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Chapter 05 - Understanding Risk

Chapter 05Understanding 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 uncertaintyB. Risk can always be avoided at no costc. Risk has a time horizond. Risk usually involves some future payoff

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2. (p. 93) All other factors held constant, an investment: a. With more risk should offer a lower return and sell for a higher priceb. With less risk should sell for a lower price and offer a higher returnC. With more risk should sell for a lower price and offer a higher returnd. With less risk should sell for a lower price and offer a lower return

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3. (p. 93) Uncertainties that are not quantifiable: a. Are what we define as riskb. Are factored into the price of an assetC. Cannot be pricedd. Are benchmarks against which quantifiable risks can be assessed


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4. (p. 93) When measuring the risk of an asset: A. There may be uncertainty about the size of future payoffsb. It is necessary to incorporate uncertainties that are not quantifiablec. One must remember that the concept of risk applies only to financial markets, not to financial intermediariesd. 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 investmentsb. Investments that pay a return over a longer time horizon generally have less riskc. Investments with a greater variance in the size of the future payoff generally pay a lower expected returnd. Risk-free investments are the best benchmark for measuring the risk of all investment strategies

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6. (p. 93) Inflation presents risk because: a. Inflation is always presentb. Inflation cannot be measuredc. There are different ways to measure itD. There is no certainty regarding what inflation will be in the future


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7. (p. 94) If the probability of an outcome equals one, the outcome: a. Is more likely to occur than the others listedB. Is certain to occurc. Is certain not to occurd. Has unquantifiable risk

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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 percentb. ZeroC. 1 or 100 percentd. Unquantifiable

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9. (p. 94) If the probability of an outcome is zero, you know: a. The outcome is more likely to occurb. The outcome is certain to occurc. The outcome is less likely to occurD. 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 soldb. Is the sum of the payoffsC. Is the probability-weighted sum of the possible outcomesd. Cannot be determined in advance


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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. $1,250b. $1,050C. $1,100d. $2,200


12. (p. 95) Another name for the expected value of an investment would be: A. The mean valueb. The upper-end valuec. The certain valued. The risk-free value


13. (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. $1,433.33b. $1,550.00c. $2,800.00D. $1,600.00


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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. $1,075b. 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. $250.00c. 6.25%D. 3.125%


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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 occurB. Believes the premium for the policy is less than the expected loss from a firec. Has calculated the probability of a fire to be highd. Has underestimated the probability that a fire will occur

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18. (p. 98) Risk-free investments have rates of return: a. Equal to zeroB. With a standard deviation equal to zeroc. That are uncertain, but have a certain time horizond. That exhibit a large spread of potential payoffs


19. (p. 98) An investment with a large spread between possible payoffs will generally have: a. A low expected returnB. A high standard deviationc. A low value at riskd. 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 dollarsb. $2,000; 250,000 dollars2c. $1,000; 250,000 dollarsD. $1,000; 250,000 dollars2


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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 dollars2b. $1,050; 20,000 dollarsc. $1,000; 40,000 dollars2d. $1,000; 80,000 dollarse. $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 dollars2b. $750; 46,875 dollarsc. $750; 62,500 dollarsD. $750; 187,500 dollars2


23. (p. 98) The standard deviation is generally more useful than the variance because: a. It is easier to calculateb. Variance is a measure of risk, where standard deviation is a measure of returnC. Standard deviation is calculated in the same units as payoffs and variance isn'td. 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 deviationb. Most people will opt for the one with the higher standard deviationc. Most people will be indifferent since the expected payoffs are the samed. Most people will calculate the variance to assess the relative risks of the two choices


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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. $90,000B. $300c. $1,700d. $30


26. (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. $217.94b. $1,650c. $47,500dollars2D. $217.94


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 riskb. Investment B has a higher expected value than A, but also greater riskC. Investment A and B have the same expected value, but A has lower risk than Bd. Investment A has a greater expected value than B, but B has less risk

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28. (p. 98) Which of the following statements is correct? a. Investment A and B have the same expected value, but A has greater riskb. Investment B has a higher expected value than A, but also greater riskc. Investment A has a greater expected value than B, but B has less riskd. Investments A and B have the same expected value and equal riskE. None of the above


29. (p. 99) The greater the standard deviation of an investment: a. The lower the returnB. The greater the riskc. The lower the riskd. The greater the return

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30. (p. 101) The difference between standard deviation and value at risk is: a. Nothing, they are two names for the same thingb. Value at risk is a more common measure in financial circles than is standard deviationC. Standard deviation reflects the spread of possible outcomes where value at risk focuses on the value of the worst outcomed. Value at risk is expected value times the standard deviation


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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; $600B. $433; $600c. $0; $1000d. $433; $1000


32. (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; $150b. $625; $275c. $275; $350d. $125; $500


33. (p. 101) The measure of risk that focuses on the worst possible outcome is called: a. Expected rate of returnb. Risk-free rate of returnc. Standard deviation of returnD. Value at risk


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34. (p. 102) Leverage: a. Reduces riskb. Is synonymous with risk-free investmentC. Increases expected rate of returnd. 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 homeb. A family considering purchasing health insurancec. A policy maker considering regulation of depository institutionsD. A mutual fund manager choosing the allocation of investments in the fund's portfolio

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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 millionb. Higher expected value for the lottery paying $5 billionC. Lower value at risk for the lottery paying $1 milliond. Higher value at risk for the lottery paying $1 million

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37. (p. 102) Which of the following statements is true? a. Leverage increases expected return while lowering riskB. Leverage increases riskc. Leverage lowers the expected return and lowers riskd. 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 riskb. Leverage increases expected return and reduces riskc. Leverage decreases expected return but has no effect on riskd. 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. Diversifyingb. Hedging riskC. Leveraged. 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 willB. Needs greater compensation for the same risk versus the risk neutral investorc. Will take the same risks as the risk neutral investor if the expected returns are equald. Needs less compensation for the same risk versus the risk neutral investor


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41. (p. 105) A risk-averse investor will: a. Always accept a greater risk with a greater expected returnb. Only invest in assets providing certain returnsc. Never accept lower risk if it means accepting a lower expected returnD. 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 returnB. Always prefer an investment with a certain return to one with the same expected return but that has any amount of uncertaintyc. Always require a certain returnd. 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 $2000b. Up to $2000C. Up to $1000d. More than $1,500


44. (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. Irrationalb. Risk-neutralc. Risk-averseD. Risk seekers


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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. $500B. An amount less than $250c. $250d. An amount not to exceed $500


46. (p. 105) The risk premium for an investment: a. Is negative for U.S. Treasury Securitiesb. Is a fixed amount added to the risk-free return, regardless of the level of riskC. Increases with riskd. Is zero (0) for risk-averse investors


47. (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 investorB. Require a higher risk premium for the same investment as a risk-neutral investorc. Place more focus on expected return and less on return than the risk-neutral investord. 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 returnB. Investments that offer the lowest standard deviation in the investments' expected rates of return for any given expected rate of returnc. Only risk-free investmentsd. Investments with the lowest risk premium, regardless of the expected rate of return


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49. (p. 106) Uncertainty associated with the expected rate of return on an individual stock reflects all of the following except: a. Idiosyncratic riskb. Changes in the performance of the individual company relative to othersc. Change in macroeconomic conditionsD. Systematic risk


50. (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 riskb. A decrease in systematic riskc. An increase in idiosyncratic riskD. A decrease in idiosyncratic risk


51. (p. 106) Which of the following statements is most correct? A. Usually higher expected returns are associated with higher risk premiumsb. Usually higher risk premiums are associated with lower expected returnsc. Usually lower expected returns are associated with higher risk premiumsd. Usually expected returns are not associated with risk premiums


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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 bondsb. There are regulations on the interest rates U.S. Treasury bonds can offerC. The risk premium is higher on common stocksd. Risk-averse investors buy more common stock


53. (p. 106) Idiosyncratic risk: a. Affects all firms in the economyB. Affects one or a few firms, not everyonec. Is fixed across all firmsd. Impacts all firms in the same industry equally


54. (p. 106) When the home construction industry does poorly due to a recession, this is an example of: A. Systematic riskb. Idiosyncratic riskc. Risk premiumd. Unique risk


55. (p. 106) Unique risk is another name for: a. Market riskb. Systematic riskc. The risk premiumD. Idiosyncratic risk

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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 riskB. Idiosyncratic riskc. Neither systematic nor idiosyncratic riskd. Both systematic and idiosyncratic risk


57. (p. 107) Changes in general economic conditions usually produce: A. Systematic riskb. Idiosyncratic riskc. Risk reductiond. Lower risk premiums


58. (p. 106) Unexpected inflation can benefit some people/firms and harm others. This is an example of: a. Systematic riskb. Unmeasured riskC. Idiosyncratic riskd. Zero risk since the effects balance


59. (p. 107) Diversification is the principle of: a. Eliminating riskb. Reducing the risk we carry to just twoC. Holding more than one risk at a timed. Eliminating investments from our portfolio that have idiosyncratic risk


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60. (p. 107) Diversification can eliminate: a. All risk in a portfoliob. Risk only if the investor is risk aversec. The systematic risk in a portfolioD. The idiosyncratic risk in a portfolio


61. (p. 107) A risk-neutral investor: a. Highly values diversificationb. Is the only type of investor who benefits from diversificationC. Gains nothing from diversificationd. 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 bondsb. Purchase shares in General Motors and buy U.S. Treasury BondsC. Purchase shares in General Motors and Amoco Oild. Put his/her invested funds in CDs


63. (p. 108) Hedging is possible only when investments have: A. Opposite payoff patternsb. The same payoff patternsc. Payoffs that are independent of each otherd. The same risk premiums


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64. (p. 109) An investor who diversifies by purchasing a 50-50 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 stocksb. Greater than the sum of the standard deviations of the individual stocksc. Greater than the standard deviation from holding the same balance in only one of these stocksD. 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 riskB. Diversification can reduce risk but only by reducing the expected returnc. Diversification reduces idiosyncratic riskd. Diversification allocates savings across more than one asset

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66. (p. 107) Systematic risk: a. Is the risk eliminated through diversificationb. Represents the risk affecting a specific companyC. Cannot be eliminated through diversificationd. Is another name for risk unique to an individual asset


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67. (p. 106) The Russian wheat crop fails, driving up wheat prices in the U.S. This is an example of: A. Idiosyncratic riskb. Diversificationc. Systematic riskd. Quantifiable risk


68. (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 riskb. Have a higher expected returnC. Not gain from diversificationd. 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 correlatedb. Be perfectly negatively correlatedC. Not be perfectly positively correlatedd. 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 correlatedB. To take advantage of the fact that returns on assets are not perfectly positively correlatedc. To lower transaction costsd. To gain from the greater returns that come from greater risk


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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 riskb. Adding ABC Inc to a portfolio that includes only XYZ Inc. will increase riskC. Adding XYZ Inc. to a portfolio that consists of only ABC Inc. will neither increase nor decrease the risk of the portfoliod. 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 $0B. The payoff is always $100c. Half of the time the payoff is $200 and the other half it is $0d. Half of the time the payoff is $200 and the other half it is $50


73. (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 averseb. Many investors are actually risk seekersC. Even risk-averse people will take risk if they are compensated for itd. Most people are risk-neutral


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74. (p. 108) Hedging risk and spreading risk are two ways to: a. Increase expected returns from a portfolioB. Diversify a portfolioc. Lower transaction costsd. Match up perfectly positively correlated assets


75. (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 directionsb. It is cheaper to spread than hedgec. Spreading increases expected returns, hedging does notd. Spreading does not affect expected returns


76. (p. 109) Spreading involves: a. Finding assets whose returns are perfectly negatively correlatedB. Adding assets to a portfolio that move independentlyc. Investing in bonds and avoiding stocks during bad timesd. Building a portfolio of assets whose returns move together


77. (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 riskb. Diversifyingc. Risk reductionD. Increasing the variance of a portfolio


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78. (p. 107) An automobile insurance company that writes millions of policies is practicing a form of: a. Mutual fundb. Hedging riskC. Spreading riskd. Eliminating systematic risk


79. (p. 107) An automobile insurance company on average charges a premium that: a. Equals the expected loss from each driverb. Is less than the expected loss from each driverC. Is greater than the expected loss from each driverd. Equals 1/(expected loss) of each driver


80. (p. 108) The variance of a portfolio of assets: A. Decreases as the number of assets increasesb. Increases as the number of assets increasec. Approaches 0 as the number of assets decreasesd. Approaches 1 as the number of assets increases


81. (p. 110) In investment matters, generally young workers compared to older workers will: a. Minimize expected return and focus more on variabilityB. Maximize expected return and focus less on variabilityc. Have equal concern for expected return and variabilityd. Be more risk-averse


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82. (p. 112) The variance of a portfolio containing n assets: a. Increases as n increasesB. Decreases as n increasesc. Is constant for any n greater than twod. 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. 1.0b. -1.0C. 0.0d. 0.5


84. (p. 107) A life insurance company can make profits because individual life spans: a. Are very similarB. Are independentc. Individual life spans are perfectly positively correlatedd. Individual life spans are perfectly negatively correlated


85. (p. 105) An individual who is risk-averse: a. Never takes risksb. Accepts risk but only when the expected return is very smallC. Requires larger compensation when the risk increasesd. Will accept a lower return as risk rises


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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 seekersb. The portfolio is attractive to investors who are risk-neutralC. The portfolio is not attractive to investors who are risk-neutrald. The portfolio is attractive to investors who are risk seekers


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".

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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.

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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.


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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) + 0.5 (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.


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.


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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.

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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) = $100


94. (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.


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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. = 0.001 ($100,000) + 0.999($0) = $100.00. Since the expected loss for each individual is $100 per year, the minimum that each would have to pay is $100.00 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.


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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)2 + 0.5(1,250-1,050)2 = 40,000 dollars2Standard deviation = the square root of the variance or in this case = $200


99. (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.


100. (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) = $1000


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101. (p. 96) Consider the following two investments. One is a risk-free investment with a $100 return. The other investment pays $2000 20% 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 risk-neutral 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) = $100Standard Deviation = √0.2*(2000-100)2 + 0.8*(-375-100)2 = √902500 = 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.


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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) + 0.75($800) = $300Standard Deviation = √0.25*(-1000-300)2 + 0.75*(800-300)2 = √750000 = 866Value at Risk = -$1200Investment (B)Expected return = 0.5(-$1000) + 0.5($2000) = $500Standard Deviation = √0.5*(-1000-300)2 + 0.5*(1600-300)2 = √1690000 = 1300Value 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).


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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) = $15.00. Since this expected loss is less than the $40 in premium savings it makes good sense to increase the deductible

AACSB: AnalyticAACSB: Reflective ThinkingBLOOMS: AnalysisBLOOMS: ApplicationBLOOMS: EvaluationLOD: 3

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.


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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.


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 PurchaseIn this case the leverage factor would be 10; so the expected return and the standard deviation would both increase by a factor of 10.


107. (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.


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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.


109. (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.


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.


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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.


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.


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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).

AACSB: Reflective ThinkingBLOOMS: SynthesisLOD: 3

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.


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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.


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).


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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.


118. (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.


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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 re-insurance.)


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.


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