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The aggregate credit spread and the business cycle Debashis Guhaa,*, Lorene Hirisb,c a

Alphanomics LLC, 110 East 59th Street, 18th floor, 10022 New York, NY, USA b C.W. Post Campus of Long Island University, Brookville, NY, USA c Economic Cycle Research Institute, NY, USA

Abstract An empirical investigation of the credit spread between yields on corporate and treasury bonds shows that it is closely related to macroeconomic fluctuations. The spread behaves counter-cyclically, that is, it narrows during business cycle expansions and widens during contractions. The results also show that the credit spread is a leading indicator of macroeconomic business conditions and turning points in the credit spread can anticipate business cycle turning points. D 2002 Published by Elsevier Science Inc. JEL classification: E44; G10; E32 Keywords: Credit risk; Interest rate spread; Business cycle; Leading indicator

1. Introduction This paper is an empirical investigation of the longer term dynamics of the credit spread and its relation to aggregate business conditions. The results show that the spread behaves counter-cyclically, i.e., it tends to widen during business cycle recessions and narrow during business cycle expansions. The dynamic behavior of the spread between the yields on corporate and treasury bonds is an important ingredient in the valuation of credit risky debt securities and credit derivatives. The yield spread has also assumed considerable importance in recent years as a determinant of the profitability of complex investment strategies that depend upon the convergence of yields on securities with differing credit risks. Some of these investment strategies apparently * Tel.: +1-646-522-0730; fax: +1-212-317-8666. E-mail address: [email protected] (D. Guha). 1057-5219/02/$ – see front matter D 2002 Published by Elsevier Science Inc. PII: S 1 0 5 7 - 5 2 1 9 ( 0 2 ) 0 0 0 7 5 - 3

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came to grief by assuming that the yield spread is mean reverting and tends to converge to an equilibrium value. The empirical results in this paper suggest that since the spread varies counter-cyclically over the longer term, there may not be any such convergence to a steadystate equilibrium value. Aggregate credit conditions in the economy have long been considered an important determinant of the dynamics of the business cycle. Monetary theories of business cycles that trace their roots back to Wicksell and Hawtrey have emphasized instabilities in credit markets, that is, the overexpansion of credit during booms and its rapid contraction during depressions, as one of the principal mechanisms that give rise to cyclical fluctuations. For an exposition of these ideas, see Haberler (1941). A modern version of this argument has been given by Bernanke and Gertler (1995) and Bernanke, Gertler, and Gilchrist (1996). Our empirical results lend support to this view by showing that turning points of the aggregate credit spread contain significant information about the future turning points of real activity.

2. The economic theory of credit spread dynamics It is well known that the spread between the yields on defaultable and risk-free bonds is determined by two stochastic variables: the default rate, interpreted as the rate of occurrence of default events, and the fractional recovery rate, i.e., the fraction of the debt recovered by the creditor after a default event has occurred. Here, a default event is defined as any missed or delayed disbursement of interest and/or principal. This is the definition adopted by Moody’s Investor’s Service, as reported for instance in Truglia (1999), to which we refer for a fuller description. The credit spread is usually expressed as the product of the expected default rate and the complement of the expected recovery rate, both expectations being taken under the risk-neutral measure. This expression can be derived from either the classical ‘‘structural’’ method of valuation of default risky bonds going back to Black and Scholes (1973) and Merton (1974) or the more recent ‘‘reduced-form model’’ used by Duffie and Singleton (1998), Lando (1998), and others. Macroeconomic fluctuations are an important influence on each of the components that together determine the credit spread: the default rate, the recovery rate, and the risk-neutral measure. It is not hard to see that rate of default would tend to rise during business cycle contractions and fall during expansions. This has been borne out by extensive empirical research and the number of business failures is a well-known business cycle indicator (see Moore, 1961). There is some reason to believe that the recovery rate is higher during expansions than during recessions. Most interestingly, the market price of risk, i.e., the market’s appetite for risk and hence its risk-reward tradeoff may also change according to the stage of the cycle, thus, changing the risk-neutral measure. Thus, there is good reason to believe that the corporate-treasury spread varies with the stage of the cycle and is higher during recessions than during expansions. Empirical investigations going back at least to Moore (1956) have shown that both the aggregate quality of credit and the aggregate level of credit risk vary systematically across

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stages of the business cycle. Chen (1991) and Fama and French (1989) have found that a related variable, the quality spread, measured as the spread between average yields on BAArated and AAA-rated corporate bonds, tends to rise during business cycle contractions and fall during expansions. Monetary theories of business cycles have, for a long time, suggested that instabilities of the credit process have a causal influence on aggregate macroeconomic dynamics. More recently, Bernanke and Gertler (1995) and Bernanke et al. (1996) have argued that the principal channel by which monetary disturbances are amplified and transmitted to the real economy is through changes in the balance sheet positions of households and firms in the economy. During good times when current income is high and prospects are hopeful, asset prices rise and this improves balance sheets. The improvement induces banks to extend credit at more favorable rates leading to a credit expansion and a boom in activity. At some point, however, the boom causes inflation and interest rates to start to rise, profit margins begin to be squeezed, and prospects for future profits have to be revised down. This leads to declines in asset prices and deterioration of balance sheets. Credit begins to be restricted, spreads start to rise, and eventually real activity turns down. Several empirical studies of the spread between corporate and treasury debt of short maturity, such as Friedman and Kuttner (1992) and Stock and Watson (1989), have found that this spread is a reliable, but not infallible, leading indicator of the business cycle. This paper adds to this literature by showing that the credit spread between yields on long maturity debt is also a good leading indicator, and in fact has performed as such for more than seven decades.

3. Methodology The analysis of business cycles depends in an essential way on the concept of turning points. According to the classical definition of Burns and Mitchell (1946), the aggregate business cycle consists of alternating periods of expansions and contractions in many economic activities. The sequence of changes is recurrent but not periodic and varies in duration from more than 1 to 10 or 12 years. The turning points are the epochs that mark the point of transition between the phases. The upper turning point, or the peak, is when an expansion ends and a recession begins and the lower turning point, or the trough, is when a recession ends and an expansion begins. Thus, the analysis of turning points is of fundamental importance in cyclical analysis. The concept of turning points and expansionary and contractionary phases as originally propounded by Burns and Mitchell (1946) can be formally modeled by some variant of the latent regime-switching time-series models introduced by Hamilton (1989). In this approach, the macroeconomic time series is represented by an AR model whose parameters are driven by an unobservable two-state Markov chain. The state of the Markov chain is 1 for the expansion phase and 0 for recessions. The transition epochs of the Markov chain are, then, the turning points of the cycle.

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A different approach to the problem of determining turning points is to define them as the local maxima and minima of the graph of the process, or equivalently, the point at which the derivative of the graph changes sign. Since the measurements of the process consist of discretely sampled observations of the output of a stochastic system, the graph must be smoothed before the true maxima or minima can be determined, or the derivative estimated. The standard data-analytic procedure for determining the turning points of an empirical timeseries was formulated by Bry and Boschan (1971) and has been widely used in business cycle analysis since then, by Balke and Wynne (1995), King and Plosser (1994), Moore (1983), Watson (1994), and many others. The investigations in this paper will explore two basic properties of the aggregate credit spread: its counter-cyclical conformity and its lead. The aggregate credit spread selected for investigation here is the difference between the average yield on Moody’s BAA-rated corporate bonds and the yield on treasury bonds of maturity 10 years or longer, which we call SPRD. A test of the counter-cyclical conformity of SPRD can be developed from the observation that counter-cyclical behavior implies that SPRD should, on average, narrow during business cycle expansions and widen during business cycle recessions, i.e., the change in the spread should be negative during expansions and positive during recessions. Also, the value of the spread should be higher, on average, during recessions than during expansions. In order to test this, we split SPRD and DSPRD, the month-to-month change in SPRD, into two samples according to the standard National Bureau of Economic Research (NBER) dates for the US business cycle turning points. The Wilcoxon signed rank-sum test is used to test whether the change in the spread is positive on average during recessions and negative on average during expansions. The Wilcoxon rank-sum test is used to test the hypothesis that the spread is higher on average during contractions than in recessions. A test for leads can be developed from the observation that if the turning points in the inverted SPRD lead business cycle turning points, then business cycle peaks would be more likely to fall in months following a trough in SPRD than in other months, and similarly, business cycle troughs would be more frequent during months following a peak in SPRD. In order to make these ideas more precise, we define the following notation.

All=the index set of all months in the sample. In our case, All={1, . . ., 900} FollowT(n)=subset of months that follow a trough in SPRD by n months or less FollowT(n)=All\FollowT(n) FollowP(n)=subset of months that follow a peak in SPRD by n months or less FollowP(n)=All\FollowP(n) Num[.]=total number of months in an index set months NumT[.]=number of business cycle troughs in an index set of months NumP[.]=number of business cycle peaks in an index set of months FP PropT=NumT[FollowP(n)]/Num[FollowP(n)] FP PropT=NumT[FollowP(n)]/Num[FollowP(n)] FT PropP=NumP[FollowT(n)]/Num[FollowT(n)] FT PropP=NumP[FollowT(n)]/Num[FollowT(n)]

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Billingsley (1961) has shown that the observed sequence of states from a finite-state Markov chain can be treated, for the purpose of statistical inference, as if they have arisen from independent samples from multinomial populations, where the multinomial probabilities are the transition probabilities from the corresponding state of the Markov chain. If we assume that the underlying process in the present case can be approximated by a two-state Markov chain, then the observed sequence of underlying states, determined by the Bry– Boschan algorithm, may be treated as samples from binomial trials where each trial is of a possible transition to the other state. This implies that a test of the hypothesis that the inverted SPRD leads overall economic activity by n months or less at business cycle troughs is simply a one-sided test of the equality of the binomial proportions FP PropT and FP PropT, and similarly for leads at peaks. There is a rather voluminous literature on the classical problem of testing the equality of two binomial proportions. Little (1989) and Santner and Duffy (1989) provide overviews of the topic. Power comparisons in Berger (1996a), Haber (1987), Martin and Silva (1994), and Storer and Kim (1990) all suggest that the exact unconditional test using the statistic proposed by Suissa and Shuster (1985) has the highest power and is to be preferred to both the usual Chi-squared test and Fisher’s exact conditional test. Both Berger and Storer and Kim suggest that the Suissa–Shuster statistic with pooled variance should be used for unequal sample sizes and this is the form of the test that will be used below. The Fortran program xun22v2.f available from Berger (1996b) was utilized to carry out these tests.

4. Results A chart of SPRD from 1925 to 1999 is shown in Fig. 1, where the business cycle recession periods are shown as gray shaded areas. An exploratory investigation of the chart clearly suggests that the spread is counter-cyclical, with a tendency to decline during expansions, shown as clear areas of the graph, and to rise during contractions, the shaded regions of the graph. The chart also suggests, somewhat less clearly, that SPRD leads the cycle. The results from the tests for counter-cyclical conformity for the period 1925–1999 are shown in Table 1. The first section of the table shows the results of the test on DSPRD0, the value of the month-to-month-change in SPRD during months when the US economy was in an NBER designated recession. If SPRD is counter-cyclical, DSPRD0 should be positive on average. The result of a Wilcoxon signed-rank test, a standard nonparametric test for sample comparison, of the null hypothesis that DSPRD0 is zero, against the alternative that it is positive, has a Z statistic of 3.3762 and a P value of .0004. We conclude that SPRD tends to rises during recessions. The second section of Table 1 shows the results of the test on DSPRD1, the value of the month-to-month-change in SPRD during months when the US economy was in an NBER-designated expansion. If SPRD is counter-cyclical, DSPRD0 should be negative on average. The result of the Wilcoxon signed-rank test of the null hypothesis that DSPRD0 is zero, against the alternative that it is negative, has a Z statistic of 3.2511 and a P value of .0006. We conclude that SPRD narrows during expansions.

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Fig. 1. Aggregate credit spread, 1925 – 1999, %, p.a.

The next section of Table 1 shows the result of a Wilcoxon rank-sum test that SPRD0, the value of SPRD during recessions, is larger than SPRD1, its value during expansions. In this case, the Z statistic is 7.8048 and the P value is .0000. We conclude that the credit spread is higher during recessions than during expansions. These three tests together Table 1 Results of tests for conformity 1. Data: DSPRD0, the value of DSPRD (the month-to-month change in SPRD), during NBER-designated recessions Signed-rank normal statistic with correction, Z=3.3762, P value=.0004, Alternative hypothesis: true mean is > 0. 2. Data: DSPRD1, the value of DSPRD (the month-to-month change in SPRD), during NBER-designated expansions Signed-rank normal statistic with correction, Z= 3.2511, P value=.0006, Alternative hypothesis: true mean is <0. 3. Data: SPRD0, the value of SPRD during NBER-designated recessions and SPRD1, the value of SPRD during NBER-designated expansions Rank-sum normal statistic with correction, Z=7.8048, P value=.0000, Alternative hypothesis: true mean of SPRD0 is greater than true mean of SPRD1.

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Table 2 Results of tests for leads Lead in months

At business cycle troughs

At business cycle peaks

3 6 9 12

0.0049 0.0080 0.0002 0.0002

0.2097 0.0269 0.0212 0.0032

provide convincing evidence of the counter-cyclical conformity of the credit spread, i.e., it widens during recessions and narrows during expansions. Table 2 presents the results for the tests for leads. The results are arranged in rows for leads of 3 months or less, 6 months or less, 9 months or less, and 12 months or less. Column 1 of each row shows the P values of the Suissa–Shuster exact unconditional test of the hypothesis that the frequency of business cycle troughs is the same, against the alternative that it is higher, in months following a business cycle peak as in other months. Column 2 shows the results of the test for leads at business cycle peaks. The results show that business cycle troughs are significantly more frequent following SPRD peaks, at all tested leads. The P values range from .0002 to .0080, and thus the null hypothesis of no leads is strongly rejected. At business cycle peaks, the null hypothesis of no leads is also rejected, except at a lead of 3 months or less. At 6-, 9-, or 12-month leads, the P values range from .0269 to .0032. The P values are higher for business cycle peaks than for troughs, but at all leads above 3 months, the null hypothesis of no leads is strongly rejected. Overall, the results of the test for leads strongly support the hypothesis that SPRD troughs lead business cycle peaks and SPRD peaks lead business cycle troughs.

5. Conclusion We found strong evidence that the spread between yields on corporate bonds and treasury bonds is closely related to the business cycle and tends to be significantly higher during recessions than during expansions. This is true not only for the postwar period, but also for the long data series from 1925 to the present. There is also evidence that the credit spread leads the business cycle. Turning points of the credit spread contain significant information about future turning points of the business cycle. The empirical results in this paper suggest that business cycle indicators could be useful in forecasting the credit spread. Results reported in Guha and Hiris (1999) show that this is indeed true. Another interesting research issue that will be left for future investigation is whether the relation discovered using the US data holds for other countries.

6. Data sources The corporate bond yield series used is the monthly series of average yields on Moody’s BAA-rated corporate bonds, published by the Federal Reserve Board. The monthly figure

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is the average of the daily figures for all the working days for that month. The history of the series is available back to January 1919 from the NBER macrohistory database. The treasury bond yield series used is the monthly series of long-term US Government bond yields (10 years or more) including flower bonds, published by the Federal Reserve Board. The monthly figure is the average of the daily figures for all the working days for that month. The history of the series is available back to January 1925 from Federal Reserve of St. Louis database. The corporate-treasury spread, denoted by SPRD, is taken to be the difference between the BAA corporate bond yield and the long-term treasury bond yield. It is calculated monthly from January 1925 to December 1999 using the two series mentioned above. The economy is designated as being in an expansion starting 1 month after a business cycle trough and continuing through the month of the next business cycle peak. The economy is designated as being in a recession the rest of the time. The peak and trough dates are the standard ones used is most business cycle analysis. These are determined by the NBER and are available from their website: www.nber.org. References Balke, N. S., & Wynne, M. A. (1995). Recessions and recoveries in real business cycle models. Economic Inquiry, 33, 640 – 663. Berger, R. L. (1996a). More powerful tests from confidence interval P values. American Statistician, 30, 314 – 318. Berger, R. L. (1996b). xun2n2v2.f, a Fortran program to perform exact unconditional homogeneity/independence tests for 22 tables for large sample sizes. Available from www.stat.ncsu.edu/~berger/tables.html. Bernanke, B. S., & Gertler, M. (1995). Inside the black box: the credit channel of monetary transmission. Journal of Economic Perspectives, 9, 27 – 48. Bernanke, B. S., Gertler, M., & Gilchrist, S. (1996). The financial accelerator and the flight to quality. Review of Economics and Statistics, 78, 1 – 15. Billingsley, P. (1961). Statistical methods in Markov chains. Annals of Mathematical Statistics, 32, 12 – 40. Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637 – 654. Bry, G., & Boschan, C. (1971). Cyclical analysis of time series: selected procedures and computer programs: technical paper, vol. 20. New York: National Bureau of Economic Research. Burns, A. F., & Mitchell, W. C. (1946). Measuring business cycles. New York: National Bureau of Economic Research. Chen, N. (1991). Financial investment opportunities and the macroeconomy. Journal of Finance, 46, 529 – 554. Duffie, D., & Singleton, K. J. (1998). Econometric modeling of term structures of defaultable bonds. Working Paper, Graduate School of Business, Stanford University. Fama, E. F., & French, K. R. (1989). Business conditions and expected returns on stocks and bonds. Journal of Financial Economics, 25, 23 – 49. Friedman, B. M., & Kuttner, K. N. (1992). Money, income, prices and interest rates. American Economic Review, 82, 472 – 492. Guha, D., & Hiris, L. (1999). Forecasting the quality spread using business cycle indicators, presented at the 1999 FMA International Conference in Barcelona, Spain. Haber, M. (1987). A comparison of some conditional and unconditional tests for 2X2 contingency tables. Communications in Statistics – Simulation and Computation, 16, 999 – 1013. Haberler, G. (1941). Prosperity and depression. A theoretical analysis of cyclical movements (3rd ed.). Geneva: League of Nations.

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