Trading The Default Swap Basis

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Trading The Default Swap Basis

The growth of the credit derivatives market has created new relative value opportunities for credit investors. One such opportunity is trading the default swap basis in which investors may take a relative value view on the spread between a bond issued by some entity, and the spread demanded by a default swap contract linked to that same entity. While there is a theoretical relationship between these two spreads, there are a number of factors that may cause this relationship to break down which have been described in a previous Learning Curve (DW, 12/17). In certain cases this can present clear investment opportunities to investors.

Before outlining how to exploit these opportunities we need to clarify our basic terminology: we define a long basis trade as one in which we buy the asset and buy protection. A short basis trade is one in which we sell the asset and sell protection.

 

Implementing A Long Basis Trade

The standard way for a credit investor to go long the basis is to purchase the bond and enter an asset swap and to then buy protection. In a standard par asset swap, the investor pays par to buy a package consisting of the bond plus an interest-rate swap to exchange the fixed coupon on the bond for payments of LIBOR plus a fixed spread known as the asset-swap spread.

How precisely the credit risk of this position should be hedged depends on a number of factors, most important of which is the initial full price (clean price plus accrued interest) of the bond. As a default swap is a par product it can only hedge the difference between par and the recovery value of the asset. This is not a problem if the asset is initially priced at par. However, if the full price of the asset is trading away from par, a default swap does not exactly hedge the initial investment.

 

Face-Value Hedge

To see this in more detail, consider the case of an investor who purchases a fixed-rate bond and enters an asset swap, and buys protection with a default swap on the full face value of the bond to maturity. We call this a face-value hedge. Assuming that the cost of funding is LIBOR flat, the difference between the asset-swap spread and the default-swap spread gives the annual carry for the investor in this trade.

In the event that the asset defaults, the investor is left with a defaulted asset and an off-market swap, which must be unwound. Initially, the value of the interest-rate swap equals 100%--the full price, but this changes over time as interest rates change and as the swap rolls down the LIBOR curve. If the asset is a premium asset, the mark-to-market will initially be negative. If the asset is a discount asset then this swap will initially be worth a positive amount and any default will result in a positive payment from the swap. As maturity is approached, the value of the swap pulls to zero so that the net position equals par at maturity in the event of default.

 

Market-Value Hedge

An alternative hedging approach for the investor is to determine the amount of default protection in order to protect their initial investment. We call this a market-value hedge. It means buying protection on a notional amount equal to the market hedge ratio times the face value of the cash where:

The effect of this approach is to change the carry on the position. The gain on default is initially zero provided our assumption of the expected recovery rate is correct. If default does occur and the actual recovery rate is different from the expected recovery then the gain on default is:

For a discount bond this means that we lose if the actual recovery is less than the expected recovery, and gain if the actual recovery is greater than the expected recovery. For a premium bond we lose if the actual recovery is greater than the expected recovery, and gain if the actual recovery is less than the expected recovery. We therefore have a recovery-rate risk, which can be for or against us.

 

Zero-Recovery Market Hedge

A third type of hedge is to buy a notional amount of protection equal to the market price of the bond. This is equivalent to the market-value hedge with an expected recovery rate of zero. We therefore call this a zero recovery market-value hedge. The cost of protection for a discount bond is between that of a face-value hedge and a market-value hedge. It guarantees that an investor can never lose more than their initial investment. However, it still leaves the investor underhedged on a mark-to-market basis as the asset accretes up to par. We view the zero-recovery market hedge as an attractive compromise between the face-value and market-value hedging strategies since it eliminates the downside recovery risk and has greater carry than a face-value hedging strategy for a discount bond.

 

The Theoretical Relationship

Using a simple model of default and recovery we can establish a theoretical relationship between the default-swap spread and the asset-swap spread for all three hedging strategies. In Figure 1(a) we plot the annualised carry versus gain in the event of default for the three hedging strategies. The first thing to note is that all three lines pass through the origin. This corresponds to the case when the asset price is at par in which case all three hedging strategies are equivalent and the carry is zero. The market-value hedge is a vertical line since, assuming that the actual recovery rate equals the expected recovery rate, there should be zero gain in the event of an immediate default. We can see this more clearly in Figure 1(b) where we have plotted the carry versus the bond price. Once again all three lines intersect at a price of par. The carry for the market-value hedge increases as the bond price falls below par, reflecting the fact that while we are hedged for an immediate default, we are underhedged as the bond accretes to par. However we are fully hedged if the bond price falls. On the other hand, the carry becomes more negative for a face-value hedge as the bond price falls since we become overhedged to an immediate default. This over-hedging reduces as the bond accretes to par.

 

Long Basis Equivalent To Covered Put

Note that one way to view a long basis (long cash, long protection) position is as a covered put option. The option's intrinsic value is 100%-P which declines to zero if the credit improves or as the bond pulls to par and increases if the credit deteriorates. The negative carry on this trade is equivalent to the amortised option premium. As the default-swap premium terminates on default, the earlier the default, the less premium we will have paid for this option.

Conclusion

In order to help investors exploit the new relative-value opportunities provided by the default swap basis, we have set out some of the issues around the implementation of basis trades for bonds which trade away from par. For non-par bonds, we have shown that there is an effective default option whose risk-return profile can be chosen by the investors hedging strategy.

This week's Learning Curve was written by Dominic O'Kaneand Robert McAdie, directors in the fixed income research group at Lehman Brothersin London.

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