Question

Consider the following information about a risky portfolio that you manage and risk-free asset: E (rp) = 12.5%, σp=16%, rf=3.5%.

a) Your client wants to invest a proportion of her total investment budget in your risky fund to provide an expected return of on overall complete portfolio equal to 9%. What proportion should she invest in the risky portfolio, P, and what proportion in the risk-free asset?

b) What will be the standard deviation of return of return on the total portfolio?

c) Consider the highest possible return subject to constraint that you limit her standard deviation to be no more than 12%. which portfolio is more appropriate if you were risk averse?

Answer 1

a. Weight of Risky Asset + weight of risk free asset = 1

Expected Return = weight of Risky Portfolio * Return of risky portfolio + Weight of risk free asset * return of risk free asset

9% = (1 - Weight of Risk Free Asset) * 12.50% + Weight of risk free asset * 3.50%

9% = 12.50% - 9% * Weight of Risk Free Asset

Weight of Risk Free Asset = 38.89%

Weight of Risky Asset + weight of risk free asset = 1

Weight of Risky Asset + 38.89% = 1

Weight of Risky Asset = 61.11%

b. Standard Deviation = Weight of Risky Asset * Standard Deviation of Risky Asset

Standard Deviation = 61.11% * 16%

Standard Deviation = 9.78%

c. If we are risk averse investor then the portfolio whose weights we made above is the good portfolio because its Standard Deviation is 9.78% which is less than 12%

But we can make another portfolio where Standard deviation equals 12% weight of such portfolio is provided below

if highest possible standard deviation is 12% then weight of risky portfolio will changes

Standard Deviation = Weight of Risky Asset * Standard Deviation of Risky Asset

12% = Weight of Risky Asset * 16%

Weight of Risky Asset = 75%

Weight of Risk Free Asset = 25%

Expected return of such portfolio = 75%*12.50% + 25% * 3.50% = 10.25%

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