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HW2Solution

# HW2Solution - =.09 or 9 b Realized return =(Ending value...

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Q1. a. Call the aggressive stock A and the defensive stock D. Beta is the sensitivity of the stock’s return to the market return, i.e., the change in the stock return per unit change in the market return. Therefore, we compute each stock’s beta by calculating the difference in its return across the two scenarios divided by the difference in the market return: 00 . 2 25 5 38 2 A = - - - = β 30 . 0 25 5 12 6 D = - - = β b. With the two scenarios equally likely, the expected return is an average of the two possible outcomes: E(r A ) = 0.5 × (–2 + 38) = 18% E(r D ) = 0.5 × (6 + 12) = 9% c. The SML is determined by the market expected return of [0.5(25 + 5)] = 15%, with a beta of 1, and the T-bill return of 6% with a beta of zero. See the following graph. Expected Return - Beta Relationship 0 5 10 15 20 25 30 35 40 0 0.5 1 1.5 2 2.5 3 Beta SML D M A α A The equation for the security market line is: E(r) = 6 + β (15 – 6)

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Q2: 2
3

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Q3. a. Expected return = weighted average of portfolio asset returns: 0.259.08)+.75(.14) = .125 or 12.5%. Std dev = the weight in the risky asset x the std deviation of the risky asset = .75 x .12
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Unformatted text preview: = .09 or 9%. b. Realized return = (Ending value – Beginning value)/ beginning value. = (60 – 75)+2+3 / 100 = -10% c. The relative portfolio weights have changed due to the decline in prices. Assume that the dividends are re-invested in the Stock portfolio and that the interest earned is re-invested in the t-bill portfolio. The endowment is now worth \$90m, with \$63m in the risky portfolio and \$27m in T-bills. As above, expected return = .122 or 12.2%. If the same expected return is desired, ie 12.5%, the endowment will have to shift funds from t-bills to the risky asset. Solving for w in an expression where expected return = the desired 12.5% , Portfolio weights work out to be .75 in the risky asset and .25 in t-bills. This implies that the managers would sell 4.5m worth of t-bills and invest the proceeds in the risky portfolio. 4 5...
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