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Measuring the yield spread of callable bonds
One of the most common ways to compare the potential returns of different municipal bonds is to compute the extent to which the bond’s yield to maturity or call date exceeds the yield of triple-A rated, general obligation (GO) bonds with the same maturity. While such comparisons have long been a factor in decisions by institutional investors, it has only been recently that retail investors have been able to make such comparisons using yield curves published by the Municipal Securities Rulemaking Board.
However, because most municipal bonds are subject to early redemption at the option of the issuer, retail investors may have difficulty discerning what the yields on a yield curve say about the relative value of a bond they may want to buy or sell. This report explores the role of yield curves in assessing a bond’s attractiveness.
A bond's relative value can be measured in two ways
The yield curve most commonly used by institutional investors is the MMD scale published by Refinitiv. One notable feature of this scale is that it assumes that the bonds have a 5% coupon and are redeemable at the option of the issuer in 10 years.
The rationale for assuming a 5% coupon is that institutional investors have favored that coupon rate on new issues. As a result, 65% of the market value of bonds in the Standard & Poor’s Municipal Bond Index have a coupon rate of between 5.00% and 5.50%. With 30-year bonds yielding 1.89% and 20-year bonds yielding 1.70% as of 23 Aug 2019, the probability that a bond with a 5% coupon will not be redeemed 10 years from now seems small.
An alternative measure of a bond’s relative value is its option-adjusted spread (OAS). Estimating a bond’s OAS requires using a pricing model that can value the issuer’s option to redeem the bond in advance of its maturity date. Such a model is designed to answer three basic questions:
1. What would the present values of the cash flows of the bond be worth if each coupon payment and the final principal payment were discounted at the yield appropriate for a triple-A rated, zero coupon bond maturing on the date of a given cash flow?
For bonds yielding higher than the yield of a triple-A rated bond with the same maturity, the sum of those present values will typically be higher than the bond’s current market price. The aggregate present value of the cash flows will also vary depending on whether the payments extend to the final maturity or end at a redemption date, which leads to the next question.
2. What is the probability that the bond will be redeemed in advance of its maturity date? The cash flows can then, in effect, be weighted by their probabilities.
3. By how much do we need to increase the discount rate applied to each cash flow in order to get the sum of the present values to equal the current market price of the bond? The OAS is the amount by which the discount rate must be increased.
Comparing callable and noncallable yield curves
For purposes of estimating the OAS of a bond, it is necessary to use a noncallable yield curve. In the first 10 years, the yields of noncallable and callable curves are the same, since the assumption is that bonds will not be called until at least 10 years have elapsed since issuance.
Ordinarily, one would expect the yields of callable bonds to be higher than the yields of noncallable bonds, since the call option has value to the issuer that reduces the value of the bond to the holder. However, because today’s interest rates are considerably lower than the 5% coupon rate that is assumed, yields of callable bonds are lower than those of noncallable bonds. For example, according to Standard & Poor’s noncallable triple-A scale, on 23 Aug 2019, a 20-year bond would yield 2.00%, while the MMD callable yield on a 20-year bond on that date was 1.70%.
The lower yield of callable bonds indicates that investors have a high degree of confidence that the bonds will be called in 10 years, and so they price the bonds using yields that are between the yield of a 20-year noncallable bond and a 10-year bond (which yielded 1.24% on 23 Aug).
Comparing OAS and spreads to a yield curve
OAS is generally considered to be more sophisticated than the spread to MMD, and we thought it would be helpful to compare the two measures. In this analysis, we computed the excess of the bond’s yield to worst over each of four values:
- The yield on S&P’s noncallable triple-A yield curve corresponding to the bond’s maturity.
- The yield on MMD’s callable yield curve corresponding to the bond’s maturity.
- The yield on S&P’s noncallable yield curve corresponding to the bond’s priced-to date (usually a call date, unless the bond is noncallable).
- The MMD yield corresponding to the bond’s priced-to date.
Figure 1 shows the spreads for a bond with a 5% coupon that matures in 13 years, but is priced to a call date in five years. The bond has a market yield of 1.40% and an OAS of 0.39%.
In this instance, the spread to either a callable or a noncallable yield based on the maturity of the bond appears to understate the bond’s value as reflected in its OAS. However, the spread based on the priced-to date exactly matches the OAS.
In our analysis of a sample of more than 200 individual bonds, we found that the bond in our example was fairly typical. Figure 2 shows the correlation (R-squared) between the OAS and the spread to priced-to date was higher than it was for spreads to maturity date, and the average difference between the OAS and the spread was smaller when the spread was based on priced-to date rather than maturity date.
In the case of bonds that mature in more than 10 years, and are priced to their maturity dates, the average difference between the OAS and the spread to the noncallable yield curve was only 0.03%, which is what one would expect when call options do not complicate the valuation.
When the difference between the maturity date and the priced-to date is 10 or more years, the difference between the OAS and the various measures of spread to a yield curve is amplified, but here too the OAS is closer to the spread based on priced-to date than the spread based on maturity date.
It makes sense that the OAS would, on average, be slightly lower than the spread based on priced-to date since the OAS is lowered to reflect the risk that the bond might remain outstanding to maturity. If investors were 100% certain that the bonds would be called at the first call date, they would be satisfied with a yield that was 0.98% higher than the yield corresponding to the priced-to date, but instead they require a yield that is 0.13% higher to compensate for extension risk.
On the other hand, if they were 100% certain that the bond would remain outstanding to maturity, they would demand a yield that was 0.98% greater than the yield of a noncallable, triple-A bond with the same maturity, but instead they are content with a yield that is only 0.15% higher. From these comparisons we can infer that, on average, investors in these bonds with long maturity dates perceive only around a 14% risk that their bonds will extend to maturity (13 / (83 + 13) = 14%).
We should also note that if the bonds remained outstanding until maturity, the return to investors would increase as a result of receiving a 5% coupon for a period that is longer than the call date that was used in pricing the bond. If the bond in our earlier example were priced to remain outstanding until maturity, its yield would rise from 1.40% to 3.29%.
Now that the Municipal Securities Rulemaking Board has begun publishing yield curves from various providers so that retail investors can have a better sense of how bonds are valued, it is important for investors to know where to look on the yield curve when they are evaluating callable bonds.
Appendix: Fixed income option pricing models
Pricing models are used to compute option-adjusted values such as effective duration, key rate durations and option-adjusted spreads. The basic structure of the model is a binomial probability tree, which assumes that there is an equal probability that the interest rate in one period will be higher or lower than the interest rate in the previous period. The result is a set of future interest rates that, when diagrammed, look like a tree whose branches become more numerous as the time between the present and future periods increases.
The tree is populated with forward rates, which are short-term, single-period interest rates. The compounded value of a series of forward rates will equal the yield of a zero coupon bond whose maturity corresponds to the maturity of the last forward rate in the series. As a result, different interest rates are used to discount the value of cash flows to be received at different times, which is unlike how bonds are priced in the market, which involves using the same yield to compute the present value of all cash flows.
At each payment date, which represents a node where two branches of the tree diverge, future cash flows are discounted to the present value as of that payment date, and that present value is discounted by the forward rates of earlier periods.
Assumptions about the volatility of interest rates will determine the size of the projected change in forward rates up and down from one period to the next.
When forward rates are so low that they cause the present value of cash flows coming after a redemption date to be greater than the redemption price on that date, the redemption price is used as the value that is to be discounted using the forward rates for periods that precede the redemption date. In this way, the call provision lowers the theoretical value of the bond.
MMD AAA municipal yield curve; https://www.refinitiv.com/en/financial-data/market-data/municipal-market-monitor-tm3 (subscription required)
Standard & Poor’s yield curves; Subscription required, not available on WebsiteMunicipal Securities Rulemaking Board; Yield Curves; https://emma.msrb.org/ToolsAndResources/MarketIndicators
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