悉尼大学资本市场与公司财务课件Lecture6精选.pptVIP

Since β is the relationship between returns on a stock and the market, it can be estimated by quantifying this historical relationship The equation for the CAPM can be more generally stated as: where: Yt = E(ri,t – rf,t ) Xt = E(rm,t – rf,t ) ri,t = the return on stock I, earned over period t rf,t = the risk-free rate of return, earned over period t rm,t = the market rate of return, earned over period t Estimation of beta (cont) (7.7) The CAPM implies that the coefficient a = 0 The coefficient b, which measures the β of stock i, is a regression coefficient that can be calculated from historical data, and is given by: The first step in calculating beta is to collect historical data and calculate a sequence of excess returns on a stock and on the market (7.8) Estimation of beta (cont) The return on the stock in any month must include the dividend paid (if any) as follows: Where: Pt is the price of the stock at the end of month t, dt is the dividend paid during month t (if any) The return on the market is simply: where It is the index level at the end of month t. (7.9) (7.10) Estimation of beta (cont) Once the monthly excess returns on the stock and market have been calculated by subtracting the risk-free rate from stock and market returns, the covariance of the excess returns on the stock and market can be calculated using the following expression: (7.11) where n is the number of observations used to estimate beta. Estimation of beta (cont) The beta is then the ratio of the covariance between excess stock returns and excess market returns to the variance of excess market returns This is further illustrated by considering the characteristic line, which is the line that best fits the relationship between excess returns on the stock and the market The slope of the characteristic line is the beta of the stock – as shown in the following example Estimation of beta (cont) Example: Characteristic line for Tabcorp Holdings Lt