Tactical Asset Allocation Alpha and The Greatest Trick the Devil Ever Pulled

“The greatest trick the Devil ever pulled was convincing the world he didn’t exist.”

– Verbal Kint, The Usual Suspects

The investment industry has investors convinced that the only path to better performance is through stock selection. As a result, most investors approach the challenge of portfolio construction exactly backward, and miss out on the most important opportunities to produce differentiated performance. The purpose of this series is to challenge the conventions that lead to misguided asset allocation priorities, and offer compelling reasons for practitioners to reverse their thinking, with the goal of delivering better outcomes for investors.

To review, Part I of this series introduced Grinold’s Fundamental Law of Active Management. Grinold proved that an investor’s opportunity to generate performance depends largely on the number of diverse investments that are available to construct portfolios. All else equal, an investor with more diverse investment choices should outperform an investor with fewer choices.

In Part II, we explained how to determine the number of truly independent sources of return in a portfolio. We used a technique called principal component analysis, and demonstrated how to isolate equity ‘beta’ from the returns of the 30 Dow stocks. We also illustrated why, according to a simple interpretation, the Dow 30 stocks are explained by just 3 independent sources of return.

In Part III, we reviewed seminal analyses on the relative importance of asset allocation and security selection from Grinold and Kahn, as well as Ibbotson and Kaplan. As these original analyses were descriptive studies of institutional returns, they really isolated the way institutions have chosen to apply active management. As such, they are less helpful in quantifying the true size of the opportunity.

Assoe et al. attempted to bridge this gap by performing a simulation study where they varied the allocation across asset classes, and independently across stocks, to determine the range of outcomes. Their analysis led the authors to conclude that individual security decisions and asset allocation decisions provide equal opportunities for differentiated performance. However, they anchored asset allocations to traditional endowment practices, i.e. 60% stocks and 40% bonds, and stock allocations to market capitalizations. As such, their analysis still did not capture the full opportunity set.

Here, in Part IV, we use the framework described in part II, along with some assumptions about the relationships between global asset classes, to illustrate the relative importance of asset allocation relative to security selection for an unconstrained strategy, such as Global Tactical Asset Allocation. We approach the problem from a theoretical perspective in order to capture the full opportunity set that is available to investors who focus in each domain. In addition, we quantify the proportion of global portfolio breadth that is available to active asset allocators versus stock-pickers given a range of correlation assumptions.

Revisiting Principal Component Analysis

Before we begin, we want to ensure that readers have a working grasp of our primary analytical tool, principal component analysis (PCA). Recall that PCA is simply a method to determine the number of independent forces that explain the dynamics of a system. It is used in voice and facial recognition, big data applications, physics, psychology, and almost any other domain you can think of where investigators want to tease out exactly what is happening in a complex process.

A metaphor may help illustrate the concept. Imagine that a man steals five dogs. Each dog is on its own leash, and has a GPS chip embedded in its collar so that it is possible to track its exact movements. As the man walks down the street the dogs move around in a seemingly random pattern, and trace out individual movements in space.

An analyst who works with the company who issues the GPS chips wishes to determine the direction that the man is walking so that the authorities can intercept him. To do so, he finds the positions of each dog, and how their positions vary from one another, at each point in time. He then performs PCA on their co-movements. The PCA reveals that, while the dogs are moving in a random pattern, there is one direction that is common to all dog movement: the movement in the direction that the thief is walking.

It’s easy to see how this concept relates to finding the dominant forces at work in a portfolio. Consider stocks: while each stock in the portfolio is reacting to a multitude of forces at any point in time, the force that dominates the movement of all securities is the direction that the market is moving in aggregate. PCA teases out this dynamic from the covariances or correlations observed between the individual stocks. Of course, the same analysis can be performed on any portfolio, including multi-asset portfolios, to determine the major forces at play.

Now that we understand how PCA works, let’s put this powerful tool to work in determining the relative impact of stocks versus asset allocation in a diversified portfolio.

A Basic Market Structure for Analysis

The analysis below is based on a framework first described by Staub and Singer (2011) in an article called “Asset allocation vs. security selection: Their relative importance.” The authors set out to see what proportion of total global breadth, across stock and bond indexes and individual stocks and bonds, is attributable to asset allocation relative to security selection. Note that the decision to invest in risky assets versus cash invokes a decision about what mix of asset classes to hold (in this case, proportion of stocks vs. bonds). Once the stock/bond proportion is chosen, the investor must choose which geographic markets to own, and once that decision is made what individual stocks and/or bonds to hold in those markets. In this way, each incremental layer of portfolio decision has a cascading impact on more granular sets of assets down the chain.