Essay Fama: Average Stock Returns

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Common factors determine the average returns of stocks and bonds (1993) by Fama & French in Journal of Financial Economics, Vol. 33, p. 3‐56. Data Span: 1963‐1990 Frequency: Monthly Assets: stocks listed on NYSE, Amex, and NASDAQ, US government and Corporate bonds. Input variables: (1) excess returns of the market RM (t )  RF (t ) , market returns minus risk free returns (2) size SMB (t )  RS (t )  RL (t ) , returns of small stocks minus returns of large stocks, details see below. (3) book‐to‐market equity ( BE / ME ) HML (t )  RH (t )  RL (t ) , returns of high ( BE / ME ) stocks minus returns of low ( BE / ME ) stocks (4) Unexpected changes in interest rates, TERM (t )  R _ LGB (t )  R _ 1mTB (t ) , returns of long‐term government bonds minus returns of 1‐month treasury bills (5) Default risks, DEF (t )  R _ LCB (t )  R _ LGB (t ) , returns of long‐term corporate bonds minus returns of long‐term government bonds Stock classifications: (a) In June of each year t from 1963 to 1991, all NYSE stocks on CRSP are rank on size (price times share). The median NYSE stock is used to split all stocks in the sample into two groups, small and big (S and B), i.e. number of small stocks is much higher. (b) Book common equity is defined as the COMPUSTAT book value of stockholder’s equity, plus balance sheet deferred taxes and investment tax credit (if available), minus the book value of preferred stocks. Book‐to‐market equity is then the book common equity for the fiscal year ending in calendar year t‐1, divided by the market equity at the end of December of t‐1. Breakpoints for the bottom 30% (Low), middle 40% (Medium), and top 30% (High) of the ranks values of ( BE / ME ) for NYSE stocks are used to classify all stocks in the sample into three groups. (c) In the beginning of July every year, six portfolios (S/L, S/M, S/H, B/L, B/M, B/H) from the intersections of the two M/E and three BE/ME groups are formed based on current year’s size rank and previous year’s ( BE / ME ) rank. Monthly value‐weighted returns on the six portfolios are calculated from July of year t to June of t+1, and the portfolios are reformed in the end of June of t+1. Output variables: (1) Excess returns on 25 stock portfolios form on size and book‐to‐market equity quintiles determined by stocks listed on NYSE as described above.

(2) Excess returns on two government bond portfolios from CRSP covering maturities from (1‐5 year) and (6‐10 year), and five corporate bond portfolios from Moody’s rating groups, Aaa, Aa, A, Baa and LG (low‐grade, that is below Baa). Empirical Models (1) Effects of bond‐market returns on the average stock returns and bond returns R (t )  RF (t )  a  mTERM (t )  dDEF (t )  e(t ) Table 3 Significant positive effects were estimated from both input factors. The explaining power for average stock returns is relatively low , with R 2 between 6% to 21%. For average bond returns, these models explain much higher variation with R 2 between 79% to 98%. Bond factors explain bond returns well. (2) Effect of excess stock market returns on the average returns of stock and bonds R (t )  RF (t )  a  b[ RM (t )  RF (t )]  e(t ) Table 4 A reverse result is found than the previous model, the market factor explains the stock returns much better than the bond returns. (3) Effects of mimicking returns for the size and book‐to‐market equity to the average returns of stocks and bonds R (t )  RF (t )  a  sSMB (t )  hHML (t )  e(t ) Table 5 The size and book‐to‐value factors explain the returns of small stocks better. SMB has positive effect and HML exhibits negative effects for stock returns. No clear patterns are found for the bond returns. (4) Effects of excess market returns and mimicking returns for the size and book‐to‐market equity to
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