Chapter 05 Understanding Risk

Transcription

1 Chapter 05 Understanding Risk Multiple Choice Questions 1. (p. 93) Which of the following would not be included in a definition of risk? a. Risk is a measure of uncertainty B. Risk can always be avoided at no cost c. Risk has a time horizon d. Risk usually involves some future payoff BLOOMS: Knowledge LOD: 1 2. (p. 93) All other factors held constant, an investment: a. With more risk should offer a lower return and sell for a higher price b. With less risk should sell for a lower price and offer a higher return C. With more risk should sell for a lower price and offer a higher return d. With less risk should sell for a lower price and offer a lower return 3. (p. 93) Uncertainties that are not quantifiable: a. Are what we define as risk b. Are factored into the price of an asset C. Cannot be priced d. Are benchmarks against which quantifiable risks can be assessed BLOOMS: Knowledge LOD: 1 5-1

2 4. (p. 93) When measuring the risk of an asset: A. There may be uncertainty about the size of future payoffs b. It is necessary to incorporate uncertainties that are not quantifiable c. One must remember that the concept of risk applies only to financial markets, not to financial intermediaries d. One cannot use other investments to evaluate the asset's risk 5. (p. 93) Which of the following is true? A. Investments with higher risk generally pay a higher return than risk-free investments b. Investments that pay a return over a longer time horizon generally have less risk c. Investments with a greater variance in the size of the future payoff generally pay a lower expected return d. Risk-free investments are the best benchmark for measuring the risk of all investment strategies BLOOMS: Analysis 6. (p. 93) Inflation presents risk because: a. Inflation is always present b. Inflation cannot be measured c. There are different ways to measure it D. There is no certainty regarding what inflation will be in the future 5-2

3 7. (p. 94) If the probability of an outcome equals one, the outcome: a. Is more likely to occur than the others listed B. Is certain to occur c. Is certain not to occur d. Has unquantifiable risk 8. (p. 94) If a fair coin is tossed, the probability of coming up with a head or a tail is: a. ½ or 50 percent b. Zero C. 1 or 100 percent d. Unquantifiable LOD: 1 9. (p. 94) If the probability of an outcome is zero, you know: a. The outcome is more likely to occur b. The outcome is certain to occur c. The outcome is less likely to occur D. The outcome will not occur 10. (p. 95) The expected value of an investment: a. Is what the owner will receive when the investment is sold b. Is the sum of the payoffs C. Is the probability-weighted sum of the possible outcomes d. Cannot be determined in advance BLOOMS: Knowledge LOD: 1 5-3

4 11. (p. 96) If an investment will return $1,500 half of the time and $700 half of the time, the expected value of the investment is: a. $1,250 b. $1,050 C. $1,100 d. $2, (p. 95) Another name for the expected value of an investment would be: A. The mean value b. The upper-end value c. The certain value d. The risk-free value BLOOMS: Knowledge LOD: (p. 96) If an investment has a 20% (0.20) probability of returning $1,000; a 30% (0.30) probability of returning $1,500; and a 50% (0.50) probability of returning $1,800; the expected value of the investment is: a. $1, b. $1, c. $2, D. $1,

5 14. (p. 96) Suppose that Fly-By-Night Airlines, Inc. has a return of 5% twenty percent of the time and 0% the rest of the time. The expected return from Fly-By-Night is: a. 10% b. 0.1% c. 0.2% D. 1.0% 15. (p. 97) An investor puts $1,000 into an investment that will return $1,250 one-half of the time and $900 the remainder of the time. The expected return for this investor is: a. $1,075 b. 5.0% C. 7.5% d. 15.0% 16. (p. 97) An investor puts $2,000 into an investment that will pay $2,500 one-fourth of the time; $2,000 one-half of the time, and $1,750 the rest of the time. What is the investor's expected return? a. 12.5% b. $ c. 6.25% D % 5-5

6 17. (p. 98) If an individual voluntarily purchases insurance on his/her home to protect against a loss due to fire, the individual: a. Is convinced a fire will occur B. Believes the premium for the policy is less than the expected loss from a fire c. Has calculated the probability of a fire to be high d. Has underestimated the probability that a fire will occur 18. (p. 98) Risk-free investments have rates of return: a. Equal to zero B. With a standard deviation equal to zero c. That are uncertain, but have a certain time horizon d. That exhibit a large spread of potential payoffs BLOOMS: Knowledge 19. (p. 98) An investment with a large spread between possible payoffs will generally have: a. A low expected return B. A high standard deviation c. A low value at risk d. Both a low expected return and a low value at risk 20. (p. 98) An investment pays $1,500 half of the time and $500 half of the time. Its expected value and variance respectively are: a. $1,000; 500,000 dollars b. $2,000; 250,000 dollars2 c. $1,000; 250,000 dollars D. $1,000; 250,000 dollars2 5-6

7 21. (p. 99) An investment pays $1,200 a quarter of the time; $1,000 half of the time; and $800 a quarter of the time. Its expected value and variance respectively are: A. $1,000; 20,000 dollars2 b. $1,050; 20,000 dollars c. $1,000; 40,000 dollars2 d. $1,000; 80,000 dollars e. $1,000; 40,000 dollars2 22. (p. 99) An investment pays $1000 three quarters of the time, and $0 the remaining time. Its expected value and variance respectively are: a. $1,000: 62,500 dollars2 b. $750; 46,875 dollars c. $750; 62,500 dollars D. $750; 187,500 dollars2 23. (p. 98) The standard deviation is generally more useful than the variance because: a. It is easier to calculate b. Variance is a measure of risk, where standard deviation is a measure of return C. Standard deviation is calculated in the same units as payoffs and variance isn't d. It can measure unquantifiable risk 24. (p. 99) Given a choice between two investments with the same expected payoff: A. Most people will choose the one with the lower standard deviation b. Most people will opt for the one with the higher standard deviation c. Most people will be indifferent since the expected payoffs are the same d. Most people will calculate the variance to assess the relative risks of the two choices 5-7

8 25. (p. 98) An investment will pay $2,000 half of the time and $1,400 half of the time. The standard deviation for this investment is: a. $90,000 B. $300 c. $1,700 d. $ (p. 98) An investment will pay $2000 a quarter of the time; $1,600 half of the time and $1,400 a quarter of the time. The standard deviation of this asset is: A. $ b. $1,650 c. $47,500dollars2 D. $ Use the following to answer questions 27-28: Investment A pays $1,200 half of the time and $800 half of the time. Investment B pays $1,400 half of the time and $600 half of the time 27. (p. 98) Which of the following statements is correct? a. Investment A and B have the same expected value, but A has greater risk b. Investment B has a higher expected value than A, but also greater risk C. Investment A and B have the same expected value, but A has lower risk than B d. Investment A has a greater expected value than B, but B has less risk BLOOMS: Analysis 5-8

9 28. (p. 98) Which of the following statements is correct? a. Investment A and B have the same expected value, but A has greater risk b. Investment B has a higher expected value than A, but also greater risk c. Investment A has a greater expected value than B, but B has less risk d. Investments A and B have the same expected value and equal risk E. None of the above BLOOMS: Analysis 29. (p. 99) The greater the standard deviation of an investment: a. The lower the return B. The greater the risk c. The lower the risk d. The greater the return BLOOMS: Evaluation 30. (p. 101) The difference between standard deviation and value at risk is: a. Nothing, they are two names for the same thing b. Value at risk is a more common measure in financial circles than is standard deviation C. Standard deviation reflects the spread of possible outcomes where value at risk focuses on the value of the worst outcome d. Value at risk is expected value times the standard deviation 5-9

10 31. (p. 101) A $600 investment has the following payoff frequency: a quarter of the time it will be $0; three quarters of the time it will pay off $1000. Its standard deviation and value at risk respectively are: a. $750; $600 B. $433; $600 c. $0; $1000 d. $433; $ (p. 101) A $500 investment has the following payoff frequency: half of the time it will pay $350 and the other half of the time it will pay $900. Its standard deviation and value at risk respectively are: A. $275; $150 b. $625; $275 c. $275; $350 d. $125; $ (p. 101) The measure of risk that focuses on the worst possible outcome is called: a. Expected rate of return b. Risk-free rate of return c. Standard deviation of return D. Value at risk BLOOMS: Knowledge LOD:

11 34. (p. 102) Leverage: a. Reduces risk b. Is synonymous with risk-free investment C. Increases expected rate of return d. Leads to smaller changes in the investment's price 35. (p. 101) Which of the following individuals is least likely to use value at risk as an important factor in his/her investment decision? a. An individual considering a mortgage to buy his first home b. A family considering purchasing health insurance c. A policy maker considering regulation of depository institutions D. A mutual fund manager choosing the allocation of investments in the fund's portfolio BLOOMS: Evaluation 36. (p. 102) Comparing a lottery where a $1 ticket purchases a chance to win $1 million with another lottery in which a $5,000 ticket purchases a chance to win $5 billion, we notice many people would participate in the first but not the second, even though the odds of winning both lotteries are the same. We can perhaps best explain this outcome by: a. Higher expected value for the lottery paying $1 million b. Higher expected value for the lottery paying $5 billion C. Lower value at risk for the lottery paying $1 million d. Higher value at risk for the lottery paying $1 million BLOOMS: Analysis 5-11

12 37. (p. 102) Which of the following statements is true? a. Leverage increases expected return while lowering risk B. Leverage increases risk c. Leverage lowers the expected return and lowers risk d. Leverage lowers the expected return and increases risk 38. (p. 102) Which of the following statements is true? A. Leverage increases expected return and increases risk b. Leverage increases expected return and reduces risk c. Leverage decreases expected return but has no effect on risk d. Leverage decreases expected return and increases risk 39. (p. 102) Which of the following investment strategies involves generating a higher expected rate of return through increasing risk? a. Diversifying b. Hedging risk C. Leverage d. Value at risk 40. (p. 105) A risk-averse investor versus a risk-neutral investor: a. Will never take a risk, while the risk neutral investor will B. Needs greater compensation for the same risk versus the risk neutral investor c. Will take the same risks as the risk neutral investor if the expected returns are equal d. Needs less compensation for the same risk versus the risk neutral investor LOD:

13 41. (p. 105) A risk-averse investor will: a. Always accept a greater risk with a greater expected return b. Only invest in assets providing certain returns c. Never accept lower risk if it means accepting a lower expected return D. Sometimes accept a lower expected return if it means less risk 42. (p. 105) A risk-averse investor will: a. Never prefer an investment with a lower expected return B. Always prefer an investment with a certain return to one with the same expected return but that has any amount of uncertainty c. Always require a certain return d. Always focus exclusively on the expected return 43. (p. 105) Up to what amount would a risk-neutral gambler pay to enter a game where on the flip of a fair coin, if you call the correct outcome the payoff is $2000? a. More than $1000 but less than $2000 b. Up to $2000 C. Up to $1000 d. More than $1, (p. 105) Professional gamblers know that the odds are always in favor of the house (casinos). The fact that they gamble says they are: a. Irrational b. Risk-neutral c. Risk-averse D. Risk seekers 5-13

14 45. (p. 105) The most a risk-averse individual would pay to participate in a flip of a fair coin with a payoff of $500 if the correct outcome is called is: a. $500 B. An amount less than $250 c. $250 d. An amount not to exceed $ (p. 105) The risk premium for an investment: a. Is negative for U.S. Treasury Securities b. Is a fixed amount added to the risk-free return, regardless of the level of risk C. Increases with risk d. Is zero (0) for risk-averse investors BLOOMS: Knowledge LOD: (p. 105) A risk-averse investor compared to a risk-neutral investor would: a. Offer the same price for an investment as the risk-neutral investor B. Require a higher risk premium for the same investment as a risk-neutral investor c. Place more focus on expected return and less on return than the risk-neutral investor d. Place less focus on expected return than the risk-neutral investor 48. (p. 105) When considering different investments, a risk-averse investor is most likely to focus on purchasing: a. Investments with the greatest spread in the expected rate of return B. Investments that offer the lowest standard deviation in the investments' expected rates of return for any given expected rate of return c. Only risk-free investments d. Investments with the lowest risk premium, regardless of the expected rate of return BLOOMS: Evaluation 5-14

15 49. (p. 106) Uncertainty associated with the expected rate of return on an individual stock reflects all of the following except: a. Idiosyncratic risk b. Changes in the performance of the individual company relative to others c. Change in macroeconomic conditions D. Systematic risk LOD: (p. 106) We observe an increase in the price for Apple stock, while other Nasdaq-listed companies experience no change in their share prices. The increase in Apple's stock price most likely reflects (with respect to Apple): a. An increase in systematic risk b. A decrease in systematic risk c. An increase in idiosyncratic risk D. A decrease in idiosyncratic risk BLOOMS: Analysis LOD: (p. 106) Which of the following statements is most correct? A. Usually higher expected returns are associated with higher risk premiums b. Usually higher risk premiums are associated with lower expected returns c. Usually lower expected returns are associated with higher risk premiums d. Usually expected returns are not associated with risk premiums BLOOMS: Analysis 5-15

16 52. (p. 106) The fact that over the long run the return on common stocks has been higher than that on long-term U.S. Treasury bonds is partially explained by the fact that: a. A lot more money is invested in common stocks than U.S. Treasury bonds b. There are regulations on the interest rates U.S. Treasury bonds can offer C. The risk premium is higher on common stocks d. Risk-averse investors buy more common stock 53. (p. 106) Idiosyncratic risk: a. Affects all firms in the economy B. Affects one or a few firms, not everyone c. Is fixed across all firms d. Impacts all firms in the same industry equally BLOOMS: Knowledge 54. (p. 106) When the home construction industry does poorly due to a recession, this is an example of: A. Systematic risk b. Idiosyncratic risk c. Risk premium d. Unique risk LOD: (p. 106) Unique risk is another name for: a. Market risk b. Systematic risk c. The risk premium D. Idiosyncratic risk BLOOMS: Knowledge LOD:

17 56. (p. 106) High oil prices tend to harm the auto industry and benefit oil companies; therefore, high oil prices are an example of: a. Systematic risk B. Idiosyncratic risk c. Neither systematic nor idiosyncratic risk d. Both systematic and idiosyncratic risk LOD: (p. 107) Changes in general economic conditions usually produce: A. Systematic risk b. Idiosyncratic risk c. Risk reduction d. Lower risk premiums BLOOMS: Knowledge LOD: (p. 106) Unexpected inflation can benefit some people/firms and harm others. This is an example of: a. Systematic risk b. Unmeasured risk C. Idiosyncratic risk d. Zero risk since the effects balance BLOOMS: Knowledge LOD: (p. 107) Diversification is the principle of: a. Eliminating risk b. Reducing the risk we carry to just two C. Holding more than one risk at a time d. Eliminating investments from our portfolio that have idiosyncratic risk BLOOMS: Knowledge LOD:

18 60. (p. 107) Diversification can eliminate: a. All risk in a portfolio b. Risk only if the investor is risk averse c. The systematic risk in a portfolio D. The idiosyncratic risk in a portfolio 61. (p. 107) A risk-neutral investor: a. Highly values diversification b. Is the only type of investor who benefits from diversification C. Gains nothing from diversification d. Does not believe that diversification can reduce risk 62. (p. 108) An investor practicing hedging would be most likely to: a. Avoid the stock market and focus on bonds b. Purchase shares in General Motors and buy U.S. Treasury Bonds C. Purchase shares in General Motors and Amoco Oil d. Put his/her invested funds in CDs 63. (p. 108) Hedging is possible only when investments have: A. Opposite payoff patterns b. The same payoff patterns c. Payoffs that are independent of each other d. The same risk premiums BLOOMS: Knowledge LOD:

19 64. (p. 109) An investor who diversifies by purchasing a mix of two stocks that are not perfectly positively correlated will find that the standard deviation of the portfolio is: a. The sum of the standard deviations of the two individual stocks b. Greater than the sum of the standard deviations of the individual stocks c. Greater than the standard deviation from holding the same balance in only one of these stocks D. Less than the standard deviation from holding the same balance in only one of these stocks 65. (p. 107) Which of the following statements is false? a. Diversification can reduce risk B. Diversification can reduce risk but only by reducing the expected return c. Diversification reduces idiosyncratic risk d. Diversification allocates savings across more than one asset BLOOMS: Analysis 66. (p. 107) Systematic risk: a. Is the risk eliminated through diversification b. Represents the risk affecting a specific company C. Cannot be eliminated through diversification d. Is another name for risk unique to an individual asset 5-19

20 67. (p. 106) The Russian wheat crop fails, driving up wheat prices in the U.S. This is an example of: A. Idiosyncratic risk b. Diversification c. Systematic risk d. Quantifiable risk LOD: (p. 107) If the returns of two assets are perfectly positively correlated, an investor who puts half of his/her savings into each will: a. Reduce risk b. Have a higher expected return C. Not gain from diversification d. Reduce risk but lower the expected return 69. (p. 107) In order to benefit from diversification, the returns on assets in a portfolio must: a. Be perfectly positively correlated b. Be perfectly negatively correlated C. Not be perfectly positively correlated d. Have the same idiosyncratic risks 70. (p. 107) The main reason for diversification for an investor is: a. To take advantage of the fact that returns of assets are perfectly positively correlated B. To take advantage of the fact that returns on assets are not perfectly positively correlated c. To lower transaction costs d. To gain from the greater returns that come from greater risk 5-20

21 71. (p. 107) If ABC Inc. and XYZ Inc. have returns that are perfectly positively correlated: a. Adding XYZ Inc to a portfolio that consists of only ABC Inc. will reduce risk b. Adding ABC Inc to a portfolio that includes only XYZ Inc. will increase risk C. Adding XYZ Inc. to a portfolio that consists of only ABC Inc. will neither increase nor decrease the risk of the portfolio d. Adding XYZ Inc to a portfolio that consists of only ABC Inc. will neither increase nor decrease idiosyncratic risk but will lower systematic risk 72. (p. 98) If an investment offered an expected payoff of $100 with $0 variance, you would know that: a. Half of the time the payoff is $100 and the other half it is $0 B. The payoff is always $100 c. Half of the time the payoff is $200 and the other half it is $0 d. Half of the time the payoff is $200 and the other half it is $ (p. 105) The fact that not everyone places all of his/her savings in U.S. Treasury bonds indicates that: a. Most investors are not risk averse b. Many investors are actually risk seekers C. Even risk-averse people will take risk if they are compensated for it d. Most people are risk-neutral 5-21

22 74. (p. 108) Hedging risk and spreading risk are two ways to: a. Increase expected returns from a portfolio B. Diversify a portfolio c. Lower transaction costs d. Match up perfectly positively correlated assets LOD: (p. 108) Sometimes spreading has an advantage over hedging to lower risk because: A. It can be difficult to find assets that move predictably in opposite directions b. It is cheaper to spread than hedge c. Spreading increases expected returns, hedging does not d. Spreading does not affect expected returns BLOOMS: Analysis 76. (p. 109) Spreading involves: a. Finding assets whose returns are perfectly negatively correlated B. Adding assets to a portfolio that move independently c. Investing in bonds and avoiding stocks during bad times d. Building a portfolio of assets whose returns move together LOD: (p. 109) Investing in a mutual fund made up of hundreds of stocks of different companies is an example of all of the following except: a. Spreading risk b. Diversifying c. Risk reduction D. Increasing the variance of a portfolio 5-22

23 78. (p. 107) An automobile insurance company that writes millions of policies is practicing a form of: a. Mutual fund b. Hedging risk C. Spreading risk d. Eliminating systematic risk 79. (p. 107) An automobile insurance company on average charges a premium that: a. Equals the expected loss from each driver b. Is less than the expected loss from each driver C. Is greater than the expected loss from each driver d. Equals 1/(expected loss) of each driver 80. (p. 108) The variance of a portfolio of assets: A. Decreases as the number of assets increases b. Increases as the number of assets increase c. Approaches 0 as the number of assets decreases d. Approaches 1 as the number of assets increases BLOOMS: Analysis 81. (p. 110) In investment matters, generally young workers compared to older workers will: a. Minimize expected return and focus more on variability B. Maximize expected return and focus less on variability c. Have equal concern for expected return and variability d. Be more risk-averse 5-23

24 82. (p. 112) The variance of a portfolio containing n assets: a. Increases as n increases B. Decreases as n increases c. Is constant for any n greater than two d. Does not change in a predictable way when n increases 83. (p. 108) The expected return from a portfolio made up equally of two assets that move perfectly opposite of each other would have a standard deviation equal to: a. 1.0 b C. 0.0 d (p. 107) A life insurance company can make profits because individual life spans: a. Are very similar B. Are independent c. Individual life spans are perfectly positively correlated d. Individual life spans are perfectly negatively correlated 85. (p. 105) An individual who is risk-averse: a. Never takes risks b. Accepts risk but only when the expected return is very small C. Requires larger compensation when the risk increases d. Will accept a lower return as risk rises 5-24

25 86. (p. 107) A portfolio of assets has lower risk than holding one asset, but the same expected return and higher transaction costs. Which of the following statements is most correct? a. The portfolio is attractive to people who are risk-averse and risk-neutral, but not to risk seekers b. The portfolio is attractive to investors who are risk-neutral C. The portfolio is not attractive to investors who are risk-neutral d. The portfolio is attractive to investors who are risk seekers BLOOMS: Analysis Short Answer Question 87. (p. 96) An individual faces two alternatives for an investment: Asset A has the following probability return schedule: Asset B has a certain return of 8.0%. If the individual selects asset A does she violate the principle of risk aversion? Explain. Asset A provides an expected return of 8.65%. For the investor the 0.65% premium may be a large enough differential to compensate for the additional risk, so she may still be "risk averse". BLOOMS: Synthesis 5-25

26 88. (p. 105) An individual faces two alternatives for an investment. Asset 'A" has the following probability of return schedule: Asset 'B' has a certain return of 10.25%. If this individual selects asset 'A' does it imply she is risk averse? Explain. Since both assets provide the same expected return, they would be equally attractive to an investor who is risk neutral. An investor who is risk averse would prefer Asset B, which provides the same expected return but with less risk than asset A. BLOOMS: Synthesis 89. (p. 106) Explain why returns on assets compensate for systematic risk but not for idiosyncratic risk. Idiosyncratic risk can be reduced through diversification. Systematic risk cannot since it affects all assets. 5-26

27 90. (p. 99) Consider the following two assets with probability of return = Pi and return = Ri. Calculate the expected return for each and the standard deviation. Which one carries the greatest risk? Why? For asset A, the expected return = 0.4(12) (8.5) + 0.1(-2.0) = 8.85% For asset B, the expected return = 0.2(11.5) +0.5(10.0) + 0.3(0) = 7.30% For asset A, the standard deviation is 3.98 = For asset B, the standard deviation is 4.81 = Since asset B has a higher standard deviation than asset A, its return has higher risk. BLOOMS: Analysis 91. (p. 105) Explain why an asset that carries more risk should sell for a lower price but offer a higher expected return. An asset that carries more risk will sell for a lower price because the asset should have less demand which would cause the price to be lower. At the same time, due to the higher risk, savers will require a risk premium be added to the risk free return to hold this asset. 5-27

28 92. (p. 104) Explain why casinos will find professional gamblers participating in the various games of chance even though these professionals know the odds are in favor of the house and against them. Most professional gamblers are aware the odds are against them but continue to participate. They do this because part of their compensation may come in the form of the "thrill" of gambling, which to some degree reflects that, at least in terms of playing games of chance, they are risk seekers. BLOOMS: Synthesis 93. (p. 96) What is the expected value of a $100 bet on a flip of a fair coin, where heads pays double and tails pays zero? The expected value of this event is calculated as E.V. = PH (H) + PT (T); where H is the payoff from the coin turning up heads and T is the payoff if the coin turns up tails. PH and PT are the probabilities of the coin turning up heads or tails respectively. Substituting actual values in out formula reveals: E.V. = 0.5 ($200) + 0.5($0) = $ (p. 101) An individual owns a $100,000 home. She determine that her chances of suffering a fire in any given year to be 1/1000 (0.001). She correctly calculates her expected loss in any year to be $100. Explain why this really isn't a good way to measure her potential for loss. While all of her calculations may be accurate this individual may be better off considering value at risk, which is the worst outcome. The value at risk from a fire for her in this case is $100,000 which, if suffered, could prove devastating. 5-28

29 95. (p. 110) Identify at least three possible sources for a risk an individual may face in planning for retirement. In planning for retirement an individual faces at least the following uncertainties: Life span, there is uncertainty regarding how long an individual's life will be. Unexpected inflation, no one knows what the inflation rate will be in the future. This makes earning a targeted real return difficult. Health problems or other unforeseen contingencies can use up funds that were being set aside for retirement. 96. (p. 96) What is the probability of tossing a pair of dice once and getting a 1? How about a 7? It is impossible to toss two dice and get a 1, since the smallest number you can roll is a 2. So the probability of getting a 1 is 0. On the other hand a seven can be obtained a 6 different ways, and since there are 36 possible outcomes from a single roll of a pair of dice, the answer is 6/36 or 1/6 or 16.7% 97. (p. 96) If there are 1,000 people, each of whom owns a $100,000 house, and they each stand a 1/1,000 chance each year of suffering a fire that will totally destroy their house, what is the minimum that they would have to pay annually for fire insurance? We can calculate the expected loss for any one individual as: E.L. = ($100,000) ($0) = $ Since the expected loss for each individual is $100 per year, the minimum that each would have to pay is $ a year, in fact, given the probability of 1 in a 1000 homeowners in this group suffering a fire each year, at $100 each, on average, there should be just enough to compensate the person suffering the fire. 5-29

30 98. (p. 96) Calculate the expected value, the expected return, the variance and the standard deviation of an asset that requires a $1000 investment, but will return $850 half of the time and $1,250 the other half of the time. Expected value is = 0.5($850) + 0.5($1,250) = $1,050. Expected return = $1,050/$1,000 = 0.05 or 5.0% Variance = 0.5( 850-1,050) (1,250-1,050)2 = 40,000 dollars2 Standard deviation = the square root of the variance or in this case = $ (p. 93) Explain the following: Risk results from the fact that more outcomes could happen than will happen. Risk results from uncertainty, not knowing what will happen. For example before a coin is flipped we know that there are two possible outcomes, heads or tails. Once the coin is flipped, there will only be one outcome. The risk is in not knowing a priori what is going to happen. If there is only one possible outcome, there is certainty and therefore, no risk (p. 96) Calculate the expected value of an investment that has the following payoff frequency: a quarter of the time it will pay $2,000, half of the time it will pay $1,000 and the remaining time it will pay $0. The expected value = ¼($2000) + ½($1000) + ¼($0) = $

31 101. (p. 96) Consider the following two investments. One is a risk-free investment with a $100 return. The other investment pays $ % of the time and a $375 loss the rest of the time. Based on this information, answer the following: (i) Compute the expected returns and standard deviations on these two investments individually. (ii) Compute the value at risk for each investment. (iii) Which investment will risk-averse investors prefer, if either? Which investment will riskneutral investors prefer, if either? (i) The expected rate of return is $100 for the risk-free investment. The risk-free investment has a standard deviation of zero because the return is certain. For the risky investment: Expected return = 0.2($2000) + 0.8(-$375) = $100 Standard Deviation = 0.2*( ) *( )2 = = 950 (ii) The value at risk for the risk-free investment is $100 because it pays a certain return. The value of risk for the risky investment is -$375, this is the maximum amount the investor can lose. (iii) The risk-averse investor will prefer the risk-free investment. The risk-neutral investor will not have a preference between the two investments because they pay the same expected return. BLOOMS: Analysis 5-31

32 102. (p. 97) Compute the expected return, standard deviation, and value at risk for each of the following investments: Investment (A): Pays $800 three-fourths of the time and a $1200 loss otherwise. Investment (B): Pays $1000 loss half of the time and a $1600 gain otherwise. State which investment will be preferred by each of the following investors, and briefly explain why. (i) a risk-neutral investor (ii) an investor who seeks to avoid the worst-case scenario. (iii) a risk-averse investor. Investment (A) Expected return = 0.25(-$1200) ($800) = $300 Standard Deviation = 0.25*( ) *( )2 = = 866 Value at Risk = -$1200 Investment (B) Expected return = 0.5(-$1000) + 0.5($2000) = $500 Standard Deviation = 0.5*( ) *( )2 = = 1300 Value at Risk = -$1000 (i) The risk-neutral investor is indifferent between these two investments because they pay the same expected return. (ii) The investor who seeks to avoid the worst-case scenario will choose Investment (B) because it has the lower value at risk. (iii) The risk-averse investor will prefer Investment (A) because it has a lower standard deviation. This suggests that there is less uncertainty about the expected return relative to Investment (B). BLOOMS: Analysis 5-32

33 103. (p. 101) You do some research and find for a driver of your age and gender the probability of having an accident that results in damage to your automobile exceeding $100 is 1/10 per year. Your auto insurance company will reduce your annual premium by $40 if you will increase your collision deductible from $100 to $250. Should you? Explain. An increase of a deductible from $100 to $250 exposes you to an out-of-pocket possible loss of $150 when you have an accident. But the chances of incurring this out-of-pocket loss is 1/10 (0.10) each year, so we can calculate the expected loss as E.L. = 0.1($150) + 0.9($0) = $ Since this expected loss is less than the $40 in premium savings it makes good sense to increase the deductible BLOOMS: Analysis BLOOMS: Evaluation 104. (p. 99) What would be the standard deviation for a $1000 risk-free asset that returns $1,100? The standard deviation for this asset would have to be $0. If it is truly risk-free the return is certain, and if the return is certain thee is no variance in the return, therefore no standard deviation. 5-33

34 105. (p. 99) You buy an asset for $2500. The asset will return $3300 half of the time and $2700, the other half. The expected return is 20% (a gain of $500) and the standard deviation is 12% ($300). How would using $1,250 of borrowed funds change the expected return and standard deviation specifically? Borrowing 50% of the funds needed to purchase the asset is using leverage. It will double the expected return as well as the standard deviation. For example, if the asset returns the $3,300, the lender will have to be repaid $1,250, but this leaves $2,050 for you. If the asset returns $2,700 the lender still needs to be repaid, leaving $1,450 for you. Since each of these outcomes is equally likely, we can calculate the expected return and standard deviation of leverage. Expected value = ½($2,050) + ½ ($1,450) = $1,750. The $1,750 expected value on a $1,250 investment is an expected return of 40%. So the expected return doubled using leverage. The standard deviation can also be calculated: = $300 or 24% of the actual amount invested. So while the expected return doubled, so did the standard deviation. BLOOMS: Analysis 106. (p. 102) What would be the impact of leverage on the expected return and standard deviation of purchasing an asset with 10% of the owner's funds and 90% borrowed funds? We can use the general formula: Leverage factor = Cost of Investment/ Owner's Contribution to the Purchase In this case the leverage factor would be 10; so the expected return and the standard deviation would both increase by a factor of (p. 105) Why isn't it correct to say that people who are risk averse avoid risk? This statement really isn't correct. A better statement would be that people who are risk averse need to be compensated to take additional risk. The degree of additional compensation is referred to as the risk premium and this will vary depending on the degree of risk aversion. 5-34

35 108. (p. 106) Briefly explain the difference between idiosyncratic risk and systematic risk. Provide an example of each. Systematic risk is risk resulting from something that will impact all firms, such as a general slowdown in the economy. Idiosyncratic risk will impact specific firms or industries, such as a harmful bacterium that is discovered in beef (p. 107) Explain why a company offering homeowners insurance policies would want to insure homes across a wide geographic area. One of the lessons from this chapter is the ability to reduce risk through diversification, and one way to effectively diversify is through spreading of risk. Since the homes can be exposed to losses which can hit specific areas, like hurricanes, tornadoes, wild fires, floods, etc. (a form of idiosyncratic risk). An insurance company would not be spreading risk effectively if all or most of the homes they insured were located in one specific area. By insuring homes across a wide geographic area the insurance company can effectively spread risk. BLOOMS: Analysis 110. (p. 107) Explain the rapid rise in popularity of mutual funds. The chapter covered the topic of spreading risk and one of the ways for an individual investor to spread risk is to purchase many different financial assets. The problem for any one individual is it could be expensive, both in terms of absolute dollars but also in transaction costs to purchase many different assets. Mutual funds allow individuals to pool their funds and purchase many different assets, thereby achieving most of the benefits of diversification without requiring a lot of funds to invest or high transaction costs. 5-35

36 111. (p. 102) Considering leverage, can you explain why a mortgage lender would want borrowers to have larger down payments, and when the borrower doesn't the mortgage lender may require mortgage insurance? We saw that leverage can do two things for the borrower: it will increase the expected return but it also increases risk. As an example, a homebuyer putting 10% down rather than 20% increases the leverage factor from 5 to 10, this will double the expected return for the borrower but also double the risk. The mortgage lender (the counterparty) is certainly concerned with the risk since the doubling of the risk also works against them. As a result, they would want a larger down payment or insurance protection in the event that the borrower does not meet their obligations. BLOOMS: Analysis 112. (p. 104) You study horse racing avidly and discover for this year's Kentucky Derby you think you have the field pretty well figured out. In fact, you calculate the expected return and it is the same as the expected return you are getting from the stock market. Is this investment in the race valuable to you? While the opportunity to win at the horse race is present, so is the opportunity to lose your investment. The same situation exists with the stock market. One key difference, however, is the stock market offers the opportunity to diversify risk through spreading, this opportunity does not exist with a single horse race, it will be all or nothing. 5-36

37 113. (p. 105) Consider an individual who plans to buy a new home. He has two options: (i) pay for mortgage insurance (that insures the lender in case the borrower defaults), or (ii) pay the lender a higher interest rate for the mortgage. Describe how these two options are related to the concept of risk premium and the lender's aversion to risk. Why does the interest rate on the mortgage differ in these two options? In option (ii), the risk premium on the mortgage is positive because the lender realizes there is some risk in the homeowner's ability to repay the loan. Therefore, the borrower will have to pay the risk premium in order to obtain a mortgage from the lender. If the homeowner takes option (i), he pays no premium to the lender. This is because the policy holder is paying someone else to take the risks associated with the mortgage. This is why the borrower will not need to pay a risk premium to the lender in option (i). If the borrower pays a risk premium to the mortgage lender, the lender takes on the risk (option i). If the borrower pays for insurance, then the insurance company takes the risk (option ii). BLOOMS: Synthesis 114. (p. 107) How are the decisions of government policy makers, such as the Federal Reserve, related to risk and an individual investor's portfolio? The decisions of government policy makers, such as the Federal Reserve, affect macroeconomic conditions, which in turn, affect the degree of systematic risk in the financial system. When the economy has low GDP growth and/or high inflation, this creates systematic risk that cannot be eliminated through diversification. BLOOMS: Synthesis 5-37

38 115. (p. 110) You read about the employees and others who invested their retirement funds in Enron stock. What lesson(s) should be learned from this? Actually there are a few; one is that employees need to pay more attention to the decisions being made regarding retirement funds. Another lesson is that a high return in the past does not guarantee a high return in the future and attention should always be paid to the probabilities of certain returns. Perhaps the most valuable lesson is that diversification works. Many of the employees had large percents of their retirement funds in Enron stock, so that when the company went bankrupt much of their retirement fund was lost. Had the employees better diversified Enron's bankruptcy would not have been so catastrophic for them. BLOOMS: Evaluation Essay Questions 116. (p. 99) Apply the definition of risk provided in the textbook to an individual's decision to purchase a car insurance policy. Suppose that the individual has two possibilities: no accident ($0 gain/loss) and accident (-$30,000 loss). If the probability of an accident is lower than the probability of an accident occurring (say the probability of an accident is 10%), then why do people buy car insurance? How is this related to the concept of value at risk and the time horizon of investment decisions? People buy car insurance in order to share risk with other policy holders. Even the risk-neutral investor would purchase car insurance because the expected return from driving one's car on a regular basis is involves a loss and never a financial gain. Risk-averse investors are willing to pay even more because of the uncertainty in outcomes and the possibility of a large loss. Value at risk refers to the worst possible outcome. This is often something drivers consider because if they drive often, and plan to drive over long periods of time, the probability of observing the worst-case scenario is higher over one's lifetime (compared with a situation where an individual drives for one day only). BLOOMS: Synthesis 5-38

39 117. (p. 98) What is the difference between standard deviation and value at risk? Consider the difference between purchasing a one-year bank CD compared with purchasing a homeowner's insurance policy. Which scenario do you believe is more likely to consider value at risk over standard deviation? Explain. Standard deviation measures the uncertainty about a payoffs expected return, whereas the value at risk is the worst possible scenario. The decision to purchase an insurance policy is more likely to consider value at risk. When people decide to purchase insurance, they are more likely to consider the worst-case scenario because the time horizon is an individual's lifetime. For a one-year bank CD, the worst-case scenario is less likely to occur simply because the time horizon is shorter (p. 105) Discuss how well financial markets would work if people all had the exact same tolerance for risk. Financial markets may not work nearly as well if people all shared the same tolerance for risk. The strength of financial markets is that risks are borne by those most willing to handle them or those who can bear them at the lowest cost. Because individuals vary across many characteristics (including age, wealth, income, lifestyle, etc.), people have different tolerances for risk and as a result risk can be passed to others. If everyone had the same tolerance for risk the ability to pass risk would be severely curtailed and financial markets would not work as well. Also the ability to diversify risk would be lost further inhibiting financial market operation. 5-39

40 119. (p. 108) Explain why insurance companies may find themselves at times having to refuse business. Insurance companies accept risk from individuals and then spread this risk, a form of diversification. As an example, an insurance company that provides home insurance accepts the risk from an individual and pools these risks in a portfolio of policies. One situation the insurance company must be aware of is accepting too many risks from one area so that the portfolio is not diversified as well as it may be. If the company finds that it has too many homes insured in Florida, say, and not enough in other parts of the country it may leave itself exposed to larger losses due to hurricanes. As a result, the company may deny any more policies from Florida until the percentage of homes in Florida represents the percentage the company predicted in determining its expected return. Also, value at risk issues come into play in these situations. A hurricane or other natural disaster can have a very large impact on one concentrated area and insurance companies must always be aware of the value at risk. If this becomes too large for a certain area or possible event, the company may not accept any additional business from that area, (this is one reason why insurance companies purchase reinsurance.) BLOOMS: Analysis 120. (p. 104) Suppose a saver is looking for the opportunity to make a very large return in a very short period of time. Would you recommend diversification for this individual? An individual looking to make a very large return in a short period of time will not likely benefit from diversification. As we saw from the chapter one of the benefits of diversification is the reduction in risk that results. But another lesson was that the lower the risk the lower the return. If an individual is interested in a large, short-term return he/she is going to have to be willing to accept a larger risk. In this case the individual is more likely to want to concentrate on one or two assets (or gambles) and put all of his/her eggs in that basket and hope for the best. If it turns out well the actual return is likely to be higher than it would have been under a diversification strategy, however, he/she is more likely to lose using this approach as well. So while the expected return may be the same, without diversification the risk is far greater which is why the actual return could be larger. BLOOMS: Evaluation 5-40