frm level test 1

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frm level test 1

Postby shah.vishal » Sun May 12, 2013 10:00 pm

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%?
Please explain

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Posts: 20
Joined: Mon Apr 08, 2013 1:36 pm

frm level test 1

Postby vnraghuveer » Tue May 14, 2013 11:42 am

It's a question on OLS estimates of regression line, slope of which is of the form
A = k + (Beta of B w.r.t A) x B
Beta of B with respect to A = Covar(A,B)/Var of A = 0.1 x 0.1 x 0.9 / 0.1^2 = 0.9
k = mean(A) - Beta x Mean(B) = 2% - 0.9 x 2% = 0.2%
So the equation is A = 0.2% + 0.9 B
and the equation for calculating expected returns of A given expected return of B is
E(A|B) = mean(A) + 0.9 (B-mean(B))
= 2%+0.9(3-2) = 2.9%

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