Question

a stock has a variance of 100%^2 its idyosyncratic risk is 64%^2 if its market portfolio is 25%^2 what is its beta?

1.2 or -1.2

1 or -1

.83 or -.83

.25 or -.25

Answer 1

Answer: Option 1 = 1.2

Below is the working for the answer:

Total Variance of a stock = Systematic Risk Variance + Unsystematic Risk Variance

Idyosyncratic risk is also known as unsystematic risk which can be reduced by diversification.

Given details:

Variance of the stock = 100%^2

Variance is represented by . Therefore, Standard deviation of the stock = = 10%

Similarly unsystematic risk variance = 64%^2

Standard deviation of the unsystematic risk or unsystematic risk would be = 8%

Systematic risk variance = Total variance of the stock - Unsystematic risk variance

Variance of systematic risk = 100% - 64% = 36%

Standard Deviation of systematic risk or systematic risk = = 6%

Systematic Risk =

Variance of the market = 25%^2

= 5%

Therefore Beta = Systematic risk /

Beta = 6%/ 5% = 1.2