# Flexible Asset Allocation With Conditional Correlations

Recently, I have been engaged in some research collaboration with Ilya Kipnis from QuantStrat TradeR. Ilya is a talented quant with a passion for testing new ideas. One of the ideas relates to a recent post he wrote on replicating an heuristic method for constructing portfolios called “Flexible Asset Allocation”. A while back I was forwarded an interesting article by Wouter Keller on “Flexible Asset Allocation” (FAA) that gained popularity for its novel approach for blending momentum, correlations and volatility into one composite ranking scheme for tactical asset allocation. The correlation component of the ranking was apparently inspired by the Minimum Correlation Algorithm. The general ranking method is essentially a weighted average of the ranking of each asset versus the universe in terms of momentum (return over a chosen window, higher is better), volatility (standard deviation, lower is better) and correlation. For the correlation component, Mr. Keller suggests ranking assets relative to their average correlation to all other assets- since that is a good proxy for the diversification potential (lower is better). The final result is that FAA manages to demonstrate both good performance and also robustness across time. For a good review of FAA, Wes Gray of Alpha Architect (which is a very good research resource) wrote a good post showing the superiority of the approach over simpler methods here.

In an email to the author, I was of course flattered, but suggested as an improvement that he use “conditional” correlation rankings since the real diversification of adding the “nth” asset was dependent on what was currently selected in the portfolio. In other words, you can’t rank everything all at once, it needs to be done in the sequence in which you choose assets: for example- holding all other factors constant (ie momentum and volatility), if I first select a bond fund (owing to its low correlation to other assets) the next lowest correlation or best diversifying asset would be a stock index rather than say another bond fund. This conditional correlation ranking approach avoids redundancy and leads to superior diversification and presumably better risk-adjusted performance than using the original method. However, it is important to note that it still does not solve the thorny issue of how many assets to choose from the portfolio- ie selecting the “top n” by composite rank. Furthermore, the choice of “top n” to hold in the portfolio is compounded by the original selection of the asset universe. These are separate problems that can be solved by using a more elegant framework, and Mr. Keller has several new articles out using variations on standard MPT in a dynamic format. The drawback to these approaches (and many other viable alternatives) is that they tend to have complex mathematical implementations that are not as simple and intuitive as the original FAA.

Getting back to the concept of conditional correlations , one should replace the correlation component in FAA with a dynamic version of the average asset correlation. This means that the average correlation relates only to new assets not already included in the portfolio to the current assets included in the portfolio. After selecting the first asset, you would rank all remaining assets in terms of their correlation to the first asset (lower is better). For example, if I select a bond fund first, I would then rank all remaining assets in the universe based on their correlation to the bond fund. Once you have two or more assets, you would find the average correlation of each remaining asset to the current portfolio assets. This average correlation becomes the ranking method for the remaining assets (lower is better). So if I have a bond fund and a stock fund in the portfolio, I would find the average of the correlation of each asset remaining (not included in the portfolio) in the universe to the bond fund and the stock fund. So if for example I was doing this calculation for a gold fund, this would be the average of the correlation of gold to the stock fund and the correlation of gold to the bond fund. This would be calculated for each remaining asset, from which point you can rank them accordingly. This process continues recursively until you reach the desired target “top n” /number of assets in the portfolio. So if you choose say 5 assets from a 15 asset universe, you would have to compute the regular average correlation method from the original FAA to select the first asset and then calculate this conditional correlation four separate times.

I know this sounds confusing, so Ilya at QuantStrat Trader plans to post a spreadsheet soon showing how this is calculated and also associated R Code for the full implementation. Presumably, this approach will be more robust when applied to a wider range of universes and also will be less sensitive to the choice of “top n”. This new version of FAA is still fairly simple, it just requires a few more calculations and it is much less complex than implementing MPT-type optimization. There are several adjustments that can be made to this new version of FAA that would make it robust to the issues mentioned above. Its just always a question of how deep one is willing to go down the rabbit hole- for hands-on practitioners, this modified version of FAA will probably be practical enough with some common sense calibration. For quants (and ultimately for the end investor), it is more beneficial to consider a more nuanced/sophisticated approach- and probably a different framework altogether. In reality, there are many dimensions to creating investor portfolios that require not only precise consideration of how to blend different elements (such as momentum, correlation, and volatility) but more importantly there needs to be a method for dealing with constraints and matching investor risk preferences. Of course, this brings back the necessity for a framework that computes a set of portfolio weights. There are some very interesting solutions to this problem that I will present at some point in the future.

Hi Dave,

Of all your research I dare say that Conditional Correlations (CC) may be one of the most important findings you’ve published. I’m glad to hear that we will see a formula for it in Ilya’s R code.

It is amazing to me how may trading systems are made or broken based on the set of assets (asset stable) selected for the system. Even the fabled FAA is proven ineffective when the “wrong” stable of assets is chosen.

I can envision future directions for research on CC defined “asset stables.” In addition to dual momentum systems like FAA, there are simple momentum systems such as the one tracked on the CXO web site – with the CXO 1,2,3 asset momentum system, will the 3 asset class performance improve with a CC-selected asset stable? Also, there are different concerns that can be addressed, such as negative semi correlation – can a CC-defined asset stable be selected to minimize the amount of negative semi-correlation in the herd, and will that improve performance? And then timelines – do short term trading systems benefit more or less from short vs long term CC-defined asset stable characteristics. Finally, can asset stables at the equity level (instead of asset class level) impact stock portfolios; i.e., could one use CC-defined universes on Portfolio123 for more consistency/better results in the ranking-style of systems developed there?

Again, Conditional Correlations is a great insight and so is the work done in quantifying them David. Once again I feel you are pushing forward the science of quantitative investing and shining a light on why things work.

Carl

Carl,

The post detailing a recursive algorithm for computing conditional correlation rankings is on my blog now. I call it a stepwise correlation rank algorithm, since that’s what it ranks correlation in a stepwise fashion, as opposed to conditional correlation, but that’s semantics.

Here:

http://quantstrattrader.wordpress.com/2014/10/27/introducing-stepwise-correlation-rank/

Excellent, I’ll take a look. Thanks for putting this together Ilya!

thanks carl, i appreciate the kind words. i thought it was a subtle point at the time rather than a breakthrough, but im glad to hear that it inspires a lot of new ideas- some of which you have mentioned are certainly worth exploring. there are in fact lots of subtleties that i alluded to in the post, and i think the most important thing is being able to find solutions that address them directly rather than focus on a strategy- which comes with a set of rules and a universe which does not clearly expose the strengths/weaknesses of a system in a backtest.

best

david

This is a really original work on the subject and I think will lead to many other future findings.

https://nightlypatterns.wordpress.com

thanks aimdal, i appreciate that. i certainly hope so.

best

david

David,

When talking about “the” correlation do you refer to an average correlation since quite some years or the current correlation? Wouldn’t it be good to calculate with AT LEAST the average correlation, MAYBE the current correlation and FOR SURE the average correlation in past down markets? Personally I would want to have some (calculated) protection against a worst case scenario so I would like to use correlation calculations when markets tank or have tanked. Is this kind of information available as far as you know?

Thanks!

drftr

hi drftr, i think that what you are talking about is a fundamental flaw in using correlations altogether–they don’t capture all the information that you would want to know, and there is no easy solution. however some of the ideas you are mentioning can improve upon just using a short-term historical window for calculation. unfortunately, for many assets with the explosion of ETFs etc, we do not have sufficient history to gauge what would happen since the data is limited. that is why it is important to use a single index model or something like that to better estimate such situations.

best

david