Question

The standard deviation of the market index portfolio is 10%. Stock A has a beta of 2 and a residual standard deviation of 20%.

A) calculate the total variance for an increase of .10 in its beta.

B) calculate the total variance for an increase of 1% in its residual standard deviation.

Answer 1

Total variance = (Beta * Standard deviation of market)^2 + (Residual Standard deviation)^2

A) New Beta = 2 + 0.10 = 2.10

Total variance = (2.10 * 10%)^2 + (20%)^2

= 0.21 + 0.04

= 0.25 or 25%

B) New residual Standard deviation = 20% + 1% = 21%

Total variance = (2 * 10%)^2 + (21%)^2

= 0.20 + 0.0441

= 0.2441 or 24.41%