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