# Chapter 6: Interest Rates

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question
Due to recent political and economic events, general prices of goods and services are expected to increase significantly over the next five years. You were about to purchase a five-year bond. You now require a higher return on the bond than you did before you found out about these expected price increases. Determine which of these fundamental factors is affecting the cost of money in the scenario described: Risk Inflation Time preferences for consumption
Inflation Inflation is the amount by which prices increase over time. You are ensuring that you will be compensated for the expected inflation over the next five years when purchasing this five-year bond. If you are not adequately compensated for future inflation, you may be better off using your money for current consumption.
question
A friend comes to you and asks you to invest in his business instead of investing in Treasury bonds. You think he has a good business model, so you tell him you are willing to invest as long as the expected return on the investment is at least four times the return you would have received on the Treasury bonds. Determine which of these fundamental factors is affecting the cost of money in the scenario described: Inflation Time preferences for consumption Risk
Risk You were already planning on investing money and saving for future consumption. Your debate was how to invest your money. Investing in your friend's business is much riskier than investing in Treasury bonds, so you require a greater expected return on the investment to compensate for the additional risk.
question
Which tend to be more volatile, short- or long-term interest rates?
Short-term interest rates Short-term interest rates reflect expectations of short-term inflation, but they also respond to current economic conditions; long-term interest rates reflect long-run expectations of inflation. As a result, long-term interest rates tend to be smoother than short-term rates. Short-term interest rates are more volatile because they respond to short-term shocks to the economy.
question
If the inflation rate was 3.40% and the nominal interest rate was 5.60% over the last year, what was the real rate of interest over the last year? Disregard cross-product terms; that is, if averaging is required, use the arithmetic average. Round intermediate calculations to four decimal places. 2.53% 1.87% 2.20% 2.75%
2.20% The nominal interest rate consists of the real rate of interest and inflation. In this case, the nominal interest rate is 5.60%, and the inflation rate is 3.40%. So the real rate of interest is 5.60% - 3.40% = 2.20%. The problem's instructions told you to ignore the cross-product term and just use arithmetic averages, but be aware that economists calculate this slightly differently (as you may recall from your economics courses). If you consider the cross-product terms and use geometric average rates, you would calculate the following: (1+ Real Rate)(1 + Inflation Rate) = (1 + Nominal Rate) (1+ Real Rate)(1 + 0.0340) = (1 + 0.056) Real Rate = 2.13% The difference between the two methods is usually fairly minor, especially if expected inflation is relatively low. But it's good to be aware that this calculation can be done in alternate ways. In many foreign countries where inflation is large, this difference can be quite substantial.
question
If the inflation rate was 3.60% and the nominal interest rate was 4.20% over the last year, what was the real rate of interest over the last year? Disregard cross-product terms; that is, if averaging is required, use the arithmetic average. Round intermediate calculations to four decimal places. 0.69% 0.75% 0.51% 0.60%
0.60% The nominal interest rate consists of the real rate of interest and inflation. In this case, the nominal interest rate is 4.20%, and the inflation rate is 3.60%. So the real rate of interest is 4.20% - 3.60% = 0.60%. The problem's instructions told you to ignore the cross-product term and just use arithmetic averages, but be aware that economists calculate this slightly differently (as you may recall from your economics courses). If you consider the cross-product terms and use geometric average rates, you would calculate the following: (1+ Real Rate)(1 + Inflation Rate)=(1 + Nominal Rate) (1+ Real Rate)(1 + 0.0360)=(1 + 0.042) Real Rate=0.58% The difference between the two methods is usually fairly minor, especially if expected inflation is relatively low. But it's good to be aware that this calculation can be done in alternate ways. In many foreign countries where inflation is large, this difference can be quite substantial.
question
Based on your understanding of the determinants of interest rates, if everything else remains the same, which of the following will be true? A BBB-rated bond has a lower default risk premium as compared to an AAA-rated bond. An AAA-rated bond has less default risk than a BB-rated bond.
An AAA-rated bond has less default risk than a BB-rated bond. Bond ratings are assigned considering several factors, including the ability of the issuing entity to pay back its investors. A bond with an AAA-rating means that the risk of default is less, thus it has a lower default risk premium. Rating agencies, such as Standard & Poor's and Moody's, assign ratings to bonds based on several factors, including the ability of the issuing entity to pay back its investors—that is, the risk of default. The higher the risk, the higher the return will be. An AAA-rated bond has less default risk than a BBB-rated bond. Thus, a BBB-rated bond will have a higher default risk premium than an AAA-rated bond.
question
There are three factors that can affect the shape of the Treasury yield curve (r*t, IPt, and MRPt) and five factors that can affect the shape of the corporate yield curve (r*t, IPt, MRPt, DRPt, and LPt). The yield curve reflects the aggregation of the impacts from these factors. Suppose the real risk-free rate and inflation rate are expected to remain at their current levels throughout the foreseeable future. Consider all factors that affect the yield curve. Then identify which of the following shapes that the US Treasury yield curve can take. Check all that apply. Downward-sloping yield curve Upward-sloping yield curve Inverted yield curve
Upward-sloping yield curve The only factors that affect the US Treasury yield curve are the real risk-free rate, inflation premium, and maturity risk premium. The yield on a US Treasury bond is calculated using the following equation: T-Bond Yield = r*t+IPt+MRPt According to the question, the real risk-free rate and the inflation rate are expected to remain constant. So, if there is no maturity risk premium (MRP = 0), the US Treasury yield curve will be flat. If the maturity risk premium is positive, it should increase as maturity increases. In other words, securities with longer maturities should have higher maturity risk premiums. Therefore, if the maturity risk premium is positive, the US Treasury yield curve is upward sloping. The yield curve cannot be downward sloping or inverted, because the maturity risk premium cannot decrease with increasing maturity.
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True or False: If inflation is expected to decrease in the future and the real rate is expected to remain steady, then the Treasury yield curve is downward sloping. (Assume MRP = 0.)
True
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True or False: The default risk on Walmart's short-term debt will be higher than the default risk on its long-term debt.
False
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True or False: The yield curve for a BBB-rated corporate bond is expected to be above the US Treasury bond yield curve.
True
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True or False: All else equal, the yield on new bonds issued by a leveraged firm will be less than the yield on the new bonds issued by an unleveraged firm.
False
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True or False: The yield curve for an AA-rated corporate bond is expected to be above the US Treasury bond yield curve.
True
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True or False: Yield curves of highly liquid assets will be lower than yield curves of relatively illiquid assets.
True
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Based on an upward-sloping normal yield curve as shown, which of the following statements is correct? -There is a positive maturity risk premium. -If the pure expectations theory is correct, future short-term rates are expected to be higher than current short-term rates. -Inflation must be expected to increase in the future. -Pure expectations theory must be correct.
If the pure expectations theory is correct, future short-term rates are expected to be higher than current short-term rates. The pure expectations theory of interest rates merely states that you can infer expected future short-term rates by comparing spot short- and long-term rates. Pure expectations theory does not depend on the yield curve being either upward or downward sloping. An upward-sloping yield curve can be an indication of expected increases in inflation. However, it also can be an indication of a positive maturity risk premium. For example, if inflation and the real risk-free rate were constant, a positive maturity risk premium would likely increase over time, which would lead to an upward-sloping yield curve. An upward-sloping yield curve could indicate a positive maturity risk premium, but it also could indicate increased inflation expectations. If there is no maturity risk premium, expectations about future short-term interest rates determine the yield curve's shape. The upward slope indicates that future short-term rates are expected to be greater than current short-term rates.
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True or False: The pure expectations theory assumes that investors do not consider long-term bonds to be riskier than short-term bonds.
True The pure expectations theory assumes that the maturity risk premium is zero (MRP = 0). This suggests that investing consecutively in short-term bonds will provide the same return as a long-term bond. This means that investing in a one-year bond and then in another one-year bond in one year will give the same return as investing in a two-year bond.
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The yield on a one-year Treasury security is 5.8400%, and the two-year Treasury security has a 7.0080% yield. Assuming that the pure expectations theory is correct, what is the market's estimate of the one-year Treasury rate one year from now? (Note: Do not round your intermediate calculations.) 8.1889% 9.3353% 6.9606% 10.3999%
8.1889% If the pure expectations theory is correct, there is no maturity risk premium, and future short-term rates may be inferred from spot short-term rates and longer-term rates. Calculate the implied one-year-forward rate one year from now as follows: (1 + 1-Year Rate)(1 + 1-Year Rate in 1 Year) = (1 + 2-Year Rate)22 Solve as follows: (1+0.0584)(1+X)1+0.05841+X = = (1+0.07008)21+0.0700821+X1+X = = (1.07008)2/1.05841.070082/1.05841+X1+X = = 1.145071/1.05841.145071/1.0584XX = = 1.081889−11.081889−1 = = 0.081889, or 8.1889%0.081889, or 8.1889%
question
Recall that on a one-year Treasury security the yield is 5.8400% and 7.0080% on a two-year Treasury security. Suppose the one-year security does not have a maturity risk premium, but the two-year security does and it is 0.3%. What is the market's estimate of the one-year Treasury rate one year from now? (Note: Do not round your intermediate calculations.) 6.4456% 7.5831% 9.6305% 8.6447%
7.5831% The pure expectations theory does not hold in this case. The two-year Treasury security requires a maturity risk premium. If you want to calculate the implied one-year Treasury rate one year from now, adjust the two-year rate by subtracting the maturity risk premium (MRP) as follows: (1 + 1-Year Rate)(1 + 1-Year Rate in 1 Year) = (1 + 2-Year Rate - MRP)22 Solve as follows: (1+0.0584)(1+X)1+0.05841+X = = (1+0.07008−0.003)21+0.07008−0.00321 + X1 + X = = (1.06708)2/1.05841.067082/1.05841 + X1 + X = = 1.13866/1.05841.13866/1.0584XX = = 1.075831−11.075831−1 = = 0.075831, or 7.5831%
question
Suppose the yield on a two-year Treasury security is 5.83%, and the yield on a five-year Treasury security is 6.20%. Assuming that the pure expectations theory is correct, what is the market's estimate of the three-year Treasury rate two years from now? (Note: Do not round your intermediate calculations.) 6.45% 6.53% 6.69% 5.46%
6.45% Using an approach similar to the previous problem, calculate the implied three-year forward rate two years from now. In this case, the five-year rate is the geometric average of the two-year rate and the three-year rate two years from now. (1 + 2-Year Rate)22(1 + 3-Year Rate in 2 Years)33 = (1 + 5-Year Rate)55 Solve as follows: (1+5-Year Rate)51+5-Year Rate5 = = (1 + 2-Year Rate)2(1 + 3-Year Rate in 2 Years)3(1 + 2-Year Rate)2(1 + 3-Year Rate in 2 Years)3(1+0.0620)51+0.06205 = = (1+0.0583)2(1+X)31+0.058321+X31.062051.06205 = = (1.0583)2(1+X)31.058321+X31.35091.3509 = = (1.1200)(1 + X)3(1.1200)(1 + X)3(1+X)31+X3 = = 1.3509/1.12001.3509/1.1200(1+X)31+X3 = = 1.20621.20621+X1+X = = 1.20621/31.20621/31+X1+X = = 1.06451.0645XX = = 0.0645, or 6.45%
question
True or False: The larger the federal deficit, other things held constant, the higher are interest rates.
True When the federal government spends more money than it takes in, it runs a deficit. The deficit must be covered by additional borrowing (selling more Treasury bonds) or by printing money. If the government borrows additional money, it will increase the demand for funds and thus push up interest rates. If the government prints money, there will be increased inflation, which will also increase interest rates.
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True or False: Actions that lower short-term interest rates will always lower long-term interest rates.
False During a recession, short-term rates commonly decline more than long-term rates. This occurs because the Fed operates mainly in the short-term and long-term rates reflect the average expected inflation rate over the next 20 to 30 years.
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True or False: During recessions, short-term interest rates decline more sharply than long-term interest rates.
True In the United States, the Federal Reserve Board controls the money supply. The money supply has a significant effect on the level of economic activity, inflation, and interest rates.
question
True or False: The Federal Reserve Board has a significant influence over the level of economic activity, inflation, interest rates in the United States.
True Actions that lower short-term interest rates will not necessarily lower long-term rates, because long-term rates are not affected as much as short-term rates by the Fed's intervention.
question
Which of the following best explains why a firm that needs to borrow money would borrow at long-term rates when short-terms rates are lower than long-term rates? -A firm will only borrow at short-term rates when the yield curve is downward-sloping. -The firm's interest payments will be the same whether it uses short-term or long-term financing, so it is essentially indifferent to which type of financing it uses. -The use of short-term financing over long-term financing for a long-term project will increase the risk of the firm.
The use of short-term financing over long-term financing for a long-term project will increase the risk of the firm. When a firm uses short-term debt, it will have to renew its loan every year. The interest rate charged on each new loan will reflect the then-current short-term rate. It is possible for short-term interest rates to increase, which would result in higher interest payments. Higher interest payments would cut into and possibly eliminate the firm's profit. The reduced profitability could increase the firm's risk to the point where its bond rating was lowered, causing lenders to increase the risk premium built into the firm's interest rate. This would further increase the firm's interest payments, which would reduce the firm's profitability even more. Eventually, lenders could perceive the firm to be so risky that they would not be willing to renew the firm's loan and demand its repayment. At that point, the firm might have to sell its assets at a loss, which could result in bankruptcy. Bankruptcies increase dramatically when interest rates rise, primarily because many firms use so much short-term debt. A firm can reduce its risk by matching its financing term with the expected life of the project it is financing.
question
Impact on yield (increases/decreases) and the cost of borrowing money from bond markets is (more/less) expensive for the following scenario: XYZ Co.'s credit rating was downgraded from AA to BBB.
Increase; More A downgrade in credit ratings means that the company's default risk has increased, leading to an increased default risk premium and thus higher interest rates. Therefore, it will be more expensive for a company to borrow money from bond markets, and yields will increase.
question
Impact on yield (increases/decreases) and the cost of borrowing money from bond markets is (more/less) expensive for the following scenario: A company uses debt to buy another company. Such an event is called a leveraged buyout.
Increase; More If a company uses debt for a buyout, both its debt load and the chances of defaulting on making committed payments will increase. In such a situation, yields will increase and it will be more expensive for a company to borrow money from bond markets.
question
Impact on yield (increases/decreases) and the cost of borrowing money from bond markets is (more/less) expensive for the following scenario: A company's financial health improves.
Decrease; Less A decrease in the liquidity premium means that the company can issue debt at a lower interest rate. In contrast, if perceived liquidity of a firm's debt falls, it'll have to pay a higher interest rate due to a higher liquidity premium.
question
Impact on yield (increases/decreases) and the cost of borrowing money from bond markets is (more/less) expensive for the following scenario: There is an increase in the perceived marketability of a company's bonds, so the liquidity premium decreases.
Decrease; Less If a company's financial health improves, investors will be confident that the issuer is capable of making committed payments. Thus, yields will decrease and it will be less expensive for the company to borrow money from bond markets.
question
The real risk-free rate (r*) is 2.8% and is expected to remain constant. Inflation is expected to be 3% per year for each of the next four years and 2% thereafter. The maturity risk premium (MRP) is determined from the formula: 0.1(t - 1)%, where t is the security's maturity. The liquidity premium (LP) on all Smith and Carter Inc.'s bonds is 1.05%. The following table shows the current relationship between bond ratings and default risk premiums (DRP): Rating Default Risk Premium U.S. Treasury — AAA 0.60% AA 0.80% A 1.05% BBB 1.45% Smith and Carter Inc. issues 8-year, AA-rated bonds. What is the yield on one of these bonds? Disregard cross-product terms; that is, if averaging is required, use the arithmetic average. 6.80% 5.35% 7.85% 7.15%
7.85% You need to solve for the yield on a Smith and Carter Inc. 8-year corporate security, so enter the data that you know and solve for the remaining data. The table tells you the default risk premium on Smith and Carter Inc.'s bonds is 0.80%. The calculation is done as follows: rC-bond = r*+IP+DRP+LP+MRPr*+IP+DRP+LP+MRP The first four years of inflation was 3% and 2% thereafter, so take the arithmetic average of the inflation over the entire life of the bond, which is 8 years. Solve for the inflation premium (IP) as follows: IP8 = [4(3%) + (8 − 4) × (2%)]/8 = 2.50% The bonds mature in 8 years (t = 8). Solve for the maturity risk premium as follows: MRP8 = 0.1(t−1)% = 0.1(8−1)% = 0.70% Now, use the values of the inflation premium and maturity risk premium and apply them in the equation for calculating interest rates. Solve as follows: rC-bond8 = r*+IP+DRP+LP+MRPr*+IP+DRP+LP+MRP = =2.8%+2.50%+0.8%+1.05%+0.70% = 7.85%
question
The real risk-free rate (r*) is 2.8% and is expected to remain constant. Inflation is expected to be 4% per year for each of the next five years and 3% thereafter. The maturity risk premium (MRP) is determined from the formula: 0.1(t - 1)%, where t is the security's maturity. The liquidity premium (LP) on all Nitreca Chemicals Inc.'s bonds is 1.05%. The following table shows the current relationship between bond ratings and default risk premiums (DRP): Rating Default Risk Premium U.S. Treasury — AAA 0.60% AA 0.80% A 1.05% BBB 1.45% Smith and Carter Inc. issues ten-year, AA-rated bonds. What is the yield on one of these bonds? Disregard cross-product terms; that is, if averaging is required, use the arithmetic average. 5.55% 8.00% 8.15% 9.05%
9.05% You need to solve for the yield on a Nitreca Chemicals Inc. ten-year corporate security, so enter the data that you know and solve for the remaining data. The table tells you the default risk premium on Nitreca Chemicals Inc.'s bonds is 0.80%. The calculation is done as follows: rC-bond = r*+IP+DRP+LP+MRPr*+IP+DRP+LP+MRP The first five years of inflation was 4% and 3% thereafter, so take the arithmetic average of the inflation over the entire life of the bond, which is ten years. Solve for the inflation premium (IP) as follows: IP10 = [5(4%) + (10 − 5) × (3%)]/10 = 3.50% The bonds mature in ten years (t = 10). Solve for the maturity risk premium as follows: MRP10 = 0.1(t−1)% = 0.1(10−1)% = 0.90% Now, use the values of the inflation premium and maturity risk premium and apply them in the equation for calculating interest rates. Solve as follows: rC-bond8 = r*+IP+DRP+LP+MRPr*+IP+DRP+LP+MRP = =2.8%+3.50%+0.8%+1.05%+0.90% = 9.05%
question
Based on your understanding of the determinants of interest rates, if everything else remains the same, which of the following will be true? Higher inflation expectations increase the nominal interest rate demanded by investors. The yield on U.S. Treasury securities always remains the same.
Higher inflation expectations increase the nominal interest rate demanded by investors.
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True or False: The pure expectations theory assumes that a one-year bond purchased today will have the same return as a one-year bond purchased five years from now.
False
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This is the premium added to the equilibrium interest rate on security that cannot be bought or sold quickly enough to prevent or minimize loss. This is the premium added when a security lacks marketability, because it cannot be bought and sold quickly without losing value. It is based on the bond's marketability and trading frequency; the less frequently the security is traded, the higher the premium added, thus increasing the interest rate.
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It is calculated by adding the inflation premium to r*. This is the rate on a Treasury bill or a Treasury bond. This is the rate for a riskless security that is exposed to changes in inflation.
Nominal Risk-Free Rate; r(subRF)
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This is the premium added as a compensation for the risk that an investor will not get paid in full. It is based on the bond's rating; the higher the rating, the lower the premium added, thus lowering the interest rate. This is the difference between the interest rate on a US Treasury bond and a corporate bond of the same profile--that is, the same maturity and marketability.
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This is the premium that reflects the risk associated with changes in interest rates for a long-term security. As interest rates rise, bond prices fall, and as interest rates fall, bond prices rise. Because interest rate changes are uncertain, this premium is added as a compensation for this uncertainty.
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Over the past several years, Germany, Japan, and Switzerland have had lower interest rates than the United States due to lower values of this premium. This is the premium added to the real risk-free rate to compensate for a decrease in purchasing power over time. This is the premium added to the risk-free rate that reflects the average sustained increase in the general level of prices for goods and services over the security's entire life.
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This is the rate for a short-term riskless security when inflation is expected to be zero. This is the rate on short-term US Treasury securities, assuming there is no inflation. It changes over time, depending on the expected rate of return on productive assets exchanged among market participants and people's time preferences for consumption.
Real Risk-Free Rate; r*
question
True or False: When the Fed increases the money supply, short-term interest rates tend to decline.
True If the Fed increases the money supply by making more money available to the banking system, banks can offer lower interest rates on loans. This leads to a decline in short-term interest rates.
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True or False: When the economy is weakening, the Fed is likely to increase short-term interest rates.
False
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True or False: During the credit crisis of 2008, investors around the world were fearful about the collapse of real estate markets, shaky stock markets, and illiquidity of several securities in the United States and several other nations. The demand for US Treasury bonds increased, which led to a rise in their price and a decline in their yields.
True
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True or False: The Federal Reserve's ability to use monetary policy to control economic activity in the United States is limited because US interest rates are highly dependent on interest rates in other parts of the world.
True
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True or False: Countries with strong balance sheets and declining budget deficits tend to have lower interest rates.
True
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True or False: If the Fed injects a huge amount of money into the markets, inflation is expected to decline and long-term interest rates are expected to rise.
False
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True or False: Long-term interest rates are not as sensitive to booms and recessions as are short-term interest rates.
True
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True or False: When the economy is weakening, the Fed is likely to decrease short-term interest rates.
True
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Impact on yield (increases/decreases) and the cost of borrowing money from bond markets is (more/less) expensive for the following scenario: ABC Real Estate is a commercial real estate firm that primarily uses short-term financing, while its competitors primarily use long-term financing. Interest rates have recently increased dramatically.