The book broadly deals with two strategies, “mean reversion” and “momentum”.These strategies cover six chapters of the book, out of which four of them are on mean reversion and two of them are on momentum strategies. Besides these six chapter, there is one chapter on backtesting strategies and there is another on risk management.

Given the importance of backtesting in any strategy, the first chapter starts off with some of the pitfalls of backtesting. It also gives three general methods for backtesting any strategy. First method is the usual frequentist method of testing whether the null : “returns from the strategy is 0”. Second method is to simulate various return paths and check for the number of times the strategy beat the returns based on historical data. The third method involves randomizing the longs and shorts and seeing whether the strategy makes sense. One can also think about a fourth method where you resample the returns series and general price path and then check out your strategy. The author also cautions about the relevance of backtesting and says that any regime shifts will make all the backtesting irrelevant and hence the strategy, despite looking good on paper, is going to fall flat. The author ends with a brief account of the various software available for a algo trader. Even though there are software that are mentioned that could help a non-programming trader, I fail to see what value such software can add. A basic requirement of anybody thinking of algo trading is working knowledge of at least one or two programming languages. UI driven interfaces can only supplement the code and not replace it.

The second chapter goes in to some basic stat/math skills to test stationarity of a series, check for a cointegration etc. Four methods are used to check for the stationarity of a time series, i.e. Dickey Fuller test, Hurst exponent, Variance ratio test, Half life of AR(1) process. Well, one can say, what’s the point in all these tests such as unit tests, variance ratio tests etc. Why not just backtest and decide whether to go ahead with the strategy or not. One point to consider is that these tests are far more statistically significant that what your strategy results show. The strategy by its very nature will have limited data points whereas the above tests use almost all the data points. Besides that if a series shows stationarity or a set of series show stationarity, then one can atleast put an effort in coming up with a strategy. What’s the point in testing strategy after strategy when the series itself is close to random ?.

For finding cointegrated assets, the chapter discusses 2 step Engle-Granger method and Johansen procedure. The former is easy to understand and implement but is plagued by some problems that are explained in this chapter. To understand Johansen procedure, one needs to sweat it out by reading the math from some other book. This chapter is more of “here is how Johansen function can be used to find cointegrating relations”. If your concern is merely to know the method, then you don’t need any further reference. But if you are like me who wants to understand what the test does, i guess there is no option but to spend time understanding the math behind it.

The third chapter begins with a very interesting take on the input to a cointegration exercise. What can be the input ? raw prices or log prices or ratio of two stocks ? The first variant of pair trading that is typically seen is the ratio trade, compute the ratio between two stocks and trade the spread. The stocks might not be cointegrating but the spread might be mean reverting in a shorter time frame. In fact this was a recurrent theme in almost all the pair reports that I used to see from Brokerage houses. These were pushed under the title cointegrated pairs. I always use to wonder why should a ratio of two stocks be stationary ? Equivalently, why should the hedge ratio between two stocks be 1 ? This chapter kind of nails that question down by saying that ratio based trading is convenient and works if the spread is stationary on a short time frame. So, given a choice between a cointegrating vector based trading and ratio based trading, which one should be selected? The author says he has no clear answer except his backtesting shows that it is better to take cointegration based hedge than to rely on ratio based trades. The chapter introduces Bollinger bands and Kalman filter based strategies for getting a higher return and Sharpe ratio compared to naive strategies.

The fourth  starts off with the author discussing about the difficulties with pursuing mean reverting strategies that involve stocks.Subsequently, mean reverting strategies for ETFs are explored. One of the first strategy that is explored in the book is Buy-on-Gap strategy. The author says he had used this strategy for his fund as well as his personal account and it made money till 2009. The chapter explores arbitrage strategies between ETFs and its constituent stocks. MATLAB results for the strategy are given and the author provides his interesting commentary on the results. The chapter ends with an exploration of cross sectional mean reversion where stocks are longed or shorted based on the relative movement with respect to sector index or a market index.

The  fifth chapter deals with some specific aspects of pairs trading in currencies. After reading this section I had a feeling that it is more important to identify the correct instruments for setting up a cointegrating equation. It is easy to make a mistake while backtesting the strategy.The strategies explored are trading currency cross rates, trading futures calendar spreads. The basic message that the author tries to convey is the decomposition of returns in to spot returns and roll returns. It is often that a strategy performs well over long backtesting period because of roll returns. One must be careful in attributing the performance of a strategy to the respective return types. The author tests out various Futures intermarket spreads and shows that none of the spreads form a stationary series. The chapter has a section where VIX futures and E-mini S&P 500 futures contracts are used to create a cointegrating pair. At least on paper, the strategy looks promising.

The sixth and seventh chapters deal with interday and intraday momentum strategies.The author says that interday momentum strategies have been performing badly since crisis and the entire action nowadays is in the intraday game. The last chapter deals with Kelly criterion and other risk management techniques. In fact the author covers quite extensively the topic of Kelly criterion in his previous book. If you are new to Kelly criterion, it is worthwhile to read the paper by Thorpe and understand various aspects of Kelly criterion. The paper is so well organized that you will have many aha moments along the way. After going through the paper, I could understand most of the material in this chapter. The book ends with discussing stop losses and CPPI techniques for dealing with the problems of applying Kelly criterion in a practical scenario.

All the code is written in MATLAB. Thanks to the author’s site, I could find most of the datasets that are used in the book. If you are a non MATLAB user like me, you can easily through the MATLAB code and translate the code in to whatever language you are comfortable with, to verify the strategy results mentioned in the book.

image Takeaway

The book discusses “mean reverting strategies” and “momentum strategies” at length. This book helped me tie a couple of loose ends in my thought process relating to mean reversion strategies. The practical insights in to Kelly criterion and Risk management makes this book a great resource for risk managers and prop traders.