Question

Question You manage an equity fund with an expected risk premium of 10% and an expected standard deviation of 14%. The rate on Treasury bills is 6 %. Your client chooses to invest $60,000 of her portfolio in your equity fund and $40,000 in a T-bill money market fund What is the expected return and standard deviation of return on your client's portfolio?

Answer 1

Ans

Information given

Expected Risk Premium = 10%

Expected Standard Deviation of Equity fund = 14%

Risk free rate of return = 6%

Expected rate of return on equity fund is calculated as

Risk free rate of return + Expected Risk Premium = 6% + 10% = 16%

The client portfolio consist of $ 60,000 of equity funds and $ 40,000 of T- Bills. Hence, Total amount invested = $ 60,000 + $ 40,000 = $ 100,000.

So the weight of Equity funds = $ 60,000 / $ 100,000 = 0.6

And the weight of T Bills = $ 40,000 /$ 100,000 = 0.4

Expected return of client’s overall portfolio = Weight of equity fund * Return on equity fund + Weight of T-Bills * Return on T-Bills

Expected return of client’s overall portfolio = ( 0.6 * 16) + (0.4 * 6) = 9.6% + 2.4% = 12%

The T-Bills have no risk i.e The Standard Deviation of T- Bills is 0

Expected Standard Deviation on Client's overall portfolio = Weight of equity fund * Standard Deviation of equity fund + Weight of T-Bills * Standard Deviation of T-Bills

Expected Standard Deviation on Client's overall portfolio = (0.6 * 14) + (0.4 * 0) = 8.4% + 0 = 8.4%

Expected Return = 12%

Expected Standard Deviation = 8.4%