In keeping with the theme of redundant asset pricing models (Insider March Issue, Completely Redundant Asset Pricing Model) I decided to base this piece on an article I read in Wired Magazine titled “Recipe for Disaster: The Formula That Killed Wall Street”, where the author talks about the formula used by financial institutions to price mortgages and ultimately devise those hybrid investment vehicles that are responsible for the mess we are in today.

The Gaussian copula function is a mathematical equation devised by David X. Li, which measures the correlation between two assets and determines the probability that it will default at the same time. Instead of using historical default data to price these assets, Li looked at what it would cost to insure the asset against default, which is the largest component of risk in fixed income securities. When the price of a credit default swap goes up, it implies that the default risk on the underlying asset has risen. Now to take this a step further, banks used this model to slice pools of mortgages into collateralized debt obligations and separate them into risky and less risky tranches. The underlying assumptions as we all know by now were that housing prices would keep rising and that there would be no correlation in default trends. Li’s formula also uses the assumption that CDS’s can price risk correctly, which, if you think about it, puts too much faith in the Efficient Market Hypothesis. To elaborate, David Li’s theory suggests that the probability of default on the underlying asset in the future is already factored into the price. In retrospect this seems a little sketchy, especially when home owners saw a drop in equity. 

Like most pricing models used in finance, the quality of the output is only as good as its underlying assumptions; so a small change in the inputs can cause massive fluctuations to output. Unfortunately, it is the blatant abuse of this formula that has lead to the collapse of the markets. During booms and rising prices, everyone is a cheerleader and we tend to ignore warning labels – “Do not use to price risk!” or “Enjoy formula responsibly”. I guess president Bush was not joking when he said Wall Street got drunk and is now dealing with a massive hangover. In 1998, before Li had even invented his copula function, Paul Wilmott wrote that "the correlations between financial quantities are notoriously unstable". This model was not intended to be used as a tool for risk management but was popularly used regardless of its limitations due to its mathematical elegance. Which leads me to my next point- investors love risk (because high risk means high reward), but hate anxiety. To counter this anxiety they tend to follow experts in empty suits.

            A close friend recently lost a large sum of money on a fund run by MFS Investment Management. I remember being at the presentation when the fund was first launched three years ago. There were these well dressed bankers with their fancy power point slides and different scenarios that showed us (then irrational and naive investors) how we could make gobs of money. Funny how there was no scenario to show us how we could stand to lose money. Bankers feed on the irrational behaviour of human beings. After all, isn’t the whole industry based on expectations of the future? Using math to force a sense of logic into the head of naive or sophisticated investors is always part of a bankers’ arsenal.

This is not the first time something like this has happened. The collapse of Long Term Capital management in 1998 was also caused by a “tell all formula”. The Black-Scholes formula, is the cornerstone of modern finance and was devised by two Long-Term Capital partners, Robert C. Merton and Myron S. Scholes, along with one other scholar. It is based on the idea that bond prices are random.

This is quite the opposite of the Copula formula, where the idea is based on correlations rather than randomness. In this case, the company collapsed when Russia defaulted on its debt in 1998 and investors dumped their securities for more liquid, risk free assets. In times of financial crisis, most investor moves are correlated and can be defined as “the flight to quality” or as Keynes put it, the psychological propensity towards liquidity

To put all of this in layman’s terms, these formulas serve two purposes. Firstly, they provide a false sense of security to unsuspecting investors by filling the void created by anxiety. Second, they serve as an alchemist’s potion and turn garbage into gold. From the beginning, there have been rational arguments against Li’s formula, but it seems as if it was like fighting a losing battle. The irrational use of mathematics to explain the fluctuations of different variables based on expectations about expectations isn’t something to be proud about. In fact, after a reading an article in the NY times about retraining business schools to focus on actually running a business and not just increasing shareholder value, I am convinced that we are perpetuating a bad trend and need to stop listening and start questioning.

What I find slightly ironic is that financial institutions have figured out a way to turn a risk adverse investors’ security of choice (bonds) into something much more toxic. This isn’t about the numbers any more. What is happening in the industry is nothing short of shameful. And I am not even talking about Madoff and Allen Stanford. Who do we trust (not in Cramer, I hope!)? Do these models work outside the realms of academia with real world factors in play? As a final word of caution, I would advise you to learn from the words of Warren Buffet and “beware of geeks bearing formulas”.

Sources: http://www.nytimes.com/2008/09/07/business/07ltcm.html?_r=2,

http://www.nytimes.com/2008/09/07/business/07ltcm.html?_r=2, Portfolio.com, The Daily Show with Jon Stewart