Mathematics is used in Financial Markets extensively. Beyond basic number crunching mathematics is used to design profitable trading and hedging strategies. I have studied mathematics at Masters level courses in North America, but unfortunately not all of it is useful in every day life. That said, there are parts of mathematics which is used every day in financial markets- resulting in turnovers of billions of dollars on NYSE (New York Stock Exchange), NASDAQ and CME ( Chicago Merchantile Exchange). These are Probability Theory and Statistics( also called Quantitative Analysis).

The probability theory is used to identify trades which have positive expectancy, trades which have a short term edge. Probability theory depends on a reasonable sample size. For example if a trading system has a positive expectation of 70% (win-loss ratio) , it implies, chances are 70% that you will have a profitable trade. If the sample size was only one, the chances are equal (50%) that the trade will actually be a loser. That means these expectation play out only when you have a reasonable sample size. You take 20 trades, on a 70% expectancy system, 14 will work out, 6 will not. The outcome is on a totally random basis, you don’t know which one will and which one will not. These systems work on unshakable belief of uncertain nature of the markets and that any trade could be a loser. This is why a risk management strategy has to go side by side with probability based trading strategy. Now is the time to introduce the second part of applied mathematics which is used for risk management in the financial markets. This is called Statistical analysis or quantitative analysis. The quantitative analysis helps in defining risk parameters, like for all the trade that fails we will have a stop loss at 1 s.d( standard deviation), or a break of some kind of moving average (20 period EMA- exponential moving average) or movement of 2 ATR ( Average True Range) in the opposite direction of trade. Probability theory is also used by Casinos who have a positive expectations out of all the games that are played. They also need a large sample size ( read gamblers) to have profitable outcome and that is why you see the ads inviting you to go and make your bets in Vegas! I could not help chuckle when I saw the Kevin Spacey starer 21, which touches on this subject in context of beating the house in their own game using MIT grad mathematicians!

There you have it probability theory is used to design profitable trading systems ( which most of the hedge funds use) whereas statistical theory is used to define risk parameters ( and also profit targets- I will exit the trade once it hits the top of the bollinger bands- these bands are based on standard deviation parameters). These tools help put a structure to the financial markets, a crutch to analyze the markets and put some sense on what is by nature an uncertain endeavor ( who could have predicted a melt down in top notch investment bank like Lehman Brothers and Bear Sterns and GSEs like Freddie Mac and Fennie Mae), I certainly could not. My risk parameters based on statistical theory is the one which helped me survive this mess, and to come back and fight for another day! I thank my mentors, my teachers, the researchers and the books I have read (most notable by Kenneth Grant) on this aspect of applied mathematics which helps me survive- and not only survive, even thrive when the lady luck smiles on me

If you asked me which subject I like most, nope- not mathematics! Although it is a close second, my first love is physics!! I will write about the applied aspect of physics on a different blog post, but just to have you thinking, here is a brief introduction. Whole engineering disciplines have branched out of fundamental concepts of physics. For example, Thermodynamics, which is part of physics, is used by Mechanical Engineers to design turbines in power plants and jet engine of your boeing planes. Every time you take off, your life depends on it- literally!!! How do I know, I am a qualified Mechanical Engineer, that’s why!!

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Mathematics is used in Financial Markets extensively. Beyond basic number crunching mathematics is used to design profitable trading and hedging strategies. I have studied mathematics at Masters level courses in North America, but unfortunately not all of it is useful in every day life. That said, there are parts of mathematics which is used every day in financial markets- resulting in turnovers of billions of dollars on NYSE (New York Stock Exchange), NASDAQ and CME ( Chicago Merchantile Exchange). These are Probability Theory and Statistics( also called Quantitative Analysis).

The probability theory is used to identify trades which have positive expectancy, trades which have a short term edge. Probability theory depends on a reasonable sample size. For example if a trading system has a positive expectation of 70% (win-loss ratio) , it implies, chances are 70% that you will have a profitable trade. If the sample size was only one, the chances are equal (50%) that the trade will actually be a loser. That means these expectation play out only when you have a reasonable sample size. You take 20 trades, on a 70% expectancy system, 14 will work out, 6 will not. The outcome is on a totally random basis, you don’t know which one will and which one will not. These systems work on unshakable belief of uncertain nature of the markets and that any trade could be a loser. This is why a risk management strategy has to go side by side with probability based trading strategy. Now is the time to introduce the second part of applied mathematics which is used for risk management in the financial markets. This is called Statistical analysis or quantitative analysis. The quantitative analysis helps in defining risk parameters, like for all the trade that fails we will have a stop loss at 1 s.d( standard deviation), or a break of some kind of moving average (20 period EMA- exponential moving average) or movement of 2 ATR ( Average True Range) in the opposite direction of trade. Probability theory is also used by Casinos who have a positive expectations out of all the games that are played. They also need a large sample size ( read gamblers) to have profitable outcome and that is why you see the ads inviting you to go and make your bets in Vegas! I could not help chuckle when I saw the Kevin Spacey starer 21, which touches on this subject in context of beating the house in their own game using MIT grad mathematicians!

There you have it probability theory is used to design profitable trading systems ( which most of the hedge funds use) whereas statistical theory is used to define risk parameters ( and also profit targets- I will exit the trade once it hits the top of the bollinger bands- these bands are based on standard deviation parameters). These tools help put a structure to the financial markets, a crutch to analyze the markets and put some sense on what is by nature an uncertain endeavor ( who could have predicted a melt down in top notch investment bank like Lehman Brothers and Bear Sterns and GSEs like Freddie Mac and Fennie Mae), I certainly could not. My risk parameters based on statistical theory is the one which helped me survive this mess, and to come back and fight for another day! I thank my mentors, my teachers, the researchers and the books I have read (most notable by Kenneth Grant) on this aspect of applied mathematics which helps me survive- and not only survive, even thrive when the lady luck smiles on me

If you asked me which subject I like most, nope- not mathematics! Although it is a close second, my first love is physics!! I will write about the applied aspect of physics on a different blog post, but just to have you thinking, here is a brief introduction. Whole engineering disciplines have branched out of fundamental concepts of physics. For example, Thermodynamics, which is part of physics, is used by Mechanical Engineers to design turbines in power plants and jet engine of your boeing planes. Every time you take off, your life depends on it- literally!!! How do I know, I am a qualified Mechanical Engineer, that’s why!!

I came across an interesting article which talks about the 3 s.d( standard deviation or sigma) moves in financial markets. You know the kind of outlier events which are expected only to happen once in gosh..like 10 years, 15 years as per all the statistical models and supposedly the risk management we have built into our models should let us take corrective action on time. That the markets have tendency to revert to mean.. so actually you can bet against an abnormal movement..hope to revert it to mean and make some decent chunk of cash!! Nice strategy, only that these don’t work when you have an outlier event!!
Turns out these outlier events happen more frequently in financial markets then you are made to believe. Do you think the collapse of LTCM ( Long Term Capital Management) was a relatively isolated event? Well think again, it has been happening with amazing regularity. The top financial institutions like Citibank, Country Wide, Merry Lynch and who can forget Bear Stearns- writing of bad bets to the tune of billions of dollars!!These companies wiped out years of their profit in couple of quarters. Being a Mechanical engineer I have relied on 1 s.d , 2 s.d, 3.d even 6 s.d for years and these are pretty reliable indicators of quality control. It is just that when you apply the same thing to financial markets, it may not hold up….the investment managers have to be ready for any eventuality and playing defensively is the only way to survive these markets in the long term. My mantra..be ready for the outlier events and if possible profit from it..one of the reason I believe more in the trend following philosophy of the technical analysis of the markets then anything else.
Yes the markets have the tendency to revert to mean 99 out of 100 times, but when they don’t ..watch out for your head being handed in these markets. Wall street is littered with such carcasses, and yet we keep saying, hah it’s an outlier event..can’t worry much about it. Get real..get defensive..expect the unexpected..you survive! Otherwise you are another Citibank in the making!!

>I came across an interesting article which talks about the 3 s.d( standard deviation or sigma) moves in financial markets. You know the kind of outlier events which are expected only to happen once in gosh..like 10 years, 15 years as per all the statistical models and supposedly the risk management we have built into our models should let us take corrective action on time. That the markets have tendency to revert to mean.. so actually you can bet against an abnormal movement..hope to revert it to mean and make some decent chunk of cash!! Nice strategy, only that these don’t work when you have an outlier event!!
Turns out these outlier events happen more frequently in financial markets then you are made to believe. Do you think the collapse of LTCM ( Long Term Capital Management) was a relatively isolated event? Well think again, it has been happening with amazing regularity. The top financial institutions like Citibank, Country Wide, Merry Lynch and who can forget Bear Stearns- writing of bad bets to the tune of billions of dollars!!These companies wiped out years of their profit in couple of quarters. Being a Mechanical engineer I have relied on 1 s.d , 2 s.d, 3.d even 6 s.d for years and these are pretty reliable indicators of quality control. It is just that when you apply the same thing to financial markets, it may not hold up….the investment managers have to be ready for any eventuality and playing defensively is the only way to survive these markets in the long term. My mantra..be ready for the outlier events and if possible profit from it..one of the reason I believe more in the trend following philosophy of the technical analysis of the markets then anything else.
Yes the markets have the tendency to revert to mean 99 out of 100 times, but when they don’t ..watch out for your head being handed in these markets. Wall street is littered with such carcasses, and yet we keep saying, hah it’s an outlier event..can’t worry much about it. Get real..get defensive..expect the unexpected..you survive! Otherwise you are another Citibank in the making!!