Question

Assume that you manage a risky portfolio with an expected rate of return of 14% and a standard deviation of 38%. The T-bill rate is 5%. Your client chooses to invest 85% of a portfolio in your fund and 15% in a T-bill money market fund.

a. What is the expected return and standard deviation of your client's portfolio? (Round your answers to 2 decimal places.)

What is the reward-to-volatility ratio (S) of your risky portfolio and your client's overall portfolio? (Round your answers to 4 decimal places.)

Answer 1

Expected Return on client portfolio = (Weight of risky portfolio * Expected return of risky portfolio) + (Weight of T-Bills * T-Bill Returns)

= (0.85 * 0.14) + ( 0.15 * 0.05)

= 0.1265 = 12.65%

Standard Deviation on client portfolio = sqrt ( Weight of risky portfolio * Standard Deviation of risky portfolio + Weight of T-Bills * standard deviation of T-Bills + 2 * Weight of risky portfolio *Standard Deviation of risky portfolio*Weight of T-Bills*standard deviation of T-Bills*correlation between risky portfolio and T-Bills)

Standard Deviation on client portfolio = sqrt(0.85 * 0.38 + 0.15* 0 + 0)

Since standard deviation of T-Bill will be zero. So last two terms in formula will be zero.

Standard Deviation on client portfolio = sqrt(0.85 * 0.38 )

= 0.2307 = 23.07 %

Reward to volatility ratio of risky portfolio (Sharp Ratio) = ( Portfolio Return - T Bill returns) / Portfolio standard deviation

= (0.14 - 0.05) / 0.38 = 0.2368

Reward to volatility ratio of client portfolio (Sharp Ratio) = ( Portfolio Return - T Bill returns) / Portfolio standard deviation

= (0.1265 - 0.05) / 0.2307 = 0.3317