Continuing the review of the BBC documentary of the Trillion Dollar Bet from Part 1
The Black-Scholes model were blocked by a need to instantaneously recalculate the dynamic hedging to keep eliminating the risk based on stock price changes continuously. Unknown to Black-Scholes at that time, someone else has found the way. Professor Robert C Merton (Harvard Business School) is a great analyst and already recognized as a pioneer for his intellectual capabilities. He was proficient in analyzing savings and investment behavior and has addressed age old questions in Economics.
Even during his college days, he was very interested in stock markets and visited the trading visiting galleries very frequently.
Black and Scholes contacted Merton in the fall, went over their formula and their problem and Merton tried to re-model their problem in his model that he had created. He had a reputation of using abstract and exotic mathematical ways to study financial contracts such as OPTIONS has the reputation of exploring theories that no one in finance theory have even heard of.
For this particular problem, he turned to rocket science.He studied the theory of a Japanese mathematician, Itô’, who faced a similar problem. Some reference material is available here and here. In rocket science, to plot the trajectory of rockets, we need to know where the missile was, not just second by second, but right at that moment and literally all the time. Itô’ has developed a way to divide time as infinitely small parcels, smoothing it out to a continuum so that the trajectory is constantly updated.
Bob Merton used this idea and adapted it for Black-Scholes problem. Using the notion of continuous time (Itô’ calculus), the value of the option can be constantly re-calculated and risk eliminated continuously. In doing so, Bob Merton created an alternative proof that the Black-Scholes model that works in a more elegant and more robust way.
The final equation was parse and deceptively simple. Academics wondered at this formula’s insights and its sheer audacity and simpleness. Barely had the academics started to celebrate, when someone started using the formula in real life. Traders, especially OPTIONS traders started augmenting their skills by adding the Black-Scholes formula to their calculators to compute any OPTIONs value at any time ,even before the model has been officially published.
Other traders started noticing the usage of the model and started using it to hedge their risks constantly and made them feel safe enough to conduct trades in scales never dreamt of before. Risks in stocks can be hedged against futures, Risk in futures can be hedged against currency transactions and they all hedged against a panoply of complex financial derivatives — which were expressly invented to exploit the Black-Scholes formula.
“Dynamic Hedging” meant that risk is eliminated by constantly trading a lot which resulted as a great news for the exchanges and led to the thinking of — “More we trade, better off the society is, since lesser the risk”
This led to more contracts, more futures exchanges, options in Germany, Nikkei futures in Japan — in order to avoid risk, we have to trade everywhere and all the time.
After 25 years of its discovery, the architects of this formula received the Nobel prize. Fischer Black passed away by that time.
Rise of Long Term Capital Management
In 1995, Scholes and Merton went into business, at the height of their reputation and created LTCM (Long Term Capital Management) — a hedge fund. They promised to use mathematical models to generate unheard amounts of profits and due to their reputations, most prestigious investors (banks, pension funds etc.,) lined up to be part of LTCM and were dubbed the “Team of the Century”.
Most of these investors had either studied under them or read their books and had a “High Priest Visit” kind of visceral notion when they were invited to invest and felt even honored to be a part of LTCM. Within months, they had raised 3 Billion dollars and started investing across the globe. Surprisingly, instead of Wall Street, they setup in a rich little town Greenwich, Connecticut.
Read more about LTCM here
From Greenwich, they devised a top secret investment strategy which even their investors did not know. it combined all their Academic insights, using probability to bet that key prices will move like how they had moved in the past, but in case the predictions go wrong, they can protect themselves using the Black-Scholes formula by dynamic hedging, in effect by taking out Options in the opposite direction.
Supremely confident, they placed vast sums of money on the market and followed a broad strategy with hedging out the risks of the positions, and did a lot of it.
Their strategy worked gloriously. LTCM outperforming all other investment companies with returns of 20% (after fees) in the first year, 43% in the second year and 41% in the 3rd year.
As per LTCM, the world is acting as per their blackboard and they seem to have identified the path to Nirvana
Their day-to-day routine became golfing, attending conferences, raising funds etc., while the strategy kept churning money. But then slowly and from an unexpected area, a change in market dynamics began to become apparent.
The Market strikes back
In the summer of 1997, across Thailand, property prices collapsed, which sparked a Asia wide panic and Banks went bust all over Asia from Japan to Indonesia. People took to the streets rioting and such extreme improbabilities were never attributed in any mathematical models.
Everyone in the markets all over the world started panicking. The market indexes broke down and rallied back up and then broke again and with lot of volatility, creating lots of uncertainty and chaos. As prices leapt and plunged, the models used by LTCM began giving strange results.
So the regular traders started relying on their instincts instead of the Black-Scholes Model. In a time of crisis, Cash is supreme leader. So traders stopped borrowing and dropped investments in risky places. As any seasoned trader would say —
You need to get out when getting out is good an this is valid for any investment strategy.
Good traders on the floor always follow the strategy
Once you realize an error, it is always good to get out of that error and start again fresh
However LTCM models predicted that the prices would return to normal and no reason to panic. After all, if any of their bets are wrong, they just needed another bet in the opposite direction.
But as panic spread, OPTIONS cost increased, LTCM did the opposite of a good trader . They borrowed heavily and traded more and took on debts of almost 100 billion dollars.
As a trader would say — “If I have a position of 100B, a 1% loss is 1 billion dollars. And if all I have to start with was 3 billion dollars, then a 3% loss essentially means I am wiped out”
But all is not lost for LTCM as they were just about on the brink with their hedging and will be able to hold out as long as one other improbable thing does not happen.
Revenge of the Market
Almost similar to a well crafted sweet revenge movie, the market did exactly that one improbable incident. As the old market saying goes,
Market would test you and will do what you don’t expect it to do
On August 1998, the biggest country in the world, Russia default on all their loans with no explicit reason and refused to pay all its debts. The LTCM models completely went out of kilter and after the default, all the relations that tended to exist in the recent past — disappeared
Mathematical models (not just Black-Scholes, but all of them) were based on normal behavior in the market. For such wild unpredictable events, models were not prepared to identify and react correctly. The standard models predicted that they should not be losing more than 50M or so, but they were losing 100M each day. And four days after Russia defaulted, they lost 500M in a single day.
Taxpayers to the rescue
In Greenwich, LTCM faced the bankruptcy. But if they go under, so does the positions they held across the globe which was staggering. On final count, the models have led them to bet a trillion dollars, which equal to a year’s turnover of American government.
World’s top financial regulators met in crisis and there was a widespread fear of, one firm which is linked up to every major firm in Wall street, is going to be seized up and markets might just stop functioning totally. To prevent a global economic collapse, American Central Bank and Federal reserve organized a bailout of LTCM with humiliating terms.
Merten and Scholes and their investors lost millions. Among them were pension funds, Central Bank of Italy, Britain’s Barclay Bank who lost around 200 million dollars each.
Then the public recriminations began for the 3.5B dollar bailout. Rep. Bernie Sanders chided the gambling practices of the wall street elite. Federal Reserve Chairman, Alan Greenman, spoke on the dependency on Financial Modelling with all of its sophistication and how too far away it is from human judgement. Rep. Carolyn Malone profoundly remarks that if Nobel Prize winners did not fully understand the risks involved, then who can.
Rep. Paul Kanjorski questions who is truly responsible for the losses of LTCM and how the Federal Reserve just tapped into the savings accounts of every senior citizen to bailout LTCM’s losses.
Myron Scholes and Robert Merten were devastated. They had a great idea and a franchise and devised an application to problem solving, but did not realize the full extent of difficulty to put that into effect.
Black-Scholes model still continue to used by traders who use their judgement to either trust the model or their intuition on a case by case basis.
In the market, it always boils down to one simple ideology upon which we all have to make the biggest decision on —
“When do you admit you are wrong and start all over again, or decide to hang on and assume that the markets will turn around in your way”
After this whole fiasco, Investors definitely need to understand that over the last several hundred years, some people are able to do it better than others. They might not be from MIT and they don’t necessarily have mathematics degrees (though they cannot be ruled out). They are the kind of people who can make that judgement “Something’s different here, I am going back to harbor, untiI I figure this out” — That is the kind of people you want running your money.
“Elegance is for tailors” — Einstein
The fatal fascination of mathematics lies in its deceptive simplicity and we should be forewarned to believe in something just because it is beautiful — like the Black-Scholes formula.