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 

As a student entering the finance stream, I feel this is the best time to learn as much as you can. Focusing purely on the Lehman bankruptcy, these are the lessons that I have learnt over the last month.

Bad news doesn’t go away
There are so many factors that can be attributed to Lehman’s collapse. (Apart for the obvious over dependence on mortgage backed assets and securitization. In 2006, 65% of the banks income came from what is now toxic waste.) Dishonesty is one such factor. Thanks to some tricky asset classification, the bank hid its mortgage backed securities (MBS) in “harder to value” categories on the balance sheet, sheltering them from the conservative and inevitable write downs. Unfortunately for Erin Callan, ex CFO at Lehman, David Einhorn raised a red flag and labeled this move as “dishonest and misleading”. After making his views about the company very public, he started the short sell trend in May earlier this year. If you can’t price assets, you can’t buy them.

Psychology of the financial markets
Fear and greed run the financial markets, not the iBankers, not the traders, not Henry Paulson. Lehman brothers was well capitalized days before its collapse, but when the mortgage giants had to be rescued by the government, everybody lost faith in the system.

Blaming the bears is really easy in retrospect, but the S.E.C.’s September 19^th ban on short selling 799 finical firms artificially inflated the market, sending the stocks of firms like Goldman and Merrill as high as 20%. Expect the market to go up, then back down when the ban is lifted.     

The bigger you are the harder you fall
Why dint the fed help out Lehman brothers? I mean it did take on Bear Sterns debt obligations so JP Morgan could take the firm under its wing. AIG, Freddie Mac and Fannie Mae were just recently privatized, so why let Lehman die? Well, if you’re not big enough then you simply don’t matter. Lehman was foolish enough to blow its self up, but not big enough to take down the rest of the economy. AIG, the mortgage giants and Bear Sterns on the other hand had much wider exposure to these wacky securities and the underlying mortgage crisis.

The Human Element
On   September 15^th, Lehman filed for bankruptcy and but Merrill Lynch agreed to sell its self to Bank of America. Again there are many reasons to why Lehman fell, in this case, a major factor was that the firm’s inability to find a buyer. Sure prospective private equity firms wanted the same guarantee Bear Sterns got from the government, but it was more to do with CEO Richard Fuld’s pride. After being with the firm since 1993, he was simply unable to face the fact that his firm was worth far less than he thought it was, discouraging the Koreans and other prospective buyers from placing a bid.

Moral hazard?
Don’t talk to me about moral hazard. The Fed is just promoting more irresponsible behavior from investment banks by removing illiquid debt securities from banks balance sheets. The shareholders of Lehman had no more say in the operation of their company than in the case of Bear or Fannie Mae. Furthermore, it doesn’t solve anything. By passing debt from the financial institutions (that created this mess in the first place) to the U.S. Treasury just puts a burden on the US tax payer’s money. Last I checked, this “bail out” was going to cost the country a whopping USD$738 billion. Couple this with the spending due to the war in Iraq, massive lay-offs on Wall street, investments firms that are either going bankrupt or take on huge losses, increased expenditure due to rising prices and you have a problem… everybody is broke! Where does the government think this money his coming from?

In my opinion, the bailout is going to cause long term problems in the future. Whatever is spent will add to a budget deficit already projected at more than $500 billion next year. Not mention indirect costs by promoting irresponsible behavior and “moral hazard”.

On the other hand, the influx of capital may just be the economy’s saving grace. A certain amount of faith will be restored into the system; a great complement to the fact that housing debt that would have just vanished. Maybe a large capital injection is what we(they?) really need. For now, all we can do is watch from a safe distance, and keep betting on what the government is going to do next.

Nothing is too big to fail
Murphy’s Law, the Black Swan, use whatever theory you want, the main idea remains the same. Perception is everything in financial markets (lesson number two). A major bank that survived the great depression and everything else the world threw at it in the last 158 years was reduced to bits and pieces over the rumors of short sellers in a uncertain market. Every bank in the system has taken a hit, some more than others, some losing everything, others losing billion’s of dollars in terms of market cap over the span of a few weeks. There is no safety in numbers and “value” is a very relative term.

What next?
Last month I talked about redistribution of wealth and the lack of regulation. This month we are going to see a large number of mergers, acquisitions and failures. We are going to see the government start the blame game. Chief executives are going to be heavily scrutinized and a number of scams and frauds will come to surface. Personally, I feel that somebody is going to jail for shifting around those “level three assets” on Lehman Brothers balance sheets. Again, only time will tell…

Down my presentation titled "Lehman Brothers: a house of cards"