ANSWERS TO END-OF-CHAPTER QUESTIONS
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.
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 ½ 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. Interest rates are more competitive, making it easier for small borrowers, and borrowers in rural areas, to obtain lower cost loans.
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.
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 that 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.
Short-term interest 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 interest 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.
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.
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.
A significant increase in productivity would raise the rate of return on producers’ investment, thus causing the investment curve (see Figure 4-2 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.
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.
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 in-crease. 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.
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 Chapter 5 (with respect to risk) and Chapters 7 and 8 (with respect to price).
A trade deficit occurs when the U.S. buys more than it sells. In other words, a trade deficit occurs when the U.S. imports more than it exports. When trade deficits occur, they must be financed, and the main source of financing is debt. Therefore, the larger the U.S. trade deficit, the more the U.S. must borrow, and as the U.S. increases its borrowing, this drives up interest rates.
The two leading stock markets today are the New York Stock Exchange and the Nasdaq stock market.
The physical location exchanges are tangible physical entities. Each of the larger ones occupies its own building, has a limited number of members, and has an elected governing body. A dealer market is defined to include all facilities that are needed to conduct security transactions not made on the physical location exchanges. These facilities include (1) the relatively few dealers who hold inventories of these securities and who are said to “make a market” in these securities; (2) the thousands of brokers who act as agents in bringing the dealers together with investors; and (3) the computers, terminals, and electronic networks that provide a communication link between dealers and brokers.
SOLUTIONS TO END-OF-CHAPTER PROBLEMS
k* = 3%; I1 = 2%; I2 = 4%; I3 = 4%; MRP = 0; kT2 = ?; kT3 = ?
Since these are Treasury securities, DRP = LP = 0.
kT2 = k* + IP2. IP2 = (2% + 4%)/2 = 3%. kT2 = 3% + 3% = 6%.
kT3 = k* + IP3. IP3 = (2% + 4% + 4%)/3 = 3.33%. kT3 = 3% + 3.33% = 6.33%.
4-2 kT10 = 6%; kC10 = 8%; LP = 0.5%; DRP = ?
kT10 = 6% = k* + IP + MRP; DRP = LP = 0.
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.
kC10 = 8% = k* + IP + MRP + 0.5% + DRP. But we know from above that k* + IP + MRP = 6%; therefore,
kT2 = k* + IP + MRP = 6.2% kT2 = 3% + 3% + MRP = 6.2% MRP = 0.2%.
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%.
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.
kT7 = 0.03 + 0.035 + 0.003 = 0.068 = 6.8%.
Solving for k1 in Year 2, 1k1, we obtain
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 percent. Therefore, all of our results are consistent.
Alternative solution: Solve for the inflation rates in Year 1 and Year 2 first:
Then solve for the yield on the one-year bond in the second year: Year 2: k1 = 1% + 5% = 6%.
k* = 2%; MRP = 0%; k1 = 5%; k2 = 7%; 1k1 = ?
1k1 represents the one-year rate on a bond one year from now (Year 2).
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 security’s life.
But here IP is the only premium, so kt = k* + IPt.
We know that I1 = IP1 = 3% and k* = 2%. Therefore,
kT1 = 2% + 3% = 5%. kT3 = k1 + 2% = 5% + 2% = 7%. But,
We also know that It = Constant after t = 1.
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%.
8.3% = 2.5% + (2.8% × 4 + 3.75% × 4)/8 + 0.0% + DRP8 + 0.75% 8.3% = 2.5% + 3.275% + 0.0% + DRP8 + 0.75% 8.3% = 6.525% + DRP8 DRP8 = 1.775%.
T-bill rate = k* + IP 5.5% = k* + 3.25% k* = 2.25%.
4-12 We’re given all the components to determine the yield on the Cartwright bonds except the
default risk premium (DRP) and MRP. Calculate the MRP as 0.1%(5 - 1) = 0.4%. Now, we can solve for the DRP as follows: 7.75% = 2.3% + 2.5% + 0.4% + 1.0% + DRP, or DRP = 1.55%.
4-13 First, calculate the inflation premiums for the next three and five years, respectively. They
are IP3 = (2.5% + 3.2% + 3.6%)/3 = 3.1% and IP5 = (2.5% + 3.2% + 3.6% + 3.6% + 3.6%)/5 = 3.3%. The real risk-free rate is given as 2.75%. Since the default and liquidity premiums are zero on Treasury bonds, we can now solve for the default risk premium. Thus, 6.25% = 2.75% + 3.1% + MRP3, or MRP3 = 0.4%. Similarly, 6.8% = 2.75% + 3.3% + MRP5, or MRP5 = 0.75%. Thus, MRP5 – MRP3 = 0.75% - 0.40% = 0.35%.
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:
Thus, the yield curve would be as follows:
b. The interest rate on the Exxon Mobil bonds has the same components as the Treasury
securities, except that the Exxon Mobil bonds have default risk, so a default risk premium must be included. Therefore,
For a strong company such as Exxon Mobil, 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 Mobil 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 Mobil bonds. The return should equal 6.3% + 1% = 7.3%.
c. Exelon bonds would have significantly more default risk than either Treasury
securities or Exxon Mobil 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 Exelon bonds and 2.0 percentage points on the 20-year bonds. The 20-year return should equal 6.3% + 2% = 8.3%.
a. The average rate of inflation for the 5-year period is calculated as:
inflation = (0.13 + 0.09 + 0.07 + 0.06 + 0.06)/5 = 8.20%.
b. k = k* + IPAvg. = 2% + 8.2% = 10.20%.
Year Inflation Inflation k* Premium Rates
1 13% 13.0% 2% 0.1% 15.1% 2 9 11.0 2 0.2 13.2 3 7 9.7 2 0.3 12.0 5 6 8.2 2 0.5 10.7 . . . . . . . . . . . . . . . . . . 10 6 7.1 2 1.0 10.1 20 6 6.6 2 2.0 10.6
d. The “normal” yield curve is upward sloping because, in “normal” times, inflation is
not expected to trend either up or down, so IP is the same for debt of all maturities, but the MRP increases with years, so the yield curve slopes up. During a recession, the yield curve typically slopes up especially steeply, because inflation and consequently short-term interest rates are currently low, yet people expect inflation and interest rates to rise as the economy comes out of the recession.
e. If inflation rates are expected to be constant, then the expectations theory holds that
the yield curve should be horizontal. However, in this event it is likely that maturity risk premiums would be applied to long-term bonds because of the greater risks of holding long-term rather than short-term bonds:
If maturity risk premiums were added to the yield curve in Part e above, then
the yield curve would be more nearly normal; that is, the long-term end of the curve would be raised. (The yield curve shown in this answer is upward sloping; the yield curve shown in Part c is downward sloping.)
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