Question

Problem 5-18 You manage an equity fund with an expected risk premium of 13% and a standard deviation of 44%. The rate on Treasury bills is 6.6%. Your client chooses to invest $90,000 of her portfolio in your equity fund and $60,000 in a T-bill money market fund. What is the expected return and standard deviation of return on your client’s portfolio? (Round your answers to 2 decimal places.) Expected return % Standard deviation %

Answer 1

Calculating expected return of Client's portfolio

Since T bill is a risk free asset, hence Return on T bill money market fund = Rt = Risk free rate = 6.6%

Equity fund risk premium = Return on equity fund - risk free rate

13% = Return on equity fund - 6.6%

Return on equity = 13% + 6.6% = 19.6%

Return on equity fund = Re = 19.60%

Total amount invested by client = T = investment in equity fund + investment in T market fund bill = 90000 + 60000 = 150000

Weight of equity fund = We = investment in equity fund / T = 90000 /150000 = 60%

Weight of T bill market fund = Wt = investment in T bill / T = 60000 / 150000 = 40%

Expected return of Client's portfolio = Wt x Rt + We x Re = 40% x 6.6% + 60% x 19.60% = 2.64% + 11.76% = 14.40%

Hence Expected return on Client's Portfolio = 14.40%

Calculating Standard deviation of Client's portfolio

Standard deviation of Equity fund = Se = 44%,

It is known that risk free asset has zero standard deviation and zero correlation with a risky asset(equity fund)

Since T bill market fund is risk free , hence Standard deviation of T bill money market fund = St = 0, Correlation between T bill money market fund and Equity fund = Corr = 0

Variance of portfolio = (Wt x St)² + (We x Se)² + 2 x Wt x We x St x Se x Corr = (40% x 0)² + (60% x 44%)² + 2 x 40% x 60% x 0 x 44% x 0 = (60% x 44%)² = (26.40%)²

Hence Standard deviation of Client's portfolio = 26.40%