### Table 2 Properties of Yield Spreads and Changes

"... In PAGE 3: ...ator (2.074). None of these estimates appear to be the result of a small number of extreme observations. Even for these three, the evidence of kurto- sis is much weaker than for yield spreads and changes ( Table2 ). The question is how to reconcile Tables 2 and 3.... ..."

### Table 8 Summary Statistics of Yield Spread Changes

"... In PAGE 27: ... In any case, if we accept on economic grounds that the credit spread series are stationary, it is clear from the high autocorrelation coefficients that they revert only slowly to their long-run average. In Table8 summary statistics for changes in credit spreads are presented. To some extent these are more important in a risk management context, as it is important to understand how credit spreads behave through time.... In PAGE 29: ...06 0.07 percentages In Table8 the first three order autocorrelation coefficients of the spread changes are also shown. Without any exception, all first order coefficients are negative and usually significantly different from zero.... In PAGE 29: ... Higher order autocorrelation does hardly seem present in the series. In any case, from the skewness and kurtosis coefficients in Table8 , it is clear that spread changes are not normally distributed. This is both due to skewness and kurtosis.... In PAGE 33: ... A second indication of the effect of risk reduction characteristics across the rating and maturity dimensions can be found in Table 10. This table reports similar summary statistics as in Table8 (Summary Statistics of Yield Spread Changes) but now for value weighted aggregate indices. We computed average spreads for the different credit rating classes and maturity buckets.... In PAGE 49: ...46 7. Mean Reversion The summary statistics for spread changes shown in Table8 as well as the Durbin- Watson statistics in Table 13 show that the series contain significant negative first order serial correlation. This may be an indication of some kind of mean reversion: the tendency of spreads to return to some long-term value after deviations from this value.... ..."

### Table 4 Summary Statistics of Yield Spreads Average

"... In PAGE 10: ...1 3. Descriptive statistics of the credit spreads Summary statistics of the daily series can be found in Table4 . As could have been expected, average spreads increase monotonically the lower the credit rating.... ..."

### Table 7 Summary Statistics of Yield Spreads

"... In PAGE 25: ...3. Summary statistics Summary statistics of the series can be found in Table7 . As could have been expected, average spreads increase monotonically the lower the credit rating.... In PAGE 51: ... Also, all the slope coefficients are negative, which implies mean-reversion. Second, the estimated implied long-run spread levels to which spreads should eventually revert (shown in the last column of Table 15) are very comparable to the reported average spreads in Table7 . The long-term levels are also internally consistent in the sense that lower rating classes have higher long-term spread levels than better rated classes in comparable maturity buckets.... ..."

### Table 2 Properties of Yield Spreads and Monthly Changes in Yields

"... In PAGE 11: ... In the data, however, long yields and yield spreads exhibit, respectively, higher and lower autocorrelations than the short rate. A related issue is the decline in volatility with maturity, such as the standard deviations of one-month changes reported in Table2 B. These models imply less variability of long rates than short rates, but the rate of decline is greater in both models than we see in the data.... In PAGE 18: ... In fact, innovations in interest rates appear markedly non-normal, typically with fat tails indicative of kurtosis. Table2 B is suggestive: one-month changes in the short rate exhibit excess kurtosis of about 10. Since departures from normality can have a signi cant impact on prices of options and related derivatives, we discuss them at some length.... In PAGE 19: ... We estimate this to be 9.302, a slightly smaller value than we report in Table2 B for short rate changes. This value is computed from the residuals of a rst-order autoregression for the short rate.... In PAGE 28: ... In the Vasicek model, a unit fall in the short rate is associated with a rise in the logarithm of the n-period bond price of (1 + apos; + + apos;n?1) = (1 ? apos;n)=(1 ? apos;), which follows (with some e ort) from (12). Thus mean reversion attenuates the impact of short rate innovations on long bond prices, an implication we see in the declining volatilities of yield changes with maturity ( Table2 B). These patterns come from a relatively simple model, but they illustrate the challenges facing a practitioner who would like to value options that vary across both maturities (option and bond).... ..."

### Table 2 Properties of Yield Spreads and Monthly Changes in Yields

"... In PAGE 11: ... In the data, however, long yields and yield spreads exhibit, respectively, higher and lower autocorrelations than the short rate. A related issue is the decline in volatility with maturity, such as the standard deviations of one-month changes reported in Table2 B. These models imply less variability of long rates than short rates, but the rate of decline is greater in both models than we see in the data.... In PAGE 18: ... In fact, innovations in interest rates appear markedly non-normal, typically with fat tails indicative of kurtosis. Table2 B is suggestive: one-month changes in the short rate exhibit excess kurtosis of about 10. Since departures from normality can have a signi cant impact on prices of options and related derivatives, we discuss them at some length.... In PAGE 19: ... We estimate this to be 9.302, a slightly smaller value than we report in Table2 B for short rate changes. This value is computed from the residuals of a rst-order autoregression for the short rate.... In PAGE 28: ... In the Vasicek model, a unit fall in the short rate is associated with a rise in the logarithm of the n-period bond price of (1 + apos; + + apos;n?1) = (1 ? apos;n)=(1 ? apos;), which follows (with some e ort) from (12). Thus mean reversion attenuates the impact of short rate innovations on long bond prices, an implication we see in the declining volatilities of yield changes with maturity ( Table2 B). These patterns come from a relatively simple model, but they illustrate the challenges facing a practitioner who would like to value options that vary across both maturities (option and bond).... ..."

### Table 1 US Corporate Bond Yield Spread 1985-95

"... In PAGE 9: ... This is mirrored in empirical studies where it is always found that the credit spread widens at an increasing rate as the credit rating worsens. This can for instance be seen in Table1 taken from Duffee (1998) for US investment grade... In PAGE 10: ... By re-valuing the debt instrument assuming a transition to a given credit rating class and then taking expectations, the MTM-mode of credit risk management models effectively take this empirical evidence into account. However, the relatively large standard deviations shown in Table1 should also be taken into account when computing unexpected losses. 3.... In PAGE 25: ... The relation is clearly not linear: the difference between the BBB-rated indices and AA-rated indices is generally much higher than between other adjacent rating classes. Remarkably, the spreads are considerably lower than the spreads reported by Duffee (1998) and given in Table1 . For AAA- rated bonds, our spreads vary between 17 basispoints (bp) and 31 bp, whereas Duffee finds at least 67 bp.... In PAGE 46: ... They can therefore be seen as the contribution of spread changes in return variance. Given the fact that the relationship between spread changes and interest rate changes is negative (see Table1 3), the covariance term will be negative, inducing two off- setting effects: the variance of spread changes implies higher return variance, but the negative covariance term reduces return variance. A priori, it is unclear which effect dominates.... In PAGE 51: ... Also, all the slope coefficients are negative, which implies mean-reversion. Second, the estimated implied long-run spread levels to which spreads should eventually revert (shown in the last column of Table1 5) are very comparable to the reported average spreads in Table 7. The long-term levels are also internally consistent in the sense that lower rating classes have higher long-term spread levels than better rated classes in comparable maturity buckets.... ..."

### Table 6: Simultaneous Equations: Ras Gas Yield Spread Changes

"... In PAGE 18: ...hich decreases the demand, i.e., direct breach of contract risk all other things being equal. In Table6 , we replicate the simultaneous equation analysis for RGS and KORELES in first differences. As in the previous analysis (see Table 4) levels of the explanatory variables perform better than their differences with the exception of the rating variable KRR.... ..."

### Table 1 provide the autocorrelation in level shifts and yield spreads.

1995

"... In PAGE 7: ...Table1 a.... In PAGE 8: ...Table1 b.... ..."

### Table 6: Correlations of Yields, Spreads, and Ex Post Average Rates Ex Post Ex Post Yield Short

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