Question

You invest $1,000 in a final combination portfolio. The final combination portfolio is composed of a risky portfolio with an expected rate of return of 16% and a standard deviation of 20% and a treasury bill with a rate of return of 6%. If you want your final combination portfolio to have a standard deviation of 9%, what proportion of it should be invested in the risky portfolio?

A. 100%

B. 90%

C. 10%

D. 45%

Answer 1

Given that,

Standard deviation on a risky portfolio SDr = 20%

A portfolio is made from this risky portfolio and Risk free asset T-bill.

So, standard deviation of the new portfolio is Weight in risky asset*Standard deviation of risky asset

Or Weight of risky asset = Standard deviation of the portfolio/Standard deviation of risk free asset

Required standard deviation of the portfolio is 9%

=> Investment in risky portfolio = 0.09/0.2 = 45%

Option D is correct.