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Theme: Big banks around the world are continuing to use Value at Risk (VAR) models to deceive investors into believing that the risk of their trading book is low. This is despite VaR proving to be grossly inadequate in measuring risk in the recent past. Bank investors need to look at the quanta of Level 2 and Level 3 assets in a bank's trading book and not go by stated VaR.

VaR, as Value at Risk is affectionately referred to by its practitioners, is a measure of how much money a trading institution can lose. VaR is quoted in terms of two parameters- time period over which the losses can occur and the probability with which you state that trading losses in the time period will not exceed the stated amount. For instance, if a bank states that its 10-day 99% VAR is $ 100 million, the bank, from its internal models, is estimating that 99% of the time, an adverse change in its trading portfolio will not result in losses more than $ 100 million in a 10 day period. You could also have a 1 day 99.99% VAR or other variations.

Anyone who lived through 2007 and 2008 would have empirically known that VaR's claims were bogus. We will not go into bank CEOs making statements to their gullible stakeholders (perhaps they were fooling themselves too) regarding VaR of their trading books. These CEOs were later to prove to be embarrassments to themselves and to the institutions they headed. What we, as credit analysts (or equity analysts who want the truth and not those who want to do a short-term pumping up of a stock), would need to ascertain is whether the theoretical underpinnings of VaR are justified and if yes, can the weaknesses noticed empirically over the last few years be rectified through tweaking.

Engineers who build airplanes and nuclear reactors deal with complex and intractable equations, those that in the years prior to cheap computing could not be readily solved. The engineer had to make those equations more tractable- so he made simplifying assumptions. One must remember a few things here- firstly the engineer was dealing with the unchanging laws of nature- the relationship between the left hand side and the right hand side of a physics equation can be split asunder, like Moses parting the Red Sea, only under divine intervention. Secondly, when the engineer ignores terms of equations to make the equation solvable, he knows exactly the order of magnitude of the terms he is ignoring. Only when a person solving an equation knows the order of magnitude of the terms he is ignoring, he can tweak the final results by multiplying his findings with a factor for safety. If he was multiplying his findings with a factor of safety without a clear and timeless understanding (i.e. the magnitude of the assumptions made doesn't change with time) of the impact of the assumptions made, an airplane thus built will be flying less on a wing and more on a prayer.

To calculate VaR of a trading book, the bank first establishes the relationship between the value of an asset and a driver of value such as interest rates, exchange rates etc. Now, this relationship does not change. So, if the value of a 10 year zero coupon government security held in the portfolio is worth $ 100 today when the 10 year rate is 8%, he can calculate what the value of the asset would be if the rate changes to 8.1%. Also, if the portfolio has a call option on Euros to be settled in US Dollars, a bank can estimate is value today. But an analyst is not only interested in the value of the two assets today. A financial analyst would be interested in knowing the worst case drop in value of the two assets over a particular time period. What is the likelihood that the ten year interest rates would rise to 8.3% in 10 days? What would be the likelihood of the Euro/USD exchange rates moving to a particular level in that period? And most important, what is the correlation in the movement of the 10 year rates and the exchange rates between Euros and USD. Alas, while the relationship between the movements in the value of the 10 year bond with 10 year rates is invariant, the movement in the 10 year rates is not governed by immutable laws. Likewise, while one can estimate the value of the call option in response to currency movements, the movement in the exchange rate does not happen in an immutable manner like the laws of gravitation or electromagnetism. And the correlation between the two underlying (the 10 year rate and the exchange rate) factors never stays constant.

To get around the fact that the value of exchange rate and the 10 year rate tomorrow is an unknown today, the VaR methodology ascribes a probability distribution for the exchange rate and the 10 year rate based on past volatility of such values and based on past correlation between the two parameters. There is no underlying reason why the parameters should follow the chosen distribution even if they did in the past (which actually they would not have). The distribution was chosen based on ease of computation- not because it reflected the underlying phenomenon. Worst of all, there is no earthly reason why the correlation between interest rates and exchange rates should have the same distribution as in the past. Exchange rate changes would reflect deep structural relationships between two economies- which drastically change with time.

The absurdity of the VaR framework is evident even when one uses only two parameters. In the real world, a bank would consider correlations among several parameters such as several exchange rates, commodity prices, and interest rates. That compounds the absurdity. In April 2008, S&P finally came to the conclusion that the losses posted by banks in 2007 and 2008 were much higher than what could be explained by VaR. As usual, they came up with the wrong thesis- "VaR is not a measure of losses in times of stress but rather of large losses under normal trading conditions". VaR does not work because the building blocks do not reflect the underlying phenomenon of movement in market prices, a phenomenon which unlike the laws of physics is not uninfringeable. So what does S&P do? They decided to scale up regulatory VaR capital by a factor of 3 to reflect "fat tail" outlying risks and other risks. Remember, when the engineer did a scaling up using a factor of safety, he understood the dynamics of the underlying phenomenon and he knew the bounds of error of his model in reflecting the underlying phenomenon. Neither is true for financial markets. So applying a factor merely compounds the absurdity called VaR. In 2008, Goldman Sachs' (NYSE:GS) CEO referred to several days of 25 sigma happenings, when even a single day should not occur if the modeling had any resemblance to reality. The terrible truth was that emperor VaR had no clothes on.

VaR, in short, was, is and never will be ready for prime time and needs to be junked- at least by financial analysts and investors. But academically discredited techniques such as technical analysis still survive, and even create a bit of self fulfilling prophecy in the short run. Astrology has survived thousands of years by masquerading as a science. Sensible people know that just because an astrologer gazes at stars like an astronomer, it does not make astrology less of a mumbo jumbo. Sensible financial analysts know that just because VaR uses techniques from mathematics and physics, it does not make it less gibberish. Only in the climate controlled environment described by quantitative finance did VaR ever make sense. To raise VaR to an elevated status in a bank's risk management pantheon is no different from Roman emperor Caligula elevating his horse to a consul.

Source: A Horse Called VaR (Value At Risk)