THREE FACTOR MODEL: FAMA AND FRENCH (1992) Oren Hovemann Yutong Jiang Erhard Rathsack Jon Tyler.
-
Upload
madeline-garrison -
Category
Documents
-
view
212 -
download
0
Transcript of THREE FACTOR MODEL: FAMA AND FRENCH (1992) Oren Hovemann Yutong Jiang Erhard Rathsack Jon Tyler.
THREE FACTOR MODEL: FAMA AND FRENCH (1992) Oren HovemannYutong JiangErhard RathsackJon Tyler
Cross Section of Expected Returns A Firm’s Size and its Book/Market ratio combine
to become a strong predictor of the Firm’s expected return
The value of Beta as a predictor of return is challenged
Additional known factors used to predict stock returns are the firm’s Leverage and Earnings/Price ratios
Size and B/M absorb the roles of Leverage and E/P ratios in the Three Factor Model
Pricing Data
Pricing data includes stocks from: NYSE AMEX NASDAQ
Date Ranges from 1962 to 1989 Data collected from CRSP and COMPUSTAT Historical reporting of Book Value limits data
range
Financial Reporting vs. Returns Matching of returns with accounting data has a six month
minimum gap. December accounting values are used to calculate (t – 1)
Book/Market Leverage Earning/Price
June accounting values are used to calculate (t) Size (price factor)
The six month gap between financial reporting and realized returns insure the reflection of all information into the stock pricing
Different fiscal year-ends between firms complicate the timing of matching accounting values with returns
100 Size–Beta Portfolios
Portfolio Assignments First stocks are divided into Size ranked deciles Then each Size based decile is sub-divided into Pre-
Ranked Beta deciles A stock can move between portfolios over time if either
its size or pre-ranked Beta changes Estimated Betas for each Portfolio
Historical monthly returns are regressed against CRSP derived market returns to estimate Post-Ranked Betas
Estimated Betas for portfolios based on a Size-Beta ranking magnify the range of Beta values
Allows tests that distinguish between the effects of size and beta upon stock returns
Size-Beta Portfolios increase range of estimated Betas
Size based beta variation is 1.44 – 0.92 = 0.52 Size-Beta Portfolio based beta variation is 1.79 – 0.53 = 1.26 The range of variation of Beta in Size-Beta based Portfolios is
1.26 / 0.52 = 2.4 times greater than Size based portfolios
Table II
Strong negative relation between size and average return.
Strong positive relation between average return and beta.
Table II
Table II
No relation between average return and beta during the 1964-1979 period.
Table III
Firm size ln(ME) is measured in June of year t If earnings are positive, E(+)/P is the ratio of total earnings
to market equity and E/P dummy is 0. If earnings are negative, E(+)/P is 0, E/P dummy is 1. T-statistic is the average slope divided by its time-series
standard error.
Fama-Macbeth Regressions The Fama-Macbeth regression is a method used to
estimate parameters for asset pricing models. The method estimates the betas and risk premium
for any risk factors that are expected to determine asset prices.
The method works with multiple assets across time (panel data).
The parameters are estimated in two steps: First regress each asset against the proposed risk
factors to determine that asset's beta for that risk factor.
Then regress all asset returns for a fixed time period against the estimated betas to determine the risk premium for each factor.
Table III
Size helps explain the cross-section of average stock returns.
Market beta does not help explain average stock returns for 1963-1990
Table IV
Portfolios ranked by values of book-to-market equity (BE/ME) and earnings-price ratio (E/P)
13 portfolios formed with the lowest and highest portfolios split and stocks with negative E/P in a separate portfolio (only for E/P)
Negative BE firms not included (on average, there are about 50/2317 per year)
Table IVProperties of Portfolios Formed on Book-to-
Market Equity (BE/ME)
Table IVProperties of Portfolios Formed on Earnings-
Price Ratio (E/P)
Variables in Table IV
Return – Time-series average of the monthly equal-weighted portfolio returns (%)
β – Time-series average of the monthly portfolio Bs Ln(ME) – Market equity representing firm size
(outstanding shares x share price) Ln(BE/ME) – Book equity divided by market equity Ln(A/ME) - Book assets divided by market equity Ln(A/BE) – Book assets divided by book equity E/P dummy – Dummy variable used to distinguish
between positive and negative earnings E(+)/P – Positive earnings to price ratio Firms – average number of stocks in the portfolio each
month
Average Returns
Average returns sorted by BE/ME Strong positive relationship Difference of 1.53% from lowest to highest
portfolios Unlikely a β effect Negative BE and high BE/ME have similar returns as
a result of capturing relative distress Average returns sorted by E/P
Returns have a U shape Portfolio 0 (negative earnings) has higher than
average returns Returns increase as positive E/P portfolios increases
Table IVProperties of Portfolios Formed on Book-to-
Market Equity (BE/ME)
Table IVProperties of Portfolios Formed on Earnings-
Price Ratio (E/P)
BE/ME
Monthly regressions of returns on book-to-market equity has strong relationship More significant than the size effect
Book-to-market equity does not replace size Monthly returns of regressions on book-to-
market equity and size: Size has a slope of -.11 and a t-statistic of -1.99 Book-to-market equity has a slope of .35 and a t-
statistic of 4.44
Table IIIAverage Slopes (T-Statistics) from Month-by-Month
Regressions of Stock Returns on β, Size, Book-to-Market Equity, Leverage, and E/P
Leverage
Two leverage ratios are used A/ME (book assets to market equity) -
Measure of market leverage A/BE (book assets to book equity) - Measure
of book leverage Both leverage ratios are related to
average returns, with opposite signs but similar absolute values
The difference between these ratios is what helps explain average returns
Table IIIAverage Slopes (T-Statistics) from Month-by-Month
Regressions of Stock Returns on β, Size, Book-to-Market Equity, Leverage, and E/P
Leverage & Book-to-Market
ln(BE/ME) = ln(A/ME) – ln(A/BE) Close link between leverage and BE/ME Two interpretations:
High book-to-market ratio could be low stock price compared to book value
High book-to-market ratio could be a firms market leverage is high relative to its book leverage
Relative distress (captured by BE/ME) can also be viewed as a leverage effect (captured by the difference between A/ME and A/BE)
E/P
It is believed that earnings are a proxy for future earnings E/P dummy is used because negative earnings
are not a proxy for future earnings E/P dummy (negative earnings) has a
strong relationship with returns Add size to the regression and the relationship
becomes insignificant This shows that the high returns for negative E/P is
better explained by size E(+)/P has a strong relationship with
returns
Table IIIAverage Slopes (T-Statistics) from Month-by-Month
Regressions of Stock Returns on β, Size, Book-to-Market Equity, Leverage, and E/P
Table IVProperties of Portfolios Formed on Earnings-
Price Ratio (E/P)
E/P & Book-to-market
Regressions of returns on ME, BE/ME and E/P gives insignificant results for E/P
Regressions of returns using ME, BE/ME and E/P produce very similar results to regressions using just ME and BE/ME for ME and BE/ME Suggests that E/P is insignificant in explaining
returns when book-to-market ratios are used Results suggest that the relationship between
E(+)/P and average return is mostly due to the positive correlation between E/P and BE/ME Firms with high E/P have high book-to-market ratios
IV. A Parsimonious Model For Average Returns1) When we allow for variation in β that is unrelated to
size, there is no reliable relation between β and average return
2) The opposite roles of market leverage and book leverage in average returns are captured well by book-to-market equity
3) The relation between E/P and average return seems to be absorbed by the combination of size and book-to-market equity.
Do not use β
Size and book-to-market equity are better indicators
A. Average Returns, Size and Book-to-Market Equity
A) Controlling for size, book-to-market equity captures substantial variation in average returns
B) Controlling for BE/ME leaves a size effect in average returns.
A. Average Returns, Size, and Book-to Market Equity
Table V: Average Monthly Returns on Portfolios Formed on Size and Book-to-Market Equity; Stocks Sorted by ME (Down) and then BE/ME (Across): July 1963 to December 1990
0.58% per month average spread of returns
B. The interaction Between Size and Book-to-Market Equity Low Market Equity
Low stock prices High book-to-market equity
Table III Correlation between ln(ME) and ln(BE/ME) = -0.26
C. Subperiod Averages of FM Slope Table III
Size has a negative premium Book-to-Market has a positive premium Market β has a neutral 0 premium
Table VI Subgroups created and tested with FM Slope β weak and inconsistent Size Effect lacks power Book-to-Market consistently reliable January Effect also found to be significant
D. Β and the Market Factor: Caveats Average premiums for β, size, and book-
to-market equity depend on the definitions of the variables used in the regressions. Using B/E will change slope SLB model
Overturns simple relationship between return and β being flat
Leaves β as the only variable
V. Conclusions and Implications Sharpe-Linter-Black (SLB) Model
Positive simple relation between average return and market β (1926-1968)
Reinganum (1981) and Lakonishok and Shapiro (1986) (1963-1990)
V. Conclusions and Implications What variables can explain return?
Banz (1981) Strong Negative Relationship between return and firm size
Bhandari (1988) Positive Relationship between return and leverage
Basu (1982) Positive Relationship between return and E/P
Rosenberg, Reid and Lanstein (1985) Positive Relationship between return and book-to-market equity
Chan, Hamao, and Lakonishok (1992) find that BE/ME is powerful for predicting returns
A. Rational Asset-Pricing Stories What is the economic explanation for the roles of size and
book-to-market equity in average returns? Regression on returns in ln(ME) and Ln(BE/ME) are returns
on portfolios that mimic the underlying common risk factors in returns proxied by size and book-to-market equity.
Relation between size and average return proxies for a more fundamental relation between expected returns and economic risk factors.
Relation between size and average return is a relative-prospects effect. More distressed firms are more sensitive to economic conditions
BE/ME should be a direct indicator of the relative prospects of a firm Low BE/ME strong performance
B. Irrational Asset-Pricing Stories Asset pricing effects are not always
rational Market overreaction to the prospects of the
firm
C. Applications
Size and Book-to-market equity describe the cross-section of average stock returns. Will it persist? Does it result from rational or irrational asset-
pricing? Explanatory power does not deteriorate over time
Long-term average returns Form portfolios and measure success
Alternate investment strategies Measure expected returns and evaluate
performance