The use of credit-default swaps as a hedge for all or a portion of the credit risk embedded in a convertible bond has increased dramatically over the past few years. One reason is that convertible arbitrage funds attempt to profit by buying embedded equity options cheaper through a convertible bond than is possible by purchasing the option separately in the equity derivatives market. Thus, although arbitrage funds are typically focused on isolating the equity option's value, the repackaging of the equity option in the convertible bond gives rise to other risks inherent in bonds--such as interest rate and credit risk--that are frequently hedged.
Credit-default swaps provide a credit risk hedge to the purchaser of protection. As the credit derivatives market has grown, more convertible arbitrage funds have employed this hedge. Fortuitously, as buyers of protection, the hedge funds have benefited during the recent secular spread widening, thereby increasing the hedge's popularity.
How It Works
As a trade example, a convertible arbitrage fund purchases a desired convertible issue after taking into account the offer price, the implied price of the option and other hedging costs. The fund will then hedge the various risks associated with the issue and will typically hedge the bond's credit risk via a default swap. The protection is most frequently matched to the convertible bond's put date, typically three years or less. The put date is the natural maturity date for the credit-default swap, because on that date the bonds will either convert to stock or be put back to the issuer--in either case, eliminating the need for credit protection. Furthermore, purchasing protection beyond the put date on the convertible bond exposes the convertible fund to risk on the unwind of the credit protection. In other words, the fund is overhedged and may face a loss on the unwind if no credit event occurs before the put date or the date the bond is converted to equity.
Credit-default swap activity in the convertible sector has created inversions in premiums from the put dates on converts to the liquid five-year tenors. This technical inversion must be considered analytically in terms of a comparison to the cost of the tail risk of a five-year position. There should be an approximate equilibrium for this inversion; in other words, convertible arbitrage funds should look at quantifying the tail risk to compare with the inversion level in premiums to the put date.
A simple example shows this equilibrium. Assume ABC Corp. has a zero-coupon convertible bond maturing in 2021 but has a put date exactly two years from today. Also assume the default swap is quoted in the two- and five-year tenors at 100 basis points and 50bps, respectively, an inversion of 50bps. The convertible fund must decide whether to hedge the credit risk to the put date at 100bps per annum or hedge in a five-year tenor for 50bps per annum with the understanding that there will be tail risk on the unwind of the five-year trade two years from today. A mathematical description of this decision process is detailed below.
Using a PV01 factor of a two-year trade of 1.92, the present value of premium savings to the hedger is 96bps to the put date of the convert. Table 2 details the unwind scenarios and corresponding present value gains and losses on the unwind levels. The fourth column shows the net gain or loss, including the 96bps savings based on the five-year default swap premium at trade inception.
As depicted, there is a loss to the hedger if the unwind level (the three-year credit-default swap two years from now) is tighter than the 50bps level on the original trade. Taking the savings into account, however, there is a net gain in all of the above scenarios until the default swap tightens to 10bps (all of the numbers are present valued to today). In fact, there is an equilibrium whereby the net gain is zero. That equilibrium is 14bps in this calculation, a tightening of 36bps.
This example shows funds must evaluate inverted protection curves because five-year trading levels more closely reflect the true credit risk of the entity, whereas levels priced to put dates are technically biased.
Other Important Considerations
No restructuring versus modified restructuring. The inclusion or exclusion of modified restructuring as a credit event in the U.S. default swap market has been a hot topic lately. There has been some accommodation in the market to trade credit-default swaps in a bifurcated manner, with names quoted with and without the modified restructuring credit event. The premium assigned to the inclusion of modified restructuring is frequently 1020% of the default swap level without modified restructuring. Given that credit-default swaps to put dates on converts most frequently trade without modified restructuring and five-year trades include modified restructuring, there is a tangible benefit to be considered when buying five-year swaps versus swaps to the put date.
Bid/offer spreads. The bid/offer spreads quoted for default swaps to the put dates of a convertible are frequently wider than the more liquid five-year tenors for the same credit. This can be especially important for early unwinds. We have seen a number of convert hedgers unwinding trades with the swaps market flat, thereby subjecting themselves purely to the bid-offer spreads. Table 3 shows some examples of bid-offer spreads from some indications as of Oct. 28.
Conclusion
It is important for convertible arbitrage funds that hedge credit risk through the default swap market to consider the economic impact of the tenor of their hedges. The swaps market has become technically inefficient because these considerations are being ignored. Furthermore, it is important to consider the market characteristics of trades with different tenors, especially with respect to the inclusion of restructuring as a credit event and the higher transaction costs often associated with shorter tenors with wider bid/offer spreads.
This week's Learning Curve was written by Nichol Bakalar, head of structured product research, and Chad Strean, v.p., at Wachovia Securities.
