Chapter 7 The Risk and Term Structure of Interest Rates Conceptual and Analytical Problems Consider a firm that issued a large quantity of commercial paper in the period leading to a financial crisis. How would you expect the credit rating of the commercial paper to evolve as the crisis unfolds? Would you alter your prediction if, rather than commercial paper, the firm was instead issuing asset-backed commercial paper? Answer: Commercial paper is generally issued without collateral, so that its rating will depend on the creditworthiness of the issuer, which faces downgrade risk in a crisis. If the commercial paper is asset-backed, the probability of a downgrade would depend on the creditworthiness of the collateral. Suppose that a major foreign government defaults on its debt. What, if anything, will happen to the position and slope of the U.S. yield curve? Answer: If Treasury debt is a substitute for the foreign government debt, then U.S. yield curve would shift downward, reflecting a flight to quality. If the holders of the foreign government debt were concentrated at the short end of the maturity spectrum, then the U.S. yield curve would shift down and become more steeply sloped; if the holders were concentrated at the long end of the maturity spectrum, then the U.S. yield curve would shift down and become flatter. What was the connection between house price movements, the growth in subprime mortgages, and securities backed by these mortgages—on the one hand—and on the other hand—the difficulties encountered by some financial institutions during the 2007-2009 financial crisis? Answer: The viability of many subprime mortgages – and in particular ARMs – depended on being able to refinance the loan before the interest rate reset to a higher level. When house prices began to fall in 2006, pushing home values below the loan amount for many of these mortgages, refinancing was no longer an option. Unable to pay the higher interest rates, borrowers began to default on these subprime mortgages at an increasing rate. This, in turn, led to significant falls in the prices of securities backed by subprime mortgages, causing difficulties for institutions that had sizable holdings of these securities. Suppose that the interest rate on one-year bonds is currently 4 percent and is expected to be 5 percent in one year and 6 percent in two years. Using the expectations hypothesis, compute the yield curve for the next three years. Answer: Yield for one-year bond = 4% Yield for two-year bond = (4% + 5%)/2 = 4.5% Yield for three-year bond = (4% + 5% + 6%)/3 = 5% According to the liquidity premium theory, if the yield on both one-and two-year bonds are the same, would you expect the one-year yield in one-year’s time to be higher, lower or the same? Explain your answer. Answer: According to the liquidity premium theory, the two-year yield (i2, t) is an average of this year’s and next year’s one-year yields (i1,t + ie 1, t + 1) divided by 2 plus a risk premium (rp) to compensate for the inflation and interest-rate risk associated with the longer maturity. i2,t = rp + (i1,t + ie 1, t + 1)/2 As we can see from the formula, if the current one-and two-year yields are the same and there is a risk premium included in the two-year yield, then next year’s one-year yield must be lower than this year’s. You have $1,000 to invest over an investment horizon of three years. The bond market offers various options. You can buy (i) a sequence of three one-year bonds; (ii) a three-year bond; or (iii) a two-year bond followed by a one-year bond. The current yield curve tells you that the one-year, two-year, and three-year yields to maturity are 3.5 percent, 4.0 percent, and 4.5 percent respectively. You expect that one-year interest rates will be 4 percent next year and 5 percent the year after that. Assuming annual compounding, compute the return on each of the three investments, and discuss which one you would choose. Answer: Expected return for (i) = (1.035) × (1.04) × (1.05) – 1 = 13.02% Expected return for (ii) = (1.045)3 - 1 = 14.12% Expected return for (iii) = (1.04)2 × (1.05) – 1 = 13.57% The second and third options have higher expected returns than the first, but both options involve investing in longer-term bonds (three-year and two-year bonds, respectively). Long-term bonds have higher inflation risk and interest-rate risk; investors require compensation for this additional risk, which is why longer-term bonds generally have higher yields than would be suggested by the expectations hypothesis. In selecting an investment strategy, it is important to take these additional risks into account. An investor’s investment horizon is also important; to reduce interest rate risk, someone with a short-term horizon would be better off choosing the first option, while someone with a three-year horizon should probably choose the second option. Suppose that the yield curve shows that the one-year bond yield is 3 percent, the two-year yield is 4 percent, and the three-year yield is 5 percent. Assume that the risk premium on the one-year bond is zero, the risk premium on the two-year bond is 1 percent, and the risk premium on the three-year bond is 2 percent. What are the expected one-year interest rates next year and the following year? If the risk premiums were all zero, as in the Expectations Hypothesis, what would the slope of the yield curve be? Answer: With iit = 0.03, the risk premium on the two-year bond at 0.01, and with the two-year yield at 4 percent, the implied one-year rate next year will solve: i2t = 0.01 + (0.03 + i1,t + 1) / 2 = 0.04, which implies that the one-year interest rate next year will be 0.03. Using this result, with a risk premium on the three-year bond of 0.02, we have: i3t = 0.02 + (0.03 + 0.03 + i1,t + 2) / 3 = 0.05 which implies that the one-year rate in two years will also be 0.03. As the solutions in part (a) show, the current and prospective one-year rates are all3 percent, so the expectations hypothesis yield curve would be flat. If inflation and interest rates become more volatile, what would you expect to see happen to the slope of the yield curve? Answer: Investors are likely to demand a higher risk premium in the face of increased volatility. There is more uncertainty regarding the real return on investments and the price for which you could sell a bond before maturity. Assuming the uncertainty rises the longer the term to maturity, you should expect the yield curve to become steeper. As economic conditions improve in countries with emerging markets, the cost of borrowing funds there tends to fall. Explain why. Answer: As economic conditions improve, the chance that businesses will default on their loans decreases. The decline in default risk reduces the return demanded by lenders. Suppose your local government, threatened with bankruptcy, decided to tax the interest income on its own bonds as part of an effort to rectify serious budgetary woes. What would you expect to see happen to the yields on these bonds? Answer: You would expect the yields to rise to compensate investors for the loss of the tax-exempt status. These yields also would have to compensate investors for the heightened probability of default by the local government. If, before the change in tax status, the yields on the bonds described in Problem 10 were below the Treasury yield of the same maturity, would you expect this spread to narrow, to disappear, or to change sign after the policy change? Explain your answer. Answer: We can attribute the lower yields on the local government bonds versus Treasury issues to their tax-exempt status, as investors would view the federal government as being at least as creditworthy as the local government. Given the serious budgetary woes of the local government, investors likely would regard these bonds as riskier than Treasury issues. The local bond yield also would have to compensate investors for the new tax obligation, so the spread would change sign. Suppose the risk premium on U.S. corporate bonds increases. How would the change affect your forecast of future economic activity, and why? Answer: An increasing risk premium can be a sign of an impending recession, so you would be more likely to forecast an economic downturn. During cyclical downturns, private companies have a more difficult time repaying their debt, while the U.S. Treasury typically is not affected, increasing the risk premium on company debt. If regulations restricting institutional investors to investment grade bonds were lifted, what do you think would happen to the spreads between yields on investment grade and speculative grade bonds? Consider a struggling emerging-market economy where, in contrast to developed economies, the perceived risk associated with holding sovereign bonds is affected by the state of the economy. Suppose vast quantities of valuable minerals were unexpectedly discovered on government-owned land. How might the government’s bond rating be affected? Using the model of demand and supply for bonds, what would you expect to happen to the yields on that country’s government bonds? Answer: The ratings of the bonds would likely be upgraded, as the outlook for the economy would improve and the reduction in the perceived riskiness of the bonds would shift the demand curve to the right. Revenues from the minerals could also mitigate the government’s need to borrow, shifting the supply of bonds to the left. Bond prices would increase and yields would fall. Consider again the economy described in Problem 14. Under which of the following scenarios would you expect the impact of the mineral discovery on bond yields to be larger? Before the discovery, the government was heavily indebted with a crippling debt-service burden or, Before the discovery, the government had a very low debt burden. Explain your choice. Answer: The impact would be larger in the case of a heavily indebted government, especially if the debt was denominated in another currency, such as U.S. dollars. These factors make the government more vulnerable to global interest- rate and currency movements. The benefit of an additional source of revenue through taxing the mineral discoveries would be greater for a government at risk of defaulting due to high debt servicing costs than in a country where this risk was not an issue. The misrating of mortgage-backed securities by rating agencies contributed to the financial crisis of 2007-2009. List some recommendations you would make to avoid such mistakes in the future. Answer: In the run-up to the 2007-2009 crisis, the absence of data capturing a period of falling house prices at a national level caused models to underestimate the default risk of the mortgages underlying the mortgage-backed securities. Running tests to see what outcomes these models would predict in extreme circumstances (stress testing) may help avoid such underestimations in the future. Publishing data on the accuracy of various bond rating firms in anticipating bond defaults also could encourage more reliable ratings. Similarly, encouraging professional asset managers to develop their own risk assessments would diminish the influence of credit ratings in portfolio selection. Finally, changing the relationship between the rating agencies and the securities issuers could reduce potential conflicts of interest. These conflicts can arise from payments by the bond issuers to the credit rating agencies in return for having their bonds rated. How do you think the abolition of investor protection laws would affect the risk spread between corporate and government bonds? Answer: These laws were likely to be much more important in protecting purchasers of corporate bonds rather than purchasers of government bonds. Their abolition would raise the relative riskiness of corporate bonds, widening the spread between corporate and government bond yields. You and a friend are reading The Wall Street Journal and notice that the Treasury yield curve is slightly upward sloping. Your friend comments that all looks well for the economy but you are concerned that the economy is heading for trouble. Assuming you are both believers in the liquidity premium theory, what might account for your difference of opinion? Answer: The difference in opinion could reflect different views on the size of the risk premium. If the risk premium is large enough, a slightly upward-sloping yield curve could mean that interest rates are expected to fall, indicating a weak economy. However, if the risk premium is small, the slight upward slope could reflect expectations that interest rates will rise and that the economy is expected to be healthy. Do you think the term spread was an effective predictor of the recession that started in December 2007? Why or why not? Answer: An inverted yield curve (negative term spread) is often a sign that the economy is about to go into recession. Looking at the term spread (10-year yield minus the three-month interest rate) in Figure 7.9, we see that the term spread did indeed turn negative in late 2006/early 2007. On the other hand, the severity of the recession was not predicted by the yield curve. Given the data in the accompanying table, would you say that this economy is heading for a boom or for a recession? Explain your choice.
3-month Treasury-bill 10-year Treasury bond Baa corporate
10-year bond
January 1.00% 3.0% 7.0%
February 1.05% 3.5% 7.2%
March 1.10% 4.0% 7.5%
April 1.20% 4.3% 7.7%
May 1.25% 4.5% 7.8%
Answer: The information in both the term structure and the risk structure point to a healthy economy. The term spread (the gap between the 10-year Treasury bond yield and the three-month Treasury bill rate) is positive and widening. This tells us that the yield curve is upward sloping and getting more steeply upward sloping. This implies that interest rates are expected to continue to rise in the future—a sign that the economy is expected to do well. The risk spread (the gap between the Treasury and corporate 10 year bonds) is narrowing. This is a sign of a healthy economy as people do not require such a high risk premium on corporate bonds. Suppose recent regulatory reforms relating to credit rating agencies are perceived to improve the reliability and accuracy of credit ratings of corporate bond issues. Imagine further that you manage a corporation interested in issuing new bonds, in addition to past issues by the firm that already trade in the market. Identify one way in which your firm might lose and one way in which it might gain from these reforms. Explain your answer. Answer: If, prior to the reforms, your bond issues enjoyed inflated credit ratings, you may receive a lower rating and therefore face higher borrowing costs if the reforms are successful in bringing about more accurate ratings. Core Principle 3 states that information is the basis for decisions. If, prior to the reforms, lack of investor confidence in credit ratings made it difficult or impossible to issue bonds, the reforms may improve market access. Put differently, if the reforms restore investor confidence in credit ratings, your corporation may be better able to issue new bonds at a reasonable price. Data Exploration Did the financial crisis of 2007-2009 affect financial and nonfinancial firms to the same extent? For the period beginning in 2006, plot the spread between the interest rates on three-month non-financial commercial paper (FRED code: CPN3M) and three-month Treasury bills (FRED code: TB3MS). Plot a similar spread using the interest rates on three-month financial commercial paper (FRED code: CPF3M) and Treasury bills (FRED code: TB3MS). Compare the evolution of these two spreads. Answer: The spreads between commercial paper (CP) rates and the Treasury bill rate rose significantly in the second half of 2007 as the financial crisis began to unfold and spiked even higher in the latter part of 2008 in the wake of the collapse of Lehman Brothers. Before the onset of the crisis, these spreads were below 50 basis points (or 0.5 percent). Over most of the next 18 months, the spreads more than doubled. Concerns about the health of the financial system had a particularly severe impact on financial CP. The financial spread peaked at 2.52 percent in October 2008, reflecting both the liquidity shortage and heightened default risk. The narrowing of the CP spreads in 2009 marked an important turning point in the crisis. The Federal Reserve Bank of St. Louis publishes a weekly index of financial stress (FRED code: STLFSI) that summarizes strains in financial markets, including liquidity problems. For the period beginning in 1994, plot this index and, as a second line, the difference between the weekly Baa corporate bond yield (FRED code: WBAA) and the weekly 10-year U.S. Treasury bond yield (FRED code: WGS10YR). Does the index STLFSI provide an early warning of stress?
Answer: The stress index deteriorated – rose in value - in 2007 before the bond yield spread widened. It also improved - fell in value - in 2009 before the bond yield spread narrowed. Movements in this stress index summarize 18 different data series, including various interest rates, yield spreads, and volatility indexes, in order to capture stress from various parts of the financial system. How did the Great Depression (1930-33) and the Great Recession of 2007-2009 affect expectations of corporate default? To investigate, construct for each of those periods a separate plot of the corporate bond yield spread. For the depression period, plot from 1930 to1933 to the difference between the Baa corporate bond yield (FRED code: BAA) and the long-term government bond yield (FRED code: LTGOVTBD). For the Great Recession, plot from 2007 to 2009 the difference between the Baa yield (FRED code: Baa) and the 10-year Treasury bond yield (FRED code: GS10). Compare the plots. Answer: The two data plots are below. The patterns are quite similar, though the risk spread was modestly larger in the Great Depression than in the Great Recession. If investors view an expected return as equivalent to a certain return of the same magnitude (economists call such investors “risk neutral”), then these spreads imply that the probability of corporate default rose similarly in both episodes and remained above pre-crisis levels several years later. How reliably does an inverted yield curve anticipate a recession? How far in advance? Plot from 1970 (as in Figure 7.9A) the difference between the 10-year Treasury yield (FRED code: GS10) and the three-month Treasury bill rate (FRED code: TB3MS). Discuss the variability of the time between an inversion of the yield curve and the subsequent recession. Answer: The data plot is below. The yield curve inverts when the term spread becomes negative, so we examine the spread for values around zero. Regarding the downturn in 1973 the yield curve appears to have inverted several months in advance of the recession. For the brief recession beginning in 1980, the inversion appears to occur about a year ahead of the onset. For the recession beginning in late 1981, the inversion is several months in advance. Prior to the 1990 recession, the yield curve did not invert, but it did flatten a year prior to the recession. The 2001 recession was preceded by an inversion over a year in advance that reversed itself just prior to the actual economic downturn. For the 2007-2009 episode, the yield curve inverted several years prior to the fall in real GDP and again reversed itself prior to the onset of the downturn. So, while the yield curve is a useful leading indicator of business cycles, this variability in timing makes it an imperfect one. Download the data used in Data Exploration Problem 4 and (a) find the most recent period for which the yield curve was (approximately) flat and (b) the longest time period for which yield curve was inverted. Answer: The most recent period when the yield curve was approximately flat was in May, 2007, when the spread was about 2 basis points. The most prolonged period of yield curve inversion was the 17-month period between December, 1978 and April, 1980 indicates more difficult problems. Solution Manual for Money, Banking and Financial Markets Stephen G. Cecchetti, Kermit L. Schoenholtz 9781259746741, 9780078021749, 9780077473075
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