Assume you manage a risky portfolio with an expected rate of return of 12% and a...

Assume you manage a risky portfolio with an expected rate of return of 12% and a standard deviation of 21%. The T-bill rate is 3%. Your client decides to invest in your risky portfolio a proportion (y) of her total investment budget so that her overall portfolio will have an expected rate of return of 8%. What is the standard deviation of the rate of return on your client's portfolio? Convert your answer to percentages with two decimal points

Solutions

Expert Solution

Proportion invested in risky portfolio = y

Proportion invested in T bill = (1-y)

Expected rate of return for risky portfolio = 12% = 0.12

Return on T bill = 3% = 0.03

Expected rate of return on overall portfolio = 8% = 0.08

(Proportion invested in risky portfolio * Expected rate of return for risky portfolio) + (Proportion invested in T bill * Return on T bill) = Expected rate of return on overall portfolio

Putting the values

(y * 0.12) + ((1-y) * 0.03) = 0.08

y = 5/7

So, Proportion invested in risky portfolio = 5/7

Standard Deviation of T bill = 0

Standard Deviation of risky portfolio = 28% = 0.28

The standard deviation of the rate of return on your client's portfolio = Proportion invested in risky portfolio * Standard Deviation of risky portfolio

= 5/7 * 0.28

= 0.20 = 20.00%

jeff jeffy answered 2 years ago

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