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Probability of Shortfall and Expected Shortfall with or without Basel III – Financial Risk Management Training Course – Day Three Update

Jawwad Farid

Every since the Basel and BIS Committee that formulates the Basel Standard announced a preference for exploring an alternate metric for Risk Management there has been a resurgence of interest in Shortfall methods. There has been a renewed focus on research some led by the NYU’s Volatility Labs on the topic of Capital Shortfall as well as the exposure to their shortfall research results in mainstream as well as market focused specialist media. There has been BIS endorsed research that compares the “new” expected Shortfall method with VaR and how the two methods fared or “would have fared” under recent market based crisis.

The challenge though is not one of switching a broken method with a more sophisticated, complex and “coherent” measure. We have always felt that the primary challenge with Value at Risk was its exotic nature which sounded simple and basic to the statistically minded but tended to be a message presented in formal Greek as far as most members of the board and executive management were concerned. Even if with some miracle of comprehension and presentation they could decipher what was being said behind the numbers and the charts, it would take another act of God and divine intervention for them to interpret the implication of what they had just heard.

In the words immortalized now by Margin Call, “Speak to me as if you were speaking to a child, or perhaps a golden retriever”, the problem is presenting risk measures in a language board members can understand, relate to and appreciate. Not in the language we (the risk managers) have grown comfortable with.

So we have now fixed this problem by replacing one exotic risk measure drawn from the annals of statistical tools with yet another exotic measure with just as sophisticated a derivation as before. And we expect risk management to suddenly pick itself up again and give a good solid soldierly account when the next crisis rolls up to our doors.

How are the two measures different? In simple terms Value at Risk (VaR) estimates the worst that can happen under “unexpected scenarios”. The new expected shortfall method calculates the average of the worst case scenarios visualized under Value at Risk.

The first one (VaR) says there is only a 1% chance that we will book a loss of more than 2 million US$ on this portfolio over the next 30 days. The second one (Expected Shortfall or ES) says, if we ever breach that 1% threshold, on average we should expect to book about 6 million US$ in losses.

The first one picks what we view as an impossible number under impossible conditions. The second one quantified and monetizes that impossible number under impossible conditions by taken the average of all possible “impossible” scenarios.

In statistical terms think of Value at Risk as your Z Score. Think of Expected shortfall as the area under the curve. One is a risk threshold that you hope to never breach or breach under a controlled environment. The second is an insurance policy or better yet an option premium.

But thinking doesn’t solve the presentation problem. Is there a solution?

While for regulatory reporting purposes our hands are tied by what the Basel Committee suggest there is an old, slightly out of favor measure that has been in use in the insurance industry and by market day traders for generations. It is called probability of ruin or using current language or terminology probability of shortfall.

A fair warning or qualification. We are not evaluating probability of shortfall as an alternate to Expected Shortfall or Value at Risk. We are simply recommending its use as a presentation tool that would help us solve some of the problems around explaining the impact of a VaR or Expected Shortfall number.

Recommended Readings

Killing Value at Risk

Day Trading and the Probability of Ruin

The Capital Shortfall Model at NYU VLabs

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