Question

You manage an equity fund with an expected risk premium of 10% and an expected standard deviation of 15%. The rate on Treasury bills (risk-free rate) is 5%. Your client chooses to invest $60,000 of her portfolio in your equity fund and $40,000 in a T-bill money market fund. The expected return and standard deviation of your client's overall portfolio is:__________ a. 11.0% and 9.0% b. 10.0% and 8.4% c. 15.0% and 9.0% d. 5.0% and 15.0%

Answer 1

Portfolio Mean return = 11%

Portfolio Stdev = 0.09 or 9%

Option a is the correct answer

Step-by-step explanation:

The mean return of a portfolio consisting of two securities can be calculated by multiplying the weight of each security in the portfolio by the mean return of that security and adding the products for each security. The formula for two asset or security portfolio return (mean) can be written as follows,

Portfolio Mean = wA * rA + wB * rB

Where,

• w represents the weight of each security

• r represents the mean return of each security

The return on the equity fund = risk free rate + risk premium

The return on the equity fund = 5% + 10% = 15%

Portfolio Mean return = 60% * 15% + 40% * 5%

Portfolio Mean return = 11%

The standard deviation is a measure of the total risk. The standard deviation of a portfolio consisting of two securities, one of which is a risk free security and has zero standard deviation, can be calculated as follows,

Portfolio Stdev = Weight of risky security * Standard deviation of risky security

Portfolio Stdev = 0.6 * 0.15

Portfolio Stdev = 0.09 or 9%