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.) 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

Answer 1

Answer:

• 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

Answer 2

Answer:

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