Back to Basics Part 3: Backtesting in Algorithmic Trading. Nearly all research related to algorithmic trading is empirical in nature. That is, it is based on observations and experience. This is in contrast with theoretical research which is based on assumptions, logic, and a mathematical framework. Often, we start with a theoretical approach (for example, a time- series model that we assume describes the process generating the market data we are interested in) and then use empirical techniques to test the validity of our assumptions and framework. But we would never commit money to a mathematical model that we assumed describing the market without testing it using real observations, and every model is based on assumptions (to my knowledge no one has ever come up with a comprehensive model of the markets based on first principles logic and reasoning). Download For Mountain Lion.

So, empirical research will nearly always play a role in the type of work we do in developing trading systems. So why is that important? Empirical research is based on observations that we obtain through experimentation. Sometimes we need thousands of observations in order to carry out an experiment on market data, and since market data arrives in real time, we might have to wait a very long time to run such an experiment. If we mess up our experimental setup or think of a new idea, we would have to start the process all over again. Clearly this is a very inefficient way to conduct research. A much more efficient way is to simulate our experiment on historical market data using computers.

In the context of algorithmic trading research, such a simulation of reality is called a backtest. Backtesting allows us to test numerous variations of our ideas or models quickly and efficiently and provides immediate feedback on how they might have performed in the past. This sounds great, but in reality backtesting is fraught with difficulties and complications, so I decided to write an article that I hope will illustrate some of these issues and will provide some guidance on how to deal with them. Why Backtest? Before I get too deeply into backtesting theory and its practical application, let’s go back up and talk about why we might want to backtest at all.

I’ve already said that backtesting allows us to carry out empirical research quickly and efficiently. But why do we even need to do that? Everyone knows that we should just buy when the Relative Strength Index drops below 3. OK, so that was obviously a rhetorical question. But I just wanted to highlight one of the subtly dangerous modes of thinking that can creep in if we are not careful.

Now I know that for the vast majority of Robot Wealth readers, I am preaching to the converted here, but over the last couple of years I’ve worked with a lot of individuals who have come to trading from non- mathematical or non- scientific backgrounds who struggle with this very issue, sometimes unconsciously. This is a good place to address it, so here it goes. In the world of determinism (that is, well- defined cause and effect), natural phenomena can be represented by tractable mathematical equations. Engineers and scientists reading this will be well- versed for example in Newton’s laws of motion. These laws quantify a physical consequence given a set of initial conditions and are solvable by anyone with a working knowledge of high school level mathematics.

The markets however are not deterministic (at least not in the sense that the information we can readily digest describes the future state of the market). That seems obvious, right?

The RSI dropping below 3. And if prices were to rise, it didn’t happen because the RSI dropped below 3. Sometimes prices will rise following this event, sometimes they will fall and sometimes they will do nothing. We can never tell for sure and often we can’t describe the underlying cause beyond more people buying than selling. Most people can accept that fact.

However, I have observed time and again a paradox: the same person who accepts that markets are not deterministic will believe in a set of trading rules because they read them in a book or on the Internet. I have numerous theories about why this is the case but one that stands out is that it is simply easy to believe things that are nice to believe. That’s human nature.

This particular line of thinking is extraordinarily attractive because it implies that if you do something (simple) over and over again, you will make a lot of money. But that’s a dangerous trap to fall into. And you can even fall into it if your rational self knows that the markets are not deterministic, but you don’t question the assumptions underlying that trading system you read about. I’m certainly not saying that all DIY traders fall into this trap, but I have noticed it on more than a few occasions. If you’re new to this game or you’re struggling to be consistently profitable, maybe this is a good thing to think about. I hope it is clear now why backtesting is important. Some trading rules will make you money, most won’t.

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But the ones that makes money don’t work because they accurately describe some natural system of physical laws. They work because they capture a market characteristic that over time produces more profit than loss. You’ll never know for sure if a particular trade is going to work out, but sometimes you can conclude that in the long run your chances of coming out in front are pretty good. Backtesting on past data is the one tool that can help provide a framework in which to conduct experiments and gather information that supports or detracts from that conclusion. Simulation versus Reality. You might have noticed that in the descriptions of backtesting above I used the words simulation of reality and how our model might have performed in the past.

These are very important points! No simulation of reality is ever exactly the same as reality itself. Statistician George Box famously said, “All models are wrong, but some are useful” (Box, 1.

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It is critical that our simulations be accurate enough to be useful. Or more correctly, we need our simulations to fit for our purpose, after all a simulation of a monthly ETF rotation strategy may not need all the bells and whistles of a simulation of high frequency statistical arbitrage trading. The point is that any simulation must be accurate enough that it supports the decision- making process for a particular application, and by “decision making process” I mean the decisions around allocating to a particular trading strategy.

So how do we go about building a backtesting environment that we can use as a decision- support tool? Unfortunately, backtesting is not a trivial matter and there are a number of pitfalls and subtle biases that can creep in and send things haywire. But that’s OK, in my experience the people who are attracted to algorithmic trading are usually up for a challenge! At its most simple level, backtesting requires that your trading algorithm’s performance be simulated using historical market data, and the profit and loss of the resulting trades aggregated. This sounds simple enough, but in practice it is incredibly easy to get inaccurate results from the simulation, or to contaminate it with bias such that it provides an extremely poor basis for making decisions. Dealing with these two problems requires that we consider: The accuracy of our simulation; and.

Our experimental methodology and framework for drawing conclusions from its results. Both aspects need to be considered in order to have any level of confidence in the results of a backtest. I can’t emphasize enough just how important it is to ensure these concepts are taken care of adequately; compromising them can invalidate the results of the experiment.

Most algorithmic traders spend vast amounts of time and effort researching and testing ideas and it is a tragic waste of time if not done properly. The next sections explore these concepts in more detail. Simulation Accuracy. If a simulation is not an accurate reflection of reality, what value is it?

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An appendix covers background material in probability. Markov decision processes, and mathematical.