Consider two stocks A and B. Assume their annual returns are jointly normally distributed, the marginal distribution of each stock has mean 2% and standard deviation 10%, and the correlation is 0.9. What is the expected annual return of stock A if the annual return of stock B is 3%?
We are trying to take out return for stock A. The equation used is OLS where A is the dependent variable and B is the independent variable. So we are using the regression equation to derive the returns for Stock A.
the explanation is given below slope or beta(A with respect to B) is Slope (A regressed on B) = Beta (A with respect to B) = Covariance(A,B) /Variance(A,B) = correlation(A,B)*StdDev(A)*StdDev(B)/Variance(B) = correlation(A,B)*StdDev(A)/StdDev(B). Slope (A regressed on B) = 0.9*10%/10% = 0.9 A(i) = intercept + slope*B(i) = 0.2% + 0.9*3%; i.e., this is the regression A(i) = E[A|B] = A(i) = intercept + slope*B(i) = 0.2% + 0.9*3% so the calculation is E[A|B=3%] = 0.2% + 0.9*3% = 2.9%
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