ch_06_sol - CHAPTER 6: RISK AND RETURN: PAST AND PROLOGUE...

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CHAPTER 6: RISK AND RETURN: PAST AND PROLOGUE 1. V(12/31, 2000) = V(1/1/1994) × (1 + g) 7 = 100,000 × 1.05 7 = $140,710.04. 2. i and ii. The standard deviation is non-negative. 3. c. Determines most of the portfolio’s return and volatility over time. 4. E(r) = .3 × 44% + .4 × 14% + .3 × (–16%) = 14%. Variance = .3 × (44 – 14) 2 + .4 × (14 – 14) 2 + .3 × (–16 – 14) 2 = 540 Standard deviation = 23.24% The mean is unchanged, but the standard deviation has gone up. 5. a. The holding period returns for the three scenarios are: Boom: ( 50 – 40 + 2 ) / 40 = .30 or 30% Normal: ( 43 – 40 + 1) / 40 = .10 or 10% Recession: ( 34 – 40 + .5) / 40 = –.1375 or 13.75% E(HPR) = .33 × 30% + .33 × 10% + .33 × (–13.75%) = 8.75%. Variance(HPR) = .33 × (30 – 8.75) 2 + .33 × (10 – 8.75) 2 + .33 × (–13.75 – 8.75) 2 = 319.8 Standard deviation = = 17.88 b. E(r) = .5 × 8.75% + .5 × 4% = 6.375%. Standard deviation = 0.5 × 17.88% = 8.94% 6. a. Time-weighted average returns are based on year-by-year rates of return. Year Return [(capital gains + dividend)/price] 1996-1997 (110–100+4) / 100 = 14% 1997-1998 (90–110+4) / 110 = –14.55% 1998-1999 (95 – 90+4) / 90 = 10% 6-1
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Arithmetic mean: 3.15% Geometric mean: 2.33% b. time Cash flow Explanation 0 –300 Purchase of three shares at $100 each. 1 –208 Purchase of two shares at $110 less dividend income on three shares held. 2 110 Dividends on five shares plus sale of one share at price of $90 each. 3 396 Dividends on four shares plus sale of four shares at price of $95 each. 396 | | | | 110 | | | | | Date: 1/1/96 1/1/97 1/1/98 1/1/99 | | | | | | | | | 208 300 Dollar-weighted return = Internal rate of return = –.1661%. 7. a. r – r f = .5A σ 2 = .5 × 4 × .2 2 = .08 (8%). b. .09 = .5A × . 2 2 . A = .09 / (.5 × .04) = 4.5. c. Increased risk tolerance means decreased risk aversion (A) which will result in a decline in risk premiums. 8. The mean risk premium for stocks over T-bills is 9.2% (13 – 3.8%) per year for the period of 1926 – 1998. E(r) = Risk free rate + Risk premium E(r) = 5% + 9.2% = 14.2%. 6-2
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9. The average rate of return and standard deviation are quite different in the sub-periods: 1926 - 1942 1969 - 1998 Average Std. Dev. Average Std. Dev. Small stocks 17.50 60.81 12.92 27.08 Large stocks 7.23 29.58 13.95 16.49 LT T-bonds 4.48 4.19 9.40 10.04 Inter-term T-bonds 3.43 3.65 8.77 8.01 T-bills 1.04 1.70 6.85 2.66 I would prefer to use the risk premiums and standard deviations estimated over the more recent period 1967-1996, because the latter period seems to have been a
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ch_06_sol - CHAPTER 6: RISK AND RETURN: PAST AND PROLOGUE...

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