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.