Fa Ma French Article

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The Journal of Financial Research Vol. XXX, No. 1 Pages 111127 Spring 2007

APPLICABILITY OF THE FAMA-FRENCH THREE-FACTOR MODELIN FORECASTING PORTFOLIO RETURNS

Ou Hu

Youngstown State University

Abstract

For the model-based estimation of the equity cost of capital, evidence shows

that the common practice of using the average historical factor premiums as the

estimates of the next-period factor premiums generates inaccurate estimates. I

propose an alternative way to estimate factor premiums by using the structural

variables that are important predictors of future asset returns. Based on the out-

of-sample results from a trading strategy with four in-sample model-selection

criteria, I find that my estimation procedure performs better than the common

practice even when transaction costs are considered.

JEL Classification: G12, G31, C13, C22

I. Introduction

Since its origination in the 1960s, the capital asset pricing model (CAPM) has beenused by most project managers to estimate the equity cost of capital. In reality,

practitioners estimate the future market risk premium by averaging the long-term

historical market risk premium. However, many studies show that the historical

average market excess return is higher than the actual market risk premium. Thus,

the estimate of equity returns overstates what rational investors would have expected

to earn. The poor performance of this common practice has cast doubt on the

application of the CAPM.

As Fama and French (1997) demonstrate, the imprecise use of the CAPM

to estimate equity returns has two sources: the estimation error of the risk loadings

and the estimation error of the risk premiums. They conclude that the uncertaintyabout risk premiums is responsible for a larger part of the problem in estimating

the equity cost of capital.

Ferson andLocke (1998), who analyze the sources of errors in CAPM-based

estimates of expected returns on industry portfolios, reach a similar conclusion:

that errors in estimating betas (factor loadings) probably do not matter as much as

The author is grateful for the comments from Ronald J. Balvers, Joseph Palardy, and especially William

T. Moore (the former editor) and an anonymous referee.

111


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112 The Journal of Financial Research

errors in estimating market premium. Pastor and Stambaugh (1999) use a Bayesian

approach to examine the estimation of costs of equity for individual firms and

to compare estimates of three factor-based pricing models. They find that model

uncertainty is less important than parameter uncertainty within any given model,and without mispricing uncertainty, estimation errors of factor premiums probably

account for more of the uncertainty about the cost of capital.

In this article, I examine the effectiveness of the Fama and French (1993)

three-factor model in predicting future returns. Following Elton (1999),1 I propose

an alternative way to estimate factor premiums. I do so by using several structural

variables, such as term premium, default risk premium, and dividend yield. Instead

of imposing a fixed model in forecasting risk premiums, I assume that investors do

not know the model specification but search for the optimal specification according

to somemodel selectioncriteria. To see whether the predictability of portfolio excess

returns can be exploited successfully, I use a trading strategy: to hold the portfolio(s)with the highest expected excess return and to sell the portfolio(s) with the lowest

expected excess return. Then, I calculate the realized excess returns for long and

short positions, and the excess profits for a zero-investment strategy (long minus

short).

Based on the empirical results, my estimation procedure performs bet-

ter than the common practice. Without consideration of transaction costs, almost

all the trading strategies generate significant positive zero-investment profits. Al-

though the transaction costs can reduce the profit, by imposing a transaction cost

filter, investors can still earn significant positive profits from most of their trading

strategies.Moreover, a risk analysis study shows that the excess returns from the

trading strategies cannot be explained by risk factors. The abnormal return from

the long position is significantly higher than that from the buy-and-hold benchmark,

the market portfolio. Finally, Bossaerts and Hillions (1999) forecast betas provide

some support for the Fama-French (1993) model in predicting asset returns.

The method I apply is fundamentally different from that used in previous

studies. For example, Ferson and Harvey (1999) allow factor loadings to be condi-

tional on some predetermined variables to test the Fama-French (1993) three-factor

model for the cross-section of stock returns. Cooper, Gulen, and Vassalou (2001)

use business-cycle variables and macroeconomic variables to predict asset future

returns. These authors find some evidence that the size factor and book-to-market

(B/M) factor are representatives of fundamental economic risks. However, those

studies do not examine the applicability of any particular asset pricing model.

1While arguing that the average realized returns are poor proxies for expected returns, Elton (1999)

proposes some alternative ways to estimate expected returns.


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Forecasting Portfolio Returns 113

II. Endogenization of Model Selection

The Fama-French (1993) three-factor model is as follows:

rit rft= bi (rmt rft)+si rSMB,t+ hi rHML,t+ eit, (1)

where rit is the return on asset i; rft is the return on the risk-free asset; rmt is the

return on the overall market; the size factor, r SMB,t, is the return on a zero-investment

portfolio that is long on small stocks and short on big stocks; the B/M factor, rHML,t,

is the return on a zero-investment portfolio that is long on high-B/M stocks and

short on low-B/M stocks;2 bi, si, andhi are factor loadings; andeit is a mean-zero

regression disturbance. Fama and French (1993) generate 25 portfolios sorted by

size and B/M factors. For each of the 25 regressions in the form of model (1), the

typical R2 is above 0.9. Fama and French (1997) use the same regression on 48industries and find that the average R2 (0.68) is slightly higher than that (0.63) of

the CAPM. This and other evidence support the power of the Fama-French (1993)

three-factor model in explaining asset returns.

To investigate its forecasting ability, I rewrite model (1) in a conditional

form:

rit rft = biEt1(rmt rft)+ siEt1rSMB,t+ hiEt1rHML,t+ it. (2)

As model (2) indicates, I must estimate all the three-factor premiums at time t bymeans of historically available information up to time t1. But instead of taking the

average of historical risk premiums, I propose using structural variables to estimate

the three-factor premiums. Moreover, I assume that investors have no knowledge

of what specific model will be applied to predict risk premiums but that they can

select an optimal model specification based on some criteria.

Following Pesaran and Timmermann (1995), I apply four model-selection

criteria: adjusted R2, Akaikes information criterion (AIC), Schwarzs Bayesian

information criterion (BIC), and the sign criterion. Once investors choose a model,

they can make one-period-ahead predictions of risk premiums. As time progresses

and more historical information is available, investors with no assumption on themodel specification must reevaluate their model selection. Consequently, investors

might not choose the same model at time t+1 as they did at time t.

Suppose that at period t an investor searches over a set of k variables to

make one-period-ahead predictions of risk premiums (r mt rft), rSMB,t, andrHML,t.

The total number of all the possible combinations of k variables [x 1,x 2, . . . ,x k]

2Details on how to construct the SMB and HML factors are available on Kenneth Frenchs Web site

(http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/).


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is 2k, where ki denotes the ith combination of k variables. For each of the 2k

combinations, I conduct a linear regression as follows:

rps = Xi,s1i + i,s s = 1, 2, . . . , t , (3)

where rps is a risk premium at time s, and Xi,s1 is a row vector that contains a

combination ofkvariables ki. To predict r pt+1, I obtain an ordinary least squares

(OLS) estimate i for each of the 2k regressions. Next, I choose an optimal i

according to a model-selection criterion and calculate an estimatedrpt+1 by multi-

plying the optimal i with its corresponding Xi,t.

III. Data, Method, and In-Sample Estimation

All variables are measured at monthly frequencies from 1954:04 to 2001:10. The

start and end dates are determined by data availability. I examine the 17 equally

weighted industry portfolios3 defined by Fama and French (1993). The Fama-

French three factorsthe market excess return (MKTEXRT ), the size factor (SMB),

and the B/M factor (HML)are obtained from Kenneth Frenchs Web site (http://

mba.tuck.dartmouth.edu/pages/faculty/ken.french/).

To predict the three factor premiums, I use the following variables: divi-

dend yield (DIV, the difference between market return with dividend and market

return without dividend), the nominal one-month Treasury bill rate (TB), the in-

dustrial production growth rate (IP), the term premium (TERM, the differencebetween 10-year and three-month Treasury yields), and the default risk premium

(DEFP, the spread between Moodys Bbb and Aaa corporate bond yields). I obtain

DIV from the Center for Research in Security Prices (CRSP); TB from Ibbot-

son and Associates; and IP, TERM, andDEFP from the Federal Reserve Bank of

St. Louis.

Table 1 reports descriptive statistics of the 17 equally weighted industry

portfolios and predictive variables. No obvious patterns are evident across the means

and standard deviations of the 17 industries. Unlike the portfolios formed on size

or B/M ratio, the 17 industries were formed according to the characteristics andactivities of individual firms. Therefore, the advantage of examining 17 industries

is that I can avoid the inherent relation between the two factors (SMB andHML)

and the size and B/M portfolios.

3Besides the 17 equally weighted industry portfolios, I apply the same method to 17 value-weighted

industry portfolios, and 30, 38, and 48 value-weighted and equally weighted industry portfolios. The results

are consistent over all portfolios grouped by different definitions, although the results of value-weighted

portfolios are not as significant as those of equally weighted portfolios.


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TABLE 1. Summary Statistics of 17 Equally Weighted Industry Portfolios and Other Predictive

Variables: Monthly Data from 1954:04 to 2001:10.

Panel A. Industry Portfolios

IndustryPortfolio Mean Std. Dev. 1 6 12 36

Food 1.14 4.40 0.20 (.000) 0.027 (.512) 0.12 (.006) 0.07 (.104)

Mines 1.22 6.58 0.13 (.002) 0.012 (.777) 0.08 (.062) 0.18 (.000)

Oil 1.32 6.60 0.14 (.001) 0.022 (.596) 0.09 (.032) 0.08 (.091)

Clths 1.00 6.03 0.25 (.000) 0.014 (.747) 0.13 (.003) 0.11 (.016)

Durbl 1.14 6.17 0.22 (.000) 0.038 (.361) 0.11 (.009) 0.07 (.143)

Chems 1.23 5.27 0.15 (.000) 0.040 (.341) 0.08 (.072) 0.09 (.051)

Cnsum 1.57 6.57 0.18 (.000) 0.016 (.702) 0.02 (.585) 0.05 (.345)

Cnstr 1.21 5.91 0.22 (.000) 0.025 (.553) 0.13 (.003) 0.09 (.042)

Steel 1.08 6.16 0.14 (.001) 0.013 (.759) 0.04 (.409) 0.08 (.091)

FabPr 1.21 5.62 0.19 (.000) 0.006 (.894) 0.12 (.006) 0.09 (.043)

Machn 1.39 6.91 0.21 (.000) 0.004 (.930) 0.05 (.303) 0.07 (.133)Cars 1.15 6.06 0.21 (.000) 0.018 (.666) 0.10 (.018) 0.07 (.090)

Trans 1.16 5.80 0.20 (.000) 0.040 (.342) 0.10 (.019) 0.07 (.089)

Utils 1.07 3.36 0.09 (.040) 0.015 (.719) 0.04 (.322) 0.04 (.320)

Rtail 1.09 5.71 0.25 (.000) 0.014 (.740) 0.09 (.044) 0.08 (.074)

Finan 1.25 4.87 0.25 (.000) 0.036 (.389) 0.13 (.002) 0.05 (.239)

Other 1.31 6.43 0.21 (.000) 0.013 (.755) 0.06 (.205) 0.07 (.119)

Panel B. Explanatory Variables

Explanatory

Variable Mean Std. Dev. 1 6 12 36

MKTEXRT 0.57 4.31 0.06 (.140) 0.03 (.503) 0.03 (.525) 0.01 (.749)

SMB 0.13 3.02 0.08 (.065) 0.06 (.146) 0.15 (.001) 0.06 (.136)HML 0.38 2.80 0.14 (.001) 0.08 (.063) 0.04 (.372) 0.04 (.450)

TB 0.44 0.23 0.96 (.000) 0.86 (.000) 0.76 (.000) 0.46 (.000)

IP 0.25 0.92 0.42 (.000) 0.03 (.536) 0.15 (.000) 0.04 (.282)

TERM 0.11 0.10 0.95 (.000) 0.65 (.000) 0.43 (.000) 0.09 (.032)

DEFP 0.08 0.04 0.97 (.000) 0.83 (.000) 0.69 (.000) 0.35 (.000)

DIV 0.29 0.18 0.13 (.001) 0.92 (.000) 0.92 (.000) 0.84 (.000)

Note: Data and definitions of 17 industries are available on Kenneth Frenchs Web site (http://mba.

tuck.dartmouth.edu/pages/faculty/ken.french/). MKTEXRT is the excess return of market portfolio

over the risk-free rate. SMB is the excess return from a zero-investment strategy of buying small

portfolios and selling large portfolios. HML is the excess return from a zero-investment strategy

of buying value portfolios (high book-to-market (B/M) ratio) and selling growth portfolios (low

B/M ratio). TB is the nominal one-month Treasury bill rate. IP is industrial production growth rate.TERM is the term premium, defined as the difference between 10-year and three-month Treasury

yields. DEFP is the spread between Moodys Bbb and Aaa corporate bond yields (i.e., default risk

premium). DIV is the dividend yield (i.e., the difference between market return with dividend and

market return without dividend). TB, IP, TERM, and DEFP are all obtained from Federal Reserve

Bank of St. Louis. DIV is obtained from the Center for Research in Security Prices (CRSP) tapes.

The variable i represents the autocorrelation coefficient over i month(s). The p-values are given in

parentheses.


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I find significant positive first-order autocorrelation over the 17 indus-

tries, with all p-values less than .05. This result is not surprising, based on the

finding in Moskowitz and Grinblatt (1999) that there is a strong and prevalent mo-

mentum in industries. Autocorrelations ofMKTEXRT are weak. In contrast, SMBandHML both exhibit strong first-order autocorrelation with p-values of .065 and

.001, respectively. Therefore, I use lags of SMB and HML as predictors for their

next periods values. The other explanatory variablesTB, IP, TERM, DEFP, and

DIVexhibit strikingly significant autocorrelations over almost all time intervals

(from 1 month to 36 months), and the magnitude of autocorrelations tends to de-

crease as the time interval increases.

I evaluate the predictability of portfolio returns by using a trading strategy

that includes in-sample estimation and out-of-sample evaluation. For the in-sample

estimation, I apply 5- and 10-year rolling windows as well as a 5-year expanding

window. For instance, with the 5-year expanding window, the data from 1959:04to 1964:03 are used to estimate excess returns of the 17 industry portfolios for

1964:04. First, I obtain the estimates of the three risk premiums: Et1(r mt rft),

Et1r SMB,t, and Et1rHML,t. Next, I develop the risk loadingsbi, si , andhifor

each industry portfolio by estimating model (1). Then, I calculate the estimated

excess returns of the 17 industry portfolios at month 1964:04 by

Et1(rit rft) = biEt1(rmt rft)+ siEt1rSMB,t+ hiEt1rHML,t. (4)

There is no intercept in this equation. If I assume that the Fama and French (1993)three-factor model correctly prices assets, the intercept that measures mispricing

should be zero.

Based on the estimated excess returns of the 17 industry portfolios, the

trading strategy is to hold the industry portfolio with the highest expected excess

return and sell the industry portfolio with the lowest expected return. The next step

is to record the realized returns of the long position, the short position, and the

zero-investment strategy (the difference between the long position and the short

position) for 1964:04. With the in-sample window moving one month forward, the

same steps are repeated 451 times until the end of the entire period, 2001:10. Finally,

the average realized excess returns are calculated. Using the same starting point,

1964:03, the same procedure is applied to the 5- and 10-year rolling windows.

Table 2 presents the monthly in-sample estimation of the Fama-French

(1993) three factors over the entire period 1954:04 to 2001:10. As indicated by the

p-values, among all the predictive variables, the 12-month lagged value ofTERM,

the 1- and 12-month lagged values of DEFP, the 12-month lagged value of DIV,

and the 1-month lagged value of TB are important in predicting market excess

returns. In contrast, only the 1-month lagged value ofMKTEXRT and the 12-month

lagged value ofTERM play a significant role in predicting the size factor, SMB. In


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estimating the future value of HML, the important variables include the 1-month

lagged values of MKTEXRT, HML, TERM, and DEFP, and the 12-month lagged

values of DEFP and DIV. The adjusted R2s for the three regressions have about

the same value of 0.04, which indicates that over the entire period, the overallpredictability of the three factors is about the same.

IV. Out-of-Sample Performance of a Trading Strategy

Performance of the Common Practice

To report out-of-sample performance,Max1 is the return from the long position, that

is, to hold the portfolio with the highest estimated excess return; Min1 is the return

from the short position, that is, to sell short the portfolio with the lowest estimated

excess return; andMax1Min1 is the profit from a zero-investment trading strategy,

that is, to hold (long) the portfolio with the highest expected excess return and sell

(short) the portfolio with the lowest expected excess return.Max3Min3 is the profit

from a zero-investment strategy of holding the three portfolios with the highest

expected excess returns and selling the three portfolios with the lowest expected

excess returns.

Following the common practice, I use the historical averages of the Fama-

French (1993) three-factor premiums as the estimates of their future values. The

factor loadings bi, si, and hi are estimated by model (1). Then, using equa-

tion (4), I calculate the expected excess returns. Table 3 shows that the out-of-sample performance of the common practice is poor indeed. ForMax1Min1 with

the five-year expanding window, the difference (Max1Min1 = 1.506%) between

the average realized annualized return (9.115%) of the long position (Max1) and

the average annualized return (7.506%) of the short position (Min1) is not signifi-

cantly different from zero (t= 0.571), which contravenes the spirit of the trading

strategy in which Max1 is expected to be significantly greater than Min1. More-

over, if the market excess return is treated as a benchmark, Max1 is expected to

be significantly greater than MKTEXRT, andMin1 is expected to be significantly

lower thanMKTEXRT. However, based on the common practice, not only areMax1

andMin1 similar over all the in-sample windows, but they also are not statisticallydifferent from annualized market excess return (5.352%). A similar result holds

forMax3Min3. Therefore, I conclude that this trading strategy provides evidence

against the common practice.

Performance of the New Approach

In contrast, Tables 4 and 5 present different results for the performance of the Fama-

French (1993) three-factor model based on the estimation procedures described in

section III. Both the fixed model and the model with the adjusted R2demonstrate


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a consistently significant performance of the Fama-French three-factor model in

predicting the excess returns of the 17 industry portfolios.

For the strategy of Max1Min1 (Panel A in both Tables 4 and 5), the av-

erage annualized return of Max1 for the fixed model and the adjusted R

2

modelover all three in-sample windows is about 13%, which is positive and significant,

and the zero-investment profit (Max1Min1) is positive and significant with an

average 10% annualized return. The out-of-sample result shows that with the help

of some structural variables, the Fama-French (1993) three-factor model can pre-

dict asset returns and correctly distinguish the portfolios with different expected

returns. Moreover, Max1mkt is positive and significant. The average annualized

return ofMax1mktis about 8%, and both the terminal wealth and the Sharpe ratio

indicate that holding the portfolio with the highest expected returns outperforms

the benchmark of buying and holding the market portfolio.

As a robustness check, Panel B in both Tables 4 and 5 presents the result forthe strategy ofMax3Min3. Although the returns ofMax3Min3 are not as high as

those ofMax1Min1, they are positive and significant, with an average annualized

return of 7%, and the returns of Max3mktfrom all the strategies are positive and

significant. Therefore, the results from Max3Min3 provide additional support for

the performance of the Fama-French (1993) three-factor model with risk premiums

estimated by structural variables.

A comparison between Table 3 and Tables 4 and 5 shows that using fore-

casted premiums performs better than using realized values of the premiums. In

Table 3, Max1mkt andMax3mkt are not different from zero; neither are Min1

mkt and Min3mkt. In contrast, in Tables 4 and 5, Max1mkt and Max3mkt arepositive and significant, andMin1mktandMin3mktare not statistically different

from zero.

In addition, I conduct formal statistical tests to compare the common prac-

tice with the proposed estimation procedures. I directly compare the out-of-sample

realized returns (Max1Min1 and Max3Min3) from the common practice with

those from the five estimation procedures: the fixed model and the four models

with different criteria. For the 5-year expanding window and the 10-year rolling

window, all five estimation procedures outperform the common practice. For in-

stance, from the 5-year expanding window, the difference of the realized annual

returns ofMax1Min1between the fixed model and the common practice is 10.64%

(t= 2.54). I generalize that the difference in annualized returns is statistically

significant, with about 10% for Max1Min1 and about 6% for Max3Min3. Al-

though the results for the 5-year rolling window are not as significant as both

the 5-year expanding window and the 10-year rolling window, the difference re-

turns is still positive and the fixed model still performs better than the common

practice.

This analysis shows that by using structural variables, the estimated risk

premiums MKTEXRT, SMB, and HMLdo a better job in forecasting


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industry-based portfolios than do the realized values of those premiums, which

presumably contain some noisy information that dilutes their forecasting ability.

Transaction Costs

In reality, transaction costs are incurred in trading assets. Previous studies such as

those by Pesaran and Timmermann (1995), Carhart (1997), and Grundy and Martin

(2001) show that transaction costs can be substantial when portfolios are switched

monthly. Therefore, it is important to analyze the effect of transaction costs for a

more reasonable assessment of stock market predictability.

Following Pesaran and Timmermann (1995), I investigate transaction costs

of 0.5% and 1% per switch. A switch involves selling one portfolio and purchasing

another. Following Balvers and Wu (2004), for Max1Min1, Max3, and Max3

Min3, I count each switch of one of the two, three, or six portfolios as 1/2, 1/3, and1/6 of a switch, respectively.

The higher the percentage of the switched portfolio is, the higher are the

transaction costs, and the lower are the realized profits. In fact, forMax1Min1, the

average percentage of switch is 32% for all five estimation procedures across all

three in-sample windows. Formal out-of-sample tests show that with a transaction

cost of 0.5%, Max1Min1 is no longer consistently positive and significant. For

example, with the adjusted R2 as the model-selection criterion, only the 5-year

expanding window and the 10-year rolling window generate positive returns of

Max1Min1. Max3Min3 is not significantly different from zero for all trading

strategies.With a transaction cost of 1% per switch, Max1Min1 and Max3Min3

become even smaller. Max1Min1 is not statistically positive, and Max3Min3

becomes negative and significant for a few cases, such as the 5-year rolling window

using adjustedR2 as the criterion and the 5- and 10-year rolling windows using AIC

as the criterion. The results indicate that a reasonable amount of transaction costs

could wipe out a significant portion of the realized excess returns generated by the

trading strategies.

The results also imply that once transaction costs are taken into consid-

eration, it is not optimal to switch portfolios whenever the expected return of one

portfolio exceeds that of the currently held portfolio. Therefore, I impose a thresh-

old on the expected return differential; that is, if the portfolio with the highest

expected return is different from the currently held portfolio, a switch will happen

only when the expected return differential between these two portfolios reaches a

minimum level. For a 0.5% transaction cost, the expected return differential for a

switch is at least 0.5%, and for a 1% transaction cost, the differential is at least

1%.

The results show that for the 0.5% transaction cost per switch, the fixed

model and the model selected by adjusted R2, AIC, and sign generate significant


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positive zero-investment profit (Max1Min1) across all three in-sample windows.4

However, BIC does not perform as well. Only the five-year rolling window produces

a significant positiveMax1Min1profit. For instance, with the five-year expanding

window, the fixed model produces an annualized return of 10.31% (t= 2.902) andthe adjustedR2 generates 7.64% (t= 2.264). These results are similar to those in

Peseran and Timmerman (1995).

For the 1% transaction cost per switch, although all four model-selection

criteria generate nonsignificant zero-investment profit (Max1Min1), the fixed

model still demonstrates strong and statistically significant performance, showing

an average annualized return of 7%. ForMax3Min3 for both low and high trans-

action costs, none of the four criteria generates significant positive zero-investment

profits. However, the fixed model performs better than all the criteria. Only the

10-year rolling window fails to generate significant positive Max1Min1 returns.

In addition, both the terminal wealth andSharpe ratio show that thetrading strategiesofMax1 andMax3 outperform the buy-and-hold strategy of the market portfolio.

I also perform formal tests to compare the common practice with the es-

timation procedures when transaction costs are present. The results show that the

estimation procedures outperform the common practice for most trading strategies,

although the results for high transaction costs are less significant than are those for

low transaction costs. In general, even after considering transaction costs, with a

reasonable prerequisite on the switch of portfolios, the Fama-French (1993) three-

factor model with forecast risk premiums still exhibit economic significance in

predicting asset returns.

Risk Analysis

The preceding analysis provides evidence on the predictability of asset returns.

Whether the predictability of asset returns indicates market inefficiency depends

on whether the excess returns can be explained by some risk factors. I use the

CAPM and the Fama-French (1993) three-factor model to identify whether the

excess returns are related to some standard risk factors. I treat the excess returns of

Max1Min1 (Max3Min3), Max1mkt(Max3mkt), andMin1mkt(Min3mkt) as

the dependent variables in the following two regressions:

erit = i + bi (rmt rft)+ eit, (5)

erit = i + bi (rmt rft)+si rSMB,t+ hi rHML,t+ eit, (6)

where erit refers to the excess return of one trading strategy at time t. I test excess

returns from six trading strategies. These tests include Max1Min1 (Max3Min3),

4Because of limited space, I do not include the results from formal tests.


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Max1mkt(Max3mkt), andMin1mkt(Min3mkt). The nonzero value ofi indi-

cates whether an asset is overpriced or underpriced.

The results show that the ofMax1Min1 is positive and significant except

for the 5-year rolling window using R

2

and sign as selection criteria. The ofMax1mkt is also positive and significant except for a few cases in which the

Fama-French (1993) three-factor model is not statistically different from zero,

such as the 10-year expanding window with model-selection criteria ofR2, AIC, and

sign.

In general, the results provide evidence that even with a risk adjustment,

the mean return of the long portfolio (Max1) is still significantly larger than that of

the buy-and-hold benchmark, the market portfolio. For some cases ofMin1mkt, the

value of is negative and significant. However, for other cases, it is not statistically

different from zero. Therefore, the evidence that the short portfolio performs worse

than the benchmark is not as strong as the evidence that the long portfolio performsbetter than the benchmark. Although showing less statistical significance, Max3

Min3, Max3mkt, andMin3mktexhibit a similar pattern in the CAPM and the

Fama-French (1993) three-factor model .

Bossaerts and Hillions (1999) Forecast Beta

The analysis of the forecasting ability of the Fama-French (1993) three-factor model

indicates that the structural variables capture the variations in risk premiums and

that using forecasted risk premiums results in better forecasts of asset returnsthan does using average historical risk premiums. I next examine the compari-

son between realized and expected excess returns. This comparison provides addi-

tional information on how well the Fama-French three-factor model forecasts asset

returns.

The method I apply is the Bossaerts and Hillions (1999) forecast beta.

They investigate the forecasting ability (external validity) of a model by projecting

the actual excess returns onto the expected excess returns:

erit+1 = ai + bizit+ vt+1, i = 1, 2, . . . , 17, (7)

where zit is the expected excess return of industry portfolio i at time t and is

calculated using the Fama-French (1993) three-factor model with risk premiums

forecasted by structural variables.

After examining all 17 industry portfolios, I find that for all four model-

selection criteria and the fixed model, at least 10 of 17 forecast betas are positive

and significant with the five-year expanding window, and that the actual ratio is

between 10/17 and 16/17. With the two rolling windows, the ratio is between 2/17

and 10/17, and in most cases, the ratio is about 7/17. As a result, I find that all five

estimation procedures perform well out of sample.


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V. Conclusion

The common practice in the model-based estimation of the equity cost of capital

uses the average historical factor premiums as estimates of future factor premiums.However, much evidence shows that the common practice generates inaccurate

estimates.

I propose using structural variables to estimate risk premiums and imple-

ment trading strategies on 17 equally weighted industry portfolios to evaluate the

forecasting ability of the Fama-French (1993) three-factor model. Assuming that

investors do not possess foreknowledge of what model they should use to estimate

risk factors, I apply four model-selection criteria to choose an optimal model for

every point in the trading strategy.

The empirical results show that based on the common practice, all trading

strategies generate nonsignificant zero-investment profits, but with the proposedestimation procedures, most trading strategies generate significant positive zero-

investment profits. When transaction costs are considered, the zero-investment

profits are materially reduced. However, an adjustment on trading strategies with a

transaction cost threshold can still prevent the profits from being completely eroded

by transaction costs, at least for low transaction costs.

A risk analysis shows that the returns generated by the trading strategies

cannot be explained by the CAPM or the Fama-French (1993) three-factor model.

Finally, to determine how well the Fama-French model forecasts asset returns, I

calculate Bossaerts and Hillions (1999) forecast betas. For the five-year expanding

window, the forecast betas are positive and significant for more than half of the17 industry portfolios.

All results demonstrate that the Fama-French (1993) three-factor model

with factor premiums estimated from structural variables is more reliable than the

common practice in forecasting portfolio returns.

References

Balvers, R. J. and Y. R. Wu, 2004, Momentum and mean reversion across national equity markets, Workingpaper.

Bossaerts, P. and P. Hillion, 1999, Implementing statistical criterion to select return forecasting models:

What do we learn? Review of Financial Studies 12, 40528.

Carhart, M. M., 1997, On persistence in mutual fund performance, Journal of Finance 52, 5782.

Cooper, M., H. Gulen, and M. Vassalou, 2001, Investing in size and book-to-market portfolio using infor-

mation about the macroeconomy: Some new trading rules, Working paper.

Elton,E. J., 1999, Expected return,realized return,and asset pricing tests,Journal of Finance 54, 11991220.

Fama, E. F. and K. R. French, 1993, Common risk factors in the returns on stocks and bonds, Journal of

Financial Economics 33, 356.

Fama, E. F. and K. R. French, 1997, Industry costs of equity, Journal of Financial Economics 43, 153

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