Losing money is one of the loneliest feelings. It was Oct 22nd, 2008. Lehman Brothers, the investment bank, had filed for bankruptcy the month before. The markets were panicking. A thousand people surrounded me, almost all of us slouched in our seats, staring at computer screens. I had eight, all flashing prices of assets that I couldn’t touch, but, oh, I could feel.

I myself was waiting for one price to flash, an interest rate in Brazil. I had bet that rates would lower over time, from 15.10% to 14.50% or so. The size of my bet was 20,000 USD for every one hundredth of a percent (or 20k per basis point). A move from 15.10% to 15.00% would make me 200,000 USD. A move to 15.20% would lose me the same amount.

I sat with a knot in my stomach, nervously chewing a swizzle stick, waiting for the markets to open in Brazil at 7 am. I jotted down worst-case scenarios, and then turned them into doodles. The default of Lehman had unleashed market hell. I closed my eyes. You could hear the markets, a trading floor filled with murmurs and sighs, the cumulative sounds of disappointment.

The Brazilian rate was a tiny yellow box on one of my screens. I had been in the office since 4 am, waiting, trying to extrapolate from other prices, from other assets how much money I would lose (or make). The price the following day had closed at 15.90%.

This day all assets, stocks, bonds, commodities, interest rates, everything, were trading in two distinct camps, going opposite ways. Most prices were falling, dramatically. A full-on Guppy Suck: Prices were spiraling lower like dead fish flushed down a toilet. Money was going into a few lucky assets, safe havens they were called, things considered having no market risk. Short maturity US bonds. Cash. The correlation between assets was approaching one or negative one.

My Brazilian rate started trading. It blinked 17.40%, 1.50% wider than the prior day. I was out 3 million dollars, and I had no chance to trade. No chance to get out at 15.50% or 16.00%. The market had gapped. I got up, shot a bird at my screen, punched it, and then walked to the bathroom.

Markets are not supposed to do this. Almost all of modern finance, all of trading of assets, is predicated on continuity, on transactions able to be made at every price along a path. Traders, banks, risk management all use mathematical models that have as an assumption continuous liquid markets.

The days following Lehman were notable not only because of the large moves, but because I, and many others, could never have traded at any price. Fists punched screens all across the globe.

It was a self-reinforcing problem. A feedback loop developed. I couldn’t sell my Brazilian rates so instead I sold another investment, Argentinian bonds. Others were doing the same, selling whatever they could, whatever was trading, moving the money into cash. The process devolved down the ladder of securities, from the least liquid to the most liquid. By the end, some of the largest stocks in the world, blue-chip stocks in the S&P 500 were also gapping.

The months following Lehman’s collapse saw the entire financial system start to fail, in a cascade of interconnected plummeting securities, and with them, the world economy. Major banks were broke, hedge funds decimated, and the average investor left feeling fleeced. The process only ended when the Federal Reserve stepped in, bailed out banks, and acted as the buyer and lender of last resort.

Those months reminded many that liquidity, how much of something you can trade per day and convert into cash, without affecting its price, is the most misunderstood variable in finance.

How did we get here?

Finance now is a complex field buttressed by hundreds of mathematical models. At its heart is the Black-Scholes equation for pricing of options.

Published in 1973, it slowly revolutionized finance, leading to a boom in financial contracts and new way of looking at markets in terms of relative value and models. It also changed the type of person who worked on Wall Street. It became people like me, with a PhD in Physics, who could build models, like Black-Scholes, to price complex products like options.

What is an option? It is the right, but not the obligation to purchase (a call) or sell (a put) an asset at a predetermined future date for an agreed price. You might be offered an option to buy a share of stock S in one month at 105 when it’s now trading at 100. What is the value of that? Because the risk is asymmetric (you own the upside of the price, but not the downside) it has a positive value to you. Until 1973 most traders used ad hoc valuations. They knew an option was more valuable the longer the maturity (more upside!), the more volatile the stock (more upside again), but no exact relation existed.

Economists Fisher Black, Myron S. Scholes, and Robert C. Merton derived an equation that valued options on most assets. They did this by making the assumption that assets move over time in a continues motion with a given volatility, so that the future price of an asset was a probability distribution. By finding a strategy of buying and selling the asset that exactly replicated the ownership of the option they derived an equation that specified the value of an option. The sole undetermined variable was the asset’s volatility.

The Black-Scholes model was revolutionary for two reasons. Not only did it put an exact value on the option, but also more importantly, it did so by showing traders how to decrease their exposure to changes in the value of the option. Buying or selling options was now less risky.

It also started people thinking about relative value in financial markets.

If an option was trading less than the value assigned to it by the model, they would suggest buying the option (it was cheap) and employing the strategy of buying and selling stocks against it. Or, in the words of Wall Street, selling the hedge. Or opposite of that, if the option was trading expensively, the model would suggest selling the option and buying the hedge (the replicating portfolio of stock that matched the behavior of the option).

This way of thinking about finance, using mathematical models to view assets as either rich or cheap and to diminish the risk associated with ownership, steadily grew in the 1980s and 1990s.

Hubris rarely is associated with math, but Black-Scholes gave the markets a sense of greater control, greater clarity. Most important, it gave the markets the belief that risk could be understood and lessened, and value better understood. Over time some traders started to focus only on using models to buy cheap assets and sell rich ones.

Mathematical hubris reached its zenith with the founding of LTCM, a hedge fund started in 1994 by John Meriwether and based in Greenwich, Connecticut.

It was one of the first, and the most famous institution, to embrace the “model driven relative value” approach to trading. Not only did it employ many mathematicians and economists, two of the seminal economists to have worked on Black-Scholes, Myron S. Scholes and Robert C. Merton, were partners in the firm.

By 1994 mathematical modeling of financial assets had gone far beyond just options. Almost every traded security could have a “fair value” price associated with it, using proprietary models. LTCM used their closely guarded models to buy the “cheap” securities and sell the “rich” ones. They did this on a huge scale, using leverage provided by the banks.

LTCM was initially wildly successful, producing hefty returns and growing from one billion dollars under management to five billion by early 1998. During that time they were the rock stars of Wall Street. Magazines wrote glowing articles about the geniuses in Greenwich. Rarely had mathematicians ever acquired such a smooth media veneer.

Then in September 1998 they lost everything, all five billion, in a spectacular crash that threatened to engulf banks and other funds. It only ended when a consortium of investors, prodded by the government, stepped in to salvage LTCM from infecting the broader markets and economy.

What happened? In September 1998 Russia defaulted on its local bonds and froze its currency. Like the days following Lehman, the markets broke, and asset prices jumped or fell with little trading. LTCM found itself unable to buy or sell assets without materially changing the price. Again, markets were anything but continuous.

Others in the markets, seeing LTCM in distress, jumped. If they thought LTCM owned bond X, they would sell it themselves, even if they did not own it, knowing it would force LTCM to have to sell. The process became self-fulfilling.

LTCM found that the assets it had bought, the ones it thought were cheap, proved to be the most illiquid, the ones that fell fastest with the fewest trades. What it had sold against the purchase, assets the model told were expensive, proved to be the most liquid. Those assets held up well. The spread between the two grew, rather than contracted as their model said it should. LTCM was, in the words of one senior trader, “Getting royally fucked.”

The models, as built, were utterly inadequate at describing the world, as they did not taken into account liquidity. Not to the appropriate degree. More important, the events surrounding LTCM showed that the liquidity of an asset was a tenacious variable, hard to define, and prone to large swings.

The problem was even more complex than that. LTCM itself, by owning certain positions, affected the eventual liquidity of securities. It created a self-reinforcing problem that the models could not address. The models needed to consider that others where using, well, models.

Wall Street learned very little following September 1998. By the time Lehman defaulted and triggered the next financial crisis (and my loss on the Brazilian rates) the same model-based methodology had again taken a primacy in markets, culminating in massive investments in complex mortgage securities.

LTCM itself was reborn. Many of the original partners started a new company, JWM Partners, which launched in late 1999. For much of the early 2000s they were again profitable, but more humble (few laudatory articles this time). Not surprising to some, they fell apart a second time, losing close to 45% in their largest fund in the period surrounding Lehman.

Not all models are to be faulted. There are models that do incorporate illiquidity, or market freezes. These do so by adding rare, but large, discontinuous jumps in the price of assets. These models, however, are of a different breed than the non-jump models.

If a trader buys an option using Black-Scholes and then sells the hedge, assuming the asset’s path over the life of the option is the volatility used in the model, the trader will break even every single time.

Models that incorporate jumps, however, give the expected price, not the actual price. That model will give a higher price to the option to compensate the trader for the rare but dramatic times jumps occur.

If the asset realizes the path postulated by the model, without a jump, the trader will lose a small amount. If the rare jump occurs the trader will make money, a large sum that should equal the total losses from the times without jumps. Not surprisingly, these models will tell the traders to take less risk, a message that many do not want to hear.

It’s also about the incentives.

Wall Street compensates and judges on short-term performance. Two competing funds, one using more conservative models, the other not, will have different return profiles. The more conservative fund will have lower returns six out of seven times, but much higher returns the one year out of seven when markets dislocate, making the more cautious firm the better investment long term.

The conservative fund, however, will find itself living in the media shadow of the risky fund and its gaudy returns. Past performance is no indication of future performance, but it sure as hell is an indication of a wall of cash looking to invest.

So what happens is the LTCM story. Models that encourage risk taking get used. They make good money seven out of eight years as liquidity is well behaved. Chances are the first few years are some of the good years. They make profits, the media fawns on them, investors come, and the traders get paid a lot of money. It’s the fifth or sixth year, when markets freeze, assets go into a fire sale, and models break down, that is their downfall.

Compensation also encourages the boom-bust models. Pay in the boom years is a percentage of profits. Pay in the bust years is zero, not negative. This asymmetry encourages traders and funds to roll the dice.

This overall myopic approach, valuing short-term profits over careful investing, is what led to Wall Street embracing models that inadequately describe the reality of finance. Models were used to rationalize “too good to be true” returns, turning them into “smart cutting-edge investing.” They became just another in a long line of ways that companies and traders masked the risk that they were running.

There are smart hedge funds, smart traders that enhance their risk management and profits using models. They do this by doing what has always worked in investing: Judicious risk-taking complimented by a thorough knowledge of the markets. They take the long view on value over the short view on profits. Sadly, they are often not the ones that get the attention or rewards.