| Essay One: A New Estimate of Beta This essay examines a new method of estimating systematic risk, or "beta". Due to market imperfection, stock prices, especially those of small firms, do not move with the market index synchronously. Because of nonsynchronous or delayed reaction in price for small firms, the traditional beta estimated from the market model may not be a true reflection of systematic risk. In other words, since stock prices do not fully respond to the market in a single period, the contemporary beta may only reflect the partial systematic risk. As a result, the beta estimated from the market model is underestimated for small firms and overestimated for large firms. The same problem also causes betas estimated from the market model to vary greatly across different estimation horizons.;I develop a model of delay/lead price reactions for small/large firms. Based on this model I derive a multiple-period regression equation for the new estimation of beta. We then estimate the equation for each of the ten size-ranked decile portfolios at different estimation horizons, using monthly, weekly and daily returns. Betas estimated from the optimal estimation horizons for monthly, weekly, and daily returns are discussed.;Our results show that, betas estimated at similar horizons, using monthly, weekly, and daily returns, are consistent with each other. Betas estimated for the ten size-decile portfolios from monthly, weekly, and daily average returns are positively related to those returns, respectively.;Essay Two: Test of Capital Asset Pricing Model Based on a New Estimate of Beta This essay tests the Capital Asset Pricing Model (CAPM), based on a new estimate of beta. The test methodology follows the classic Fama-MacBeth (1973) approach, using updated data from 1926-2010. I ran each test on eleven different periods based on three different estimates of beta: the Ordinary Least Square (OLS) beta, the Scholes-Williams (1977) beta, and a new estimate of beta. From three long testing periods, 1935-1968, 1969-2010, and 1935-2010, all three hypotheses are confirmed based on the new estimate of beta. In other words there is a positive trade-off between average return and risk, and non-linearity and non-beta risk do not play a significant role in explaining the cross section of expected return. Test results from the three long periods based on the OLS beta and the Scholes-Williams beta are mixed and less supportive to CAPM. Our test results from the eight shorter periods do not confirm the CAPM. However, this may be due to the lack of power and efficiency of the test methodology when applied to short periods.;Overall, our results from long periods show that tests based on the new estimate of beta perform better than those based on the OLS beta and the Scholes-Williams beta in terms of supporting CAPM. |
