题目
We regressed daily returns of a stock against a market index. The regression produced a beta for the stock, with respect to the market index, of 1.050. The stock's volatility was 30.0% and the market's volatility was 20.0%. If the regression's total sum of squares (TSS) is 0.300, what is the regression's explained sum of squares (ESS)?
选项
A.0.0960
B.0.1470
C.0.4900
D.1.2500
答案
B
解析
As beta (stock,index) = covariance(stock,index)/variance(index) = correlation(stock, index)×volatility(stock)/volatility(index),it follows that correlation(stock,index) = beta (stock,index)×volatility(index)/volatility(stock); in this case, correlation(stock,index)= 1.050×20%/30% = 0.70,and: R2 = ρ2 = 0.72 = 0.49.SinceR2 = ESS/TSS, ESS =R2×TSS.In this case, ESS = 0.49×0.30 = 0.1470