THREE FACTOR MODEL: FAMA AND FRENCH (1992) Oren Hovemann Yutong Jiang Erhard Rathsack Jon 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

 No relation between average return and beta during the 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

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 IV Properties of Portfolios Formed on Book-to-Market Equity (BE/ME)

Table IV Properties 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 IV Properties of Portfolios Formed on Book-to-Market Equity (BE/ME)

Table IV Properties 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 Book-to-market equity has a slope of.35 and a t-statistic of 4.44

Table III Average 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 III Average 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 III Average Slopes (T-Statistics) from Month-by-Month Regressions of Stock Returns on β, Size, Book-to-Market Equity, Leverage, and E/P

Table IV Properties 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 Returns 1) 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 % 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

Table VI: Subperiod Portfolios and Subperiod Means Average Monthly Returns on the NYSE Equal-Weighted and Value-Weighted of the Intercepts and Slopes from the Monthly FM Cross-Sectional Regressions of Returns on (a) Size (In(ME)) and Book-to-Market Equity (In(BE/ME)), and (b) β, In(ME), and In (BE/ME)

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 ( )  Reinganum (1981) and Lakonishok and Shapiro (1986)  ( )

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