Chapter5_solutions

# Chapter5_solutions - Chapter 5 ANSWERS TO END-OF-CHAPTER...

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5-1 a. The probability distribution for complete certainty is a vertical line. b. The probability distribution for total uncertainty is the X-axis from - to + . 5-2 Security A is less risky if held in a diversified portfolio because of its negative correlation with other stocks. In a single-asset portfolio, Security A would be more risky because σ A > σ B and CV A > CV B . 5-3 a. No, it is not riskless. The portfolio would be free of default risk and liquidity risk, but inflation could erode the portfolio’s purchasing power. If the actual inflation rate is greater than that expected, interest rates in general will rise to incorporate a larger inflation premium (IP) and--as we shall see in Chapter 7--the value of the portfolio would decline. b. No, you would be subject to reinvestment rate risk. You might expect to “roll over” the Treasury bills at a constant (or even increasing) rate of interest, but if interest rates fall, your investment income will decrease. c. A U.S. government-backed bond that provided interest with constant purchasing power (that is, an indexed bond) would be close to riskless. The U.S. Treasury currently issues indexed bonds. 5-4 a. The expected return on a life insurance policy is calculated just as for a common stock. Each outcome is multiplied by its probability of occurrence, and then these products are summed. For example, suppose a 1-year term policy pays \$10,000 at death, and the probability of the policyholder’s death in that year is 2 percent. Then, there is a 98 percent probability of zero return and a 2 percent probability of \$10,000: Expected return = 0.98(\$0) + 0.02(\$10,000) = \$200. This expected return could be compared to the premium paid. Generally, the premium will be larger because of sales and administrative costs, and insurance company profits, indicating a negative expected rate of return on the investment in the policy. b. There is a perfect negative correlation between the returns on the life insurance policy and the returns on the policyholder’s human Answers and Solutions: 5 - 1 Chapter 5: ANSWERS TO END-OF-CHAPTER QUESTIONS

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capital. In fact, these events (death and future lifetime earnings capacity) are mutually exclusive. c. People are generally risk averse. Therefore, they are willing to pay a premium to decrease the uncertainty of their future cash flows. A life insurance policy guarantees an income (the face value of the policy) to the policyholder’s beneficiaries when the policy- holder’s future earnings capacity drops to zero.
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