Question

You plan to form a portfolio that contains only the risk free asset and stock A. The risk free rate is 2%. The expected return and the standard deviation of stock A's return are 10% and 15% respectively. The expected return of your portfolio is 8%. Find out the standard deviation of the portfolio.

7.5%

12%

11.25%

15%

10%

Answer 1

Let the weight of risk free asset be x

weight of stock A =(1-x)

Expected return of portfolio = Weight of risk free asset*return of risk free asset + weight of stock A* return of stock A

8% = x*2%+(1-x)*10%

8% =x*2% + 10% - 10%*x

10%*x - 2%*x = 10%-8%

0.08x = 2%

x = 2%/0.08

=0.25

(1-x) = 0.75

When a portfolio comprises of a risky asset and a risk free asset, the standard deviation of the portfolio is calculated as :

Standard deviation of the portfolio = Weight of the Stock A * Standard Deviation of Stock A

= 0.75*15%

= 11.25%Answer = 11.25%