Tactical MPT and Momentum: The Modern Asset Allocation (MAA)

Abstract

Modern Portfolio Theory (MPT), as developed by Markowitz (1952) and others, is often described as a nice but impractical theory. The full MPT framework is very sensitive to parameters like the expected returns which are estimated with errors, resulting in allocations with even larger errors. This is known as the multiplication of errors. The same holds for the expected covariance matrix. In this paper we combine MPT with momentum, a simple covariance model and shrinkage estimators. First, we use historical estimates based on short (up to one year) lookback periods, in contrast to the traditional (multi-year) approach. Second, we use the “single-index model” of Elton (1976) to structure the covariance matrix and to arrive at an elegant analytical formula for the optimal allocations. Finally, we reduce estimation errors by partially “shrinking” all estimates for expected returns, volatilities and cross-correlations towards their means over assets. We call the resulting “tactical” (short-term) MPT model the “Modern Asset Allocation” (MAA). We illustrate the MAA model on nine universes (with 7 to 130 assets) over 1997-2013 and show that the MAA model beats the simple EW model consistently, proving the usefulness of MPT.

Keywords: Tactical Asset Allocation, Momentum, Markowitz, Elton, MPT, mean variance, minimum variance, Sharpe, EW, SIM

JEL Classification: C00, C10, G00, G11