Chapter 05 – Understanding Risk
95. Identify at least three possible sources for a risk an individual may face in planning for
retirement.
96. What is the probability of tossing a pair of dice once and getting a 1? How about a 7?
97. 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?
Chapter 05 – Understanding Risk
98. 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.
99. Explain the following: Risk results from the fact that more outcomes could happen than
will happen.
100. 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.
Chapter 05 – Understanding Risk
101. 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?
Chapter 05 – Understanding Risk
102. 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.
Chapter 05 – Understanding Risk
103. 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.
104. What would be the standard deviation for a $1000 risk-free asset that returns $1,100?
Chapter 05 – Understanding Risk
105. 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?
106. 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?
Chapter 05 – Understanding Risk
107. Why isn’t it correct to say that people who are risk averse avoid risk?
108. Briefly explain the difference between idiosyncratic risk and systematic risk. Provide an
example of each.
109. Explain why a company offering homeowners insurance policies would want to insure
homes across a wide geographic area.
Chapter 05 – Understanding Risk
110. Explain the rapid rise in popularity of mutual funds.
111. 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?
Chapter 05 – Understanding Risk
112. 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?
113. 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?
Chapter 05 – Understanding Risk
114. How are the decisions of government policy makers, such as the Federal Reserve, related
to risk and an individual investor’s portfolio?
Essay Questions
115. 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?
Chapter 05 – Understanding Risk
116. 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.
117. Discuss how well financial markets would work if people all had the exact same
tolerance for risk.
Chapter 05 – Understanding Risk
118. Explain why insurance companies may find themselves at times having to refuse
business.
119. 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?