1. Assume that you manage a risky portfolio with an expected rate of return of 20% and a standard deviation of 25%. The T-bill rate is 7%. Suppose that you have a client that prefers to invest in your risky portfolio a proportion (y) of his total investment budget so that his overall portfolio will have an expected rate of return of 15%. (1) What is the investment proportion, y? (2.) What is the standard deviation of the rate of return on your client’s portfolio? 2. The expected rates of return for stocks A and B are 28% and 22% respectively. The T-bill rate is 12% and the expected rate of return on S&P 500 index is 24%. The standard deviation of stock A is 22% while that of B is 20%. If you could invest only in T-bills plus one of these stocks, which stock would you choose?

The computations are shown below:

Explanation:

The computation is shown below:

Overall portfolio Expected rate of return = Risky portfolio expected rate of return × investment proportion + t- bill rate × 1 - investment proportion

0.15 = 0.20(y) + 0.07(1 - y)

0.15 = 0.20y + 0.07 - 0.07y

So,

y = 61.54%

2.  Now Standard Deviation is

= investment proportion × standard deviation

= (0.6154) × (0.25)

So,

Standard Deviation = 15.38%

2. We Use Sharpe Ratio to choose out the right stock which is shown below:

Sharpe Ratio = (Expected rate of return - Risk free rate of return) ÷ Standard deviation

For Stock A, it is

= (22% - 12%) ÷ 20%

= 0.5

For Stock B, it is  

= (28% - 12%) ÷22%

= 0.73

Since the Sharpe ratio has highest in Stock B and the same is to be choose

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