Sunday, November 1, 2009

The Problem With VAR & Risk Management

Economic and Financial Theories and Models have come under considerable criticism over the last 18 months, most of it well deserved. The primary targets have been Efficient Market Hypothesis, Free Market Capitalism, and most importantly Value At Risk Models. There has been many articles written on both sides of the pond in the area of EMH and the idea of free markets.

I posted a few days ago the duel over EMH.

http://tradersutra.blogspot.com/2009/10/emh-steel-cage-death-match.html

Also Free Markets Capitalism has been roasted by the Keynesian folks.

http://tradersutra.blogspot.com/2009/10/capitalism-has-failed.html

Back in September, there was a hearing on VAR Modeling held by the Subcommittee On Oversight And Investigations. This was a meeting to discuss how the role of risk models influenced the crisis and how they should be used going forward.

They call VAR the 1% Model, meaning that with certain confidence and all else being equal, a trader or desk can stand to lose a given amount on a given day. Simply if you have a VAR of $25M, that means that you on 99% of all days will lose less then $25MM. Sounds good. Control your VAR and you control your losses. Correct?

But the problem with VAR is much more complex, much more complex then the derivatives and assets it tries to model. VAR makes some assumptions that if you look back at is quite head scratching. Some if not all of these assumptions are clearly false.

1-Not all asset classes are included in the VAR calculation, because accurate pricing is not available. This was even before the crisis, where assets rarely traded and pricing was scarce. The VAR models that were used didn't take into account future toxic assets, most of which were off balance sheets and tied up in structured investment vehicles. Even today this is true.

2-Data used in VAR calculations are based on historical data. We live in a real time dynamic world yet we are using models that are static in nature. These results are unrepresentable of future results. This is what is also called "Future Blindness." People tend not to be able to anticipate a future they have never personally experienced.

3-VAR as well as Black Scholes and other risk measurements do not and can model the basic problem of liquidity. When markets are pressured the liquidity generally dries up. LTCM was brought down because the firm held hundreds of billions of assets that were not liquid. The VAR Model doesn't make the basic allowances for liquidity risk.

4-The most important assumption that VAR makes that is empirically and academically wrong is that asset prices follow a "normal" distribution or the classical bell curve. A lot of people tend to call these type of distributions "Gaussian."

I will go into why #4 is so wrong in a moment.

Lets get one thing straight. Risk Models work great and are designed to function properly in normal market conditions, but they should not be 100% relied upon in times of crisis. Too many bank executives relied on these models during times of crisis because they were seduced by the Nobel Prize winners that designed them. Both the strange thing is going back to LTCM, everyone knew you could not rely on these models when crap hot the fan. That they were completely worthless. This is the one remarkable thing that has so bewildered market thinkers. How in the world did the regulators allow the banks to use models that they knew were worthless in times of crisis, and those same models were telling the risk managers what level of capital requirements were needed in such times of crisis? In the end there was not enough cushion to soften the blow. I can only safely assume that bank executives who in the most part are not very mathematical left the heavy lifting to the model makers. There was so much competition in the financial alchemy world that economists and financial engineers were in the game of who can build a better mousetrap. These guys had their own incentives. The economic profession is all about giving more credence to mathematical models that can crunch the numbers faster and with the least bit of parameters. There was no room for common sense.

Most importantly the people behind the VAR Models knew of their shortcomings on almost every scale, but using those models brought results to the banking world. In the end VAR helped risk managers, traders, and high level executives rationalize bad trading bets. Traders used VAR to again rationalize a situation that defied even the basic common sense of risk management. The high level executives who have no clue of the shortcomings of VAR only cared to hear what they wanted to hear. In the end most financial models only work because they meet the basic need the human beings that use them. They needed VAR during the boom, and VAR need more traders to use them. When everyone is using the same road map, we all will drive off of a cliff.

Now lets go back to my 4Th point with regards to normal distributions. This is where I think VAR made the biggest wrong assumption. Its extremely dangerous to assume that risk are normally distributed. Of course on a day to day basis they tend not to move far away from the mean, but its a widely known fact that distribution of prices in financial markets are subject to something called "Fat Tails." Fat Tails alerts you that events far away from the mean are more likely to happen then a normal distribution would alert you to. These distributions are subject to "skewness", meaning they are not symmetrical around the mean.



Stocks and bonds are subject to negative skewness which mean longer tails of negative outcome. While commodities are subject to positive skewness. This is the reason, along with their low correlation with financial asset returns makes them a useful addition to a model portfolio.

Kurtosis is also known informally as “fat tails”. That means that events far away from the mean are more likely to happen that a normal distribution would suggest.

Now this one important finding has been researched and many papers have been written proving it, yet the math in which most risk management models including VAR and Black Scholes goes to bed at night assuming a normal distribution. The French Mathematician Benoit Mandelbrot observed that distributions of price changes in various markets were not normally distributed. The observed distributions of price changes had fatter tails than the normal distribution. From this we have Nassim Nicolas Taleb, author of The Black Swan and Fooled by Randomness, who has dubbed significantly larger extreme price moves than those predicted by a normal distribution as “Black Swans.” Taleb has linked Black Swan price change events to the recent financial crisis, suggesting in effect that we all collectively misunderstood on which side of the distribution of possible risk outcomes we stood.

This is where VAR fails. It misrepresents and underestimates the nature of risk.

So the argument can be made like this:

Current risk management and derivative pricing regimes are based upon normal distributions. Price movements in the recent financial crises were unpredictable or low probability events that were also greater than predicted by normal distribution models. Hence the collective failure to anticipate Black Swan events is “responsible” for the recent crises as mis-specified risk management models failed due to fatter than normal tails.

So the argument cam also go this way. Was housing and sub prime a Black Swan event or a failure of the stated objectives of risk management and oversight?

We all know that risk management systems based solely on analysis of past price moves will at some point fail if financial markets continue to change. The problem with current risk management systems cannot be fixed by simply changing VAR parameters or other statical models. Risk management regimes must incorporate judgments about the evolution of the underlying markets, distribution of possible price changes and other dynamic sources of risk.

I can only say that risk was so badly miss priced that a black swan event was going to happen sooner or latter because of the simple fact that too many complex derivatives were created with far too much leverage, and that no model was ever created or will be subsequently created to manage this.

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