Post 3 - The LTCM Story

Post 3 can get a little heavy, so let’s start out with something a little lighter. This first metaphor was borrowed from one of my biggest influences, Nassim Nicholas Taleb:

The Turkey Problem

A turkey born on a family farm lives a luxurious life (for a turkey). He has land on which he can roam free from predators, he has its meals fed to it twice a day, and he has shelter which he can use to avoid inclement weather.

As it turns out, our turkey friend is an avid forecaster, and he’s good at it too. He has modeled his feeding schedule going forward every day for the past few months. Each morning and afternoon, just as he predicted, he gets fed his normal meal of seeds and gains. One day, our turkey friend decides that he wants an “all-in-one” model: the model of his well-being. He decides to build it.

The turkey has generally liked the way his life has trended, and he has no reason to believe that the trend will change based on historical precedent. So, as any reasonable turkey would, he models for the trend to continue using historical averages.

Our turkey friend’s well-being has generally trended upward. Like any turkey, it may have a bad day here and there, but the volatility of its life has remained fairly constant. The model he comes up with looks exactly like the graph below:

 Very impressive. A few weeks go by and he is on trend. At this point, he thinks he’s the Nostradamus of turkeys. He goes to his turkey boss and asks for a raise. Of course, he gets it (as predicted). His turkey family is ecstatic for him. He’s on top of the world.

A few weeks later, when there is a cool breeze in the air, his boss pings him for an updated model. He wants to show the rest of the farm what his impressive employee can do. Our turkey friend updates his model (it looks the same as it did) and sends it off.

Only there is one problem: tomorrow is Thanksgiving.

He had modeled Thanksgiving to be just like any other day. Instead, his morning meal of seeds and grains was substituted for the business end of a butcher’s cleaver. Our turkey friend went well-being bankrupt overnight. How could this have happened? Our turkey friend, using past data, expected to get his typical morning meal consisting of seeds and grains and for his well-being to continue on trend. He had no (analytical, statistical, etc.) reason to believe otherwise, so he thought.

The LTCM Story

Long-Term Capital Management (LTCM) was founded in February 1994 and, at the time, was the largest startup hedge fund to date. The partners largely came from one incredibly successful wing of Salomon Brothers, one the most successful investment banks in the 1980s and 1990s. The talent involved with LTCM was simply unmatched.

LTCM’s founder and principal manager was a former Salomon Brothers standout, John Meriwether. Meriweather worked as a bond trader and was widely seen as one of the best in the business (ignoring the 1991 scandal where traders under Meriweather were caught making false bids on two-year notes in order to manipulate that market. He personally was fined $50,000 in civil court). Meriwether hired a dream team of PhDs in mathematics and finance. One journalist, at the time, wrote “In the Greenwich, Conn., office of the hedge fund's management firm, Long-Term Capital Management, there may be more IQ points per square foot than in any other institution extant. There are certainly more Nobel Prize winners per square foot.” - LTCM had brought on two: Myron Scholes and Robert Merton, both of whom won the Nobel Prize in economics for the now-famous Black-Scholes equation for pricing derivatives, a revolutionary equation that changed the fabric of derivatives trading, for a time.

With a roster such as theirs, the early years of LTCM went exactly how you’d expect. They were able to raise an incredible $1.1B, $1.0B from outside investors, and $100M from the twelve partners. Their returns in 1994, 1995, 1996, and 1997 were 28%, 59%, 57%, and 25%, respectively (for context, the S&P500, or the largest 500 publicly traded companies in the United States, earns somewhere around 8% per year on average). LTCM was so successful that in 1995, just a year after its founding, it closed the fund to outside investors. They were so on fire that in 1997 they returned $2.7B to investors via a forced dividend; the firm was outgrowing the opportunity set that they saw and were “too flush” with cash.

The Fragility of LTCM

Nobel Prizes Are Better with a Side of Gravy

LTCM’s bread and butter was the convergence trade of the same assets & liabilities. Simply, they would go long, or buy, the cheap asset and go short, or sell, the more expensive liability against them and wait for their two market prices to converge. An example trade (that LTCM actually employed) will help illustrate exactly how this worked:

LTCM would buy (or long) the 29-year US treasury bond by selling (or shorting) the newly minted 30-year US treasury bond. In August of 1998, the 29-year US treasury bond was trading at a yield of 5.62% while the newly-minted 30-year US treasury bond was trading at a yield of 5.50%. This was a difference of 0.12%, or 12 basis points. If the yields of the two bonds converged towards each other, i.e. the spread went down from 12 basis points, as is “expected,” then LTCM would make money. If the spread gapped out above 12 basis points, then LTCM would lose money.

In the world of bonds, the higher the yield, the cheaper the bond, so the 29-year bond (at 5.62%) was cheaper than the 30-year bond (at 5.50%) in August of 1998. This is abnormal. Typically, in a normal yield curve environment, the further out the maturity of the bond, the higher the yield should be due to the increased uncertainty of longer and longer periods in the future (a promise to repay me in three months is much more valuable than a promise to repay me in 30 years. I have a much higher confidence in what the world/my life may be like in 3 months vs 30 years. Because of this, I demand a higher yield (or lower price) for those promises further out in the future).

So, in theory, the 30-year bond should be cheaper (and have a higher yield), than the 29-year bond. However, this is not the case in reality. The newly-minted 30-year bond has what is called a “liquidity premium” which means that more people are trading the fresh 30-year bond relative to the older 29-year bond. Because more people are buyers and sellers of the 30-year bond, it is simply easier to buy and sell. This increased relative level of liquidity comes at a price - in this case, somewhere around 12 basis points. LTCM’s bet was that once a new 30-year bond is offered to the market, the old 30-year bond (now technically the 29.5-yr bond since the US deploys new bonds into the market every 6 months) and the 29-yr bond’s yields would converge towards each other. 

LTCM, by borrowing (selling) the 30-year bond, was paying 5.50% and receiving 5.62% when buying the 29-year bond. This resulted in a profit of 12 basis points. 12 basis points isn’t a very interesting upside by anyone’s standards, so to make it more profitable, they would need to apply leverage, or debt, to make the return on the company’s equity more palatable. LTCM would lever up their convergence trades by borrowing against the 29-year bond they were buying. Usually, this would come at a price that an investment bank would charge, known in the industry as a “haircut,” in case the price of the bond was to move against the bank. However, investment banks were charging LTCM a haircut of exactly zero.

The consequence of a 0% haircut was that LTCM could make these convergence trades for zero cash down; they would short the 30-year and receive cash, use that cash to buy the cheaper 29-year bond, and then borrow against their 29-year bond for more cash to pursue other trades. With a zero haircut, one could make these trades indefinitely. In 1998, LTCM had approximately 15,000 line items on its balance sheet because they did exactly that. Because they were putting no cash up front, they were funding a majority of these trades with leverage. At their peak debt and equity levels, LTCM was operating at 25:1.

Improper Statistics

How to Make Thanksgiving Come Faster

 So how risky were these convergence trades? Dr. Eric Rosenfeld, one of the co-founders at LTCM, gave a lecture to a consortium of graduate and undergraduate students in April 2007. The way Dr. Eric Rosenfeld describes risk in his lecture is the smoking gun of this whole case. In the lecture, Dr. Rosenfeld shows a graph of the trend in 30-year US treasury bond yields from 1994 to the beginning of 1998 and relays the following.

“Here is a graph of 30-year bond yields from ‘94 to the beginning of ‘98. It has a sigma of about 85 basis points. So, the risk of an outright bond trade, if bonds are at 5.50%, is +/- 85 basis points two-thirds of the time. But, if we look at the spread trade… if we take the standard deviation of the spread, that’s at 4 basis points… because these bonds are so highly correlated.”

He refers to the level of risk as “sigma” which is a reference to the typical notation for standard deviation and the preferred measure of risk by the Gaussian Cosa Nostra. The standard deviation is a measure of variation; a higher standard deviation suggests that the data set disperses more, on average, from the mean than a data set with a lower standard deviation. Generally, an asset whose price movements have a higher standard deviation is considered “riskier.” The price moves up and down at a greater “intensity,” if you will. More importantly, however, his statement reveals him as a member of the Gaussian Cosa Nostra.

His statement that the yield fluctuates plus or minus 85 basis points “two-thirds of the time” is what gives it away - he is implicitly implying that the fluctuations in the yield follow a Gaussian distribution (normal distribution or bell curve), just like Bachelier posited long ago (in the Gaussian distribution depiction below, 68.2% of data points fall within +/- one standard deviation (sigma) of the mean, which is, approximately, the two-thirds Dr. Rosenfeld was speaking to).

Assuming the Gaussian has many probabilistic implications, one of which is particularly important here. The Gaussian distribution belongs to a class of distributions considered “thin-tailed,” i.e. the probability of an event occurring gets exponentially lower as one moves away from the mean. Said another way, it doesn’t scale: the probability of observing two consecutive 3-sigma events is (much) higher than observing one 6-sigma event.

Dr. Rosenfeld brings up an example of the spread between the 29-year bond and the 30-year bond gapping out to 28 basis points, away from its usual 12 basis points, in 1998. Remember, the standard deviation of the spread was 4 basis points, so an increase of 16 basis points would be a “4-sigma” event. Based on our Gaussian math, a 4-sigma event should only occur once every 31,560 trading days, or approximately once every 126 years. If we’re giving LTCM the benefit of the doubt, they may have just simply gotten extremely unlucky to experience a 4-sigma event. Once every 126 years is rare, but it certainly could occur during someone's lifetime. In the next example, however, one cannot give them such a benefit.

In August of 1998, Russia defaulted on its sovereign debt and sent financial markets into disorder. Dr. Rosenfeld brings up an example of another convergence trade using swaps, which typically varied by 1 basis point a day, gapping out 21 basis points during the crisis. Here, he is implying that swap spreads gapped out 20(!) standard deviations. The odds of a 20-sigma event occurring is once every 1.45x10⁸⁶ years. To put that into context, the universe is estimated to be only 1.37x10¹⁰ years old.

Even better, the number of particles in the universe, according to a recent estimate I found, is 3.28x10⁸⁰. So, by Dr. Rosenfeld and LTCM’s risk management math/logic, if I were to choose one particle from anywhere in the universe, LTCM would have had much better odds, by orders of magnitude, at guessing which particle I chose than that swap spread gapping out to 21 basis points (I’ll note that he was giving this lecture after the fact, yet still didn’t understand the probabilities he was inherently speaking to*). They lost $550M in this one trade. The firm subsequently went to zero.

Ask yourself: Did they get cosmologically unlucky, or were they using the wrong mathematical tools?

The result of their mysteriously sudden crash was a full-blown panic: the crisis caused by LTCM’s actions was so destructive that a consortium of banks, along with the Federal Reserve Bank of New York, had to step in and inject billions of dollars to prevent a full contagion within financial markets. Each of the twelve partners, who entered the fund with $100M, left with nothing.

Below is a graph of LTCM’s performance vs the S&P 500 over LTCM’s life. Does it look familiar? It would seem to me that our turkey friend and the all-star lineup of PhDs and Nobel laureates are not that different from each other.

Denouement

So what happened with John Meriweather and the LTCM crew for putting everyone, including everyday Americans, financially at risk? It is a pleasure to say justice prevailed. They eventually paid back the debt they owed, they learned from their mistakes, and they suffered legal trouble; they were barred from ever trading securities again.

Just kidding.

John Meriweather immediately started JWM Partners LCC within the same exact year that LTCM collapsed: 1998. He raised $250 million (from people living under a rock, presumably) and brought along a lot of the same LTCM talent. The fund used similar trading strategies as LTCM (but “only” used a leverage ratio of 15:1 this time). In April of 2008, they had amassed $1.6 billion in assets under management.

Then came the Great Financial Crisis. On July 7^th, 2009, JWM Partners LLC announced its closure after a 44% loss within its main fund.

Some turkeys never learn.

Thank you for reading.