Pettengill, Sundaram and mathur 107 IV. Data and Methodology A. Data The sample period for this study extends from January 1926 through Decem ber 1990. Monthly returns for the securities included in the sample and the CRSP equally-weighted index(as a proxy for the market index)were obtained from the CRSP monthly databases. The three-month Treasury bill rates(a proxy for the risk-free rate) for the period 1936 through 1990 were collected from the Federal Reserve bulletin B. Test of a Systematic Relationship between Beta and Returns A The purpose of this paper is twofold. The first is to test for a systematic, conditional relationship between betas and realized returns. The second is to test for a positive long-run tradeoff between beta risk and return Tests for a systematic relationship utilize a modified version of the three-step portfolio approach first used by Fama and MacBeth(1973). The sample period is first separated into 15-year subperiods, which are further divided into a portfolio formation period, a portfolio beta estimation period, and a test period of five years each. In the portfolio formation period, betas are estimated for each security in the sample by regressing the securitys return against the market return. Based on the relative rankings of the estimated beta, securities are equally divided into 20 portfolios. Securities with lowest betas are placed in the first portfolio, the next lowest in the second portfolio, and so on. Portfolio betas are estimated in the second five-year period within each subsample by regressing portfolio returns ( the equally-weighted return of all securities in the portfolio) against the market eturns The third step, which tests the relationship between portfolio beta and returns is modified to account for the conditional relationship between beta and realized returns. As argued in Section IL, if the realized market return is above the risk-free return, portfolio betas and returns should be positively related, but if the realized market return is below the risk-free return, portfolio betas and returns should be inversely related. Hence, to test for a systematic relationship between beta and returns, the regression coefficients from Equation (4)are examined, (4) Rir =%0r+fir*8*Bi+i2*(1-6)*B;+Er where 8= l, if(Rmt-Ra)>0(i.e, when market excess returns are positive), and 8=0, if(Rmt-Rn)<o(i. e, when market excess returns are negative), The above relationship is examined for each month in the test period by estimating either yI or 12, depending on the sign for market excess returns Since 1 is estimated in periods with positive market excess returns, the expected sign of this coefficient is positive. Hence, the following hypotheses are sted There is no material difference in the results when the value-weighted index is used he entire sample period into up markets and down markets was first performed