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Credit Risk Exposure

January 1, 2002

By H. Brett Humphreys and David C. Shimko

Will traders finally wake up to the danger?

During the Midwest power crisis and the defaults of the summer of 1998, we were sure the energy industry would wake up to credit risk. But the urgency passed with the heat wave. During the California crisis and defaults of 2001, credit risk rose to prominence again, only to be forgotten after the California markets cooled off. Now as we experience the Enron crisis, the question is, will the energy industry forget about credit yet again?

Regrettably, the recent developments within the power market highlight the risks associated with credit exposure, even with companies that were thought to exhibit pristine credit. Two years ago, trades with both Enron and PG&E were viewed as having little if any credit risk, but as of today divisions of both companies have filed for bankruptcy. These reversals of fortune reinforce the need for a solid understanding of credit risk within corporations and an active credit risk management policy.

Measures of Credit Risk

To manage credit risk effectively we first need to be able to measure it. The industry has become significantly more sophisticated in viewing credit risk and now recognizes that credit risk exists for both the seller and the purchaser of an asset and that, especially for power sales, the risks may not be equal on each side. The next step for most companies is to attempt to measure their credit exposure. The standard measure has become credit value at risk (CVaR). However, while the term CVaR is frequently mentioned it is rarely defined. In truth, we have found three major different meanings used by various companies when discussing CVaR. Each has pros and cons.

The first meaning of CVaR is also the most common and refers simply to the potential exposure to a given counterparty. If your CVaR to Mirant is $10 million, this implies that in the event of a default, there is only an X percent chance (say 5 percent, for example) of losing more than $10 million in the appreciated value of your trading position with Mirant. This measure ignores the probability of default and the recovery rate. It simply says how much money your company could make from all of the transactions to a counterparty and would therefore be at risk if the counterparty defaults. To clarify the discussion, we might better refer to this measure of CVaR as Conditional Credit VaR because this is the VaR conditional on the default of a counterparty. The benefit of this measure is that it is extremely easy to calculate. If we have internal VaR models, then we can easily generate this CVaR value by simply calculating the VaR of the portfolio consisting of all trades with a single counterparty, where the VaR is taken from the point of view of the counterparty. Some companies do a slight variation of this measure by adding the actual current exposure (accounts receivable minus accounts payable plus contract mark to market) in their calculation of CVaR.

While CVaR gives a point estimate of potential exposure, we can not compare this estimate with other CVaR measures. For example, the same set of trades with J.P. Morgan or Enron would have identical CVaRs. However, we know that, given the default probability for Enron, the trades with Enron represent a significantly greater credit risk.

The second interpretation of CVaR attempts to correct this weakness by taking the potential exposure to a given counterparty and multiplying it by the default rate (and occasionally by one minus the recovery rate) of the counterparty. This calculation, in contrast to CVaR, is believed to create a measure of the expected loss by a counterparty. It is not actually equal to the expected loss because the CVaR number is in itself a kind of worst-case outcome. Nevertheless, this calculation has some intuitive value. By accounting for default probabilities we have now created CVaR numbers that are comparable between counterparties. We will refer to this CVaR measure as PCVaR, or the probability-weighted CVaR. In the above example, assume the CVaR for both the Enron and J.P. Morgan trades was $10 million. If J.P. Morgan has a default probability of 0.1 percent and Enron has a default probability of 20 percent, then the PCVaR for J.P. Morgan would be $10,000, and for Enron it would be $2 million. We can now easily see that J.P. Morgan is much more attractive as a trading partner than Enron.

The main problem with the PCVaR measure is that while it allows for a comparison of relative risk, it does not truly represent the potential magnitude of a risk. In the above example, imagine that J.P. Morgan did in fact default. The actual exposure will likely be significantly different from the probability-weighted CVaR measure, and may also be very different from the actual CVaR number. So while PCVaR is a guidepost for making relative credit risk decisions, unlike VaR it in no way represents a reasonable upper limit to losses due to credit events.

Alternatively, to get a sense of the average credit loss conditional on default, one could calculate a probability-weighted average of all possible credit loss levels. This calculation is termed the "Average Shortfall" in the banking world. Surprisingly, under a set of simplifying assumptions, the PCVaR calculation is equivalent to the Average Shortfall method (see box) of determining VaR. Many financial professionals prefer the use of the average shortfall as a substitute for VaR, since it considers the entire shape of the loss distribution.

The third meaning of CVaR is directly equivalent to a portfolio VaR measure. It represents the maximum loss due to all credit events in the portfolio with a given probability over a given confidence interval. The main benefit of this measure is that it is directly comparable to a market risk VaR measure.

Even this measure has significant drawbacks. Unlike market risks, the distribution of credit exposures has a significant "fat tail" exposure. A credit loss could in some cases exceed portfolio CVaR by 5 or 10 times (an extremely unlikely event for market losses and VaR). Furthermore, portfolio CVaR is truly only relevant for a portfolio of counterparties. Given the extremely low probability of default for most companies, a CVaR calculation of this type by a counterparty will almost undoubtedly be zero. In truth, the company should have trades with hundreds of counterparties to make this measure meaningful.

Charging For Credit

Now that we've done the math, what should one do with this credit information? To induce traders to take credit risk appropriately, we need to appropriately charge for credit risk. No risk report will ever have the impact of a risk charge! The charge for credit risk means that the trader has eliminated the credit risk associated with his or her portfolio and this risk is now held by some other portion of the operation. For convenience we will call it the credit desk. The credit desk should not be run as a profit center, instead it should charge a fair price for credit protection to traders. Effectively, the credit desk functions by writing insurance policies. The cost of the policies depends upon the risk of the position and the default likelihood of the counterpart. As a first step the credit desk could simply charge an appropriate "option" premium for any trading position.

Getting Technical
Using Average Shortfall to Compute Expected Credit Exposures

We begin with a simple counterparty portfolio with value 0 at inception and random value X at maturity. We assume that there are no intermediate payments.

Let:

X = payoff in one year (normally distributed with risk-neutral mean 0)

ó = standard deviation in dollars computed to a one year holding period

Z = number of standard deviations for CVaR calculation (e.g., two)

CVaR = zó (by definition)

Ð = Probability of default per year

R = recovery rate as percentage of loss

L = loss rate = 1-R

The deal has two possible outcome states depending on whether the counterparty defaults or not.

Probability

1 - Ð

D <

Ð

Payment to trader

X

Min(X,0)+(1-L) max(X,0)=X-L max(X,0)

In the non-default case (top line), the trader receives the payment of X. In the default case (bottom line), one of two things may happen. If the trader is out of the money, he will still have to "pay up", so his receipt is negative, i.e. min(X,0). If his payment should have been positive, he would have received max(X,0), but loses a fraction L of the value, hence he receives (1-L)max(X,0).²

We now wish to compute the expected value and risk of the trade in the defaultable case relative to the no-default case. To do this, we take advantage of the mathematical approximation that the expected value of the min or max term in the equation is E[max(X,0)] = 0.40ó. Many traders know this rule as the 40 percent rule-an at-the-money option trades around 40 percent of the value of its total standard deviation.

Since the mean of X is zero, the overall expected value is negative at -0.40 ÐLó. This is also the reserve level for expected credit losses.

The Default Case-Risk Charges

To compute the risk, we recognize that the VaR criterion is insufficient in this case-if the probability of a credit event is less than 2.5 percent (corresponding to two standard deviations), then the credit event is ignored. Conversely, if the probability is greater than 2.5 percent, it is given full weight! Therefore we turn to the average shortfall method, but convert average shortfall back to VaR equivalents.

To see how this works, consider the no default risk case. In this case, the VaR is zó. The average shortfall is the expected loss conditional on a loss having occurred. In mathematical terms:

Average shortfall = -E[X|X<0] = -E[max(X,0)]/Pr(X<0) 0.80ó

The result was derived by taking the expectation of max(X,0) as 0.40ó and dividing by 0.50, the probability that X<0. Since the average shortfall is 0.80ó, to get to the VaR, we multiply

VaR Equivalent = [z/0.80] Average Shortfall = 1.25 z x (Average Shortfall)

We may now compute the average shortfall due to credit risk and convert this to a VaR equivalent. The average shortfall can be decomposed as follows:

Avg shortfall = Avg shortfall due to credit risk = 0.80ó
Expected Avg shortfall = ÐL(0.80ó) = 0.80óÐL
VaR equivalent = 1.25z * Expected Avg shortfall = zóÐL = CVaR * ÐL

Therefore, the PCVaR is equal to the VaR-equivalent of the average shortfall due to credit losses, under these simplifying assumptions.

-B.H. and D.S.

When we look at any trade, the counterparty has an embedded default option included within the contract. In other words, a counterparty default if you owe them money, has no financial impact. But a default when they owe you can have significant impact. Consider a short forward position. The default option in this case is equivalent to an at-the-money call option. Specifically we would calculate the option premium for the position and multiply it by the probability of default. This gives the total charge for protecting against credit risk.¹

One potential method of operation is for the credit desk to simply charge the embedded option premium for every transaction by every trader. The credit desk may then hedge some of their risks by going out into the insurance market. However, if the credit desk charges based solely on individual trades, then we would expect that over time they would make a profit. The reason is that such a method ignores the marginal effects on overall credit risk from each additional trade with a counterparty.

One problem with this method is that it ignores concentration risk. An improved implementation of this methodology would modify the simple method to depend on the existing set of trades with a given client. One possibility is to increase the rate of default (and therefore the cost of credit protection) for a given counterparty as the exposure increases. In other words, as a counterparty gets closer and closer to their credit limit we can incrementally increase the cost of doing business with them. Theoretically, we may even be able to eliminate credit limits all together-we simply make the credit cost so prohibitive that trading would automatically stop.

Another refinement to this methodology would be to charge not on the risk of a specific trade but on the marginal effect that that risk has on the overall credit portfolio. What matters then is how the new position interacts with the current portfolio. It may diversify the overall position or even function as a hedge. For example, if a company has a large long position in the Cinergy market with Biggy Energy and Trading, then a short position with BET in PJM may actually decrease the overall credit risk. In such a case, the credit desk should be willing to pay the trader for making that trade!

A Checklist

An effective credit organization within an energy trading unit performs the following tasks in addition to the standard credit function:

Determine accurate measures of CVaR by counterparty
Backtest these measures and continue to test on an ongoing basis
Assess default probabilities and recovery rates by counterparty
Update these numbers for changes in the markets
Charge traders or trading units for credit risk
Undertake credit risk mitigation strategies where appropriate
Measure success or failure of risk mitigation strategies
Allocate credit risk capital to maximize returns for the organization

If you checked two or fewer boxes, you have plenty of company, but your credit practices may have room for improvement. Three to five boxes implies you are operating in the top 25 percent of energy trading companies. More than five boxes makes your firm a credit star!

There's no time like a crisis to fix credit risk policies and practices. Especially when no one, not even the largest player in the market, is immune from default. Wait a short while and the urgency will pass until the next crisis-but then the next credit crisis could be you.

Brett Humphreys and David Shimko are founding partners of Risk Capital Management Partners, a consulting firm that focuses on energy and credit risk management. Related research is available at the company's Web site, www.e-rcm.com. They can be contacted at hbh@e-rcm.com or dcs@e-rcm.com.

This depends upon all the standard assumptions inherent in option pricing.
Note that min(X,0)=X-max(X,0), so that the lower term can be rewritten as follows: X-L max(X,0).

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