Suppose that the standard deviation of returns from a typical share is about .42

Question

Suppose that the standard deviation of returns from a typical share is about .42 (or 42%) a year. The correlation between the returns of each pair of shares is about .7.

a. Calculate the variance and standard deviation of the returns on a portfolio that has equal investments in 2 shares, 3 shares, and so on, up to 10 shares.

b. How large is the underlying market variance that cannot be diversified away?

c. Now assume that the correlation between each pair of stocks is zero. Calculate the variance and standard deviation of the returns on a portfolio that has equal investments in 2 shares, 3 shares, and so on, up to 10 shares

Explanation / Answer

a)

Variance = 1/n * (0.42^2) + (n-1) * 0.7 * 0.42*0.42

b)   underlying market risk = 0.12348

= (n-1) /n * 0.7*0.42*0.42 =0.12348

as n increase (n-1)/n tend to 1

hence

underlying market risk is 0.7*0.42*0.42 = 0.12348

c) variance =1/n * (0.42^2)

number of share variance standard devaition 1 0.1764 0.42 2 0.14994 0.387220867 3 0.14112 0.37565942 4 0.13671 0.369743154 5 0.134064 0.366147511 6 0.1323 0.36373067 7 0.13104 0.361994475 8 0.130095 0.360686845 9 0.12936 0.359666512 10 0.128772 0.358848157

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