Chapter 6: Interest Rates

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.

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.

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.

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.

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.

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.

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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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.

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.

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%

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%

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%

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.

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.

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.

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.

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.

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.

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.

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.

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.

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%

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%

Higher inflation expectations increase the nominal interest rate demanded by investors.

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Liquidity Risk Premium; LP

Nominal Risk-Free Rate; r(subRF)

Default Risk Premium; DRP

Maturity Risk Premium; MRP

Inflation Premium; IP

Real Risk-Free Rate; r*

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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Decrease; Less

Decrease; Less