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TBS 907- Spring 2005- TUTORIAL 2- Risk and return SOLUTIONS

# TBS 907- Spring 2005- TUTORIAL 2- Risk and return SOLUTIONS...

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TBS 907 TUTORIAL 2 - RISK AND RETURN SOLUTIONS QUESTION 1 (a) R y = R f + β (R m – R f ) (assuming the current cost of capital properly reflects the beta factor i.e, it is equilibrium with the marked0 Therefore β = R y - R f R m - R f Kingswick’s beta factor for it’s equity securities = 18.5% - 8% = 1.5 15% - 8% (b) & (c) Project CAPM required return Expected return A 8% + (7% x 0.3) = 10.1% 95 = 9.5% Reject 1,000 B 8% + (7% x 0.5) = 11.5% 130 = 13% Accept 1000 C 8% + (7% x 1) = 15% 280 = 18.7% Accept 1500 D 8% + (7% x 1.5) = 18.5% 385 = 19.3% Accept 2000 E 8% + (7% x 2) = 22% 400 = 20% Reject 2000 QUESTION 2 (a) The β value of Mr. Smith’s savings portfolio is simply a weighted average of the individual portfolio elements. Given that Treasury Stock has β value of zero, then the portfolio beta is: (0.20 x 0.10) + (0.80 x 0.10) + (1.20 x 0.10) + (1.6 x 0.20) + (0x 0.50) = 0.54 Similarly, the expected return is a weighted average: (7.6% x 0.10) + (12.4% x 0.10) + (15.6% x 0.10) + (18.8% x 0.20) + (6% x 0.50) = 10.32% TBS 907- T UTORIAL 2- R ISK AND RETURN AND MARKET EFFICIENFY SOLUTIONS P AGE 1 OF 7

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(b) We now need to find the return on the market portfolio. Using the CAPM expression and the Company W shares this can be found as follows: E[r w ] = r F + (E[r m ] - r F ). β w 7.6% = 6% + (E[r m ] – 6% F ) . 0.20 7.6% - 6% = (E[r m ] – 6% F ) = 8% 0.20 Therefore, E[r m ] = 8% + 6% = 14% If Mr. Smith wants a savings portfolio with an expected return of 12%, then his portfolio β will need to be found from the CAPM expression: 12% = 6% + (14% - 6%) x βp 12% - 6% = βp = 0.75 (14% - 6%) Let x equal the proportion of Mr.Smith’s savings invested in the market portfolio. β M = 1β F = 0 Therefore, solving for x : (0.10 x0.20) + (0.10 x 0.80) + (0.10 x 1.20) + (0.2 x 0.60) + ( x x 1) + ([0.5 – x ] x 0) = 0.75 0.02 + 0.08 + 0.12 + 0.32 + x + 0 = 0.75 x = 0.75 – 0.02 – 0.08 -0.12 -0.32 = 0.21 Thus Mr.Smith should place 21% of his savings in the market portfolio. This represents an amount of: 0.21 x £ 12000 = £ 2520. Thus he should sell £2520 of Treasury Bills and invest the money in the market portfolio. His total, revised portfolio would now be: Investment [Worth] Treasury Bills £3480 Market portfolio £ 2520 Company W shares £ 1200 Company X shares £ 1200 Company Y shares £ 1200 Company Z shares £ 2400 TBS 907- T UTORIAL 2- R ISK AND RETURN AND MARKET EFFICIENFY SOLUTIONS P AGE 2 OF 7
QUESTION 3 1. a. Percival’s current portfolio provides an expected return of 9 percent with an annual standard deviation of 10 percent. First we find the portfolio weights for a combination of Treasury bills (security 1: standard deviation = 0 percent) and the index fund (security 2: standard deviation = 16 percent) such that portfolio standard deviation is 10 percent. In general, for a two security portfolio: Бp 2 = x 1 Б 1 2 + 2x 1 x 2 Б 1 Б 2 р 12 + x 2 2 Б 2 2 (0.10) 2 = 0 + 0 + x 2 2 (0.16) 2 x 2 = 0.625 =>x 1 = 0.375 Further: r p = x 1 r 1 + x 2 r 2 rp = (0.375 x 0.06) + (0.625 x 0.14) = 0.11 = 11.0% Therefore, he can improve his expected rate of return without changing the risk of his portfolio.

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TBS 907- Spring 2005- TUTORIAL 2- Risk and return SOLUTIONS...

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