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NonConstancy of Credit Spread Sensitivities

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The non-constancy of credit spread sensitivities would naturally be embedded in their dependence on state variables in the RCR model. However, we would like to see how they change over time, and compare it to the simple linear regression sensitivity estimators, and find out why the RCR estimators provide better accuracy.

Let's take one bond as example, the bond with CUSIP of "001765AE", one of American Airlines' long term bonds, and depict its random coefficients and constant coefficients. The following three figures show the comparison of regression coefficients with respect to interest rate changes, leverage changes, and volatility changes.

sensitivity to r w

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• nf # # ^ ^ ^ # <$> ^ ¿P ^ ^
• beta dr linear
• beta dr RCR

Figure 4.6 Coefficient for Ar in RCR vs. Linear Model

1. 2
2. 4
3. 6
4. 8

sensitivity to lev
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3 -	fli/
2 -	1 % ay ^wv m w VJL
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♦ beta_dlev_linear —■—beta_dlev_RCR		<5? # <5? ¿0-p # # / ^ / ^

Figure 4.7 Coefficient for Avol in RCR vs. Linear Model

Figure 4.7 Coefficient for Avol in RCR vs. Linear Model

sensitivity to sig

• ^
• beta dvix linear
• beta dvix RCR

Figure 4.8 Coefficient for Alev in RCR vs. Linear Model There are three major findings from the graphs:

1. Sensitivity to Ar does change over time. In Merton's model, increased interest rate would increase the risk neutral drift term, thus decrease the default probability, and shrink the credit spread. In reality, Fed generally lowers interest rate to stimulate economy when there is a recession, which is the case during 1990-1992. Generally higher credit spreads are observed during a recession. That is the main reason for negative correlation between interest rate and credit spread. However, what about during times of economic recovery or boom? It would be interesting to compare Figure 4.6 which depicts the sensitivity of credit spread to interest rate, to Figure 4.9, the history of 3-month Treasury rate, a close reflection of Fed's policy on funding rate. When the economy is recovering, lowering interest rate would have less effect on credit spread. That is exactly the case we found during 1992-1993, when the Fed continued lowering the short interest rate, and the sensitivity of credit spread to the interest rate is close to zero. Also when economy is booming, the Fed is likely to raise the interest rate, and that seems to have little effect on the credit spread. That is likely the case for 1994-1995.
2. Sensitivity to Aa also changes over time. In structural model, increase in volatility would increase the default probability, and thus widen the credit spread. However, comparing Figure 4.8 with 4.10: the history of VIX volatility index, we found that while volatility is high both in the early 90's and the late 90's, their impact on credit spread sensitivity are quiet different. One explanation for this could be that during a recession, volatility is a bad thing, because it is likely that the volatility is a result of dropping equity, and investors will be really concerned with a volatility spike. However, when the economy is booming, it is likely that high volatility is introduced by rising stock prices, and investors are less likely to require high credit spread for this "good volatility".

Figure 4.9 Three-Month Treasury Rate from 1990 to 1997

vix

Figure 4.10 VIX index from 1990 to 1997 Of the three volatility measures we used, our results show that VIX is better than both history volatility and excess volatility, which is unanticipated. Originally we thought that since VIX is a broad market volatility index, replacing it with company specific volatility should improve our results. The reason for this phenomenon might be that credit spread response is more sensitive to market perception of risk than to historical

Figure 4.10 VIX index from 1990 to 1997 Of the three volatility measures we used, our results show that VIX is better than both history volatility and excess volatility, which is unanticipated. Originally we thought that since VIX is a broad market volatility index, replacing it with company specific volatility should improve our results. The reason for this phenomenon might be that credit spread response is more sensitive to market perception of risk than to historical volatility. Also we tried the excess return volatility, which Campbell and Taksler (2003) claims to have significant explanatory power in regression of credit spread levels. The results are disappointing, and the adjusted R2 is comparable to historical volatility, but not as good as VIX index. The reason might be that the credit spread itself already has a build-in premium associated with the standard deviation of excess return, but the change of credit spread is not sensitive to its change, so the regression on credit spread levels and changes will have different explanation.

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