When we have to calculate exposure at default (EAD) on a particular trade, we seldom have to compute it analytically (e.g. as shown here). More often we just take the current MtM of the trade and add the so-called add-on. The add-on is the notional amount of the trade multiplied by the coefficient specific to the trade type, underlying and remaining maturity:
where is the current MtM, is the add-on, is the notional amount and is the trade-specific coefficient.
This method works reasonably well for a single trade.
If we have several trades covered by a netting agreement, we have a problem. We cannot just calculate the exposure on a netted portfolio as a sum of exposures per trade: exposures are not additive. One way to tackle this problem is to use the 40-60 rule. This rule, however, is so seriously wrong that it becomes alarming how many people use it without thinking of its shortcomings.
Consider a netted portfolio of n trades with MtMs and per-trade add-ons . The 40-60 rule says that the exposure on the netted portfolio is
(if all MtMs are negative, NGR=1).
In other words, NGR (net to gross ratio) is defined as the net replacement cost of the portfolio divided by the sum of the replacement costs for each transaction.
The 40-60 rule for exposure calculation is described in the Treatment of potential exposure for off balance sheet items (1995), issued by the Basel Committee on Banking Supervision. The Committee, to my knowledge, does not provide any justification for this rule.
Worse yet, it is known that the rule is wrong. Back in 2001, ISDA published theirÂ Response to the Basel Committee on Banking Supervision’s Consultation on the New Capital Accord. There they conclude that â€œthe aggregation rule fails to measure the true risk in a portfolioâ€ (page 52). To substantiate this claim, they give a simple example (Annex A) showing that the 40-60 rule can grossly over- or underestimate the exposure. In other words, the value given by the 40-60 rule has nothing to do with the real exposure on the netted portfolio.
If this method is so bad, why is it so widely used? I don’t have a good answer to this question.