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Chapter 17 Financial Economics
QUESTIONS
1. Suppose that the city of New York issues bonds to raise money to pay for a new tunnel linking
New Jersey and Manhattan. An investor named Susan buys one of the bonds on the same day that
the city of New York pays a contractor for completing the first stage of construction. Is Susan
making an economic or a financial investment? What about the city of New York? LO1
Answer: New York is making an economic investment. Recall that an economic
investment refers either to paying for new additions to the capital stock or new
2. What is compound interest? How does it relate to the formula: X dollars today = (1 + i )tX
dollars in t years? What is present value? How does it relate to the formula: X/(1 + i)t dollars
today = X dollars in t years? LO1
Answer: Compound interest describes how quickly an investment increases in value
when interest is paid, or compounded, not only on the original amount invested but also
on all interest payments that have been previously made.
3. How do stocks and bonds differ in terms of the future payments that they are expected to
make? Which type of investment (stocks or bonds) is considered to be more risky? Given what
you know, which investment (stocks or bonds) do you think commonly goes by the nickname
“fixed income”? LO2
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Answer: Stocks pay dividends out of profits to the shareholders that own them, with the
percentage of the total dividend received being based on the percentage of stocks owned.
4. What are mutual funds? What different types of mutual funds are there? And why do you think
they are so popular with investors? LO2
Answer: Mutual funds pool investors money and buy a collection of stocks or bonds.
Some are narrowly defined, focusing on a particular sector of the economy (technology,
in the many stocks and bonds in the portfolio.
5. Corporations often distribute profits to their shareholders in the form of dividends, which are
simply checks mailed out to shareholders. Suppose that you have the chance to buy a share in a
fashion company called Rogue Designs for $35 and that the company will pay dividends of $2
per year on that share every year. What is the annual percentage rate of return? Next, suppose that
you and other investors could get a 12 percent per year rate of return by owning the stocks of
other very similar fashion companies. If investors care only about rates of return, what should
happen to the share price of Rogue Designs? (Hint: This is an arbitrage situation.) LO3
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Answer: A yearly dividend of $2 on a $35 share of stock equals a 5.71% annual rate of
return ($2/$35 = .0571 = 5.71%).
6. Why is it reasonable to ignore diversifiable risk and care only about nondiversifiable risk?
What about investors who put all their money into only a single risky stock? Can they properly
ignore diversifiable risk? LO4
Answer: It is reasonable to ignore diversifiable risk if the investor’s portfolio is already
diversified. By investing in different types of assets, diversifiable (idiosyncratic) risk can
7. If we compare the betas of various investment opportunities, why do the assets that have higher
betas also have higher average expected rates of return? LO5
Answer: The assets with the highest betas are the most risky. Potential investors in
8. In this chapter we discussed short-term U.S. government bonds. But the U.S. government also
issues longer-term bonds with horizons of up to 30 years. Why do 20-year bonds issued by the
U.S. government have lower rates of return than 20-year bonds issued by corporations? And
which would you consider more likely, that longer-term U.S. government bonds have a higher
interest rate than short-term U.S. government bonds, or vice versa? Explain. LO5
Answer: U.S. government bonds have lower rates than bonds issued by corporations
because the risk of default is lower with the Federal government. Federal government
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9. What determines the vertical intercept of the Security Market Line (SML)? What determines
its slope? And what will happen to an asset’s price if it initially plots onto a point above the
SML? LO5
Answer: The vertical intercept is the risk-free interest rate (the rate on short-term U.S.
government bonds) that is determined by Federal Reserve monetary policy.
10. Suppose that the Federal Reserve thinks that a stock market bubble is occurring and wants to
reduce stock prices. What should it do to interest rates? LO5
Answer: If the Fed wants to decrease stock prices it should raise interest rates.
11. Consider another situation involving the SML. Suppose that the risk-free interest rate stays
the same, but that investors’ dislike of risk grows more intense. Given this change, will average
expected rates of return rise or fall? Next, compare what will happen to the rates of return on low-
risk and high-risk investments. Which will have a larger increase in average expected rates of
return, investments with high betas or investments with low betas? And will high-beta or low-
beta investments show larger percentage changes in their prices? LO5
Answer: Average expected rates of return will rise on all assets except those paying the
risk-free interest rates. Higher beta investments will see a greater increase in their rates
12. LAST WORD Why is it so hard for actively managed funds to generate higher rates of return
than passively managed index funds having similar levels of risk? Is there a simple way for an
actively managed fund to increase its average expected rate of return?
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Answer: Actively managed funds have difficulty generating higher rates of return than
passively managed index funds for two reasons. First, arbitrage causes rates of return to
PROBLEMS
1. Suppose that you invest $100 today in a risk-free investment and let the 4 percent annual
interest rate compound. Rounded to full dollars, what will be the value of your investment 4 years
from now? LO1
Feedback: Consider the following example. Suppose that you invest $100 today in a
risk-free investment and let the 4 percent annual interest rate compound. Rounded to full
dollars, what will be the value of your investment 4 years from now?
2. Suppose that you desire to get a lump sum payment of $100,000 two years from now. Rounded
to full dollars, how many current dollars will you have to invest today at a 10 percent interest to
accomplish your goal? LO1
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Feedback: Consider the following example. Suppose that you desire to get a lump sum
payment of $100,000 two years from now. Rounded to full dollars, how many current
dollars will you have to invest today at a 10 percent interest to accomplish your goal?
To answer this question we start at the end of the problem.
3. Suppose that a risk-free investment will make three future payments of $100 in one year, $100
in two years, and $100 in three years. If the Federal Reserve has set the risk-free interest rate at 8
percent, what is the proper current price of this investment? What is the price of this investment if
the Federal Reserve raises the risk-free interest rate to 10 percent? LO1
Feedback: Consider the following example. Suppose that a risk-free investment will
make three future payments of $100 in one year, $100 in two years, and $100 in three
years. If the Federal Reserve has set the risk-free interest rate at 8 percent, what is the
proper current price of this investment? What is the price of this investment if the Federal
Reserve raises the risk-free interest rate to 10 percent?
Here we need to use the concept of present value.
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4. Consider an asset that costs $120 today. You are going to hold it for 1 year and then sell it.
Suppose that there is a 25 percent chance that it will be worth $100 in a year, a 25 percent chance
that it will be worth $115 in a year, and a 50 percent chance that it will be worth $140 in a year.
What is its average expected rate of return? Next, figure out what the investment’s average
expected rate of return would be if its current price were $130 today. Does the increase in the
current price increase or decrease the asset’s average expected rate of return? At what price
would the asset have a zero average expected rate of return? LO3
Feedback: Consider the following example. Consider an asset that costs $120 today.
You are going to hold it for 1 year and then sell it. Suppose that there is a 25 percent
chance that it will be worth $100 in a year, a 25 percent chance that it will be worth $115
in a year, and a 50 percent chance that it will be worth $140 in a year. What is its average
expected rate of return? Next, figure out what the investment’s average expected rate of
return would be if its current price were $130 today. Does the increase in the current
price increase or decrease the asset’s average expected rate of return? At what price
would the asset have a zero average expected rate of return?
The first exercise is to calculate the expected payoff for this asset. To do this, multiply
the probability (decimal representation of percentage) for each payoff (state) by the actual
payoff.
5. Suppose initially that two assets, A and B, will each make a single guaranteed payment of $100
in 1 year. But asset A has a current price of $80 while asset B has a current price of $90. LO3
a. What are the rates of return of assets A and B at their current prices? Given these rates of
return, which asset should investors buy and which asset should they sell?
b. Assume that arbitrage continues until A and B have the same expected rate of return. When
arbitrage ends, will A and B have the same price?
Next, consider another pair of assets, C and D. Asset C will make a single payment of $150 in
one year while D will make a single payment of $200 in one year. Assume that the current price
of C is $120 and that the current price of D is $180.
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c. What are the rates of return of assets C and D at their current prices? Given these rates of
return, which asset should investors buy and which asset should they sell?
d. Assume that arbitrage continues until C and D have the same expected rate of return. When
arbitrage ends, will C and D have the same price?
Compare your answers to questions a through d before answering question e.
e. We know that arbitrage will equalize rates of return. Does it also guarantee to equalize prices?
In what situations will it equalize prices?
Feedback: Consider the following example. Suppose initially that two assets, A and B,
will each make a single guaranteed payment of $100 in 1 year. But asset A has a current
price of $80 while asset B has a current price of $90.
Part a:
What are the rates of the return of assets A and B at their current prices? Given these
rates of return, which asset should investors buy and which asset should they sell?
return on asset A = ($100-$80)/$80 =0.25 (25%)
Part b:
Assume that arbitrage continues until A and B have the same expected rate of return.
When arbitrage ends, will A and B have the same price?
Yes, the assets will have the same price because the payoff is the same ($100).
Part c:
c. What are the rates of the return of assets C and D at their current prices? Given these
rates of return, which asset should investors buy and which asset should they sell?
return on asset C = ($150-$120)/$120 =0.25 (25%)
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Part d:
d. Assume that arbitrage continues until C and D have the same expected rate of return.
When arbitrage ends, will C and D have the same price?
Part e:
Compare your answers to questions a through d before answering question e.
e. We know that arbitrage will equalize rates of return. Does it also guarantee to equalize
prices? In what situations will it equalize prices?
payoffs are the same do we observe equal prices.
6. Advanced Analysis Suppose that the equation for the SLM is Y = 0.05 + 0.04X, where Y is the
average expected rate of return, 0.05 is the vertical intercept, 0.04 is the slope, and X is the risk
level as measured by beta. What is the risk-free interest rate for this SML? What is the average
expected rate of return at a beta of 1.5? What is the value of beta at an average expected rate of
return is 7 percent? LO5
equation for the SLM is Y = 0.05 + 0.04X, where Y is the average expected rate of
return, 0.05 is the vertical intercept, 0.04 is the slope, and X is the risk level as measured
by beta. What is the risk-free interest rate for this SML? What is the average expected
rate of return at a beta of 1.5? What is the value of beta at an average expected rate of
return is 7 percent?
The risk free is the intercept of SLM line, which is 0.05. Thus, the risk free rate is 5%.
(This represents a beta of zero, which implies no risk).