One of the things that’s been clearly illustrated throughout the current credit crisis is that hedging credit risk with credit default swaps isn’t very useful if your counterparty is Bear Stearns or Lehman Brothers. For that reason, best practice risk management of retail, small business, corporate and sovereign credit risk has focused on macro factors where there is an exchange traded derivative that one could use to hedge. In the KRIS version 3.0 Jarrow-Chava reduced form model, introduced more than 4 years ago, the 2 year return on the stock index was a statistically significant explanatory variable in explaining defaults of listed corporations. Let’s assume that ABC Bank in country X has employed this variable in separate models for retail credit risk, small business credit risk, major corporate credit risk, and sovereign credit risk. If the current stock index value is 500, the predicted level of losses at each level of the stock index in 2 years is as follows:
Can one simply short the stock index future in country X to hedge? One could, but that short position will lead to large losses if stock prices rise instead of fall. Let’s make two simplifying assumptions for purposes of exposition. First, let’s assume that losses happen exactly two years from today, with no intervening losses. Second, let’s assume that there are put options on the stock index at various strike prices and a maturity of exactly two years. We can calculate the gains or losses on the put options at every possible outcome of the stock index.
Given our example above, the perfectly hedging portfolio has the following long and short positions in the stock index put options:
The combination of puts that perfectly offsets the losses is to go long 2 contracts at a 650 strike and 8 contracts at a 450 strike, combined with a short position of 2 contracts at a 600 strike and 8 contracts at a 400.strike. The short positions are necessary because predicted credit losses do not monotonically increase as the stock index falls. Over some range of index levels, the losses do not increase, and the short positions correct what would otherwise be an “overhedge.” They also reduce the total cost of the hedge.
Two questions beg to be asked after doing this analysis.
- What if we’re not sure how accurate the credit model is?
- What if the business is not profitable after we account for the hedge?
After the last 2 years of experience, anyone who has been involved in the collateralized debt obligation business who’s not asking the first question is in serious need of counseling. The answer is this: the more one is uncertain about the model, the more one “cuts down” the magnitude of the hedge to make sure that it is not an overhedge.
The second question parallels our blog on great quotes of the credit crisis. One CEO said that the business wouldn’t be profitable if a good risk management system were put in place, but he wanted to do the business anyway. In this case, a more rational answer is a simple one. If the net present value of the lending business after a perfect hedge is put in place is a negative number, one shouldn’t be in the lending business.
This simple example is just a highly stylized general macro factor version of the tried and true “PVBP” (present value of a basis point) analysis of parallel interest rate shifts that has been around since Macauley in the 1930s. The difference is that credit losses are not symmetrical around changes in the stock index, so we use puts instead of futures to hedge. The parallels to the fixed income market, where convexity makes value shifts non-symmetric, are exact.
Donald R. van Deventer
Honolulu, June 25, 2009