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Hedging a Credit-Linked Instrument Such as an Asset-Backed Security

We have seen in Section 6.4.2 that some instruments an institution can invest in are asset-backed securities, instruments that pay a coupon linked to the receivables from a specific pool of assets. These instruments can be hedged with an asset swap, however, as they can be fairly risky, the type of hedge that isolates market and credit risk is either a total return swap or a repurchase agreement, which are similar, although the latter tends to be more present in mature and liquid markets.

Hedging an asset-backed security with an asset swap does not differ greatly from hedging a fixed or floating vanilla bond.

In Table 7.6 we show the situation in which we have purchased an ABS paying a coupon Ci, which can be either fixed (in which case Ci will be the same for all i) or floating. The value of this instrument is obtained by discounting with a cumulative discount factor . It is worth reminding that the credit correction will, of course, be different for each of the examples in this section. (In this example it is the credit correction due to the credit of the ABS issuer.) After purchasing the instrument, we enter into a swap in which we pay the coupon received from the bond and receive in return a floating rate plus a spread sASW. The net outcome is that now we are receiving floating rate plus sASW. As usual, Ф denotes the difference resulting from the different discounting of the bond and the swap.

As we have said, asset-backed securities can be considerably risky and therefore can dramatically decrease in value or can default.[1] We know that in an asset swap after the initial setting of the spread sASW, the link between the security and the swap is not a tight one. Although the value of

TABLE 7.7 The hedging of an investment in an ABS with a total return swap.

Instrument type

Pay/Receive

Leg structure

Fixed/Floating ABS

Receive

Fixed/Floating TRS Leg

Pay

Floating TRS Leg

Receive

Result

Receive

the coupon leg in the swap and the value of the bond will change in a similar (but of course opposite) fashion, this will be only if the change is linked to the coupon value or the pure interest rate element of the discount factor. If the change in the bond value is driven by the credit standing of the issuer, that is, it is driven by the discounting correction , then the bond and the coupon leg of the swap will be out of sync and, should the change be such that the bond loses value, the bond holder faces an overall loss. From the bond holder perspective, in this case the institution investing the bond, the income received from the bond is worth less than the liability represented by the coupon leg of the swap.

A type of static hedging that solves the issue presented above is one where the institution purchasing the bond enters into a total return swap. The situation is shown in Table 7.7.

The payout of the bond is, of course, similar between the situation presented in Tables 7.6 and 7.7. In a total return swap (TRS), the bond holder passes on to the swap counterpart not only the fixed coupon but also any appreciation or depreciation of the bond: of course to pass an appreciation is to pay something and to pass a depreciation is to receive something.

In Table 7.7 we have expressed the bond value at timeasand the appreciation/depreciation between two coupon datesandas . In the table the pay leg of the swap is seen from the point of view of the bond holder so, should the bond appreciate (i.e.,), the positive amount of the difference, with the negative sign in front, results in a payment on the bond holder part. Should the bond depreciate (i.e., ), the negative amount given by the difference, with the negative sign in front of the leg, results in a payment from the counterpart to the bond holder in addition to what the swap counterpart is already paying in the form of a floating rate plus spread. This does not apply to the final cash flow because, by definition, if the bond issuer has not defaulted, the bond is worth par.

We see why the transaction is called total return swap, because what is transferred between the two parties is not just the coupon of the security but the total mark-to-market (MTM) gain or loss as well. Should the bond

TABLE 7.8 The hedging of an equity investment with an equity return swap.

Instrument type

Pay/Receive

Leg structure

Equity investment

Receive

Floating Equity Swap Leg

Pay

Floating Equity Swap Leg

Receive

Result

Receive

issuer default during the life of the swap and the bond price drop to some recovery value, the swap counterpart will pay the bond holder the difference between that value and par.

We are now able to comment on the relative returns of the two types of static hedges. As the TRS offers considerable protection to the bond holder, it is not difficult to see why the return in terms of spread over the floating rate is lower than in the case of a simple asset swap and we have therefore . It is for the institution to decide whether it is worth taking the risk of hedging an ABS with an asset swap. A traditional financial institution, where the goal is the maximization of profit, would probably opt for an asset swap hedging; a development bank, whose goal is simply to gain a positive return over the benchmark (we can assume that Lj represents the benchmark), would probably opt for the TRS hedging.

Let us note as well that in Table 7.7 we do not have Ф anymore: this is because the difference between the bond price and the corresponding swap leg driven by the change in the credit, and therefore the discounting, of the bond is now included in the passing of the appreciation/depreciation of the bond between the bond holder and the swap counterpart.

  • [1] This, of course, applies to all securities, but in the case of ABS there is a stronger argument to be made.
 
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