Chapter 5 The Financial Environment: Markets, Institutions ...fnccwh/pdf/05fm9.pdf · The Financial...

Harcourt, Inc. items and derived items copyright 2002 by Harcourt, Inc. Answers and Solutions: 5 - 1

Chapter 5 The Financial Environment:

Markets, Institutions, and Interest Rates ANSWERS TO SELECTED END-OF-CHAPTER QUESTIONS

5-1 a. A money market is a financial market for debt securities with

maturities of less than one year (short-term). The New York money market is the worlds largest. Capital markets are the financial markets for long-term debt and corporate stocks. The New York Stock Exchange is an example of a capital market.

b. Primary markets are the markets in which newly issued securities are

sold for the first time. Secondary markets are where securities are resold after initial issue in the primary market. The New York Stock Exchange is a secondary market.

c. In private markets, transactions are worked out directly between two

parties and structured in any manner that appeals to them. Bank loans and private placements of debt with insurance companies are examples of private market transactions. In public markets, standardized contracts are traded on organized exchanges. Securities that are issued in public markets, such as common stock and corporate bonds, are ultimately held by a large number of individuals. Private market securities are more tailor-made but less liquid, whereas public market securities are more liquid but subject to greater standardization.

d. Derivatives are claims whose value depends on what happens to the value

of some other asset. Futures and options are two important types of derivatives, and their values depend on what happens to the prices of other assets, say IBM stock, Japanese yen, or pork bellies. Therefore, the value of a derivative security is derived from the value of an underlying real asset.

e. An investment banker is a middleman between businesses and savers.

Investment banking houses assist in the design of corporate securities and then sell them to savers (investors) in the primary markets. Financial service corporations offer a wide range of financial services such as brokerage operations, insurance, and commercial banking.

f. A financial intermediary buys securities with funds that it obtains by

issuing its own securities. An example is a common stock mutual fund that buys common stocks with funds obtained by issuing shares in the mutual fund.

g. A mutual fund is a corporation that sells shares in the fund and uses

the proceeds to buy stocks, long-term bonds, or short-term debt instruments. The resulting dividends, interest, and capital gains are

Answers and Solutions: 5 - 2 Harcourt, Inc. items and derived items copyright 2002 by Harcourt, Inc.

distributed to the funds shareholders after the deduction of operating expenses. Different funds are designed to meet different objectives. Money market funds are mutual funds which invest in short-term debt instruments and offer their shareholders check writing privileges; thus, they are essentially interest-bearing checking accounts.

h. Organized security exchanges, such as the New York Stock Exchange,

facilitate communication between buyers and sellers of securities. Each organized exchange is a physical entity and is governed by an elected board of governors. The over-the-counter market consists of all the facilities that provide for security transactions not conducted on the organized exchanges. These facilities are, basically, the relatively few dealers who hold inventories of over-the-counter securities, the thousands of brokers who act as agents in bringing these dealers together with investors, and the communications network that links the dealers and agents.

I. Production opportunities are the returns available within an economy

from investment in productive assets. The higher the production opportunities, the more producers would be willing to pay for required capital. Consumption time preferences refer to the preferred pattern of consumption. Consumers time preferences for consumption establish how much consumption they are willing to defer, and hence save, at different levels of interest.

j. The real risk-free rate is that interest rate which equalizes the

aggregate supply of, and demand for, riskless securities in an economy with zero inflation. The real risk-free rate could also be called the pure rate of interest since it is the rate of interest that would exist on very short-term, default-free U.S. Treasury securities if the expected rate of inflation were zero. It has been estimated that this rate of interest, denoted by k*, has fluctuated in recent years in the United States in the range of 2 to 4 percent. The nominal risk-free rate of interest, denoted by kRF, is the real risk-free rate plus a premium for expected inflation. The short-term nominal risk-free rate is usually approximated by the U.S. Treasury bill rate, while the long-term nominal risk-free rate is approximated by the rate on U.S. Treasury bonds. Note that while T-bonds are free of default and liquidity risks, they are subject to risks due to changes in the general level of interest rates.

k. The inflation premium is the premium added to the real risk-free rate

of interest to compensate for the expected loss of purchasing power. The inflation premium is the average rate of inflation expected over the life of the security.

l. Default risk is the risk that a borrower will not pay the interest

and/or principal on a loan as they become due. Thus, a default risk premium (DRP) is added to the real risk-free rate to compensate investors for bearing default risk.


m. Liquidity refers to a firms cash and marketable securities position, and to its ability to meet maturing obligations. A liquid asset is any asset that can be quickly sold and converted to cash at its fair value. Active markets provide liquidity. A liquidity premium is added to the real risk-free rate of interest, in addition to other premiums, if a security is not liquid.

n. Interest rate risk arises from the fact that bond prices decline when

interest rates rise. Under these circumstances, selling a bond prior to maturity will result in a capital loss, and the longer the term to maturity, the larger the loss. Thus, a maturity risk premium must be added to the real risk-free rate of interest to compensate for interest rate risk.

o. Reinvestment rate risk occurs when a short-term debt security must be

rolled over. If interest rates have fallen, the reinvestment of principal will be at a lower rate, with correspondingly lower interest payments and ending value. Note that long-term debt securities also have some reinvestment rate risk because their interest payments have to be reinvested at prevailing rates.

p. The term structure of interest rates is the relationship between yield

to maturity and term to maturity for bonds of a single risk class. The yield curve is the curve that results when yield to maturity is plotted on the Y axis with term to maturity on the X axis.

q. When the yield curve slopes upward, it is said to be normal, because

it is like this most of the time. Conversely, a downward-sloping yield curve is termed abnormal or inverted.

r. The expectations theory states that the slope of the yield curve

depends on expectations about future inflation rates and interest rates. Thus, if the annual rate of inflation and future interest rates are expected to increase, the yield curve will be upward sloping, whereas the curve will be downward sloping if the annual rates are expected to decrease.

s. A foreign trade deficit occurs when businesses and individuals in the

U. S. import more goods from foreign countries than are exported. Trade deficits must be financed, and the main source of financing is debt. Therefore, as the trade deficit increases, the debt financing increases, driving up interest rates. U. S. interest rates must be competitive with foreign interest rates; if the Federal Reserve attempts to set interest rates lower than foreign rates, foreigners will sell U.S. bonds, decreasing bond prices, resulting in higher U. S. rates. Thus, if the trade deficit is large relative to the size of the overall economy, it may hinder the Feds ability to combat a recession by lowering interest rates.

5-2 Financial intermediaries are business organizations that receive funds in

one form and repackage them for the use of those who need funds. Through


financial intermediation, resources are allocated more effectively, and the real output of the economy is thereby increased.

5-3 Regional mortgage rate differentials do exist, depending on supply/demand

conditions in the different regions. However, relatively high rates in one region would attract capital from other regions, and the end result would be a differential that was just sufficient to cover the costs of effecting the transfer (perhaps of one percentage point). Differentials are more likely in the residential mortgage market than the business loan market, and not at all likely for the large, nationwide firms, which will do their borrowing in the lowest-cost money centers and thereby quickly equalize rates for large corporate loans. If Congress were to permit nationwide branching, interest rates would become more competitive, making it easier for small borrowers, and borrowers in rural areas, to obtain lower cost loans.

5-4 It would be difficult for firms to raise capital. Thus, capital

investment would slow down, unemployment would rise, the output of goods and services would fall, and, in general, our standard of living would decline.

5-5 The prices of goods and services must cover their costs. Costs include

labor, materials, and capital. Capital costs to a borrower include a return to the saver who supplied the capital, plus a mark-up (called a spread) for the financial intermediary which brings the saver and the borrower together. The more efficient the financial system, the lower the costs of intermediation, the lower the costs to the borrower, and, hence, the lower the prices of goods and services to consumers.

5-6 Short-term rates are more volatile because (1) the Fed operates mainly in

the short-term sector, hence Federal Reserve intervention has its major effect here, and (2) long-term rates reflect the average expected inflation rate over the next 20 to 30 years, and this average does not change as radically as year-to-year expectations.

5-7 Interest rates will fall as the recession takes hold because (1) business

borrowings will decrease and (2) the Fed will increase the money supply to stimulate the economy. Thus, it would be better to borrow short-term now, and then to convert to long-term when rates have reached a cyclical low. Note, though, that this answer requires interest rate forecasting, which is extremely difficult to do with better than 50 percent accuracy.

5-8 a. If transfers between the two markets are costly, interest rates would

be different in the two areas. Area Y, with the relatively young population, would have less in savings accumulation and stronger loan demand. Area O, with the relatively old population, would have more savings accumulation and weaker loan demand as the members of the older population have already purchased their houses and are less consumption oriented. Thus, supply/demand equilibrium would be at a higher rate of interest in Area Y.


b. Yes. Nationwide branching, and so forth, would reduce the cost of financial transfers between the areas. Thus, funds would flow from Area O with excess relative supply to Area Y with excess relative demand. This flow would increase the interest rate in Area O and decrease the interest rate in Y until the rates were roughly equal, the difference being the transfer cost.

5-9 A significant increase in productivity would raise the rate of return on

producers investment, thus causing the investment curve (see Figure 5-2 in the textbook) to shift to the right. This would increase the amount of savings and investment in the economy, thus causing all interest rates to rise.

5-10 a. The immediate effect on the yield curve would be to lower interest

rates in the short-term end of the market, since the Fed deals primarily in that market segment. However, people would expect higher future inflation, which would raise long-term rates. The result would be a much steeper yield curve.

b. If the policy is maintained, the expanded money supply will result in

increased rates of inflation and increased inflationary expectations. This will cause investors to increase the inflation premium on all debt securities, and the entire yield curve would rise; that is, all rates would be higher.

5-11 a. S&Ls would have a higher level of net income with a normal yield

curve. In this situation their liabilities (deposits), which are short-term, would have a lower cost than the returns being generated by their assets (mortgages), which are long-term. Thus they would have a positive spread.

b. It depends on the situation. A sharp increase in inflation would

increase interest rates along the entire yield curve. If the increase were large, short-term interest rates might be boosted above the long-term interest rates that prevailed prior to the inflation increase. Then, since the bulk of the fixed-rate mortgages were initiated when interest rates were lower, the deposits (liabilities) of the S&Ls would cost more than the return being provided on the assets. If this situation continued for any length of time, the equity (reserves) of the S&Ls would be drained to the point that only a bailout would prevent bankruptcy. This has indeed happened in the United States. Thus, in this situation the S&L industry would be better off selling their mortgages to federal agencies and collecting servicing fees rather than holding the mortgages they originated.

5-12 Treasury bonds, along with all other bonds, are available to investors as

an alternative investment to common stocks. An increase in the return on Treasury bonds would increase the appeal of these bonds relative to common stocks, and some investors would sell their stocks to buy T-bonds. This would cause stock prices, in general, to fall. Another way to view this is that a relatively riskless investment (T-bonds) has increased its return by 7 percentage points. The return demanded on riskier investments


(stocks) would also increase, thus driving down stock prices. The exact relationship will be discussed in Chapters 5 (with respect to risk) and 8 and 9 (with respect to price).


SOLUTIONS TO END-OF-CHAPTER PROBLEMS 5-1 k* = 3%; I1 = 2%; I2 = 4%; I3 = 4%; MRP = 0; kT-2 = ?; kT-3 = ?

k = k* + IP + DRP + LP + MRP.

Since these are Treasury securities, DRP = LP = 0.

kT-2 = k* + IP2 IP2 = (2% + 4%)/2 = 3% kT-2 = 3% + 3% = 6%.

kT-3 = k* + IP3 IP3 = (2% + 4% + 4%)/3 = 3.33% kT-3 = 3% + 3.33% = 6.33%.

5-2 kT-10 = 6%; kC-10 = 8%; LP = 0.5%; DRP = ?

k = k* + IP + DRP + LP + MRP.

kT-10 = 6% = k* + IP + MRP; DRP = LP = 0.

kC-10 = 8% = k* + IP + DRP + 0.5% + MRP.

Because both bonds are 10-year bonds the inflation premium and maturity risk premium on both bonds are equal. The only difference between them is the liquidity and default risk premiums.

kC-10 = 8% = k* + IP + MRP + 0.5% + DRP. But we know from above that k* + IP + MRP = 6%; therefore,

kC-10 = 8% = 6% + 0.5% + DRP 1.5% = DRP.

5-3 kT-1, 1 = 5%; kT-1, 2 = 6%; kT-2 = ?

kT-2 = 2

6% + 5% = 5.5%.

5-4 k* = 3%; IP = 3%; kT-2 = 6.2%; MRP2 = ?

kT-2 = k* + IP + MRP = 6.2% kT-2 = 3% + 3% + MRP = 6.2% MRP = 0.2%.


5-5 Let x equal the yield on 1-year securities 1 year from now:

(5.6% + x)/2 = 6% 5.6% + x = 12% x = 6.4%.

5-6 Let x equal the yield on 2-year securities 4 years from now:

7.5% = [(4)(7%) + 2x]/6 0.45 = 0.28 + 2x x = 0.085 or 8.5%.

5-7 k = k* + IP + MRP + DRP + LP.

k* = 0.03. IP = [0.03 + 0.04 + (5)(0.035)]/7 = 0.035. MRP = 0.0005(6) = 0.003. DRP = 0. LP = 0.

k = 0.03 + 0.035 + 0.003 = 0.068 = 6.8%.

5-8 a. k1 = 3%, and

k2 = 2

2 Year in k + 3% 1 = 4.5%,

Solving for k1 in Year 2, we obtain

k1 in Year 2 = (4.5% x 2) - 3% = 6%.

b. For riskless bonds under the expectations theory, the interest rate for

a bond of any maturity is kn = k* + average inflation over n years. If k* = 1%, we can solve for IPn:

Year 1: k1 = 1% + I1 = 3%; I1 = expected inflation = 3% - 1% = 2%.

Year 2: k1 = 1% + I2 = 6%; I2 = expected inflation = 6% - 1% = 5%.

Note also that the average inflation rate is (2% + 5%)/2 = 3.5%,

which, when added to k* = 1%, produces the yield on a 2-year bond, 4.5%. Therefore, all of our results are consistent.

Alternative solution: Solve for the inflation rates in Year 1 and Year 2 first:

kRF = k* + IP


Year 1: 3% = 1% + IP1; IP1 = 2%, thus I1 = 2%.

Year 2: 4.5% = 1% + IP2; IP2 = 3.5%.

IP2 = (I1 + I2)/2 3.5% = (2% + I2)/2 I2 = 5%.

Then solve for the yield on the one-year bond in the second year:

Year 2: k1 = 1% + 5% = 6%.

5-9 k* = 2%; MRP = 0%.

k1 = 5%; k2 = 7%.

k2 = 2

2 Year in k + k 11 ,

7% = 2

2 Year in k + 5% 1 ,

9% = k1 in Year 2.

k1 in Year 2 = k* + I2,

9% = 2% + I2 7% = I2.

The average interest rate during the 2-year period differs from the 1-year interest rate expected for Year 2 because of the inflation rate reflected in the two interest rates. The inflation rate reflected in the interest rate on any security is the average rate of inflation expected over the securitys life.

5-10 First, note that we will use the equation kt = 3% + IPt + MRPt. We have

the data needed to find the IPs:

IP5 = 5

4% + 4% + 4% + 5% + 8% =

5

25% = 5%.

IP2 = 2

5% + 8% = 6.5%.

Now we can substitute into the equation:

k2 = 3% + 6.5% + MRP2 = 10%. k5 = 3% + 5% + MRP5 = 10%.


Now we can solve for the MRPs, and find the difference:

MRP5 = 10% - 8% = 2%. MRP2 = 10% - 9.5% = 0.5%.

Difference = (2% - 0.5%) = 1.5%. 5-11 Basic relevant equations:

kt = k* + IPt + DRPt + MRPt + LPt.

But here IP is the only premium, so kt = k* + IPt.

IPt = Avg. inflation = (I1 + I2 + ...)/N.

We know that I1 = IP1 = 3% and k* = 2%. Therefore,

k1 = 2% + 3% = 5%. k3 = k1 + 2% = 5% + 2% = 7%. But,

k3 = k* + IP3 = 2% + IP3 = 7%, so

IP3 = 7% - 2% = 5%.

We also know that It = Constant after t = 1.

We can set up this table:

k* I Avg. I = IPt k = k* + IPt 1 2 3 3%/1 = 3% 5% 2 2 I (3% + I)/2 = IP2 3 2 I (3% + I + I)/3 = IP3 k3 = 7%, so IP3 = 7% - 2% = 5%.

Avg. I = IP3 = (3% + 2I)/3 = 5% 2I = 12% I = 6%.

5-12 a. Real

Years to Risk-Free Maturity Rate (k*) IP** MRP kT = k* + IP + MRP 1 2% 7.00% 0.2% 9.20% 2 2 6.00 0.4 8.40 3 2 5.00 0.6 7.60 4 2 4.50 0.8 7.30 5 2 4.20 1.0 7.20 10 2 3.60 1.0 6.60 20 2 3.30 1.0 6.30


**The computation of the inflation premium is as follows:

Expected Average Year Inflation Expected Inflation 1 7% 7.00% 2 5 6.00 3 3 5.00 4 3 4.50 5 3 4.20 10 3 3.60 20 3 3.30

For example, the calculation for 3 years is as follows:

5.00%. = 3

3% + 5% + 7%

Thus, the yield curve would be as follows:

b. The interest rate on the Exxon bonds has the same components as the

Treasury securities, except that the Exxon bonds have default risk, so a default risk premium must be included. Therefore,

kExxon = k* + IP + MRP + DRP.

(%)11.0

10.5

10.0

9.5

9.0

8.5

8.0

7.5

7.0

0 2 4 6 8 10 12 14 16 18 20

Interest Rate

6.5

LILCO

Exxon

T-bonds

Years to Maturity


For a strong company such as Exxon, the default risk premium is virtually zero for short-term bonds. However, as time to maturity increases, the probability of default, although still small, is suffi-cient to warrant a default premium. Thus, the yield risk curve for the Exxon bonds will rise above the yield curve for the Treasury securities. In the graph, the default risk premium was assumed to be 1.0 percentage point on the 20-year Exxon bonds. The return should equal 6.3% + 1% = 7.3%.

c. LILCO bonds would have significantly more default risk than either

Treasury securities or Exxon bonds, and the risk of default would increase over time due to possible financial deterioration. In this example, the default risk premium was assumed to be 1.0 percentage point on the 1-year LILCO bonds and 2.0 percentage points on the 20-year bonds. The 20-year return should equal 6.3% + 2% = 8.3%.

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