Question

The standard deviation of the market-index portfolio is 20%. Stock A has a beta of 1.5 and a residual standard deviation of 30%.

a. Calculate the total variance for an increase of .15 in its beta. (Do not round intermediate calculations. Round your answer to 4 decimal places.)

b. Calculate the total variance for an increase of 3% in its residual standard deviation. (Do not round intermediate calculations. Round your answer to 4 decimal places.)

(I tried 0.1989 for both answers and it is not correct)

Answer 1

a) Assume that correlation between multi index portfolio and stock A ir r

SD(A) - standard deviation of stock A = 30%

SD(m) - standard deviation of multi index portfolio = 20%

Equation : Beta (A) = r x SD(A) / SD(m)

1.5 = r = 0.3 / 0.2

r = 1

New beta(A) = 1.5 + 0.15 = 1.65

1.65 = 1 x SD(A) / 0.2

SD(A) = 1.65 x 0.2 = 0.33

Var(A) = Square of SD(A) = 0.33² = 0.1089

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b) SD(A) = 0.33 + 0.03 = 0.36

Now Variance of A= 0.36^2 = 0.1296