During this holiday period, I want to thank you all very much for the support you have showed this nascent blog in 2010. The good discussions I have had with reader in the comment section or via email made every minute of the adventure worth it. The good feedback I received exceeded every expectations I ever had for the blog and I hope that 2011 will be just as prosperous for the Quantum Financier blog.
Now to you that take time during this time of festivities to read this post, I wish the best for the holiday period and a very successful year trading and evolving with the markets in 2011.
In this post, I want to build on a good discussion in the comment section of this post: An Intermarket Ensemble Model for the S&P500 Using Market Rewind’s “Sentiment Spreads”. One of ETF Prophet’s contributors and the initial thinker for the spreads, Mr. Pietsch commented on CSS’s use of the sentiment spreads to predict the S&P 500. The part that spiked my interest was the very last question: what can you tell us about improving performance yet again with weak learner methodologies? While originally directed to Mr. Varadi, I felt compelled to try the idea.
The setup layed out in the post linked above is a good candidate for a support vector machine prediction model. You can think of the process as mapping the information contained in the spreads in relation to the ETF tracking the S&P 500. This approach, a weak form of ensemble learning is the next level after single indicator/variable model. Conceptually, one can think of market movements as the aggregation of a high (very) quantity of information and data. Trying to process the market and generate signals using a single raw filter/signal/strategy has a small chance to succeed for a long time without adaptation. Using multi-variables adaptive models/strategies tends to increase the odds in our favour. I would argue that two of the most important variables to take in consideration are price action and inter market effects. Most technical indicator covers the price action angle. These sentiment spreads are a simple way to introduce the other very important part into a quantitative strategy. For now, I will only take these into consideration, but I plan to expand on this and show how we can combine price action and intermarket effects to our best advantage. The following results are from using a -svm classification model trained on the last 100 days of spread. Note that the sample is very small since I wanted to take all seven spreads together, it will be interesting to see how it plays out with more data to our disposition and to test it using intraday data.
In continuation with last post on market neutrality, this post will look into obtaining market neutrality for a portfolio of strategy. As mentioned in last post, investors can trade many strategies with conflicting signals. For this particular example, imagine an investor that trades two strategies; a RSI2 and the 50-200 moving average crossover on the S&P 500. You can imagine that the signals from these strategies are going to be conflicting. The RSI2 is a really short-term strategy with a high turnover, while the so termed “golden cross” is a polar opposite very slow moving low frequency strategy. Also assume this investor allocate 50% of his capital to both strategy.
Now in this particular experiment, we have that portfolio of strategies and want to short or long some SPY in order to remain market neutral. To accomplish this we will use the commonly used simple linear regression and the slightly more robust quantile regression.
Simply put, we are simply using the portfolio (dependant) and market (independent) returns series to obtain the prescribed hedge ratio approximated by the regression coefficient. Now everyone is likely familiar with the linear regression so I will skip the intro. However the quantile regression is not as mainstream. It simply estimates the tau()-th conditional quantile regression function, and give the expected value based on the current quantile (tau) of the predictor variables. The premise for using quantile regression is that we expect the regression coefficients to vary depending on the level of the predictor variable. Note that in this experiment I used the linear quantile regression but there exists a non-linear version of it.
The results below are obtained using a 60 days lookback period for the hedge ratio calculation. They represent the equity curves of the portfolio traded with the market neutral long/short hedge as prescribed by the regression coefficient. A note of caution here, doing this will reduce returns however, it also reduces volatility.
I think this result is interesting in a couple of ways. But first I want to look if market neutrality is effectively obtained. As explained in last post, we often say we are market neutral if our beta is zero. Readers that have experimented with this concept know that the beta is never going to be strictly zero, but will oscillate around it. To test whether or not my goal was accomplished I used a simple t-test for the 60 day rolling mean of the observed beta. Alternatively, I could have used a more robust bootstrap test but I wanted to keep things simple. The t-test confirmed that the observed beta was effectively not different from zero and that we obtained theoretical market neutrality with both methods.
To conclude, I was happy the result confirmed my expectation with quantile regression which tested slightly better. I think there is value in the quantile regression when considering market neutrality as an objective for a strategy or a portfolio of strategies. The dynamic linear modelling approach is left to the interested reader.