Question 3 (9 points) (1) Two investment advisers are comparing performance. Adv

Question

Question 3 (9 points) (1) Two investment advisers are comparing performance. Adviser A averaged a 20% retum with a portfolio beta of 1.5, and adviser B averaged a 15% return with a portfolio beta of 1.2. If the T- bill rate was590 and the market return during the period was 13%, which adviser was the better stock picker? (2) Consider the following SML based on the CAPM Return 15% SML 10% 2 Beta What is the expected return for a portfolio with a beta of 0.5 (3) A share of stock sells for $50 today. It will pay a dividend of S6 per share at the end of the year. Its beta is 1.2. What do investors expect the stock to sell for at the end of the year? Assuming that the risk-free rate is 6% and the expected rate of return on the market is 16%.

Explanation / Answer

1) For a good portfolio, the expected return or the actual return would be higher than the required return.

Required return can be computed using CAPM as follows -

Required return = Risk free rate + Beta x (Expected market return - Risk free rate)

Advisor A

Actual return = 20%

Required return = 5% + 1.5 x (13% - 5%) = 17%

Advisor B

Actual return = 15%

Required return = 5% + 1.2 x (13% - 5%) = 14.6%

From the above, we can see that advisor A was the better stock picker.

2) At beta 0, the return is 5%. This is the risk free return.

At beta 1, the return is 10%. This is the market return.

Expected return at 0.5 beta = 5% + 0.5 x (10% - 5%) = 7.50%

3) Stock price (P0) = $50, Dividend (D1) = $6, Beta = 1.2, Risk free rate = 6%, Market return = 16%

Required return (Ke) = 6% + 1.2 x (16% - 6%) = 18%

Stock price as per constant dividend growth model can be computed as follows -

P0 = D1 / (Ke - g)

where, g = growth rate

First, we compute the constant growth rate using the above formula -

$50 = $6 / (0.18 - g)

or, 0.18 - g = $6 / $50

or, 0.18 - g = 0.12

or, g = 0.06 or 6%

Now, to compute the price at the end of next year of P1, we require the dividend to be paid in year 2, i.e., D2.

D2 = D1 x (1 + g) = $6 x (1 + 0.06) = $6.36

P1 = D2 / (Ke - g) = $6.36 / (0.18 - 0.06) = $53

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