THE AMERICAN ECONOMIC REVIEH SEPTEMBER 1978 TABLE 1-SECOND-PASS REGRESSION WITH MONTHLY DATA B 0.00985 (0.08956) 0.00053) 0.l1129) 0.00117 0.10404 (0.00099) (0.00136) (0.12865) 0.00136 (0.00096) (0.00110) (0.12909) then, in spite of the fact that we do not have In this paper we examine the follo a perfect empirical procedure to test it, we linear regressions, with monthl expect the variance itself, of, to provide annual data and annual data planation of pri R f() R =f(S2) Ill. The Empirical Findin R;-r=f(G2) The monthly rates of return of a sample R4-r=f(1,S2) of 101 stocks traded on the New york Stock R-r=f(8,G3) Exchange(NYSE) were calculated for the period 1948-68, that is, for each security where R, is the average rate of return on the there are 240 observations. Thus, if Ril, ith security, r is the rate of return on riskless Rao were the monthly rates of re- assets, and p is the systematic risk esti- turn, on the ith security, one can calculate mated from the time-series regressions; S the bimonthly rates of return,R青,R盔, is the residual variance(taken also from the Riizo by substituting(1 +Ri(1 +R) time-series regressions)and a? stands for 1+R青,(1+R3)(1+R4)=1+ Rs etc he estimate of the ith security variance return for an investment horizon of two e These regressions are run for three dif. where ri(i= 1. 2,..., 120)are the rates of rent investment horizons (one, six, and months. Note that, by using a horizon of twelve months)since it has been shown that two months, we subdivided the period 1948-68 to 120 time units rather than to 240 time units, without changing the length of government bonds were taken from var the period covered by the empirical re- the Federal Reserve Bulletin. The sample of shares was search: namely, twenty years. Similarly, if taken from the return file of the CrSP tape. Note that we had used annual rates of return, we we employ the same set of data. This may cause some would have only 20 observations. As a statistical bias. However, I believe that by a division of proxy to the market portfolios I used the the period to two superiods (one for estimating Beta Fisher Arithmetic Index. which assumes an ther for the cre se many observations, which is undesirable. More equal investment in h of the NYSE over. the Beta may change from period to period which decreases the reliability of this procedure. 0m3303038AN654 THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1978 TABIE 1-SECOND-PASS REGRESSION WITH MONTHLY DATA Ri =yo +- 'yli + ^2 ? -32 R 0.00894 0.00196 0.04 (0.00096) (0.00094) t = 9.3 t = 2.1 0.00985 0.18369 0.04 (0.00057) (0.08956) t= 17.3 t=2.0 0.00999 0.21916 0.04 (0.00053) (0.11129) t = 19.0 t = 2.0 0.00914 0.00117 0.10404 0.05 (0.00099) (0.00136) (0.12865) t = 9.2 t = 0.86 (t = 0.81) 0.00899 0.00136 0.13736 0.05 (0.00096) (0.00110) (0.12909) t=9.3 t=1.2 t=1.l then, in spite of the fact that we do not have a perfect empirical procedure to test it, we expect the variance itself, uK, to provide a better explanation of price behavior than the traditional systematic risk, /i. III. The Empirical Findings The monthly rates of return of a sample of 101 stocks traded on the New York Stock Exchange (NYSE) were calculated for the period 1948-68, that is, for each security there are 240 observations. Thus, if Ril, Ri2. . ., Ri 240 were the monthly rates of re￾turn, on the ith security, one can calculate the bimonthly rates of return, R*, R*,.... R*120by substituting (1 + Ri) (1 + Ri2) - 1 ? R*, (1 + R13)(l + R4) = I + R * etc., where R* (i = 1,2,. ..,120) are the rates of return for an investment horizon of two months. Note that, by using a horizon of two months, we subdivided the period 1948-68 to 120 time units rather than to 240 time units, without changing the length of the period covered by the empirical re￾search: namely, twenty years. Similarly, if we had used annual rates of return, we would have only 20 observations. As a proxy to the market portfolios I used the Fisher Arithmetic Index, which assumes an equal investment in each of the NYSE stocks. In this paper we examine the following linear regressions, with monthly data, semi￾annual data and annual data: R- r = f(i3i) Ri- r = f (0) Ri - r = f(S, R- r = f(a i Ri - r = f(i3i, &i) where Ri is the average rate of return on the ith security, r is the rate of return on riskless assets,'0 and /3 is the systematic risk esti￾mated from the time-series regressions; Se. is the residual variance (taken also from the time-series regressions) and &j stands for the estimate of the ith security variance. These regressions are run for three dif￾ferent investment horizons (one, six, and twelve months) since it has been shown that I0The rates of return on Treasury Bills as well as on government bonds were taken from various issues of the Federal Reserve Bulletin. The sample of shares was taken from the return file of the CRSP tape. Note that in estimating Beta, and in the cross-section regression we employ the same set of data. This may cause some statistical bias. However, I believe that by a division of the period to two superiods (one for estimating Beta and the other for the cross-section regression) one may lose many observations, which is undesirable. More￾over, the Beta may change from period to period which decreases the reliability of this procedure. This content downloaded from 202.115.118.13 on Wed, 11 Sep 2013 03:07:38 AM All use subject to JSTOR Terms and Conditions