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The Real, and Simple, Equation That Killed Wall Street

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“If it weren’t for those meddling kids!” That was the punch line for every Scooby Doo episode. It also is the overly simple narrative that many in the media have spun about the last financial crisis. Smart meddling kids armed with math hoodwinked us all.

One article, from the March 2009 Wired magazine, even pinpointed an equation and a mathematician. The article “Recipe for Disaster: The Formula That Killed Wall Street,” accused the Gaussian Copula Function.

It was not the first piece that made this type of argument, but it was the most aggressive. Since then it has been a common theme in the media that mathematics, especially obscure advanced mathematics, is largely responsible for the catastrophe that doomed the world to the last five years of recession and slow growth.

This theme plays on the fallacy that danger always comes from complexity. It’s a fabrication that obscures the real causes, that makes it easier to say, “Hey, it wasn’t my fault, I was blinded by science.”

The reality is much simpler and less sexy. Wall Street killed itself in a time-honored fashion: Cheap money, excessive borrowing, and greed. And yes, there is an equation one can point to and blame. This equation, however, requires nothing more than middle school algebra to understand and is taught to every new Wall Street employee. It is leveraged return.

What is leveraged return? It’s the return on assets using borrowed money.

The equation for the leveraged return, L, is:

Where Y is the return of the asset, R is the cost to borrow money, and N is the “haircut,” or the percentage of money the investor must put down to secure the loan (the down payment).

A simple example. An investor wants to buy a bond returning 7% using borrowed money. The bank requires them to pay 20% in cash with the remaining 80% lent at a rate of 5%. What is the leveraged return?

So after borrowing, a 7% return is turned into 15%. Kaboom!

The equation, though simple, reveals one dangerous truth that investors love to exploit. If you can find an asset that returns more than the cost to borrow money then any return is possible with enough leverage.

How to exploit it though? Two conditions need to be met: A low borrowing cost and somebody willing to lend lots of money. Both came together perfectly in the six years preceding the meltdown of 2008.

The first condition, low rates, came courtesy of the bursting of the dot-com bubble.

In early 2001, following the collapse of the stock market, the Federal Reserve (the Fed) started aggressively lowering the Federal Funds rate (Fed funds). They did this in an attempt to stave off a recession. The Fed funds is the rate, set by the Fed, for overnight loans between banks. This rate broadly sets the cost of borrowing money for short time periods.

The goal of the Fed was to promote growth. In 2001 Fed funds was brought from 6.0% to 1.5%, and by 2003 had reached 1.0%. Small business loans, mortgages, and all borrowing become cheaper.

Those low rates, intended to boost consumption and increase employment, also boosted Wall Street. Money was cheap and many assets, which had suffered from the sell-off following the dot-com implosion, were also cheap. Money started pouring back into the markets with investors flocking to the high-returning risky assets.

As the markets moved forward the returns on assets contracted under the buying pressure. The only way to get the same returns? Borrow more, dropping the haircut to lower and lower levels increasing the leveraged return.

Still, what was needed was a way to justify the borrowing of more money. That second condition also came courtesy of the Fed. This time it was unintended.

What drives the haircut, N, the amount of money Wall Street will lend?

Most borrowing in the markets is secured lending with the asset purchased used as security against the loan. The haircut, the cash put down, is a buffer against a fall in the price of the asset.

Risk managers, who set the haircut, run simple models that posit asset prices in the future to be spread about an average with a width to the distribution. That width, the standard deviation, is also knows as the price volatility, . How do they estimate this? Mostly using historical data.

The consequence? Higher market volatility means higher haircuts (less money lent) and lower market volatility means lower haircuts (more money lent).

By 2004 the economy was on an upswing, helped in part by the Fed’s policy of low rates. Now it was time to “step on the brakes.” From the middle of 2004 until the end of 2006 the Fed started to raise rates as the economy healed.

The combination of increased borrowing cost and higher overall asset prices should have been the end of the leveraged return game. But something funny happened. The Fed raised rates in a smooth and predictable fashion, communicating to the markets that increases would be .25% at every six-week meeting.

The methodical steps higher in rates dropped market volatility to historical lows.

An index that measures market volatility, called the VIX, decreased during that period reaching a bottom of 10% in early 2007.

What did banks do in response? They lowered the cash required from 20% to 15% and eventually to 10% and lower, giving a whole new meaning to the term Dime Bag.

Now came another equation.

The profit in any year must be greater than the profit in the prior year.

2005 and 2006 were record-breaking years on Wall Street. Assets were at historical highs and lending was also. Leverage at major financial had grown from around 20 times capital to 35 times. The easy money was gone, but management felt profits had to keep pace.

Chuck Prince, CEO of Citibank, in a now infamous quote said, “When the music stops, in terms of liquidity, things will be complicated. But as long as the music is playing, you’ve got to get up and dance. We’re still dancing,”

Haircuts could not go much lower. Now simple greed took over. The banks turned to outright purchases of securities, morphing their role as lenders into investors.

This is where equations like the Gaussian Copula function enter. The market used these exotic functions to argue favorable regulatory treatment, assigning risky assets less risky weightings. This was helped by a symbiotic relationship between the rating agencies and banks. Lax oversight by regulators further enabled the corruption.

The result? Now everyone was loaded with leveraged assets many of them far riskier than reported. A tumble in one asset could precipitate a furious and fast fall in others. Lenders would be forced to sell collateral, triggering other assets to be sold as borrowers had to find cash to post against the loans.

With balance sheets engorged relative to capital, prices did not have to fall far before some institutions faced insolvency. Cross borrowing amongst institutions led to further entanglements. No fund was an island.

The result was the spectacular fall in markets in 2008 that culminated in bank defaults and the government bailout.

The Gaussian Copula Function, opaque to most, is convenient to blame. It allows us to shake off our collective sense of guilt. It obscures the real crime with a motive that doesn't take a gang of teenage sleuths and they’re dog to sniff out: greed.

From the minutes of the Aug 7, 2007 Fed meeting.

“I lived through the corrections of the S&L market, portfolio insurance, the crashes of ’87, ’97, and so on. When you sort through them, all of them have a common basis, and that is a search for greater yields or greater return, leverage in order to achieve that return….”

---Richard Fisher. Dallas Fed President.

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Data courtesy of Bloomberg Financial.

The views expressed are those of the author and are not necessarily those of Scientific American.

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