Operational Risk Correlations

Many operational and business risks are correlated. While the default assumption of independence between risks is far more realistic with operational risks than with market or credit risks, there are still large sectors of operational risk that are correlated. This is particularly the case with the adoption of a broad definition of operational risk such as including business risks associated with the state of the economy or with political change.

Obvious examples in retail banking might include the dependence of the profitability of many products on the overall health of the economy or more directly on consumer confidence and household incomes. Less evident but no less dangerous are changes in legal or tax code interpretations that might affect the viability and liability of a range of business transactions and activities. A major employee discrimation award may change understanding of employee liability across multiple businesses.

How can these be handled in the Monte Carlo measurement of risk capital for an entity or segment thereof?

An additional step is needed. With independent operational risks the Monte Carlo simulation process starts for each risk with a randomly generated number. With a correlated risk this random number is replaced by a number that both reflects the risk's unique characteristics and those of a common factor that is also present in all the other risks to which it is correlated.

If two risks were perfectly correlated then whatever number was randomly generated for the first risk in each iteration would also be used for the second risk.

In practice most correlations are partial, and many risks might be correlated together, but to different extents. A flexible correlation factor model allows for a hierarchy of correlation factors and for a risk being affected by more than one factor.

The principle is simple. Risks that are highly correlated will tend to show the same incident tendencies - an extreme loss iteration in one risk will tend to be reflected in similar extreme iterations in highly correlated risks. This automatically feeds into the operational risk measurements at the relevant segment and Group levels.

Note that unlike in market risk, correlations are not calculated pairwise from rate or incident data. In operational risk most correlations are initially estimated, either intuitively or based on econometric analysis of the relationships between factors. The subsequent pairwise correlations generated between the risks can be calculated and used as a confirmation of reasonableness.

The difference correlations make can be substantial, but most would be positive correlations tending to increase risk capital calculations. There is less chance of negative correlation assumptions (as occur more frequently in market risk and which led to the demise of Long Term Capital Management when the correlations failed to remain in stress conditions). The equivalent danger in operational and business risk would be to fail to recognise the underlying political, judicial interpretation, technological and economic trends that underpin many diverse types of operational and business risk. LTCM provides a sobering example about assumed correlations (albeit in terms of assumed negative market and credit risk correlations):

"The LTCM risk model told them that the loss they incurred on one day at the end of August 1998 should have occurred once every 80 trillion years. It happened again the following week." Howard Davies, Chairman, UK Financial Services Authority

It is not possible yet to have precision in correlation between operational risks, but it is lunacy to avoid broad judgments and just ignore them.

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Last updated:16/5/07

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