The dreadful 40-60 rule

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:

20100302-EAD

where 20100302-M is the current MtM, 20100302-A is the add-on, 20100302-N is the notional amount and 20100302-a 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 20100302-MtMs and per-trade add-ons 20100302-Addons. The 40-60 rule says that the exposure on the netted portfolio is

20100302-rule4060

where

20100302-NGR

(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 their Response to the Basel Committee on Banking Supervision’s Consultation on the New Capital Accord. There they conclude that “the aggregation rule fails to measure the true risk in a portfolio” (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.

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1 Response to The dreadful 40-60 rule

  1. Paul says:

    That is a very clear and concise explanation of something I have no prior knowledge. Thank you. I look forward to reading more of your posts.

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