Risk Management
Task Force

Risk Management Metrics (RMM) Subgroup Minutes

 

Risk Management Metrics
May 4, 2004
12:00 noon Central Time

Participants: Fred Tavan (Leader), Cliff Angstman, Steve Craighead, Emilie Gilde, David Ingram, Julie Perks, Greg Sloan

Discussion on Risk Metrics
Greg Sloan did a quick review of the Cruz textbook on "Modeling, Measuring, and Hedging Operational Risk". He found references to two types of operational risk metrics, namely Opertional TVaR and Reputational TVaR.

Operational VaR is somewhat similar to the typical VaR which we are all used to seeing in the measure of market and many other risks. For example, Operational VaR does look for a percentile from a distribution.

However, Cruz points out that Operational VaR does differ in many respects. Operational VaR does not make use of the Gaussian assumption common to VaR. Operational VaR instead use Extreme Value Theory as its basis. Also, Operational VaR is modeled using a convolution approach where frequency and severity are modeled separately then convoluted together. Operational VaR is modeled with a discrete frequency stochastic process which is contrasted against the continuous (typically Brownian Motion) stochastic process. However, the most important difference is the fact that since Operational VaR is a shortfall EVT approach, Opeartioal VaR satisfies the sub-additivity principle violated by the typical market VaR. Therefore, Operational VaR is a coherent risk measure.

The second risk metric put forward in Cruz's book is Reputational VaR. To calculate Reputational VaR, define X(Rep) as 1 if a reputational risk occurs and 0 otherwise (reputational risk indicator variable). Regress using a multifactor return model such as R = B(Market) * X(Market) + ... + B(Rep) * X(Rep) + error term. Use this regression analysis to approximate the values of the mean and standard error of Bhat(Rep). Now if we want to find the Reputational VaR with a desired quantile of 100(1-a)%, we define VaR(Rep) to be D * Y * Bplus, where D is given by a probit/logit model, Y is the market value of the business in relation to the eventual reputational losses, and Bplus is t(a/2) * se (Bhat(Rep)) (with t being the t-distribution and se being standard error).

Another approach to operational risk that was discussed was the Analog Approach. Under this approach one looks at non-financial firms which don't have much inventory. This is because financial institutions don't hold much inventory. The amount of capital held by these non-financial firms could then be used as a proxy for the amount of capital that needs to be held for perational risk since they hold very little financial risk. The ratio of expenses to capital from a non-financial company could potentially be used to determine operational risk capital for a financial institution. There are some pitfalls with this approach as the ratio of expenses to capital could vary substantially depending on the type of analog company that is chosen.

There was a lot of discussion about extending the AAA risk management framework. The group went over the suggested extension. The discussion brought out the point that the original Federal Reserve Bank risk management framework included operational risk categories. Dave Ingram agreed to distribute the Federal Reserve Bank version to the meeting participants. The group will look at these at the next call.

Next Call
The next call will be on May 25th at 1PM EST (noon central).

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