# What is an appropriate hedge ratio for hedging a credit instrument with equity of the same issuer?

Given a bond and a stock issued by the same issuer, what is the appropriate ratio of bond-to-stock one should hold in order to minimize the specific risk to that issuer? Equivalently, what is the expected change in the credit spread for a given change in equity? Knowing this, one could then use the spread duration, or credit DV01, to derive the expected price change of the bond, which could be used as the hedge ratio.

I am looking for professional or academic research that may inform the decision of how much equity to short against a given bond or credit default swap. Any research that cites a correlation or regression coefficient between equity and credit spreads (could be OAS or CDS-equivalent spreads) would be helpful.

• Hey Tal, maybe check this out: stanford.edu/class/msande444/2011/MS&E444_2011_Group1.pdf Commented Apr 27, 2012 at 11:54
• @SpeedBoots great paper on the theory, I just wish they discussed the actual numbers that came out of their analysis a bit. Commented Apr 27, 2012 at 15:12
• You can get numbers from the classical Merton structural model using Bloomberg. In both theory and practice the hedge ratio is highly dependent on leverage so you will get results even poorer than the usual dismal ones for equity/credit if you do not take that into account. Commented Apr 27, 2012 at 15:42
• @BrianB Where on Bloomberg can I get these numbers? I know there are also some reduced-form models out there, and I just want to get a sense for a typical average hedge ratio. Commented Apr 27, 2012 at 16:55
• @TalFishman Any chance you can accept my answer ?
– Dom
Commented Aug 24, 2016 at 19:41

One way to approach this is to use a structural credit model which links the price of debt and equity.

To start with, you may wish to consider the JP Morgan / Deutsche Bank Credit Grades model which came out in 2002. In those days, the growing CDS market made it possible for hedge funds to short credit and to play any perceived mispricing of debt-equity from both sides. So it got a lot of coverage for a while.

It is quite a nice extension of Merton's model and the fuzzy barrier solves the zero credit spread for short-term debt that the Merton model implies and which is not found in reality.

Whether it is useful or will let you make money is an open question as far as I know.

Here is a link to the technical paper.

http://www.creditrisk.ru/publications/files_attached/cgtechdoc.pdf

You should certainly be able to use it to calculate hedge ratios by doing simple perturbation of the stock price.