The difficulty of math level depends on education and experience. If you have a PHD or even a Master, clearly the mathematics is rather simple. Take the simple topic of GARCH. There are at least six prominent forms I know of... which out do you choose? Tough question. The selection depends on your field and level of education. An MBA might choose ARCH or ARCH- M. Personally I choose EGARCH. Anyhow, statistical arbitrage is getting very very sophisticated. Tough condiitons motivates, I guess ... I am hearing that genetic algorithm and fuzzy logic is currently being peddled .... needless-to-write the amount of math needed and programming is mindboggling. Just curious but do you have a PHD or a MSFE?
You keep saying that. I could explain stat arb to a high school kid. How long have you been on ET? This statement is just plain false. I have no idea whose pairs trading threads you have been looking at, but there are some seriously large pair traders at ET. I used to make a living doing nothing else a year ago with it. Anyone that does Pairs trading without doing _at_least_ correlation analysis is an amateur at best. There are pair traders that do nothing else and make a large amount of money doing it. In fact, most of the math is crap. The best players at it do well because they are good trader in addition to understanding pairs. Cointegration without correlation analysis is like a coin with one side. You keep mentioning that you ran a desk arb as if it means something. I routinely crush the returns these guys yearly returns in two months of trading. nitro
I could explain correlation to a high school kid. I could explain cointegration to anyone with a decent grasp of calculus. This is SIMPLE and does not require a Phd in anything. The hard part of most of Time Series Analysis is knowing when and how and why to apply what to the data. Getting the data "prepped" for TSA is harder than the application of the methods themselves. In fact, since these are all LINEAR MODELS, their usefulness is in question. But we do the best we can, and as traders, adjust accordingly... There is no replacing being a trader in any of this stuff. Most of these advanced math "traders" usually have to be carried out of a trading room on an oxygen tank... Model selection is not "chosen" by hand. The prefered way these days is to let MLE or other optimization functions tell you what the "best" model is. All these models are useful in some particular case... All of Econometric and Financial Engineering is constantly evolving. Genetic Algorithms have been around ever since I started programming and have been (tried) used in the Financial marktets ever since I can remember. Fuzzy logic the same, and equally worthless (in the face of other statistical measures.) No I have neither, but I stayed a Holiday Inn last night? nitro
What is the justification for this venting/venom? Your Comment: "You keep mentioning that you ran a desk arb as if it means something. I routinely crush the returns these guys yearly returns in two months of trading." Please refresh me... how many time did I bring this up? Once, perhaps twice... I surely dont remember bragging about this aspect. Moreover, if you look at the context rather than just plain words, you're notice that this was in RESPOND to MYD"s question. And NOT as an offhand casual remark with underpinning of oneupmanship. Your Comment: "I routinely crush the returns these guys yearly returns in two months of trading." Please elaborate. Are you taking about return on a trader positon or an institution posiiton? Big Big difference. Moreover, how have the method fare so far? Your Comment: "Cointegration without correlation analysis is like a coin with one side." Pure bullshit or sheer ignorance. If you need further discussion on this topic, visit Wilmott forum. This topic is discussed at tremendous LENGTH. Sorry if I seem harsh, but they way you shape your comment are very offensive. Your Comment: "Anyone that does Pairs trading without doing _at_least_ correlation analysis is an amateur at best" I know a good number of people who do not run correlation analysis. I guess they're not profession but rather amateur by your definition. Your Comment: "How long have you been on ET? This statement is just plain false. I have no idea whose pairs trading threads you have been looking at, but there are some seriously large pair traders at ET." You're correct in the sense that I havent been here long, but from what I gleaned, that is my observation. I think it was NYSE's trend ... that really really long one. If I remember correctly all the strategies centered around TA. RSI, MA, Stochastic, etc. Moreover, Pairs trading and statistical arbitrage are DIFFERENT entity although they share similar characteristics. Your Comment: "I could explain correlation to a high school kid. I could explain cointegration to anyone with a decent grasp of calculus. This is SIMPLE and does not require a Phd in anything. " Perhaps you're one of those great teachers or those with the articulation second to none. But explaining to correlation to a high school kid is a daunting feat, how do I know? I teach a night undergraduate class after I got my degree, if undergraduate are having difficult I can only imagine that it would be hard for HS students. You make it seems so easy and effortless. The basic concept of Cointegration is indeed easy, but how many undergraduate do you know that understand this??? Again, you're making it out to seem as if it is a cakewalk which I strongly disagree. VAR (not value at risk) is usually reserve for higher end master program and Phd. You cant just learn this via simple calculus. Your Comment: "All of Econometric and Financial Engineering is constantly evolving. Genetic Algorithms have been around ever since I started programming and have been (tried) used in the Financial marktets ever since I can remember. Fuzzy logic the same, and equally worthless (in the face of other statistical measures.)" Perhaps you misunderstood or my syntax is bad... Genetic algorithms on pairs and fuzzy logic on PAIRS trading. "Black Box" has been here since the 70s if I remember correct. Your comment: "No I have neither, but I stayed a Holiday Inn last night?" Inside joke? I have no clue. Your comment: "There is no replacing being a trader in any of this stuff. Most of these advanced math "traders" usually have to be carried out of a trading room on an oxygen tank..." Agree. In fact, a number of firms I know hire traders for this very reason. Your Comment: "The hard part of most of Time Series Analysis is knowing when and how and why to apply what to the data. Getting the data "prepped" for TSA is harder than the application of the methods themselves. In fact, since these are all LINEAR MODELS, their usefulness is in question. But we do the best we can, and as traders, adjust accordingly..." Agree except for the remarks on linearity. Nonlinear relationship can be model via linear methodsl time series is not exclusive to nonlinear relationship. There is a huge literature on nonlinear time series.... where the focus is turning nonlinearity into linear composition. Your Comment: "Model selection is not "chosen" by hand. The prefered way these days is to let MLE or other optimization functions tell you what the "best" model is. All these models are useful in some particular case..." Agreed. But you're taking the comment out of context. My comment was for illustration purpose and NOT to argue on the merits of selection. <b>Clearly you're very astute. But I find fault with the way you shape your comments, perhaps I am reading too much between the lines, but you come off arrogant and obnoxious. Perhaps, there is a misunderstanding.... I just plain dont know. Secondly, I find fault with how you make things seem so "easy." Perhaps it comes naturally to you, but not to everyone. You comment on MLE clearly denote that you're very knowledgeable. The very fact that you do NOt hold advance degree is a testimony (sp?) to your learning ability and hard work. But not everyone is like you.</b> --- Satyrican P.S. I am curious, but what is your major? And how did you learn all this stuff which is equivalent to obtaining a MSFE?
I didnt notice how long my respond was. Here's a Cliffnote. 1. Pairs Trading is different from statistical arbitrage. Would you consider longing ES and shorting NQ as statistical arbitrage? I wouldnt. I wouldnt consider long-short strategy based on technical analyais as stats arb either. 2. Correlation vs Cointegration. This has been discussed at length on other website. Correlation fails because it dependent on the number of observation. The more observation, the more likely you're have spurious correlation. THIS IS A KNOWN FACT. Cointegration is a far far better barometer. Moreover, havent you notice that a fair number of pairs dont make sense - spurious correlation is the culprit. 3. Statistical arb is highly quantitative. Take a look at job ads. All requiring MSFE, PHD or at the very minimum a master in physics/mathematics. You can explain pair trading but you cannot explain statistical arbitrage. 4. Institutional trading and individual trading. It's easy to "crush" institutional return if you doiing it via individual trading. How many stats arb fund return are above 30%?? Very very few. A 30% on daytrading "pairs" or any methodolgy would be abysmal if you're an individual daytrader. Overall, comparing return of the two is tantamount to comparing apples and oranges. ---Satyrican.
That a great trader can trade a simple system. This applies to pairs, arb, cabbage patch kids, etc. Nitro hits it on the head, in my opinion. In my opinion also, the more you need to hide behind more stats, the less you trust yourself as a trader, generally speaking. You are looking to technical analysis to compensate for the degree of lack of self trust you have in just trading. By the way, I don't know who exactly I mean when I am referring to "you", but I think its representative of some general idea that I see a lot here that really makes me feel sorry for people who are getting caught in the trap. I trade pairs and I also do merger arb. Simple algebra is all that required as far as the technical skill. You can blast me for that, but if I had to do all the stuff the 'you's claim you have to do in addition to trading and making money, I would hate this career that I love. I don't mean any disrespect for the severely math addicted that read this. Its not my intention to do that. But I think in a an analysist of time involved, you can achieve the same results by becoming a better trader in lieu of searching for the holy grail in such a refined system. Nobel laureates blow up quite often too.
I am trader, so returns are from a traders perspective. I no longer pair trade because I went cold on the method about a year ago, so I cannot tell you how the "method" is fairing so far. I have new incentives and ideas to make it work and I am working on a programming project to implement that tool. Preamble: a) Returns are short memory process. Correlation measures RETURNS. The traditional starting point for asset allocation and risk management is to DIFFERENCE (turn the raw data into returns) the price data before analysis is even begun (in the time domain), and differencing removes a priory any long term trends in the data. b) Cointegration is based on the RAW price data, rate or yield data, AS WELL as the return data. Price, rate and yield data are not normally stationary - in fact they are usually integrated of order 1, I(1). Definition: A set of I(1) series is termed 'cointegrated' if there is a linear combination of that series that is stationary. So in the case of two integrated series: x and y are cointegrated if x,y ~ I(1) but there exists an a such that x - ay ~ I(0) Algorithm: Cointegration is a TWO step PROCESS: first any long-run equilibrium realtionships between prices are established using Ordinary Least Squares (OLS) regression (plus some statistics to verify), and THEN a dynamic CORRELATION model of returns is estimated. The Error Correcting Model (ECM), so called because short-term deviations from equilibrium are corrected. [I just explained cointegration to a bright high school kid - Notice that I am CORRECT in my assertion that correlation and cointegration go HAND IN HAND in some implementations of it] I guarantee you, they are running correlation analysis if they are SHORT TERM TRADERS and not "Investors" looking for a 10% yearly return. Long/Short, or market neutral strategies are in "spirit" all the same and share most of the math with each other. The subject of Financial Engineering is not trivial by any means. However, see above for "my" explanation of cointegration - any bright high school kid with an inclination for math would understand that statement with no problem. ok. You must not be from the US. Yes it was a joke... But here is the irony: cointegration is really meant to measure LONG TERM relations between variables, usually the time frame is not in the dominion of the trader. Well, if you have solved this problem, I would like to see it and probably would win you a Noble Prize in Economics. At the core of all these analysis and statistical measures is LINEAR ALGEBRA. That was the reason for trying to bring in Neural Nets, etc, to capture the nonlinearities in the data better... Ok. I started an undergraduate degree in Algebraic Number Theory. I am well versed (but VERY rusty) in Groups, Rings, Modules, Vector Spaces, and Linear Algebra. Once you have even this relatively weak background, people can try to complicate the subject all they want, but it is pretty straight forward. One thing that I find interesting is that you keep asking me questions, and you wave your hands alot by claiming all kinds of things, but not ONCE have you shown that YOU know what you are talking about. That is where my "venting/venom" comes from - you posture alot, but offer little... nitro
Fair enough. Yes, Cointegration measure long term stabiilty but you forgetting that you can measure the speed of mean reversion! Which is the heart of stats arb. In addition with vector autoregression (VAR), you can measure the speed of mean reversion for Any set of variable, while at the same time, "holding" other variable constant. With regard to correlation, you can show that correlation converges into a stationary process if you increase the number of observation. Spurious correlation. Thus very little value to traders. You can also show that in the SHORT RUN, the time frame of interest, volatility dominate return ~white noise if you will. Thus correlation based on RETURN on a short time frame offers very little info. You can test this by running a simple Monte Carlo (sp?) setup with two randomized sets. In the short run, volatility, not return, influence correlation calculation. Cointegration is "established" as a mean of correcting this all important spurious correlation. Compounding the problem is the fact of the length of computation for correlation. How do you decide? Your comment:"Cointegration is a TWO step PROCESS: first any long-run equilibrium realtionships between prices are established using Ordinary Least Squares (OLS) regression (plus some statistics to verify), and THEN a dynamic CORRELATION model of returns is estimated. The Error Correcting Model (ECM), so called because short-term deviations from equilibrium are corrected." Wrong. The "standard process" for stats arb is to run VAR and use the mean speed of reversion as your catalyst, not correlation dynamics. Why would you use correlation model? With VAR you can "hold" other parameters constants like interest rate fluctuation, implied volatility, etc. Correlation does not, it is very very crude. Unless your're talking about some nonlinear correlation - which I never heard of it - I dont see the sense of using correlation analysis. Moreover, residual analysis would have been a better bet in of itself. If you already established with cointegration the cointegration vector, why would you need correlation???? You can simply use that cointegration vector and ECM, that would suffice. Where does correlation fall under? ----Satyrican
Agree. Trading is an "ART". Mathematics is an efficient tool to solve problems, but NOT the only tool. It also depends on the persons, who use it. I always believe that great scientists must have great physical insights. You have to love your job to excel. Hence, the most important thing is to create and implement a trading strategy that matches your personality. It does not matter whether it is a simple system, or involves the most sophisticated mathematics known to human beings. Just my two cents.
I like this. Richard Bellman was a great American Mathematician especially known for Dynamic Programming (also somewhat interested in speculation theories)! Dynamic Programming is an optimization technique used in very many space and military optimal control systems. I recall Professor Bellman once saying: "Mathematicians learn more by the way of example than by the way of induction"