Momentum, Markowitz, and Smart Beta: A Tactical, Analytical and Practical Look at Modern Portfolio Theory

Abstract

In this paper we will try to improve on the Modern Portfolio Theory (MPT) as developed by Markowitz (1952). As a first step, we combine the MPT model with generalized momentum (see Keller 2012) in order to arrive at a “tactical” MPT. In our second step, we will use the single index model (Elton, 1976) to arrive at an analytical solution for a long-only maximum Sharpe allocation. We will call this the MAA model, for Modern Asset Allocation. In our third step, we use shrinkage estimators in our formula for asset returns, volatilities and correlations to arrive at practical allocations. In addition, as a special cases, we arrive at EW (Equal Weight), Minimum Variance (MV), Maximum Diversification (MD) and (naive) Risk Parity (RP) submodels of MAA. These EW, MV, MD and RP models are sometimes called “smart-beta” models. We illustrate all these different models on three universes consisting of respectively 10 and 35 global ETFs, and 104 US stocks/bonds, with daily data from Jan. 1998 – Dec. 2013 (16 years), monthly rebalanced. We show that all these models beat the simple EW model consistently on various return /risk criteria, with the general MAA model (with return momentum) also beats nearly all of the “smart beta” models.