2012 Wishes

As we look to 2011 through the rear view mirror, I make a quick divergence from my recent lethargy to send my best wishes for 2012 to all readers. May 2012 be a trading year filled with opportunities you capitalize on.

See you in the new year.

QF

Ensemble Building 101

In continuation with last post, I will be looking at building a robust ensemble for the S&P 500 ETF and mini-sized future. The goal here will be to set-up a nice framework that will be (hopefully) of good use for readers interested in combining systems in creating strategies. In order to make it more tangible, I want to create a simplified example that will be used as we move forward in development. I would encourage readers to actively comment and contribute to the whole process.

Before we do anything, as with any project, I want to have an idea of the scope so I don’t get entangled in an infinite loop of development where I am never satisfied and continuously trying to replace indicator after indicator for a marginal increase in CAGR on the backtest. For this example, I want to use 4 indicators (two with a momentum flavour and two with a mean-reversion flavour), a volatility filter and an environmental filter. The strategy will also have an adaptive layer to it.

Now that the foundation idea has been laid, let’s examine the mechanics at a high level, keep in mind that this is only one way you could about it. Basically I will be evaluating each strategy individually, looking at performance under different volatility environment and also with the global environment filter. Based on historical performance and current environment, exposure will be determined.

This series will have R code for the backtest (still debating using quanstrat/blotter) and the simple example will be available for download. My point is to provide reader a way to replicate results and extend the framework significantly. More to follow!

QF

One Size Does Not Fit All

In our eternal search for the trading Holy Grail it is often tempting to try and find the “ultimate” signal (indicator) and apply it to as many instruments we can. This single solution approach for the most part fails miserably, think of a carpenter with only a hammer in his (or her; QF is an advocate for equal opportunity) toolbox. While making signals adaptive is definitely an improvement however, I think we sometimes miss the point.

Instead of harassing and optimizing a signal ad absurdum to improve the backtest, one would be better served by looking at the big picture. One signal in itself only contains so much information. While there are a lot of good indicators that perform very well by themselves available (the blogosphere is a really rich ecosystem in that regard); their power is only magnified when combined with other signals containing different information. The secret is in the signal aggregation. In other words, in how we form and use an ensemble of signals isolating different pieces of information to build a profitable strategy (note the use of the word strategy as opposed to system, careful wordsmithing aside, the difference is paramount). This is a topic I have been taking a close look at recently and I think the blogosphere is a perfect tribune to share some of my findings. As a starter, here are some points I will be touching on in the upcoming series of post.
1. What are the basic intuitions behind ensembles and why can they help in building trading strategies?

2. How do we isolate and quantify specific pieces of information and then observe their effect on the instruments we trade.

3. How to we evaluate current pertinence of the signals.

4. Finally, how do we aggregate all the useful information and build a strategy from the ground up.

The mechanics are going to be explained using a simplified example for readers to follow along but the intuition will be the same that the one behind the first QF strategy to be tracked real-time on the blog. I still don’t have a fancy name for it but it’ll get one for its official launch.

QF

Update, Milestone, and Unfinished Business

Update
First of all let me apologize for being off the grid for so long and not providing you with any of my geek prose recently. My final university semester classes are coming to an end today and I will resume regular posting after finals. However rest assured that my absence of the blogosphere has not caused quant power atrophy, it was merely a by-product of how busy I was with school and interviewing. Thank you all for sticking up with me during this dry spell.

Milestone
I recently obtained 50,000 views, while not an incredibly big number compared to the blogosphere’s behemoths (see blogroll), I personally am really happy. I never really thought that this blog would take these proportions and it keeps surprising me by bringing opportunities I never thought would be possible, and for that I must thank you.

Unfinished Business
I know some of you were eagerly waiting for the TAA system post I kept saying would be coming soon; I am sorry to tell you that it will not. My services were hired by a private firm and the intellectual property developed is protected by a non-disclosure agreement. I might however discuss the intuition at a high level if the interest is still present.

Finally some of you might have noticed the new “QF Strategies” tab up top. For now it shines by its emptiness but it will not for much longer. I will be tracking strategies there soon, bear with me.

QF

Model Scalability

When designing a model, an aspect that I often overlook is scalability. First a definition from Investopedia: “A characteristic of a system, model or function that describes its capability to cope and perform under an increased or expanding workload. A system that scales well will be able to maintain or even increase its level of performance or efficiency when tested by larger operational demands.”

Now most of you probably wonder why I would overlook such a crucial aspect of model building. The reason is very simple; I never had to. Most of the models I design are for my personal trading and since I don’t have millions of dollar in capital to trade (yet!), the scalability requirements are very insignificant. Most of my trading is on the mini futures and I only trade a few contracts per symbol. Keeping this in mind, I don’t have to worry too much about slippage when I place my orders since the effect of the order book are negligible. However, chances are I am not going to design models solely for my personal trading during my career.

The scalability requirement for a hedge fund for example is however, very different. Imagine trading a high-turnover strategy on a single symbol, for the sake of example, consider a RSI2 strategy. It is a very short term strategy that has a relatively high turnover for an end-of-day strategy. Now trading this strategy with 50k is feasible (not optimal but not too bad), now think about trading the RSI2 signal on a single symbol with 100mm; very impractical. Think how much slippage would affect the strategy. At time of writing, the SPY opened at 133.02, trading 100mm would end up being about 751,654 shares at open quote. Admittedly, I don’t have the exact number, but I doubt that the order book opened almost a million deep at the ask and therefore we would expect some slippage effect. Presumably, it would be quite significant and would significantly change our expectation of return for our RSI2 strategy.

Now I know that few hedge funds would trade a RSI2 on the SPY alone, it is only a conceptual example to support understanding, and I want to point out that I am not saying that RSI2 is non-scalable (nor that it isn’t). To evaluate scalability, we need robust backtesting clearly estimating the impact of the order book, latency (if intraday), and other relevant factors on the returns. Another angle to consider is scalability across assets, following our RSI2 example, if we allocate 50% to both the SPY and the QQQQ, in theory we reduce the weighted impact of slippage and other transaction costs on a given symbol (ie. the marginal transaction cost per symbol is decreasing when we diversify across assets). However, that effect is not necessary a linear one as nicely explained by Joshua in the comment section below.

Other avenues to consider in scalability are left to the interested reader who can always contact me via email if they desire since I have recently paid closer attention to the issue myself. Furthermore, for readers with similar career desires to mine, remember that models scalability is directly related to employability!

QF

S&P 500 Sectors Analysis

To follow up with last post, and also nicely tying into Engineering Returns’ recent sector rotational system I will show a factor decomposition of the S&P 500 from different sectors. In essence, you can think of it as a multifactor analysis where I try to determine what sectors are relevant for a given period in predicting the S&P 500. This kind of analysis is important since a lot of the point and click trading in proprietary firms is done based of price action and correlation across markets. It is the later part I address today.

I looked at the period going from Jan. 01 2008 to today in both analyses. When using linear least squares we perform the regression on the next day SPY returns using the current return of our sector ETFs (I used the SPDRs) as independent variables. Results are below:

What we see from the table is that the consumer discretionary, financials, materials and technology sectors have statistically significant. Additionally, the financials and technology sectors seem to be precursors of reversals as indicated by their negative coefficients. The opposite holds true with the consumer discretionary and materials sector who seem to not be so contrarian. This simple analysis seems to indicate that these four sectors are the best candidates to consider when looking into cross markets relationships.

Another aspect of trading where factor analysis can come into play is related to diversification benefits. Using principal component analysis we extract the co-movements of our sector ETFs and SPY. Similarly, we could use the same type of method to extract the co-movements across country indices, or some other discretionary breakdown. Looking at the factor loading for the first three (explain about 95% of the covariance matrix) principal components for each ETF, we can get a better feel of the value of allocating capital to an ETF versus another and puts the illusion of diversification in perspective. In our days where correlation across asset classes is high, people trading TAA systems have all the advantages to use such analysis in their asset allocation and weighting. The factor loadings are below:

Meric et al. (2006) say it best: “The sectors with high factor loadings in the same principal component move closely together making them poor candidates for diversification benefits. The higher the factor loading of a sector in a principal component, the higher its correlation is with the other sectors with high factor loadings in the same principal component. The sector indexes with high factor loadings in different principal components do not move closely together and they can provide greater diversification benefit. Some sector indexes may have high factor loadings in more than one principal component. It indicates that the movements of these sectors have some similarity to the movements of sectors with high factor loadings in more than one principal component. These sectors are not good prospects for successful sector portfolio diversification.” In depth interpretation of the table is left to the curious reader.

In conclusion, factor decomposition/analysis can be very useful for traders to get a feel of their traded instrument of predilection. Be it for establishing significant lead/lag relationship or diversification caveats, both least squares and PCA can be valuable tools. Interested readers can also look at Granger causality for similar avenues.

QF

Predictor(s)/Factor(s) Selection

Before getting in the post main subject, I want to mention a couple things. First, the TAA system talked about before on the blog is still in the works, a busy schedule and work commitment made it difficult for me to polish and publish it as soon as I wanted. Secondly, I apologize for the New Year’s hiatus; I will be back to regular posting in the coming days.

Back to the subject at hand; predictor selection. For usual readers of the blog, machine learning will not strike as an unusual topic for the blog. I really enjoy using statistical learning models for my research and trading, and talked about it a fair bit in earlier posts. However, reviewing the blog history recently, I noticed that I overlooked this very important topic.

The same way we must be careful what predictor(s) we use when using linear regression or, for that matter, any forecasting model we need to pay close attention to our input when using learning models (GIGO: garbage in = garbage out).

Using a “kitchen sink” approach and using as many predictors as one can think of is generally not the way to go. A large number of predictors often bring a high level of noise which usually makes it very hard to identify reliable patterns in the data for the models. On the other hand, with very few predictors, it is unlikely that there will be a lot of high probability patterns to profit from. In theory we are trying to minimize the number of predictors for a given accuracy level.

In practice, we usually go from what the theory suggests or discretionary observation to determine what should be included. The quantification of this process is often called Exploratory Factor Analysis (EFA); basically looking at the covariance matrix of our predictors and perform an eigenvalue decomposition. Doing this we aim to determine the number of factors influencing our response (dependant) variable, and the strength of this influence. This technique is useful to better understand the relationships between a predictor and the response variable and determine what predictors are most important when classifying. This type of covariance matrix decomposition is supposed to help us refine our predictor selection and hopefully improve classification performance; this process will be the object of the next few posts.

QF