Question

The standard deviation of the market-index portfolio is 25%. Stock A has a beta of 1.60 and a residual standard deviation of 35%.

a-1.

Calculate the total variance of stock A if its beta is increased by 0.20? (Do not round intermediate calculations. Enter your answer as a decimal rounded to 4 decimal places.)

Total variance=

a-2.

Calculate the total variance of stock A if its residual standard deviation is increased by 5.62% ? (Do not round intermediate calculations. Enter your answer as a decimal rounded to 4 decimal places.)
Total variance=

b.

An investor who currently holds the market-index portfolio decides to reduce the portfolio allocation to the market index to 90% and to invest 10% in stock A. Which of the following changes (increase of .20 in beta or increase of 5.62% in residual standard deviation) will have a greater impact on the portfolio's standard deviation?
Choose the correct answer:



A) Increase of 5.62% in residual standard deviation will have a greater impact.

B) Both will have the same impact.

C) Increase of .20 in beta will have a greater impact.

Answer 1

Check the following calculations

Step-by-step explanation:

Total variance = (β x σM)2 + σE2

Part (a) - 1

β = 1.6 + 0.2 = 1.8;

Total variance = (1.8 x 0.25)2 + (0.35)2 = 0.3250

Part (a) – 2

σE = 35% + 5.62% = 40.62% = 0.4062

Total variance = (1.6 x 0.25)2 + (0.4062)2 = 0.3250

Part (b)

The correct answer is option C) Increase of .20 in beta will have a greater impact.

Magnitude wise both the options have same effect. However, the incremental impact of residual risk can be diversified away and its impact can therefore be minimized. However, increase in beta translates into an increase in a systematic risk that can't be diversified away. Hence, the impact due to increase in beta will be higher.