Assume that you manage a risky portfolio with an expected rate of return of 16%

Question

Assume that you manage a risky portfolio with an expected rate of return of 16% and a standard deviation of 45%. The T-bill rate is 6%. Your client decides to invest in your risky portfolio a proportion (y) of his total investment budget with the remainder in a T-bill money market fund so that his overall portfolio will have an expected rate of return of 14%. a. What is the proportion y? (Enter your answer as a decimal number rounded to 2 decimal places.) Proportion y b. What is the standard deviation of the rate of return on your client's portfolio? (Enter your answer as a percentage rounded to two decimal places.) Standard deviation % per year

Explanation / Answer

Expected return = Weight1 * return of portfolio + ( 1 - weight1) * return of t-bill

0.14 = Weight1 * 0.16 + ( 1 - weight1) * 0.06

0.14 = 0.16Weight1 + 0.06 - 0.06weight1

0.08 = 0.1weight1

Weight1 = 0.8

Proportion of Y = 0.8 or 80%

b)

Standard deviation = 0.8 * 0.45

Standard deviation = 0.36 or 36%

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