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

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!

Disclaimer

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These materials do not purport to be exhaustive and although the particulars contained herein were obtained from sources ReSolve believes are reliable, ReSolve does not guarantee their accuracy or completeness. The contents hereof does not constitute an offer to sell or a solicitation of interest to purchase any securities or investment advisory services in any jurisdiction in which such offer or solicitation is not authorized.

Forward-Looking Information. The contents hereof may contain “forward-looking information” within the meaning of the Securities Act (Ontario) and equivalent legislation in other provinces and territories. Because such forward-looking information involves risks and uncertainties, actual performance results may differ materially from any expectations, projections or predictions made or implicated in such forward-looking information. Prospective investors are therefore cautioned not to place undue reliance on such forward-looking statements. In addition, in considering any prior performance information contained herein, prospective investors should bear in mind that past results are not necessarily indicative of future results, and there can be no assurance that results comparable to those discussed herein will be achieved. The contents hereof speaks as of the date hereof and neither ReSolve nor any affiliate or representative thereof assumes any obligation to provide subsequent revisions or updates to any historical or forward-looking information contained herein to reflect the occurrence of events and/or changes in circumstances after the date hereof.

General information regarding returns. Performance data prior to August, 2015 reflects the performance of accounts managed by Dundee Securities Ltd., which used the same investment decision makers, processes, objectives and strategies as ReSolve has used since it became registered and commenced operations in August, 2015. Records that document and support this past performance are available upon request. Performance is expressed in CAD, net of applicable management fees. Indicated returns of one year or more are annualized. Past performance is not indicative of future performance.

General information regarding the use of benchmarks. The indices listed have been selected for purposes of comparing performance with widely-known, broad-based benchmarks. Performance may or may not correlate to any of these indices and should not be considered as a proxy for any of these indices. The S&P/TSX Composite Index (Net TR) (“S&P TSX TR”) is the headline index and the principal broad market measure for the Canadian equity markets. The Standard & Poor’s 500 Composite Stock Price Index (“S&P 500”) is a capitalization-weighted index of 500 stocks intended to be a representative sample of leading companies in leading industries within the U.S. economy.

General information regarding hypothetical performance and simulated results. These results are based on simulated or hypothetical performance results that have certain inherent limitations. Unlike the results in an actual performance record, these results do not represent actual trading. Also, because these trades have not actually been executed, these results may have under- or over-compensated for the impact, if any, of certain market factors, such as lack of liquidity. Simulated or hypothetical trading programs in general are also subject to the fact that they are designed with the benefit of hindsight. No representation is being made that any account or fund managed by ReSolve will or is likely to achieve profits or losses similar to those being shown. The results do not include other costs of managing a portfolio (such as custodial fees, legal, auditing, administrative or other professional fees). The contents hereof has not been reviewed or audited by an independent accountant or other independent testing firm. More detailed information regarding the manner in which the charts were calculated is available on request. Any actual fund or account that ReSolve manages will invest in different economic conditions, during periods with different volatility and in different securities than those incorporated in the hypothetical performance charts shown. There is no representation that any fund or account will perform as the hypothetical or other performance charts indicate.

General information regarding the simulation process. The systematic model used historical price data from Exchange Traded Funds (“ETFs”) representing the underlying asset classes in which it trades. Where ETF data was not available in earlier years, direct market data was used to create the trading signals. The hypothetical results shown are based on extensive models and calculations that are available for any potential investor to review before making a decision to invest.