Question

Consider the CAPM model. Stock A has a risk premium of 13%, and its standard deviation is 18%. The market index has a risk premium of 12%. The T-bill rate is 2%. The correlation between A and the market index is 0.1735. What is the standard deviation of the market index?

A. 0.0255

B. 0.0212

C. 0.0288

D. 0.0831

Answer 1

Stock A expected return = Risk free rate + Risk premium of stock A

=2%+13%

=15%

Stock expected return as per CAPM = risk free rate + (Beta * market risk premium)

15% = 2% + (beta *12%)

13% = beta * 12%

Beta = 13%/12% =1.083333333

Beta of stock = 1.083333333

Standard deviation of stock =18%

Correlation between A and market = 0.1735

Beta of stock formula =Correlation * Standard deviation of stock /standard deviation of market

1.083333333 = 0.1735*18%/stadard deviation of market

standard deviation of market = 0.1735*18%/ 1.083333333

=0.02882769232

So standard deviation of Marekt is 0.0288