Risk Latte - Are the banks which lost money recently victims of Negative Skew?

Are the banks which lost money recently victims of Negative Skew?

Rahul Bhattacharya
August 23, 2007

Goldman Sachs and Bear Stearns, we are sure, must be paying hundreds of millions of dollars to hundreds of rocket scientists, traders and fund managers to manage their in house or proprietary portfolios. They should fire all these "monkeys" and simply hire one man: Nassim Taleb.

We have talked about negative skew and asymmetric payoff in detail elsewhere in this site. However, the events of the last couple of months - the sub prime and the credit crises and the blowups of several hedge funds - coupled with emails from our readers have prompted us to write about it once again.

If one were a quantitative trader in the early nineties and witnessed the currency crisis in 1992 (and thereby witnessed George Soros' shining hour) or the interest rate crises of 1994 one would have simply ignored the current turbulence in the credit, equity and the interest markets and the subsequent busting of so many hedge funds, including the ones run by big names like Bear Stearns and Goldman Sachs (losing 30% of investment capital in a week is also as good as going bust). He or she would have simply said: "oh so what? That's no big deal; it all boils down to the third moment."

But those traders or investors who were not present at that time or were simply tourists back then watching the show from the sidelines could still read Nassim Taleb (any of his work will do) and get to understand why so many hedge funds went bankrupt recently and why even the "monkeys" at Goldman and Bear Stearns fell victims to the ruthless markets. If one is too busy to go through books, then he or she can simply read up many of Taleb's papers on Negative skewness.

A negatively skewed bet is one where the investor - trader or the gambler - has a 99% percent chance of winning (making a gain) and 1% chance of making a loss. This is an asymmetric payoff. Just as in life, most human beings prefer asymmetric payoff in the financial markets.

Mathematically, one calculates negatively skewed probabilities of the payoffs multiplied by the cube (third power) of the payoffs and deducted from the mean. This is the negative third central moment of the distribution.

There are only two things that can happen if one engages buying and selling financial instruments or portfolios (like a portfolio of credit derivatives or a hedge fund manager's portfolio) which have asymmetric payoffs. Either you'll bleed or blowup! Not all hedge fund portfolios displays negative skew or asymmetric payoffs; but most portfolios do, and therefore they blow up.

Almost, all financial derivatives display asymmetric payoffs. All sold (short) option positions and sold (short) derivatives positions - something that banks, financial institutions, hedge funds and even corporations engage in regularly these days - are negatively skewed bets. These short portfolio positions will produce negative skew for the trader. He will be fooled by the variance (volatility) of the process, as the observed variance (volatility) would be lower than the true variance most of the time. This would mean the more the skewness in the distribution (of the portfolio) the more the variance will be concentrated in a small slice of time and for most part it will generate steady returns. And the trader will think that he is making money, albeit in small proportions but steadily. And then after a while - could be a long wait - the true variance will wipe out all those gains.

It is also a fallacy, one that is strangely entertained by the "monkeys" of the industry, that "market neutral" (delta hedged) strategies mitigate the third moment risk. They do not. Again a simple truth eludes these guys. Mitigation of asymmetry risks involves continuous adjustment of their positions which is not possible in the face of a rare price jump. Most of the time - 99% in fact - the market neutrality will be in place through delta hedging and they'll feel happy and get rich until one fine morning when the asset will make a large jump through a barrier.

More to the point and closer to the events at hand, all loans and credit related instruments display negative skewness.

A bank lends money to a triple A rated company (or to a family in mid western United States with prime credit rating). The bank charges a fixed rate of interest and it has a very high probability of earning a high interest amount. And then the bank gets bold and lends a lot of money to a whole lot of corporations or families with excellent credit rating. And it keeps on earning interest and keeps boosting its bottom line. Then one day, after a considerable lapse of time, one of the families or companies with prime credit rating turns sub prime or goes one notch down and there is a default on one of the loans. And all of a sudden, within a few days, there is a cascading effect and a large number of these borrowers default and the lot of money vanish. Over the years what appeared to be a steady stream of earnings on the profit and loss statement suddenly gets transformed into as a huge hole on the bank's balance sheet.

Lending money is a negatively skewed bet with asymmetric payoff and carries third moment risk. Yet banks do it regularly and have been doing it for the last couple of hundred years. Moreover banks grant credit lines to clients - generally corporate clients with a good credit rating - with the assumption that they will not be used. This is done, chiefly by the commercial banks, to gain more advisory or M & A business. The banks expect that these lines will not be drawn down; but when a client is in distress or faces severe cash flow problems (such as Xerox in 2002) it will draw down the load.

Therefore, these loan commitments are like sold option position. The bank is selling an option to the corporate client but with a credit risk. Thus such a loan can be decomposed as a portfolio of a spread option and a CDS.

Structured Loan = Spread Option + CDS

The bank is short the option and hence facing a negative third moment.

Negative skewness and asymmetric payoffs are part and parcel of financial markets. The problem is that very few pay any attention to the third moment. So much attention is focused on the second moment - volatility or the variance - that third moment is almost forgotten. Yet is the only reason why companies and hedge funds go bankrupt and "monkeys" become "monkeys on a typewriter".

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