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Essentials of Investments Chapter 2 Solutions

Essentials of Investments Chapter 2 Solutions - Essentials...

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Essentials of Investments (BKM 7 th Ed.) Answers to Suggested Problems – Lecture 2 Chapter 5 : 6. #3 For each portfolio: Utility = E(r) – (½ × 4 × σ 2 ). Investment E(r) σ U 1 0.12 0.30 -0.0600 2 0.15 0.50 -0.3500 3 0.21 0.16 0.1588 4 0.24 0.21 0.1518 The portfolio with the highest utility value is #3. 7. #4 When an investor is risk neutral, A = 0, so that the portfolio with the highest utility is the portfolio with the highest expected return. This is investment #4, with 24%. 9. 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% 10. σ X 2 = [0.2 × (–.20 – .20) 2 ] + [0.5 × (.18 – .20) 2 ] + [0.3 × (.50 – .20) 2 ] = .0592 σ X = 24.33% σ Y = [0.2 × (–.15 – .10) 2 ] + [0.5 × (.20 – .10) 2 ] + [0.3 × (.10 – .10) 2 ] = .0175 σ Y = 13.23% 15. 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. 18. a) Expected cash flow: 0.5($50,000) + 0.5($150,000) = $100,000 HPR = (P 1 - P 0 )/P 0 0.15 = (100,000 - P 0 )/P 0 P 0 = $86,956.52 b) HPR = (100,000 - 86956.52)/86956.52 = 15%
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