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

Hi,

Very promising idea – do you have a copy of Co-movements of sector index returns in the world’s major stock markets in bull and bear markets: Portfolio diversification implications to share?

Why do you have for some sectors Not Three components?

Have a good day

Hi Martin,

Email me at quantumfinancier at gmail dot com for the paper. Then regarding your question, some sectors are simply not loaded in the component. You can think of it as them not being a factor for the PC.

Best,

QF

I’m not sure what the results would look like… But combining pca with regression (partial least squares regression) might be interesting.

Hi Mike,

Good question, I have not tried it yet, but I think it would be an interesting avenue to explore. I’ll touch it in another post if the results are interesting.

Best,

QF

Quick question. In your regression analysis, did you use all the ETFs as regressors simultaneously? They are very likely to be highly correlated and thus the regression would be severely affected. A more sound approach would be to use orthogonal regression (regression of returns on the PCA factors’ realizations).

Hi Alexandre,

Good point, multi-collinearity would affect the regression but I ran them individually first and it did not notice any major changes in the coefficient significance and the direction.

Best,

QF

Hello QF,

Very nice post. I think the next step would be VAR which could include lags beyond 1. However, potential problems include not just the time varying nature of sector performance versus the index, i.e. bull versus bear market, but also the varying composition and weighting of the index and the sectors over time. Due to the difficulty of quantifying or adjusting for the latter, it seems you pretty much have to ignore it. Ideally, you’d like to catch the time-varying aspect of sector performance, given that is what you are seeking, right? Thoughts?

Best Regards,

Trey

Hi Trey,

Thanks, I think the VAR approach has some problems with it that will make it cumbersome to use. However, if we decide to sacrifice the time-varying aspect and the regime we miss on some very important information. Orthogonal regression as suggested by Alexandre would be a good idea and I think I will try it out soon and post the results. I think that sacrificing the timing of prediction performance is a big problem since it is precisely what we are trying to do. Having a regime switching model for the prediction could also be a good approach. I’ll give it some thoughts and come back to it.

Good comment!

QF