Mathematics has been called the Queen of All Sciences. Physical laws when written in the form of mathematical equations allowed scientists to calculate precisely the different phenomenons of nature. Today mathematical formulas are increasing being used to predict financial markets. It was mathematics that allowed the conquest of our surroundings and the nature. So why not apply it to financial market, predict what is going to happen and make a lot of money. Building mathematical models that can predict financial markets is the new game that everyone is loving.

### Black Scholes Stock Options Pricing Formula

You must have tried to use Black Scholes formula for stock option pricing. Does it work? Most of the time it doesn’t. Why? It uses a few assumptions that most of the time markets violate. For example it assumes stock prices to follow a log normal distribution. This assumption often breaks down in conditions of high volatility. Another assumption is about constant volatility which also doesn’t hold. Professors Robert Merton of Harvard and Myron Scholes of Stanford were the 2 persons who developed this Black Scholes stock options pricing formula. They got awarded a Nobel Prize in Economics in 1997 for developing the formula that most of the time would not work. One of the input variables that this formula requies is volatility of that stock. Till today no one has been able to figure out how to model volatility. **You can read a detailed analysis of why this formula doesn’t work and why no one actually uses it**.

### Long Term Capital Management Collapse

The creators of Black Scholes formula got hired by a hedge fund with the name of Long Term Capital Management. Both of them also got featured in the Long Term Capital Management Saga which has been dubbed the Trillion Dollar bet that went bust. Long Term Capital Management had taken huge positions in the market that had put the whole financial system at risk. **Long Term Capital Management collapse case study** is something that you should study as it will teach you how difficult it is to model risk in the market.

Two Nobel Laureates along with their other colleagues tried to model risk and failed miserably. So you can see how difficult it is to model financial markets even if you are a Nobel Laureate. Hedge funds are notorious for taking big bets in the market that often go wrong starting their death spiral. Most of the time these hedge funds are small sized. But when the hedge fund takes too big a position it can cause systemic collapse as could have happened with Long Term Capital Management if Federal Reserve did not intervene in time. **Did you read out last post on hedge funds and whether they can bring the financial system down**?

### Renaissance Technologies Hedge Fund

So you can well imagine how difficult it is consistently beat the market. Sometimes things work out but just when you increase your risk things go against you. John Simons before he started his hedge fund was hired and fired by NSA. John Simons started his investing career liked it and decided to start a hedge fund named Renaissance Technologies in 1982.

**Renaissance Technologies LLC is an investment management company dedicated to producing superior returns for its clients and employees by adhering to mathematical and statistical methods**. As you can see Renaissance Technologies is a Quantitative Hedge Fund that uses mathematical and statistical models to find hidden patterns in price that can be profitably traded. Renaissance Technologies has averaged 71% annual return between 1994 and 2014. In 2008 when the stock market was showing extreme volatility and many hedge funds went belly up, his hedge fund made 98% annual return that year. You can now compare the two hedge funds the Long Term Capital Management and the Renaissance Technologies. One went bust and the other did spectacularly well. Both hedge funds were managed by mathematician. Both used quantitative trading strategies. In the video below you can listen to him talking about his love for mathematics and how he used it in making a lot of money.

Now John Simon is very secretive about the quantitative trading strategies that are used by his hedge fund Renaissance Technologies. You can read the book “**The Quants: How a New Breed of Math Whizzes Conquered Wall Street and Nearly Destroyed It**” by Scott Patterson in which you can get a glimpse of quantitative trading strategies that are being employed by John Simons and his team of mathematicians. The focus is on Algorithmic Trading. Below is another video in which John Simons explains his love for mathematics!

We can only judge a trader, investor or for that matter a hedge fund by it performance over the years. Performance of Renaissance Technologies has been consistent over the years. The idea is to use powerful computers to solve sophisticated mathematical algorithms. Renaissance Technologies is reputed to have the best maths and physics department in the world.

**In 1988 Renaissance’s established its most famous and profitable portfolio**, the Medallion fund which used an improved and expanded form of Leonard Baum’s mathematical models improved by pioneering algebraist James Ax to explore correlations from which they could profit. Simons and Ax started a hedge fund and christened it Medallion in honor of the math awards that they had won. The mathematical models the company developed worked better and better each year, and by 1988, Simons had decided to base the company’s trades entirely on the models…

Most probably Renaissance Technologies is using a model based on Hidden Markov Chains. Not sure about that*.***Have you read Market Wizard book series by Jack Schwager**? Jack Schwager has written a great book on Hedge Fund Market Wizards but there is no mention of Renaissance Technologies or John Simons in it despite the fact that his hedge fund has been in existence for the last 30 years and has a proven track record. Maybe John Simons did not want to give interview to Jack Schwager.

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