Bond yields are customarily expressed relative to benchmarks. The old-fashioned credit risk measure was the difference between the yield-to-maturity (YTM) of a risky bond and that of a like-maturity Treasury bond. The modern-day measure is the so-called option-adjusted spread relative to a riskless benchmark yield curve.
For taxable bonds, the standard benchmark curves are specified by the yields of Treasury bonds and LIBOR swaps. In both cases the prices of the underlying securities/contracts are optionless. In contrast, longer-term muni benchmark yields are based on the prices of callable bonds. The current practice is to define benchmark curves by the yields-to-call (YTC's) of 5% NC-10 bonds (NC-10 means not callable for 10 years). Several vendors, such as MMA, MMD and Standard & Poor's publish AAA 5% NC-10 curves, and some even distribute state-specific and credit-specific 5% NC-10 curves. Although less prevalent, some vendors still report par NC-10 benchmark curves.
As discussed in my recent article in this paper — "
Bond math students are familiar with the method of 'bootstrapping' an optionless par curve into its implied spot (pure discount) rates and forward rates. These curves are 'equivalent' – any of the three implies the other two. If you believe that the par curve is correct, you must also accept the other two. Negative forward rates implied by the par curve would raise doubts about the validity of the par rates. As we'll see, similar sanity checks are also essential when it comes to callable benchmark curves.
Conversion Problems
Kalotay Analytics licenses a calculator which converts vendor-provided callable benchmark curves into optionless curves. As an example, Figure 1 displays a recent MMA 5% NC-10 curve and its implied optionless par curve (at 15% interest rate volatility). Here, the YTC of the 30-year bond is 3.10%, and the implied optionless 30-year par rate is 3.53%.
We frequently get calls from distraught clients complaining that the calculator failed to solve for an optionless curve. Their immediate reaction is that the software must be defective. However, even before troubleshooting, we already know the source of the problem. It turns out that in every case it is the curve, not the software, which is defective. Detecting bad curves is easier than you think; below we show you how.
How to Detect Bad Benchmark Curves
Two related factors simplify the specification of a par curve: the dollar price of each underlying bond is 100, and therefore for each maturity, the YTC, YTM, and coupons are the same. However, in the case of a 5% NC-10 curve the dollar prices vary by maturity, and the YTC and YTM are different. Although dollar prices are obviously important, the market participants tend to quote the corresponding YTC's. As we will see, prices can reveal bad curves just by inspection.
Par NC-10 Curves
As shown by
You can see this intuitively by putting yourself in the position of a municipality that wants to issue 20-year NC-10 bonds at par. If the coupon (yield) of a 21-year NC-10 happened to be lower, you would prefer it to the 20-year bond. You could call the 21-year bond whenever you wanted to call the 20-year bond, and if you allowed the 20-year bond to mature, you could call the 21-year bond at par after 20 years. So in every case, you would be certain to benefit from the lower debt service of the 21-year issue. Now put yourself into the position of an investor. By the same argument, you would be sure to lose by accepting a lower coupon on the 21-year bond. Thus in the case of callable bonds sold at par, the longer the maturity the higher must be the coupon/yield.
5% NC-10 Curves
As discussed above, currently the typical benchmark municipal yield curve is based on the prices of 5% NC-10 bonds. Because for investment-grade issuers the prevailing borrowing rates are well below 5%, the yields are specified as YTC's, rather than YTM's.
Once again, let's consider the perspective of an issuer who can sell callable 20-year or 21-year 5% bonds. If the market price of the 21-year bonds happened to be higher, the issuer would sell the 21-year bonds for greater proceeds, and then manage them exactly the same way it would manage the 20-year bonds. There would be no downside for the issuer. Therefore investors should pay less for 21-year bonds.
So in order for a 5% NC-10 curve to be sound, the dollar prices of the bonds must decline with maturity. Increasing YTM's alone do not guarantee that the callable curve can be converted – what's needed are declining dollar prices.
Recommendations
In summary, the municipal market is in a dire need of realistic optionless yield curves. The recommended approach is to convert a callable curve into an optionless one. However, in order to be convertible, callable curves must satisfy the conditions discussed above: the YTM's of par bonds must increase, and the prices of 5% callable bonds must decline with maturity. Otherwise the yield curve is defective and should be rejected. Anyone who tries to convert a defective callable curve into an optionless one sooner or later realizes that it cannot be done. But what happens to those who use a bad callable curve in its raw form? They will probably never realize that they are making decisions on nonsensical information.
Bottom line: Check that your callable benchmark curve is valid before using it; otherwise garbage in, garbage out.
Andrew Kalotay is president of Andrew Kalotay Associates
