December 2002: rmrf: excess return on a value-weighted market proxy smb: return on a small-stock portfolio minus the return on a large-stock portfolio (Small minus Big) hml: return on a value-stock portfolio minus the return on a growth-stock portfolio (High minus Low) umd: return on a high prior return portfolio minus the return on a low prior return portfolio (Up minus Down). All data are for the USA. Each of the last three variables denotes the dif- ference in returns on two hypothetical portfolios of stocks. These portfolios are re-formed each month on the basis of the most recent available infor- mation on firm size, book-to-market value of equity and historical returns, respectively. The hm/ factor is based on the ratio of book value to market value of equity, and reflects the difference in returns between a portfolio of stocks with a high book-to-market ratio (value stocks) and a portfolio of stocks with a low book-to-market ratio (growth stocks). The factors are mo- tivated by empirically found anomalies of the CAPM (for example, small firms appear to have higher returns than large ones, even after the CAPM risk correction). In addition to the excess returns on these four factors, we have observations on the returns on ten different "assets' which are ten port- folios of stocks, maintained by the Center for Research in Security Prices (CRSP). These portfolios are size-based, which means that portfolio I con- tains the 10% smallest firms listed at the New York Stock Exchange and portfolio 10 contains the 10% largest firms that are listed. Excess returns (in excess of the risk free rate) on these portfolios are denoted by rl to r10, respectively. In answering the following questions use rl, /10 and the returns on two additional portfolios that you select. (a) Regress the excess returns on your four portfolios upon the excess return on the market portfolio (proxy), noting that this corresponds to the CAPM. Include a constant in these regressions. (b) Give an economic interpretation of the estimated B coefficients. (c) Give an economic and a statistical interpretation of the R2. (d) Test the hypothesis that B, = I for each of the four portfolios. (e) Test the validity of the CAPM by testing whether the constant terms in the four regressions are zero