Assume that you manage a risky portfolio with an expected rate of return of 20%

Question

Assume that you manage a risky portfolio with an expected rate of return of 20% and a standard deviation of 42%. The T-bill rate is 4%. A client prefers to invest in your portfolio a proportion (y) that maximizes the expected return on the overall portfolio subject to the constraint that the overall portfolio's standard deviation will not exceed 30%. a. What is the investment proportion, y? (Do not round intermediate calculations. Enter your answer as a percentage rounded to two decimal places.) Investment proportion y b. What is the expected rate of return on your client's overall portfolio? (Do not round intermediate calculations. Enter your answer as a percentage rounded to two decimal places.) Rate of return

Explanation / Answer

Part a)

When you have some portion of your portfolio in a risky stock and some portion in a risk free stock, the standard deviation of the portfolio is given by

Standard Deviation = Weight of the Risky stock*Standard deviation of the risky stock

= y*42%

Since the standard deviation cannot exceed 30%,

30% = y * 42%

So, y = 0.3/0.42 = 0.7143 or 71.43%

In other words, the final portfolio consists of 71.43% risk stock and the rest 28.57% invested in risk free stock.

Part b)

Expected return = (weight of the risky stock*Expected Return of the risky stock) + (weight of the risk free stock*Expected Return of the risk free stock)

= (71.43%*42%)+(28.57%*4%)

= 31.14%

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