## Tuesday, May 28, 2013

Non-quants need not apply. Although sometimes even mathematically challenged readers can profit from books describing quantitative strategies, I would not recommend Ernest P. Chan’s Algorithmic Trading: Winning Strategies and Their Rationale (Wiley, 2013) to them. The book is very good, much better than his 2009 effort, Quantitative Trading. But it’s not for the casual reader or the trader in search of a couple of strategies he can mindlessly co-opt. Its target audience is traders who are comfortable navigating formulas and MATLAB code.

So now that 90% of people have stopped reading this post, let me continue for the remaining 10%.

Chan divides his book into mean reversion and momentum strategies. It is critical to understand what a mean-reverting price series is. “The mathematical description of a mean-reverting price series is that the change of the price series in the next period is proportional to the difference between the mean price and the current price.” An equivalent way of looking at the price series is stationarity, where “the variance of the log of the prices increases slower than that of a geometric random walk.” A second kind of mean reversion that bears mentioning is cross-sectional mean reversion, where “the cumulative returns of the instruments in a basket will revert to the cumulative return of the basket.” (p. 41)

Unfortunately, most financial price series are not mean reverting. This fact is not, however, a strategy killer. Chan contends that “we don’t necessarily need true stationarity or cointegration in order to implement a successful mean reversion strategy: If we are clever, we can capture short-term or seasonal mean reversion, and liquidate our positions before the prices go to their next equilibrium level.” (p. 63) Moreover, one can go beyond a single-stock strategy to a basket of “cointegrating stocks and ETFs to create our own stationary, mean-reverting portfolio.” (p. 60) In its simplest form, the trader can opt for a mean-reverting pair, although pair trading of stocks is no longer very profitable in the efficient U.S. markets. A better option is trading ETF pairs and triplets. An example of a cointegrating triplet is GLD-GDX-USO. Along the same line, traders can look for opportunities for cointegration in commodity currencies.

What about trading VX futures? “Every student of finance knows that volatility is mean reverting; more precisely, we know that the VIX index is mean reverting. In fact, an augmented Dickey-Fuller (ADF) test will show that it is stationary with 99 percent certainty. You might think, then, that trading VX futures would be a great mean-reverting strategy.” And you would be wrong: “a look at the back-adjusted front-month futures prices over time indicates that the mean reversion in VX only happens after volatility peaked around November 20, 2008 (the credit crisis), May 20, 210 (aftermath of flash crash), and then again on October 3, 2011. At other times, it just inexorably declines.” (p. 122) In fact, since VX has been in contango around three fourths of the time, we’re better off using a momentum strategy with VX.

Like mean reversion, momentum can be classified as either time series momentum or cross-sectional momentum. In time series momentum “past returns of a price series are positively correlated with future returns. Cross-sectional momentum refers to the relative performance of a price series in relation to other price series: a price series with returns that outperformed other price series will likely keep doing so in the future and vice versa.” (pp. 133-34)

Chan spends less time on momentum than on mean reversion, in part because both the concept and its implementation (especially as regards risk management) are much simpler. He also admits that he’s found it “harder to create profitable momentum strategies, and those that are profitable tend to have lower Sharpe ratios than mean-reversal strategies.” (p. 151) However, it would be unwise to focus solely on mean reversion strategies. “[A]s most futures and currencies exhibit momentum, momentum strategies allow us to truly diversify our risks across different asset classes and countries. Adding momentum strategies to a portfolio of mean-reverting strategies allow us to achieve higher Sharpe ratios and smaller drawdowns than either type of strategy alone.” (p. 154)

I’ve steered clear of math in this post, but, in doing so, I’ve only touched the surface of Chan’s book. Do you want to know whether scaling-in and scaling-out work? How to use the Kalman filter? Or do you just want to crib some Matlab code? Algorithmic Trading is an excellent source for quants and would-be quants.

#### 1 comment:

1. Great !
This is my visit to your blog and I will be a regular visitor .Though I am a discretionary trader , I am searching for strategies to be automated.Your review of books will help me in choosing the right book to go into right direction .
Keep going
Thanks.