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.) Total variance. 1989 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.) Total variance. 0098

total variance for an increase of. 15 in its beta = 0.1989± 0.001

total variance for an increase of 3% in its residual standard deviation = 0.1989±0.001

total variance for option A is correct = 0.1989 total variance for option B is also = 0.1989 the given total variance for option B (0.0098) is wrong

Explanation:

option A

standard deviation (Sd) = 20% = 0.2

stock beta = 1.5

The new stock beta value = stock beta + increase in beta

The new stock beta = 1.5 + 0.15 = 1.65

Residual standard deviation (Rd) = 30% = 0.3

Total variance = (new stock beta) ^2 * (Sd) ^2 + (Rd) ^2

= 1.65^2 * 0.2^2 + 0.3^2

= 0.1989

option B

for an increase of 3% in the residual standard deviation

total variance = (stock beta) ^2 * (Sd) ^2 + (new residual deviation) ^2

= (1.5) ^2 * 0.2^2 + (0.3 + 0.03) ^2

= 2.25 * 0.04 + 0.1089

= 0.1989