6. Assume the Following Investment Alternatives Economy Prob. T-Bill Alta Repo Am F. MP Recession 0.10 8.0% -22.0% 28.0% 10.0% -13.0% Below avg. 0.20 8.0 -2.0 14.7 -10.0 1.0 Average 0.40 8.0 20.0 0.0 7.0 15.0 Above avg. 0.20 8.0 35.0 -10.0 45.0 29.0 Boom 0.10 8.0 50.0 -20.0 30.0 43.0 1.00
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9. Calculate the expected rate of return on each alternative. r = expected rate of return. r Alta = 0.10(-22%) + 0.20(-2%) + 0.40(20%) + 0.20(35%) + 0.10(50%) = 17.4% . ^ ^
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11. What is the standard deviation of returns for each alternative?
19. Portfolio Risk and Return Assume a two-stock portfolio with $50,000 in Alta Inds. and $50,000 in Repo Men. Calculate r p and p . ^
20. Portfolio Return, r p r p is a weighted average: r p = 0.5(17.4%) + 0.5(1.7%) = 9.6% . r p is between r Alta and r Repo . ^ ^ ^ ^ ^ ^ ^ ^ r p = w i r i n i = 1
25. Large 0 15 Prob. 2 1 1 35% ; Large 20%. Return
26. # Stocks in Portfolio 10 20 30 40 2,000+ Company Specific (Diversifiable) Risk Market Risk 20 0 Stand-Alone Risk, p p (%) 35
27. Stand-alone Market Diversifiable Market risk is that part of a security’s stand-alone risk that cannot be eliminated by diversification. Firm-specific , or diversifiable , risk is that part of a security’s stand-alone risk that can be eliminated by diversification. risk risk risk = + .
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33. Use the historical stock returns to calculate the beta for PQU. Year Market PQU 1 25.7% 40.0% 2 8.0% -15.0% 3 -11.0% -15.0% 4 15.0% 35.0% 5 32.5% 10.0% 6 13.7% 30.0% 7 40.0% 42.0% 8 10.0% -10.0% 9 -10.8% -25.0% 10 -13.1% 25.0%
34. Calculating Beta for PQU r PQU = 0.83r M + 0.03 R 2 = 0.36 -40% -20% 0% 20% 40% -40% -20% 0% 20% 40% r M r KWE
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41. Required Rates of Return r Alta = 8.0% + (7%)(1.29) = 8.0% + 9.0% = 17.0%. r M = 8.0% + (7%)(1.00) = 15.0%. r Am. F. = 8.0% + (7%)(0.68) = 12.8%. r T-bill = 8.0% + (7%)(0.00) = 8.0%. r Repo = 8.0% + (7%)(-0.86) = 2.0%.
42. Expected versus Required Returns ^ r r Alta 17.4% 17.0% Undervalued Market 15.0 15.0 Fairly valued Am. F. 13.8 12.8 Undervalued T-bills 8.0 8.0 Fairly valued Repo 1.7 2.0 Overvalued
43. . . Repo . Alta T-bills . Am. Foam r M = 15 r RF = 8 -1 0 1 2 . SML: r i = r RF + (RP M ) b i r i = 8% + (7%) b i r i (%) Risk, b i SML and Investment Alternatives Market
44. Calculate beta for a portfolio with 50% Alta and 50% Repo b p = Weighted average = 0.5(b Alta ) + 0.5(b Repo ) = 0.5(1.29) + 0.5(-0.86) = 0.22 .
45. What is the required rate of return on the Alta/Repo portfolio? r p = Weighted average r = 0.5(17%) + 0.5(2%) = 9.5% . Or use SML: r p = r RF + (RP M ) b p = 8.0% + 7%(0.22) = 9.5% .
46. SML 1 Original situation Required Rate of Return r (%) SML 2 0 0.5 1.0 1.5 2.0 18 15 11 8 New SML I = 3% Impact of Inflation Change on SML
47. r M = 18% r M = 15% SML 1 Original situation Required Rate of Return (%) SML 2 After increase in risk aversion Risk, b i 18 15 8 1.0 RP M = 3% Impact of Risk Aversion Change