The US Municipal Bond Risk Model. Oren Cheyette

The US Municipal Bond Risk Model Oren Cheyette

THE US MUNICIPAL BOND RISK MODEL Overview Barra s integrated risk model includes coverage of municipal bonds accounting for marketwide and issuer-specific risks of investment grade municipal securities. The municipal bond market is affected by financial factors somewhat distinct from the primary drivers of the taxable bond market. Aside from the obvious different in tax treatment, some other key differences are: A very large number (about 2 million) of relatively small, illiquid issues Additional option features, such as pre-refunding The new model is designed with these differences in mind. Because of the large number of illiquid bonds, estimation of market valuation factors is a job we believe better left to muni market professionals. Therefore, unlike our approach in the taxable markets, where we start with asset terms and prices, in constructing our muni model we start from vendorsupplied sector yield curves. Our model is based on histories of four yield curves for national general obligation (GO) bonds rated AAA (uninsured), AA, A and BBB 1. Histories of these yields back to 1994 are the basic information used in constructing the model. 1 The Muni Risk Model The muni risk model structure is similar to though simpler than the taxable US model. Like the investment grade portion of the taxable model, the dominant contribution to risk arises from market-wide interest rate levels. These are captured in the muni model by eight key rate factors, at the same maturities as for taxable interest rates: 1, 2, 3, 5, 7, 10, 20 and 30 years. Rather than following the usual practice of calculating spot rates from yields by bootstrapping 2, we calculate the current levels for the key rates by means of a modified version of our standard spot rate estimation machinery, which minimizes rootmean-squared pricing error of a universe of bonds. We do this because the practice for reporting market yields for maturities beyond 10 years is to quote yields of callable bonds. Were we to do standard bootstrapping, then use the resulting spot rate curve to value callable bonds, we would not reproduce the market yields we started from. Figure 1 shows estimated spot rates and corresponding market yields for 2/12/2001. The pronounced dip in the 30 year spot rate is primarily due to the callability of the longer bonds. In addition to the non-taxable interest rate factors, the model includes three credit spread factors: one each for AA, A and BBB rated bonds. These are calculated as average spreads of the corresponding spot rate curves over the AAA curve. Figure 2 shows estimated muni credit spreads since 1994. 1 Yield curve data is supplied daily by Delphis-Hanover corporation. 2 Bootstrapping is a procedure for recursively calculating successively longer spot rates based on market yields. Given an interpolation scheme for spot rates or yields between specified maturities, one can find, either analytically or numerically, the spot rates implied by the yields starting at the short end and working to longer maturities.

Figure 1 AAA GO Muni yield curve and estimated spot rates on 2/12/2001 Rate 5.5 5.0 4.5 4.0 3.5 3.0 0 5 10 15 20 25 30 Term (years) 2 Figure 2 Par Yields Spot Rates Credit spreads for AA, A and BBB rated GO bonds Spread (bp) 100 90 80 70 60 50 40 30 20 10 0 1/94 1/95 1/96 1/97 1/98 1/99 1/00 1/01 BBB A AA It is interesting to compare the timeseries of Figure 2 with similar graphs of swap and credit spreads in the taxable market. While the taxable credit spreads experienced huge shocks in the second half of 1998, followed by persistently higher volatility and levels continuing to the present, no such effect is visible even in the lower-grade muni spreads. Over this period, at least, the muni market has manifestly behaved entirely independently from the taxable market.

THE US MUNICIPAL BOND RISK MODEL In total, then, the muni risk model contains 11 common factors: eight key rates and three rating spreads. In addition to common factor risk, the muni model incorporates a modified version of the taxable issuer credit risk model. Based on the Credit Metrics approach, the issuer credit risk model uses historical information about credit migration rates together with current spread levels to forecast risk due to up or downgrades and default. The muni model uses the same credit migration rates as the taxable model obtained from Standard and Poor s, these are historical averages of all issuer credit migrations. Risk calculation for a bond portfolio requires not only estimates for factor volatilities and asset-specific risks, but also estimates for the exposure of each bond to the risk factors. The exposures to key rates are the key rate durations; the exposure to credit spread (for bonds rated AA and below) is the spread duration. For straight bonds with no embedded options these exposures are easily calculated by means of standard formulas for discounted present value. However, not only are many municipal bonds callable (and some putable), already necessitating use of a conventional option model, but as noted above, many bonds carry in addition a so-called pre-refunding option. This is the issuer s option to defease an issue by creating an escrow account funded by taxable Treasury securities to make remaining interest and principal payments on an issue. This creates a tax arbitrage, whereby a municipality is able to convert taxable Treasury bond payments into tax-free municipal bond payments. While the extent to which municipalities can benefit from this arbitrage is constrained, yield curve slope effects can nevertheless permit an issuer to realize savings by pre-refunding. Both the issuer and the holder benefit from the exercise of this option. Defeasance is almost always to the first call date. 3 Barra s risk analytics provide calculation of option-adjusted spread, key rate durations, spread duration and effective duration and convexity for refundable municipal bonds accounting for the value of refunding along with the other conventional options. Recent Results Table 1 shows model forecasts as of 1/31/2001 for the muni interest rate and credit spread factors and issuer credit risk. For purposes of forecasting common factor risk, muni bonds rated below BBB are exposed to the BBB spread factor. Credit risk for such bonds is modeled as for the others, by means of the credit migration model. Table 1 Common factor and issuer credit risk forecasts for municipal bonds as of 1/31/2001 Factor Factor Volatility Credit Risk Muni Spot Rates 64 bp/yr 4.2 bp/yr Muni AA 8.5 10 Muni A 11 21 Muni BBB 14 47 Muni BB 97 Muni B 240 Muni CCC 540

Recent Treasury and swap rate volatility forecasts have been hovering around 80 90 bp/yr. The first row of Table 1 indicates that muni bond interest rate volatility has been about 75% to 80% as large. This is perhaps slightly higher than the 60% 70% one might expect based on taxable yield equivalence. Taxable credit spread volatilities, on the other hand, appear to be considerably higher by factors of 2 to 3 than those for munis, as shown in Table 2. 3 Table 2 Average common factor and issuer credit risk forecasts for taxable corporate and sovereign bonds, as of 1/31/2001 Factor Factor Volatility Credit Risk AAA 22 bp/yr 11 bp/yr AA 27 26 A 31 38 BBB 37 92 BB 100 220 B 203 363 CCC 274 732 4 Figure 3 shows historical correlations (equivalently, the history of model forecasts) between the muni AAA spot rates and muni credit spreads, US Treasury rates and the swap spread. The large correlation between muni and Treasury rates is unsurprising the tax driven link between the markets would naturally be expected to play a large role for the least credit-risky munis. The figure also shows that the other correlations are all near zero. Muni AAA spot rates are nearly uncorrelated with muni credit spreads and with the taxable swap spread. Table 3 shows correlations between the swap spread and taxable credit spreads and muni rates and spreads. The high correlation between swap spreads and the various taxable credit spreads is partly a result of the recent idiosyncratic behavior of the Treasury market. However, the near zero correlation of the muni spot rates and credit spreads with the swap spread indicates that municipal market pricing has been largely independent of the turmoil in the taxable credit market. Summary The newly released municipal market risk model is designed to capture the dominant contributors to market-wide and issuer specific risk in the tax-exempt US domestic market. The eleven factors cover interest rates and common-factor spread risk for bonds rated BBB and above, and issuer specific credit risk to CCC. Recent price movements in the muni market suggest that it has been largely unaffected by the volatility of the taxable market subsequent to the 1998 credit crash. 3 The size of corporate spread volatilities is partly due to the recent decoupling of the Treasury market from the credit markets, so this comparison somewhat overstates the difference between spread volatility in the taxable and tax-exempt markets. However, the negative correlation between taxable spreads and spot rates has actually been fairly low in recent months, so the impact of this decoupling is small.

THE US MUNICIPAL BOND RISK MODEL Figure 3 Historical correlations (two year half-life) between muni AAA spot rates and each of: Treasury spot rates, muni AA, A and BBB spreads, and the swap spread over Treasuries. Correlation 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0-0.1-0.2 12/98 6/99 12/99 6/00 12/00 BBB A AA Treasury Swap Spread 5 Table 3 Factor Group Swap Spread Correlation Correlations between the US swap spread and other factors as of 12/31/2000 AGENCY 0.60 AAA 0.60 AA 0.51 A 0.57 BBB 0.52 BB 0.46 B 0.49 CCC 0.51 MBS 0.62 MUNI SPOT 0.19 MUNI AA 0.09 MUNI A 0.11 MUNI BBB 0.17 Summary The newly released municipal market risk model is designed to capture the dominant contributors to market-wide and issuer specific risk in the tax-exempt US domestic market. The eleven factors cover interest rates and common-factor spread risk for bonds rated BBB and above, and issuer specific credit risk to CCC. Recent price movements in the muni market suggest that it has been largely unaffected by the volatility of the taxable market subsequent to the 1998 credit crash.