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Momentum and Markowitz: A Golden Combination

34 Pages Posted: 16 May 2015 Last revised: 5 Jun 2015

Wouter J. Keller

VU University Amsterdam

Adam Butler

ReSolve Asset Management

Ilya Kipnis

QuantStrat TradeR

Date Written: May 16, 2015

Abstract

Mean-Variance Optimization (MVO) as introduced by Markowitz (1952) is often presented as an elegant but impractical theory. MVO is "an unstable and error-maximizing" procedure (Michaud 1989), and "is nearly always beaten by simple 1/N portfolios" (DeMiguel, 2007). And to quote Ang (2014): "Mean-variance weights perform horribly… The optimal mean-variance portfolio is a complex function of estimated means, volatilities, and correlations of asset returns. There are many parameters to estimate. Optimized mean-variance portfolios can blow up when there are tiny errors in any of these inputs...".

In our opinion, MVO is a great concept, but previous studies were doomed to fail because they allowed for short-sales, and applied poorly specified estimation horizons. For example, Ang used a 60 month formation period for estimation of means and variances, while Asness (2012) clearly demonstrated that prices mean-revert at this time scale, where the best assets in the past often become the worst assets in the future.

In this paper we apply short lookback periods (maximum of 12 months) to estimate MVO parameters in order to best harvest the momentum factor. In addition, we will introduce common-sense constraints, such as long-only portfolio weights, to stabilize the optimization. We also introduce a public implementation of Markowitz's Critical Line Algorithm (CLA) programmed in R to handle the case when the number of assets is much larger than the number of lookback periods.

We call our momentum-based, long-only MVO model Classical Asset Allocation (CAA) and compare its performance against the simple 1/N equal weighted portfolio using various global multi-asset universes over a century of data (Jan 1915-Dec 2014). At the risk of spoiling the ending, we demonstrate that CAA always beats the simple 1/N model by a wide margin.

Keywords: Markowitz, MPT, MVO, Mean Variance, Momentum, Tactical Asset Allocation, CLA, CAA, EW, 1/N, Smart Beta

JEL Classification: C00, C10, C22, G00, G11, G10, G14

Suggested Citation

Keller, Wouter J. and Butler, Adam and Kipnis, Ilya, Momentum and Markowitz: A Golden Combination (May 16, 2015). Available at SSRN: https://ssrn.com/abstract=2606884 or http://dx.doi.org/10.2139/ssrn.2606884

Wouter Keller (Contact Author)

VU University Amsterdam ( email )

De Boelelaan 1105
Amsterdam, NH 1081 HV
Netherlands
+31622392446 (Phone)

Adam Butler

ReSolve Asset Management ( email )

1 Adelaide St. East, Suite 2000
Toronto, Ontario M5C 2V9
Canada
4165725477 (Phone)

HOME PAGE: http://www.investresolve.com

Ilya Kipnis

QuantStrat TradeR ( email )

No Address Available
United States

HOME PAGE: http://www.quantStratTrader.wordpress.com

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