Chap005 - Chapter 05 Risk and Return Past and Prologue...

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Chapter 05 - Risk and Return: Past and Prologue 5-1 CHAPTER 05 RISK AND RETURN: PAST AND PROLOGUE 1. The 1% VaR will be less than -30%. As percentile or probability of a return declines so does the magnitude of that return. Thus, a 1 percentile probability will produce a smaller VaR than a 5 percentile probability. 2. The geometric return represents a compounding growth number and will artificially inflate the annual performance of the portfolio. 3. No. Since all items are presented in nominal figures, the input should also use nominal data. 4. Decrease. Typically, standard deviation exceeds return. Thus, a reduction of 4% in each will artificially decrease the return per unit of risk. To return to the proper risk return relationship the portfolio will need to decrease the amount of risk free investments. 5. E(r) = [0.3 × 44%] + [0.4 × 14%] + [0.3 × (–16%)] = 14% σ 2 = [0.3 × (44 – 14) 2 ] + [0.4 × (14 – 14) 2 ] + [0.3 × (–16 – 14) 2 ] = 540 σ = 23.24% The mean is unchanged, but the standard deviation has increased. 6. a. The holding period returns for the three scenarios are: Boom: (50 – 40 + 2)/40 = 0.30 = 30.00% Normal: (43 – 40 + 1)/40 = 0.10 = 10.00% Recession: (34 – 40 + 0.50)/40 = –0.1375 = –13.75% E(HPR) = [(1/3) × 30%] + [(1/3) × 10%] + [(1/3) × (–13.75%)] = 8.75% σ 2 (HPR) = [(1/3) × (30 – 8.75) 2 ] + [(1/3) × (10 – 8.75) 2 ] + [(1/3) × (–13.75 – 8.75) 2 ] = 319.79 σ = 79 . 319 = 17.88% b. E(r) = (0.5 × 8.75%) + (0.5 × 4%) = 6.375% σ = 0.5 × 17.88% = 8.94%
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Chapter 05 - Risk and Return: Past and Prologue 5-2 7. a. Time-weighted average returns are based on year-by-year rates of return. Year Return = [(capital gains + dividend)/price] 2007-2008 (110 – 100 + 4)/100 = 14.00% 2008-2009 (90 – 110 + 4)/110 = –14.55% 2009-2010 (95 – 90 + 4)/90 = 10.00% Arithmetic mean: 3.15% Geometric mean: 2.33% b. Time Cash flow Explanation 0 -300 Purchase of three shares at $100 per share 1 -208 Purchase of two shares at $110, plus dividend income on three shares held 2 110 Dividends on five shares, plus sale of one share at $90 3 396 Dividends on four shares, plus sale of four shares at $95 per share Dollar-weighted return = Internal rate of return = –0.1661% 396 | | | | 110 | | | | | Date: 1/1/07 1/1/08 1/1/09 1/1/10 | | | | | | | | | 208 300
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Chapter 05 - Risk and Return: Past and Prologue 5-3 8. a. E(r P ) – r f = ½A σ P 2 = ½ × 4 × (0.20) 2 = 0.08 = 8.0% b. 0.09 = ½A σ P 2 = ½ × A × (0.20) 2 A = 0.09/( ½ × 0.04) = 4.5 c. Increased risk tolerance means decreased risk aversion (A), which results in a decline in risk premiums. 9. For the period 1926 – 2008, the mean annual risk premium for large stocks over T- bills is 9.34% E(r) = Risk-free rate + Risk premium = 5% + 7.68% =12.68% 10. In the table below, we use data from Table 5.2. Excess returns are real returns since the risk free rate incorporates inflation. Large Stocks: 7.68% Small Stocks: 13.51% Long-Term T-Bonds: 1.85% T-Bills: 0.66 % (table 5.4) 11. a. The expected cash flow is: (0.5 × $50,000) + (0.5 × $150,000) = $100,000 With a risk premium of 10%, the required rate of return is 15%. Therefore, if the value of the portfolio is X, then, in order to earn a 15% expected return: X(1.15) = $100,000 X = $86,957 b. If the portfolio is purchased at $86,957, and the expected payoff is $100,000, then the expected rate of return, E(r), is: 957 , 86 $ 957 , 86 $ 000 , 100 $ = 0.15 = 15.0%
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This note was uploaded on 04/06/2010 for the course FIN 100 taught by Professor Staff during the Fall '08 term at Penn State.

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Chap005 - Chapter 05 Risk and Return Past and Prologue...

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