 1.13 4.81 1.36 P7 8.42 9.91 5.77 4.85 5.81 2.88 0.89 1.05 0.05 0.69 0.00 1.14 P8 5.12 5.25 1.86 0.51 0.57 0.00 3.47 1.02 1.24 0.08 0.85 0.01 0.81 0.02 P9 6.06 6.43 2.70 1.18 1.56 0.15 1.67 0.23 1.41 1.81 0.31 1.59 0.26 0.22 0.32 0.20 P10 4.13 3.60 0.88 0.03 0.03 0.26 3.52 0.28 1.13 1.62 1.97 0.41 1.62 0.31 0.06 0.36 0.29 0.04
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e P2 1.64 0.62 P3 2.56 0.29 0.59 0.01 P4 4.24 1.48 0.52 0.10 0.17 0.25 P5 5.01 2.71 1.80 0.54 0.46 2.55 3.69 2.97 P6 0.68 0.06 0.60 2.98 6.30 0.15 0.08 0.14 0.01 2.98 P7 0.46 3.70 6.93 14.48 22.51 6.86 0.06 0.95 1.33 0.62 0.54 1.19 P8 0.04 0.81 2.09 6.06 10.94 1.00 2.47 0.51 2.36 2.93 2.19 0.00 3.68 0.77 P9 0.27 0.19 0.86 3.12 5.61 0.10 4.22 0.41 0.00 0.35 0.50 0.10 1.04 0.24 0.23 1.80 P10 0.45 0.06 0.49 1.82 3.28 0.00 3.20 0.45 0.07 0.60 0.08 0.05 0.44 3.21 0.42 1.91 3.86 1.52
90
Table 4.25.1: Paired Difference Test - Sensitivity of Stock Prices to Negative & Positive White-Noise Residuals of Surprises during different business cycles, by Portfolios based on Fundamental-to-Price Ratios. Table shows results of regression of the mean difference of one-day price changes between ith and jth decile portfolios, (ΔPt,i - ΔPt,j), where i ≠ j, on the negative and positive white-noise residuals of surprises during different business cycles. The tests on the type of residual shocks (POSITIVE or NEGATIVE) and during the different business cycles (CONTRACTION or EXPANSION) are shown in each sub-table below. P1 through P10 are 10 portfolios sorted by respective ratio of fundamental-to-price. All portfolios are constructed using stocks listed on NYSE, AMEX, and Nasdaq, and are obtained from CRSP. Panel A records the price response of 10 portfolios sorted by dividend yield (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). Panel B records the price response of 10 portfolios sorted by book-to-market ratio. Panel C records the price response of 10 portfolios sorted by earnings-to-price ratio. Panel D records the price response of 10 portfolios sorted by cashflows-to-price ratio. The table reports the t test of the null hypothesis β_6 = 0 and the null hypothesis β_8= 0. Bold denotes significance at the 5 percent level.
∆𝑃𝑡,𝑖 − ∆𝑃𝑡,𝑗 = 𝛼 + ��𝛽1 + 𝛽2 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� < 0�+ �𝛽3 + 𝛽4 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� > 0�� ∗ 𝐷(𝐶𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛)+ ��𝛽5 + 𝛽6 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� < 0� + �𝛽7 + 𝛽8 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� > 0�� ∗ 𝐷(𝐸𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛) + 𝜀𝑡
Impact from NEGATIVE Shocks during CONTRACTIONs (H0: b2i = 0) Impact from POSITIVE Shocks during CONTRACTIONs (H0: b4i = 0) P1 P2 P3 P4 P5 P6 P7 P8 P9 P1 P2 P3 P4 P5 P6 P7 P8 P9
Pane
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P2 -0.11 2.20 P3 -0.64 -0.53 1.89 -0.30 P4 -0.69 -0.58 -0.05 3.07 0.87 1.18 P5 -0.57 -0.46 0.07 0.12 7.27 5.07 5.37 4.20 P6 -0.84 -0.73 -0.19 -0.15 -0.26 4.28 2.08 2.38 1.21 -2.99 P7 -0.99 -0.88 -0.35 -0.30 -0.42 -0.15 4.52 2.33 2.63 1.45 -2.75 0.25 P8 -1.29 -1.18 -0.64 -0.60 -0.71 -0.45 -0.30 8.56 6.37 6.67 5.49 1.30 4.29 4.04 P9 -0.97 -0.86 -0.33 -0.28 -0.40 -0.13 0.02 0.32 5.92 3.73 4.03 2.85 -1.34 1.65 1.40 -2.64 P10 -0.74 -0.63 -0.10 -0.05 -0.17 0.09 0.25 0.54 0.23 2.80 0.61 0.91 -0.27 -4.46 -1.47 -1.72 -5.76 -3.12
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t P2 -0.44 -0.33 P3 -0.22 0.23 -1.13 -0.80 P4 -0.46 -0.01 -0.24 -0.07 0.25 1.06 P5 -0.24 0.20 -0.03 0.21 -0.75 -0.42 0.38 -0.67 P6 -1.14 -0.69 -0.92 -0.68 -0.89 -0.15 0.17 0.98 -0.08 0.59 P7 -1.60 -1.16 -1.38 -1.14 -1.36 -0.46 1.71 2.04 2.84 1.78 2.45 1.86 P8 -1.35 -0.91 -1.13 -0.89 -1.11 -0.21 0.25 0.91 1.24 2.04 0.99 1.66 1.07 -0.80 P9 -0.95 -0.50 -0.73 -0.49 -0.70 0.19 0.65 0.40 2.04 2.37 3.17 2.11 2.78 2.19 0.33 1.13 P10 -1.92 -1.47 -1.70 -1.46 -1.67 -0.78 -0.32 -0.57 -0.97 1.58 1.91 2.71 1.65 2.33 1.73 -0.13 0.67 -0.46
91
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rice P2 0.43 -0.89
P3 0.63 0.20 0.62 1.50 P4 0.58 0.15 -0.04 -0.94 -0.05 -1.55 P5 0.83 0.40 0.20 0.25 -0.17 0.72 -0.78 0.77 P6 -0.42 -0.85 -1.05 -1.01 -1.25 0.82 1.71 0.20 1.76 0.99 P7 -0.25 -0.69 -0.88 -0.84 -1.09 0.17 1.45 2.33 0.83 2.39 1.61 0.63 P8 -1.09 -1.52 -1.71 -1.67 -1.92 -0.66 -0.83 1.37 2.26 0.75 2.31 1.54 0.55 -0.08 P9 -0.52 -0.95 -1.15 -1.10 -1.35 -0.10 -0.27 0.57 3.06 3.95 2.44 4.00 3.22 2.24 1.61 1.69 P10 0.64 0.21 0.01 0.05 -0.19 1.06 0.89 1.72 1.16 -0.18 0.71 -0.79 0.76 -0.01 -1.00 -1.62 -1.55 -3.23
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e P2 -0.13 0.11 P3 -0.58 -0.45 0.11 0.00 P4 0.00 0.12 0.58 0.16 0.05 0.05 P5 0.31 0.44 0.89 0.31 -3.28 -3.39 -3.39 -3.44 P6 0.97 1.10 1.55 0.97 0.66 -1.94 -2.06 -2.05 -2.11 1.33 P7 0.41 0.54 0.99 0.41 0.10 -0.56 -2.07 -2.19 -2.18 -2.24 1.21 -0.13 P8 0.77 0.90 1.35 0.78 0.46 -0.20 0.36 -1.66 -1.77 -1.77 -1.82 1.62 0.29 0.41 P9 0.87 1.00 1.45 0.87 0.56 -0.10 0.46 0.10 -2.11 -2.23 -2.22 -2.28 1.17 -0.17 -0.04 -0.46 P10 0.69 0.82 1.27 0.69 0.38 -0.28 0.28 -0.08 -0.18 -2.63 -2.74 -2.74 -2.79 0.65 -0.69 -0.56 -0.97 -0.52
92
Table 4.25.2 (continued from Table 4.25.1): Paired Difference Test - Sensitivity of Stock Prices to Negative & Positive White-Noise Residuals of Surprises during different business cycles, by Portfolios based on Fundamental-to-Price Ratios. Table shows results of regression of the mean difference of one-day price changes between ith and jth decile portfolios, (ΔPt,i - ΔPt,j), where i ≠ j, on the negative and positive white-noise residuals of surprises during different business cycles. The tests on the type of residual shocks (POSITIVE or NEGATIVE) and during the different business cycles (CONTRACTION or EXPANSION) are shown in each sub-table below. P1 through P10 are 10 portfolios sorted by respective ratio of fundamental-to-price. All portfolios are constructed using stocks listed on NYSE, AMEX, and Nasdaq, and are obtained from CRSP. Panel A records the price response of 10 portfolios sorted by dividend yield (P1 being the smallest value and P10 being the largest value), excluding utility firms (SIC 4900-4949). Panel B records the price response of 10 portfolios sorted by book-to-market ratio. Panel C records the price response of 10 portfolios sorted by earnings-to-price ratio. Panel D records the price response of 10 portfolios sorted by cashflows-to-price ratio. The table reports the t test of the null hypothesis β_6 = 0 and the null hypothesis β_8= 0. Bold denotes significance at the 5 percent level.
∆𝑃𝑡,𝑖 − ∆𝑃𝑡,𝑗 = 𝛼 + ��𝛽1 + 𝛽2 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� < 0� + �𝛽3 + 𝛽4 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� > 0�� ∗ 𝐷(𝐶𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛)+ ��𝛽5 + 𝛽6 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� < 0�+ �𝛽7 + 𝛽8 ∗ ∆𝑊𝑁𝑡��𝐷�∆𝑊𝑁𝑡� > 0�� ∗ 𝐷(𝐸𝑥𝑝𝑎𝑛𝑠𝑖𝑜𝑛) + 𝜀𝑡
Impact from NEGATIVE Shocks during EXPANSIONs (H0: b6i = 0) Impact from POSITIVE Shocks during EXPANSIONs (H0: b8i =0) P1 P2 P3 P4 P5 P6 P7 P8 P9 P1 P2 P3 P4 P5 P6 P7 P8 P9
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P2 1.28 -0.71 P3 2.86 1.58 -1.03 -0.31 P4 2.67 1.40 -0.18 -0.07 0.65 0.96 P5 2.58 1.30 -0.28 -0.10 -0.91 -0.19 0.12 -0.84 P6 3.32 2.04 0.46 0.64 0.74 -0.99 -0.28 0.04 -0.92 -0.08 P7 2.62 1.34 -0.24 -0.06 0.04 -0.70 -2.76 -2.04 -1.73 -2.69 -1.85 -1.77 P8 4.38 3.10 1.52 1.70 1.80 1.06 1.76 -2.39 -1.67 -1.36 -2.32 -1.48 -1.40 0.37 P9 3.82 2.54 0.96 1.15 1.24 0.50 1.20 -0.56 -2.29 -1.58 -1.26 -2.22 -1.38 -1.30 0.47 0.10 P10 2.70 1.42 -0.16 0.02 0.12 -0.62 0.08 -1.68 -1.12 -3.06 -2.34 -2.03 -2.99 -2.15 -2.07 -0.30 -0.67 -0.77
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t P2 0.36 0.17 P3 1.20 0.84 0.37 0.20 P4 1.70 1.33 0.49 -0.54 -0.71 -0.91 P5 2.04 1.68 0.84 0.34 -0.14 -0.32 -0.52 0.39 P6 2.09 1.73 0.89 0.39 0.05 -0.69 -0.86 -1.06 -0.15 -0.55 P7 2.89 2.53 1.69 1.20 0.85 0.80 -1.53 -1.70 -1.90 -1.00 -1.39 -0.84 P8 2.98 2.62 1.78 1.29 0.95 0.89 0.09 -1.55 -1.72 -1.92 -1.01 -1.40 -0.86 -0.02 P9 3.99 3.62 2.78 2.29 1.95 1.90 1.09 1.00 -2.35 -2.52 -2.72 -1.81 -2.20 -1.66 -0.82 -0.80 P10 0.76 0.40 -0.44 -0.93 -1.28 -1.33 -2.13 -2.22 -3.22 -2.36 -2.53 -2.73 -1.82 -2.21 -1.67 -0.83 -0.81 -0.01
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Pane
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rice P2 0.60 -0.30
P3 1.50 0.90 -1.45 -1.14 P4 2.12 1.52 0.62 -1.01 -0.71 0.44 P5 2.12 1.52 0.62 0.00 -1.72 -1.42 -0.27 -0.71 P6 2.52 1.92 1.02 0.40 0.40 -2.46 -2.16 -1.02 -1.45 -0.74 P7 3.27 2.67 1.76 1.15 1.15 0.75 -1.70 -1.40 -0.26 -0.69 0.02 0.76 P8 2.50 1.90 0.99 0.38 0.38 -0.02 -0.77 -1.79 -1.49 -0.34 -0.78 -0.07 0.67 -0.09 P9 2.70 2.10 1.20 0.58 0.58 0.19 -0.56 0.21 -2.10 -1.79 -0.65 -1.09 -0.38 0.37 -0.39 -0.31 P10 2.22 1.62 0.72 0.10 0.10 -0.30 -1.04 -0.27 -0.48 -2.24 -1.93 -0.79 -1.23 -0.52 0.23 -0.53 -0.45 -0.14
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e P2 0.71 -0.70 P3 0.99 0.28 -0.76 -0.07 P4 1.37 0.66 0.38 -0.34 0.35 0.42 P5 1.67 0.97 0.68 0.30 0.81 1.51 1.57 1.15 P6 0.56 -0.15 -0.43 -0.81 -1.12 -0.42 0.27 0.34 -0.08 -1.23 P7 -0.49 -1.19 -1.47 -1.85 -2.16 -1.04 0.27 0.97 1.04 0.62 -0.54 0.70 P8 0.15 -0.56 -0.84 -1.22 -1.53 -0.41 0.63 0.84 1.54 1.60 1.18 0.03 1.26 0.57 P9 0.41 -0.29 -0.57 -0.95 -1.26 -0.14 0.90 0.27 -0.06 0.63 0.70 0.28 -0.87 0.36 -0.34 -0.90 P10 0.54 -0.17 -0.45 -0.83 -1.14 -0.02 1.02 0.39 0.12 -0.99 -0.30 -0.23 -0.65 -1.80 -0.57 -1.27 -1.83 -0.93
94
CHAPTER 5
DISCUSSIONS AND CONCLUSIONS
My paper uses an equity duration framework to conduct an empirical analysis on the
impact of changes in Federal Funds target rates on equity prices. It makes the following
contributions.
First, in this paper I decompose the Federal Funds rate change to its predictable and
unpredictable components to examine price sensitivity. I find that (i) only the surprise
component has a significant and negative effect on portfolio returns, (ii) the expected component
has no effect on portfolio returns, (iii) the coefficient on the surprise component is typically
higher than the coefficient on nominal change in interest rate, and (iv) the R-squares of
regressions on the surprise are almost twice as large compared to those of regressions on nominal
change in interest rate.
Second, my study extends the work Bernanke and Kuttner (2005) who also report the
effects of unanticipated monetary policy actions of stock prices. While their study only focus on
the price reactions of broad based equity portfolios, I use an equity duration framework to
analyze stock price reaction to Federal fund rate shocks by segmenting portfolios, based on their
inherent levels of interest sensitivity. I differentiate equity portfolios along the growth-value axis
through four fundamental-to-prices ratio: dividend yield, book-to-market value, earnings-to-
price, and cashflows-to-price. In each case, I find that price reactions are more pronounced for
portfolios with low fundamental-to-prices characteristics, thus providing further support for the
presence of an equity duration effect.
Third, this paper reexamines whether portfolio returns react asymmetrically to the
direction of rate surprise. Although from a pure DFC standpoint, a negative (positive) target rate
95
surprise is considered to be good news (bad news), it would be unrealistic to expect the Federal
Reserve to announce rate changes that are independent of the prevailing business conditions. I
therefore test the hypothesis that asymmetric price reaction to positive or negative interest rate
shocks is conditional on the prevailing business cycle. I find strong evidence of asymmetric price
reaction, especially across business cycles. I specifically find that a one basis point positive
interest rate surprise will produce a 21 to 31 basis point price increase in the market portfolio
during a recession, but no will have no effect during an expansion. On the other hand, a one basis
point negative interest rate surprise will produce a 5 to 6 basis point price increase in the market
portfolio during an expansion, but no will have effect during a recession. Also, the magnitude of
the price reaction to a rate decrease is 5 to 6 time larger than that observed for a rate increase.
While my results appear to be counter-intuitive from a purely DCF perspective, I offer a
behavioral finance explanation that bad news tends to be discount less rigorously than good
news.
Finally, to improve the robustness of above mentioned results, I control for any possible
serial correlation across time series shocks. Although there is no economic implication for the
correlation among time series shocks, I replace target rate change shocks with white noise
residuals of target shocks in all regression models. Most of the robustness test results using white
noise residuals of target shocks are quite consistent with the ones tested with pure shocks except
for two contradictions. First, when I use white noise residual to examine whether portfolio
returns react asymmetrically to the direction of rate surprise, I find that portfolio returns only
react positively to negative signs. Second, when testing whether asymmetric price reaction to
positive or negative interest rate shocks is conditional on the prevailing business cycles, I find
that portfolio returns react positively to negative signs during expansions but fewer portfolios
96
react to the positive surprise during contractions. Overall, the results generated from using white
noise residuals are consistent with the ones using pure target shocks. From the DCF perspective,
I find that price reactions testing with white noise residuals are more pronounced for portfolios
with low fundamental-to-prices characteristics, thus providing further support for the presence of
an equity duration effect.
97
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