Feb 6, 2010

Why VaR fails and actuaries can do better

Perhaps the most important challenge of an actuary is to develop and train the capability to explain complex matters in a simple way.

One of the best examples of practicing this 'complexity reduction ability' has been given by David Einhorn, president of Greenlight Capital. In a nutshell David explains with a simple example why VaR models fail. Take a look at the next excerpt of David's interesting article in Point-Counterpoint.

Why Var fails
A risk manager’s job is to worry about whether the bank is putting itself at risk in the unusual times - or, in statistical terms, in the tails of distribution. Yet, VaR ignores what happens in the tails. It specifically cuts them off. A 99% VaR calculation does not evaluate what happens in the last1%.

This, in my view, makes VaR relatively useless as a riskmanagement tool and potentially catastrophic when its usec reates a false sense of security among senior managers and watchdogs.

VaR is like an airbag that works all the time,except when you have a car accident

By ignoring the tails, VaR creates an incentive to take excessive but remote risks.

Consider an investment in a coin-flip. If you bet $100 on tails at even money, your VaR to a 99% threshold is $100, as you will lose that amount 50% of the time, which obviously is within the threshold. In this case, the VaR will equal the maximum loss.

Compare that to a bet where you offer 127 to 1 odds on $100 that heads won’t come up seven times in a row. You will win more than 99.2% of the time, which exceeds the 99% threshold. As a result, your 99% VaR is zero, even though you are exposed to a possible $12,700 loss.

In other words, an investment bank wouldn’t have to put up any capital to make this bet.

The math whizzes will say it is more complicated than that, but this is idea. Now we understand why investment banks held enormous portfolios of “super-senior triple A-rated” whatever. These securities had very small returns.

However, the risk models said they had trivial VaR, because the possibility of credit loss was calculated to be beyond the VaR threshold. This meant that holding them required only a trivial amount of capital, and a small return over a trivial capital can generate an almost infinite revenue-to-equity ratio.

VaR-driven risk management encouraged accepting a lot of bets that amounted to accepting the risk that heads wouldn’t come up seven times in a row. In the current crisis, it has turned out that the unlucky outcome was far more likely than the backtested models predicted.

What is worse, the various supposedly remote risks that required trivial capital are highly correlated; you don’t just lose on one bad bet in this environment, you lose on many of them for the same reason. This is why in recent periods the investment banks had quarterly write-downs that were many times the firm wide modelled VaR.

The Real Risk Issues
What. besides the 'art of simple communication', can we - actuaries - learn from David Einhorn?

What David essentially tries to tell us, is that we should focus on the real Risk Management issues that are in the x% tail and not on the other (100-x)% .

Of course we're inclined to agree with David. But are we actuaries truly focusing on the 'right' risks in the tail?

I'm afraid the answer to this question is most often : No!
Let's look at a simple example that illustrates the way we are (biased) focusing on the wrong side of the VaR curve.

Example Longevity
For years (decades) now, longevity risk has been structurally underestimated.

Yes, undoubtedly we have learned some of our lessons.

Todays longevity calculations are not (anymore) just based on simple straight on mortality observations of the past.

Nevertheless, in our search to grasp, analyze and explain the continuous life span increase, we've got caught in a interesting but dangerous habit of examining more and more interesting details that might explain the variance of future developments in mor(t)ality rates.

As 'smart' longevity actuaries and experts, we consider a lot of sophisticated additional elements in our projections or calculations.

Just a small inventory of actuarial longevity refinement:
  • Difference in mortality rates: Gender, Marital or Social status, Income or Health related mortality rates
  • Size: Standard deviation, Group-, Portfolio-size
  • Selection effects, Enhanced annuities
  • Extrapolation: Generation tables, longitudinal effects, Autocorrelation, 'Heat Maps'


In our increasing enthusiasm to capture the longevity monster, we got engrossed in our work. As experienced actuaries we know the devil is always in the De-Tails, however the question is: In which details?

We all know perfectly well that probably the most essential triggers for longevity risk in the future, can not be found in our data.
These triggers depend on the effect of new developments like :

It's clear that investigating and modeling the soft risk indicators of extreme longevity is no longer a luxury, as also an exploding increase of lifespan of 10-20% in the coming decades seems not unlikely.
By stretching our actuarial research to the the medical arena, we would be able to develop new (more) future- and shock-proof longevity models and stress tests. Regrettably, we don't like to skate on thin ice.....

Ostrich Management

If we - actuaries - would take longevity and our profession as 'Risk Manager' more serious, we would warn the world about the global estimated (financial) impact of these medical developments on Pension- and Health topics. We would advice on which measures to take, in order to absorb and manage this future risk.

Instead of taking appropriate actions, we hide in the dark, maintaining our believe in Fairy-Tails. As unworldly savants we joyfully keep our eyes on the research of relative small variances in longevity, while neglecting the serious mega risks ahead of us.

This way of Ostrich Management is a worrying threat to the actuarial profession. As we are aware of these kind of (medical) future risks, not including or disclaiming them in our models and advice, could even have a major liability impact.

In order to be able to prevent serious global loss, society expects actuaries to estimate and advice on risk, instead of explaining afterwards what, why and how things went wrong, what we 'have learned' and what we 'could or should' have done.

This way of denying reality reminds me of an amusing Jewish story of the Lost Key...

The lost Key
One early morning, just before dawn, as the folks were on their way to the synagogue for the Shaharit (early morning payer) they notice Herscheleh under the lamp post, circling the post scanning the ground.

“Herschel” said the rabbi “What on earth are you doing here this time of the morning?”

“I lost my key” replied Herscheleh

“Where did you lose it?” inquired the rabbi

“There” said Herscheleh, pointing into the darkness away from the light of the lamp post.

“So why are looking for you key in here if you lost it there”? persisted the puzzled rabbi.

“Because the light is here Rabbi, not there” replied Herschel with a smug.

Let's conclude with a quote, that - just as this blog- probably didn't help either:

Risk is not always apparent,
but its invisibility is no longer an excuse for ignoring it.

-- Bankers Trust on risk management, 1995 --

Interesting additional links:

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