The credit derivatives market has created a number of relative value opportunities. Diverging slightly from our credit theme, relative value is a term traditionally employed to describe strategies predominantly within the fixed income marketplace which are not directional in nature.
For example if you buy a bond out right you are taking a view on yields.
You either make or loose money depending on the direction that the yield changes. To exploit a relative value opportunity however, you would short a bond and from the proceeds buy another bond so you are neu- tral with regard to the direction of the market (usually only duration is hedged). The hope is to gain from a change in shape from the existing yield curve.
The default swap basis is the spread between a bond and the premium demanded by the market for credit protection on the bond. We would expect a strong relationship between these two spreads but often this
0 100 200 300 400 500
0% 10% 20% 30% 40% 50% 60%
Correlation
Spread (bps) Worst
First to default Sum
Figure 3.19 The first to default note bps against correlation.
can breakdown, the relative value default swap trade seeks to exploit these opportunities. There are two ways of exploiting this difference the first is the long basis trade in which the investor buys the assets and simultaneously buys protection. The converse is a short basis trade in which the investor sells the asset and simultaneously sells protection.
Long basis trade
There are a number of ways of going along the basis for a particular credit, the choice to a certain extent will depend on the types of instru- ments the borrower has issued into the market. We begin with an analy- sis of a basis trade which is carried out by purchasing a par FRN and protection. This will illustrate the relationship between the spread on the floater and the default protection premium. From Figure 3.20 we can see that the default spread is equal to the asset swap spread when the asset is at par.
Buying protection
If an investor wishes to be immunized against the default of the issuer there are a number of assumptions which must be considered prior to constructing the hedge. It is not a simple case of sourcing protection, but rather the details depend on the nature of the underlying asset.
We consider the case of a common example; an asset swap on a vanilla bond. (The motivation and arrangement of this have been discussed in some depth within Section 3.8.)
Hedged investor Asset
Funding Protection seller
Borrows 100 Libor
Default swap spread Pays 100
L spread
Figure 3.20 The risk free basis trade. Source:Lehman.
Asset swap
Our investor purchases the bond through an asset swap. But is con- cerned about the credit in the short term, and thus takes out protection on the bond. The rather frustrating aspect of the hedge is that it is only partial. We can elaborate with regard to Table 3.7, which features a bond with a notional of €100.
We can see from the Table 3.7 that the initial hedge of taking out protection on the nominal value of the bond subsequently asset swapped leaves some unedifying consequences. The entry price, assuming the purchaser funds at libor, is flat. Further the carry on the trade, assum- ing the asset swap margin is fairly valued and equal to the default swap premium, is close to zero.
If the bond was to default immediately the investor would be in the unfortunate position of not being fully hedged if the bond was trading away from par, which could be due to a change in the prevailing inter- est rate relative to the inception. Thus the effectiveness of the hedge depends on the underlying interest rate environment, together with the perceived credit risk of the issuer supplying the bond.
To be a little bit more specific we will work through some numbers.
The bond on asset swap unfortunately involves some mental gymnastics.
(However it represents the most common arrangement of hedging rate risk inherent in a bond.)
The carry on the structure will be
which nets out to be
marginpremium.
What about the profit assuming immediate default? That depends on where the bond is trading relative to par. If the bond is above par then we lose money because the protection only gets us back 100 recovery.
But we gain on the carry. The converse is true when the bond is trading below par.
Bond asset swap default swap funding
coupon libor margin coupon premium libor,
Table 3.7 The payoff for a hedger of protection.
An asset swapped bond with credit protection
Component Bond Swap Funding CDS
Entry Price (100Price) 100 0
Immediate Recovery 100Price 100 100recovery
Default later Recovery M to M 100 100recovery
We reproduce the graph (Figure 3.21) which illustrates these characteristics.
These results can be obtained by examining any bullet bond with a fixed coupon on asset swap and the model described in Table 3.8.
To determine the gain we need to calculate the price of the bond this is given by the formula:
where DFtis the discount factor at time tand rec.is the recovery value in the event of default. The survival probability is normally implied from the default swap market, and we refer the reader to Section 3.14 where there is a worked example of this ‘bootstrap’ methodology. How- ever in the example displayed in Figure 3.21, the survival probability was taken as the standard function of a uniform hazard rate.
Having determined the bond price, the carry is the difference between the asset swap margin and the default spread (which is just an expres- sion involving the survival probability, the recovery rate (which has to
Survival probability( ) exp(t t).
Bond price coupon survival probability
100 survival probability ( ) 100 marginal probability ,
coupon coupon
all coupons
coupon
maturity maturity
coupon all coupons
coupon coupon
Â
Â
DF
DF rec.
DF Bond on asset swap
40 20
6 4 2 2
Gain % of par
Carry (bp)
4 6 8
0
Figure 3.21 The gain on a face value hedge 5 year 6% bullet bond.
Source:Lehman.
Table 3.8 The inputs required to determine the hedging payoff.
Characteristic Source
Hazard rate Simulated
Risk free rate Prevailing libor
Recovery rate Assumption
be assumed) and the risk free rate.) The asset swap margin can be determined through the standard formula:
Finally the chart is obtained by simulating over different values of the hazard rate.
To circumvent the above we could always consider buying differing amounts of protection. In particular we would like to hedge the initial investment. This means buying more or less protection depending on the price of the bond. The amount of protection we should buy is given by the formulae below:
This is determined by equating the loss on the bond with the gain on the default swap bearing in mind that the latter instrument is par based. The shortcoming with this approach is that it is only good if the actual recovery matched the estimated, otherwise there will be a loss or gain of
To guard against this investors will occasionally take out what is termed a ‘zero recovery’ hedge. This assumes nothing is recovered when the bond defaults, as such her capital is safe because an amount of protec- tion is purchased equal to the price of the bond. However it over hedges and leaves her unable to benefit from any opportunistic situations.