Question

The return on the risky portfolio is 15%. The risk-free rate, as well as the investor's borrowing rate, is 10%. The standard deviation of return on the risky portfolio is 20%. If the standard deviation on the complete portfolio is 25%, how much is the expected return on the complete portfolio?

Answer 1

Given,

Return on risky portfolio = 15%

Risk free rate = 10%

Standard deviation on risky portfolio = 20%

Standard deviation on complete portfolio = 25%

Solution :-

Weight of risky asset = Standard deviation on complete portfolio/Standard deviation on risky portfolio

= 25%/20% = 1.25

Weight of risk free asset = 1 - weight of risky asset

= 1 - 1.25 = -0.25

Now,

Expected return on complete portfolio

= (Return on risky portfolio x weight of risky asset) + (risk free rate x weight of risk free asset)

= (15% x 1.25) + (10% x -0.25)

= 18.75% - 2.50%

= 16.25%