Suppose that you construct an equally weighted portfolio of N stocks, each with the same expected return
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Suppose that you construct an equally weighted portfolio of N stocks, each with the same expected return E(r1)=E(r2)=...= E(rN)=15% and standard deviation s1=s2 =...=sN=s =25%. All N stocks have a common correlation coefficient r (that is, corr(ri, rj)=r for all pairs of stocks i, j).
- For four cases r=0, 0.2, 0.5, and 1.0, plot the portfolio standard deviation as a function of N (from N=1 to N=50).Put all the graphs on the same plot.
Hint: To compute the portfolio variance, use formula (7.16) in BKM. Take w1=w2=...= wN=1/N, Cov(ri, ri)=s2, and Cov(ri, rj)=rs2 for all i, j.
Then sP2 = s2 (1 + (N-1) r)/N. (This is the same formula as (7.21) in BKM)
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