A Century of Evidence for Mean-Variance Optimization: Can We Finally Declare Victory?

By in Investing & Economics, Statistics

There’s really no nice way to say this, so we’ll just be plain: If mean-variance optimization (MVO) isn’t working for you, there’s a very good chance you’re doing it wrong. After all, we’ve been applying MVO with momentum-based estimates to manage live portfolios for years (see our strategy page, here).

Our most recent research, developed in collaboration with friend and colleague Dr. Wouter Keller of Flex Capital BV, confirms the simple reality of the method’s efficacy over a full century of data in a Global Tactical Asset Allocation context. To access the full paper, entitled Momentum and Markowitz: A Golden Combination, click here.

Recall that we at BPG & Associates have been advocating for the use of MVO methods with momentum for Global Tactical Asset Allocation since 2012, when in the introduction to our paper Adaptive Asset Allocation: A Primer, we wrote:

“Practitioners, academics, and the media have derided modern Portfolio Theory (MPT) over much of its history, but the grumbling has become outright disgust over the past ten years. This is largely because the dominant application of the theory, Strategic Asset Allocation, has delivered poor performance and high volatility since the millennial technology crash, and the traditional assumptions of MPT under the Efficient Markets Hypothesis offer no explanation or hope for a different outcome in the future.

Strategic Asset Allocation probably deserves the negative press it receives, but the mathematical identity described by Markowitz in his 1967 paper is beyond reproach. The math is the math.

Modern Portfolio Theory requires three parameters to create optimal portfolios from two or more assets:

1. Expected returns
2. Expected volatility
3. Expected correlation

The trouble with Strategic Asset Allocation is that it applies MPT using long-term averages of these parameters to create diversified portfolios. Unfortunately for SAA investors, long-term averages turn out to be poor estimates of returns, volatility and correlation…”

In the 2012 paper we laid out methods for making accurate and reliable parameter estimates over momentum-friendly lookback horizons, and applied these methods to 20-year backtests (which initiated in 1995). As parameters were layered on, there was an impressive stepwise improvement. And yet, despite feeling comfortable with our 20-years of backtest history, we are the first to admit that in the world of investing, larger sample sizes generally yield more reliable conclusions.

Which brings us back to our most recent paper, in which we present a practical and effective application of mean-variance optimization by pairing it with the well-documented asset class momentum factor. We target portfolio volatility on the efficient frontier in order to examine the performance of “aggressive” (target volatility=10% annualized) and “conservative” (target volatility = 5% annualized) implementations on three universes spanning a century of data.

We consistently observe Sharpe ratios for optimized portfolios of 2x to 3x that observed for a naive equal weight portfolio as a result of delivering both higher returns and lower risk. Maximum drawdown risk is also reduced by 3x to 5x. Results are robust to 1-way transaction costs as high as 0.8% for returns alone, and higher on a risk-adjusted basis.

A visual representation of just one of the tests included in the paper is quite compelling:


A paper examining the impact of universe selection and rebalance date effects based on randomized portfolios and rebalancing dates is forthcoming, along with formal hypothesis testing on means, Sharpe ratios, and alphas.

In the meantime, we invite you to download the paper and contact us with comments or questions. Enjoy!