# Hedging a CDS sold

How would a bank that sold a CDS to a client hedge its position?

Is there a replication method similar to what is done with option hedging or other methods used?

Many thanks

## 3 Answers

The most basic answer to your question, is that the CDS contract is not hedgeable and there is no replication strategy.

As @ZRH rightly points out, you can in theory net out the position with another CDS trade, or effectively net out the position if you short one of the bonds. I don't really think of the first case as hedging, and shorting of corporate bonds is super-rare in practice so it's not actually done.

Another trade you can do to "sort-of" hedge the position is buy a bunch of equity puts (if they are traded on the same corporate entity). It's usually not feasible to get that much size done, but it's easy to compute how many puts you want to own given some recovery rate assumption. Another problem with the puts I that you effectively pay for more than you need, because they are not digital like the CDS. Those potential payoffs at, say, a 30% drop in equity, are something you pay for in option premium, even though that's not a default scenario.

There also exist Merton style debt-equity models, which pretend to help you replicate and hedge. They model the firm equity $$E$$ as an option on the economic value $$A$$ of firm assets, less the debt $$D$$. $$A$$ follows a random process, and default happens if there ever comes a time when the firm owners would "exercise" by selling $$A$$ to pay off $$D$$ and taking home $$A-D$$. In a Black-Scholes version you get

$$E = BS(A, D, \sigma_A, \tau_A)$$

From all this you can work out the parameters from observed prices and price series, and thence a hedge ratio $$\frac{\partial D}{\partial E}$$ or an equivalent $$\frac{\partial \, CDS}{\partial E}$$.

In practice the investment bank corporate debt desks don't bother with Merton models, and almost never with puts. Instead they just hold a big portfolio, keep the exposure to any one name or industry low, and take their hits occasionally. They don't try to replicate.

If it is a single name CDS, the transaction leaves the bank short the credit spread of that bond vs a risk-free bond in the same currency.

To go long the spread, the bank would i) buy the same CDS from another bank or ii) sell short the same bond, and get rid of general interest rate risk by going long a risk-free bond (or interest rate swap) of the same tenor.

• What does “single name” mean here? – Theodore Feb 8 '19 at 0:08
• Single name means it's not an Index CDS. Other imperfect ways to hedge the risk would be short selling the company, buying index CDS (works better if you have a diversified CDS portfolio). – Lliane Feb 8 '19 at 2:57

When you go long (i.e. buy risk) a bond position, you're explicitly running both interest rate and credit risk, as any fluctuation in the general interest rate (i.e. USD yield curve for a USD denominated bond) or credit spread of the bond issuer will result in P&L.

A CDS replicates the credit risk of the bond without any (material) interest rate risk. So if you sell (as in sell protection, which is equivalent to buying risk) a CDS, you've replicated the credit risk component of an equivalent bond position without the interest risk rate.

So in direct answer to your question - no, there is no single other instrument that you would hedge only your credit spread risk. As mentioned earlier - a bond would hedge both interest rate and credit spread risk. Similarly, an option would hedge credit spread risk and credit volatility risk.

However, you can replicate a CDS by adding two or more instruments together. For example, if you add a bond (interest rate risk + credit spread risk) to an offsetting interest rate swap (only interest rate risk), you have technically synthetically created the risk profile of a CDS.

Hope this helps.