Minimum Variance Portfolios: Theory and Empirics at Odds

Minimum Variance Portfolios: Theory and Empirics at Odds

October 23, 2013 Uncategorized
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(Last Updated On: October 23, 2013)

Sitting here working on my lecture for advanced investment management.

I’ve been working through mean-variance-analysis and came across the good old-fashioned “Mean Variance Frontier.”

click to enlarge


In the chart above you’ll notice I’ve highlighted two important portfolios: The minimum variance portfolio and the tangency portfolio.

As any good investor focused on mean and standard deviation will tell you, the minimum variance portfolio is a portfolio nobody would theoretically own.

Why not?

Well, look at the portfolio opportunity set created by pairing the tangency portfolio and the risk-free rate (the straight line). Notice how the straight line rests well above the minimum variance portfolio? Well, if an investor could hold a basket that is part tangency portfolio and part risk-free, that investor can achieve a higher risk/reward than by simply holding the minimum variance portfolio. To repeat, NOBODY SHOULD HOLD A MINIMUM VARIANCE PORTFOLIO (in theory).

And yet, the world is full of minimum variance portfolios:

Did the biggest fund providers in the world forget to attend their MBA 101 classes?

Well, not really. These folks are obviously bright and many of the underlying assumptions associated with mean variance analysis are absolutely ludicrous. However…

The biggest fund providers are in the business of selling and one of the more effective ways to sell is to data-mine for a great backtest, ignore robustness tests, and tell a great story.

The minimum volatility pitch is great:

  • Investor: “Hi financial advisor, what do you have that involves low-risk equity investing?”
  • RIA: “Well sir, we are screening for a portfolio that minimizes your volatility. Low risk, no doubt–its even in the name!”

It turns out that, historically, the minimum variance portfolio (minimizes volatility) has outperformed the theoretically superior “tangency” portfolio (maximizes sharpe) construction.

However, the basis for creating portfolios based on a minimum variance approach has little in regard to theoretical underpinnings…as far as I can tell…

Moreover, some of the work I’ve done on my own (and from others) suggests that investors have many reasons to question the robustness of any portfolio formed based on mean variance analysis (to include the minimum variance portfolio!).

Minimum volatility to the rescue?

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Definitions of common statistics used in our analysis are available here (towards the bottom)

About the Author

Wesley R. Gray, Ph.D.

After serving as a Captain in the United States Marine Corps, Dr. Gray earned a PhD, and worked as a finance professor at Drexel University. Dr. Gray’s interest in bridging the research gap between academia and industry led him to found Alpha Architect, an asset management that delivers affordable active exposures for tax-sensitive investors. Dr. Gray has published four books and a number of academic articles. Wes is a regular contributor to multiple industry outlets, to include the following: Wall Street Journal, Forbes,, and the CFA Institute. Dr. Gray earned an MBA and a PhD in finance from the University of Chicago and graduated magna cum laude with a BS from The Wharton School of the University of Pennsylvania.