I’ve picked a fight with the default, static 60/40 industry portfolio many, many times before.  My general go to slogan is “an asset allocation is not a risk profile.”  Normally I go after the mis-matched risk contribution and the potential for correlations to dramatically shift.

A paper I stumbled across, “Computing implied returns in a meaningful way” by Ulf Herold gave me a new angle to explore this topic.  That angle is: does a static allocation line up with my excess return beliefs?

As I said in my last post, I view asset allocations decisions to be about whether we believe excess return premia offered by the market are rich or cheap relative to their respective risks.  Traditional mean-variance optimization uses this framework as well, balancing expected premia with their (shared) risks (measured via asset covariances).  But as we all know, errors in premia estimation are magnified by the mean-variance framework, making it a precarious tool to work with.

But, it may still be useful.  In the paper, Ulf uses the framework to back out the excess returns that would have lead to the weights we’re utilizing.  The one computational catch is that we have to assume knowledge of at least one (or two) risk premia.

To test out the methodology, I assume the following fixed portfolio weights: 30% S&P 500, 20% European Equity, 10% Emerging Market Equity, 5% High Yield Bonds, 15% 10-Year Treasuries, and 20% Corporate Grade bonds.  I chose the 500bp for the S&P 500 and 150bp for the 10-Year Treasuries for my assumed excess returns.  Below are the backed out implied excess returns.  weight implied returns


What is interesting about this technique is that it allows us a way to cross-reference our beliefs with our weights.  If September 2008 rolls around and I believe that US High Yield bonds should have a 2.5% premium and I see that my weights are implying a premium of nearly 4%, it is a good indication that my weights are not lining up with my beliefs and that my weights should be tweaked in some way.

This methodology suffers from one of the main critiques of MVO: it assumes that volatility is the appropriate measure to capture all risk associated with an asset class and that correlation is the appropriate measure to capture the entirety of asset class relationships.  This is important, because risk premia are the excess return we are paid for all associated risks.  Therefore, since the premia are being backed out relative to our assumptions, we have to realize that they are the premia associated with risks accurately measured by volatility and relationships accurately measured by correlation.

If you are interested in trying this out with your current weights, I put together a simple Excel workbook that matches the results from the paper.  It will take a bit of tweaking, but hopefully you can figure out the formulas and calculate your implied returns.

Corey is co-founder and Chief Investment Officer of Newfound Research, a quantitative asset manager offering a suite of separately managed accounts and mutual funds. At Newfound, Corey is responsible for portfolio management, investment research, strategy development, and communication of the firm's views to clients. Prior to offering asset management services, Newfound licensed research from the quantitative investment models developed by Corey. At peak, this research helped steer the tactical allocation decisions for upwards of $10bn. Corey holds a Master of Science in Computational Finance from Carnegie Mellon University and a Bachelor of Science in Computer Science, cum laude, from Cornell University. You can connect with Corey on LinkedIn or Twitter.