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# 5 3 5 4 10 real interest rates are expected to rise

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5-4 10. Real interest rates are expected to rise. The investment activity will shift the demand for funds curve (in Figure 5.1) to the right. Therefore the equilibrium real interest rate will increase. 11. The expected dollar return on the investment in equities is \$18,000 compared to the \$5,000 expected return for T-bills. Therefore, the expected risk premium is \$13,000. 12. E(r) = [0.2 × ( 25%)] + [0.3 × 10%] + [0.5 × 24%] =10% 13. E(r X ) = [0.2 × ( 20%)] + [0.5 × 18%] + [0.3 × 50%] =20% E(r Y ) = [0.2 × ( 15%)] + [0.5 × 20%] + [0.3 × 10%] =10% 14. σ X 2 = [0.2 × (– 20 – 20) 2 ] + [0.5 × (18 – 20) 2 ] + [0.3 × (50 – 20) 2 ] = 592 σ X = 24.33% σ Y 2 = [0.2 × (– 15 – 10) 2 ] + [0.5 × (20 – 10) 2 ] + [0.3 × (10 – 10) 2 ] = 175 σ X = 13.23% 15. E(r) = (0.9 × 20%) + (0.1 × 10%) =19% 16. The probability that the economy will be neutral is 0.50, or 50%. Given a neutral economy, the stock will experience poor performance 30% of the time. The probability of both poor stock performance and a neutral economy is therefore: 0.30 × 0.50 = 0.15 = 15% 17. E(r) = (0.1 × 15%) + (0.6 × 13%) + (0.3 × 7%) = 11.4%
5-5 18. a. Probability Distribution of the HPR on the Stock Market and Put: STOCK PUT State of the Economy Probability Ending Price + Dividend HPR Ending Value HPR Boom 0.30 \$134 34% \$ 0.00 100% Normal Growth 0.50 \$114 14% \$ 0.00 100% Recession 0.20 \$ 84 16% \$ 29.50 146% Remember that the cost of the index fund is \$100 per share, and the cost of the put option is \$12. b. The cost of one share of the index fund plus a put option is \$112. The probability distribution of the HPR on the portfolio is: State of the Economy Probability Ending Price + Put + \$4 Dividend HPR Boom 0.30 \$134.00 19.6% = (134 112)/112 Normal Growth 0.50 \$114.00 1.8% = (114 112)/112 Recession 0.20 \$113.50 1.3% = (113.50 112)/112 c. Buying the put option guarantees the investor a minimum HPR of 1.3% regardless of what happens to the stock's price. Thus, it offers insurance against a price decline. 19. The probability distribution of the dollar return on CD plus call option is: State of the Economy Probability Ending Value of CD Ending Value of Call Combined Value Boom 0.30 \$114.00 \$19.50 \$133.50 Normal Growth 0.50 \$114.00 \$ 0.00 \$114.00 Recession 0.20 \$114.00 \$ 0.00 \$114.00
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