Chapter 5
Understanding Risk
Conceptual and Analytical Problems
1. Consider a game in which a coin will be flipped three times. For each heads you will
a. Construct a table of the possibilities and probabilities in this game.
d. Consider the effect of a change in the game so that if tails comes up two times in a
row, you get nothing. How would your answers to parts a-c change?
Answer:
a. The first step is to list all possible outcomes for the three coin tosses (heads (H),
tails (T)).
Toss 1 Toss 2 Toss 3
HHH
H H T
T H T
We can see that there are four distinct options—3H and 0T, 2H and 1T, 1H and
Next, we will need to assign a probability to each of these four options, taking
a certain outcome for each coin toss.
Possibilities Probability Outcome
1 1/27 0 heads, 3 tails
c. A person who is risk-averse will want to pay less than $200; a person who is
d.
Possibilities Probability Outcome Payoff
1 1/27 3 tails $0
2 2/27 Tails, heads, tails $100
6 8/27 3 heads, 0 tails $300
8/27($300) = $185
A person who is risk-averse will want to pay less than $185; a person who is risk-
2. *Why is it important to be able to quantify risk? (LO2)
Answer: Core Principle 2 tells us that risk requires compensation. In order to
bear it.
3. You are the founder of IGRO, an Internet firm that delivers groceries. (LO4, LO5)
b. As founder of the company, you own a significant portion of the firm, and your
Answer:
a. An idiosyncratic risk is that someone could create another Internet firm to deliver
groceries, which would reduce IGRO’s share of the market. A systematic risk
return to buying groceries from a supermarket instead of online to save on
delivery costs).
b. You could suffer large losses if IGRO does poorly; your stock holdings could
IGRO stock.
4. Assume that the economy can experience high growth, normal growth, or recession.
State of the Economy Probability Return
High Growth 0.2 +30%
a. Compute the expected value of a $1,000 investment over the coming year. If you
the percentage expected rate of return?
b. Compute the standard deviation of the percentage return over the coming year.
investment?
Answer:
b. Standard Deviation
=
%7.11%)9.1215(1.0%)9.1212(7.0%)9.1230(2.0
222
c. Risk Premium = 12.9% – 7% = 5.9%
5. Using the information from the table in Problem 4, in dollar terms what is the value at
risk associated with the $1,000 investment? (LO2)
6. Car insurance companies sell a large number of policies. Explain how this practice
minimizes their risk. (LO5)
Answer: Individual automobile accidents are uncorrelated in the sense that one person
having an accident doesn’t have any effect on whether someone else will have one.
they will face 10,000 claims.
7. Mortgages increase the risk faced by homeowners. (LO2)
a. Explain how.
b. What happens to the homeowner’s risk as the down payment on the house rises
Answer:
b. From the formula in the Tools of the Trade we know that with 10 percent down,
the leverage factor is 10 [1/ (1 – 90/100)], and with 50 percent down, it is 2 (1/ 1 –
8. Banks pay substantial amounts to monitor the risks that they take. One of the primary
Answer: The first concern of a bank’s management is to stay open. This means
9. Explain how liquidity problems can be an important source of systemic risk in the
financial system. (LO4)
Answer: Lack of liquidity can make it difficult or impossible for certain firms to
meet their obligations to other firms in the system. For example, if one firm cannot
obligations and so on, leading to system-wide problems.
10. *Give an example of systematic risk for the U.S. economy and how you might reduce
your exposure to such a risk. (LO4, LO5)
Answer: A recession is one kind of systematic risk facing the U.S. economy. You
could diversify your investments internationally. You could hedge against a
independent of each other.
11. For each of the following events, explain whether it represents systematic risk or
idiosyncratic risk and explain why. (LO4)
a. Your favorite restaurant is closed by the county health department.
cellphone service worldwide.
Answer:
a. This is idiosyncratic risk since it is unique to this particular establishment.
the Florida freeze.
d. This is systematic risk as communications around the globe are disrupted, perhaps
until new satellites can be constructed and put into orbit.
12. You are planning for retirement and must decide whether to purchase only your
and systematic risk, explain how you would make your decision. (LO4, LO5)
Answer: From both perspectives, you should purchase the more highly diversified
portfolio containing the 500 large companies. If you own only your company’s stock,
challenge. In neither case would you expect to be worse off holding the mutual fund,
but you would be better protected against idiosyncratic risk.
13. For each of the following actions, identify whether the method of risk assessment
underlying probability distribution. (LO2)
a. You buy life insurance.
Answer:
a. Life insurance only pays off when you die and your heirs are left without your
b. You are taking steps to reduce idiosyncratic risk in a portfolio, attempting to
decision.
c. Emergency loans to support the financial system are an attempt to avoid the worst
d. You are trying to smooth out the earnings of the business across seasons. This is
14. Which of the following investments in the following table would be most attractive to
a risk-averse investor? How would your answer differ if the investor were described
as risk-neutral? (LO3)
Investment Expected Value Standard Deviation
A 75 10
Answer: A risk-averse investor requires a higher return for taking on more risk. This
investor will also prefer an investment with a higher expected value given a certain
indifferent between Investments B and C.
15. Consider an investment that pays off $800 or $1,400 per $1,000 invested with equal
probability. Suppose you have $1,000 but are willing to borrow to increase your
Answer: If you just invest your own $1,000, the expected value = 0.5($800) +