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
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