optimization - Why does the minimum variance portfolio provide good returns?

I've been a researching minimum variance portfolios (from this link) and find that by building MVPs adding constraints on portfolio weights and a few other tweaks to the methods outlined I get generally positive returns over a six-month to one year time scale.

I am looking to build some portfolios that are low risk, but have good long term (yearly) expected returns. MVP (as in minimum variance NOT mean variance) seems promising from backtests but I don't have a good intuition for why this works.

I understand the optimization procedure is primarily looking to optimize for reducing variance, and I see that this works in the backtest (very low standard deviation of returns).

What I don't have an intuitive feel for is why optimizing variance alone (with no regards to optimizing returns, i.e. no mean in the optimization as in traditional mean-variance optimization) gives generally positive returns. Any explanations?

Answer

The minimum variance solution loads up on securities that have low variances and co-variances. Theoretically you are correct that this should have a low expected return profile.

However, it turns out - in contradiction to modern portfolio theory - that securities that have low-volatility or low-beta experience higher returns than high-volatility or high-beta stocks. This is well-documented in the literature as the low-volatility anomaly. As a result, many funds and ETFs have been launched in recent years to exploit this phenomenon.

There are a couple arguments as to why the anomaly exists. The paper I cite above argues that institutional investor objectives and constraints create the anomaly:

Over the past 41 years, high volatility and high beta stocks have substantially underperformed low volatility and low beta stocks in U.S.markets. We propose an explanation that combines the average investor's preference for risk and the typical institutional investor’s mandate to maximize the ratio of excess returns and tracking error relative to a fixed benchmark (the information ratio) without resorting to leverage. Models of delegated asset management show that such mandates discourage arbitrage activity in both high alpha, low beta stocks and low alpha, high beta stocks. This explanation is consistent with several aspects of the low volatility anomaly including why it has strengthened in recent years even as institutional investors have become more dominant.