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28 February, 20:31

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?

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  1. 28 February, 23:54
    0
    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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