Why The Low-Volatility Anomaly Exists

Why The Low-Volatility Anomaly Exists

March 5, 2015 Research Insights, Low Volatility Investing, $SPY
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(Last Updated On: January 18, 2017)

Benchmarks as Limits to Arbitrage: Understanding the Low-Volatility Anomaly


Contrary to basic finance principles, high-beta and high-volatility stocks have long underperformed low-beta and low-volatility stocks. This anomaly may be partly explained by the fact that the typical institutional investor’s mandate to beat a fixed benchmark discourages arbitrage activity in both high-alpha, low-beta stocks and low-alpha, high-beta stocks.

Alpha Highlight:

Empirical research shows that low-volatility stocks earn higher risk-adjusted returns than high-volatility stocks. An anomaly that flips the entire financial economics profession on hits head.

We’ve done some simple tests with the strategy in the following posts:

  • Historical data (here)
  • and Simulation results (here).

This paper verifies the existence of low-vol anomaly. Data is obtained from CRSP, and ranges from 1968 to 2008. The paper sorts stocks into five groups for each month according to their 5-year trailing total volatility or trailing beta. The figure below shows the performances of the 5 groups of stocks. The conclusion is clear: Low-beta stocks outperform high-beta stocks.

2015-01-28 16_43_51-Why Low-Volatility Anomaly Exists_ - Alpha Architect

But How is this Possible?

Part 1: Bad Investor Behavior

The preference for high-volatility stocks derives from the biases that afflict the individual investor.

(1) Preference for lotteries. Here’s a good example from the paper:

  • A 50% chance of losing $100 vs. a 50% chance of winning $110;
  • A near-certain chance of losing $1 and a 0.0099 percent chance of winning $10,000. (Gamble: low-priced but volatile)

Which bet will you take? Although the first choice has a positive expected payoff,  most people prefer the second one with the negative expected payoff. Here’s how the paper explains the finding:

Buying a low priced, volatile stock is like buying a lottery ticket: There is a small chance of its doubling or tripling in value in a short period and a much larger chance of its declining in value.

(2) Representative Bias: Another example from the paper: Investors purchased Microsoft Corp. and Genzyme Corp. at their IPOs in 1986, which were considered “great investments.” However, people’s representative bias leads them conclude that “the road to riches is paved with speculative investments.” So investors are inclined to overpay for volatile stocks and ignore the failures of other speculative investments.

(3) Overconfidence: Both normal people and finance professionals suffer from overconfidence, or the inability to appropriately calibrate forecasts. Overconfidence enhances disagreement around stock price forecasts, especially for stocks with more uncertainty, such as high-vol stocks.

Part 2: Limits of Arbitrage

An institutional investor with a fixed benchmark is surprisingly unlikely to exploit such mispricings. In fact, in empirically relevant cases, the manager’s incentive is to exacerbate them.

The paper hypothesizes that the presence of delegated investment management with a fixed benchmark causes the CAPM relationship to fail. A quote from the paper is below:

2015-01-29 11_18_36-SSRN-id1585031.pdf - Adobe Reader

2015-01-29 11_20_11-SSRN-id1585031.pdf - Adobe Reader


In a nutshell, the paper reviews the low-volatility anomaly through the lens of behavioral finance: understand how behavioral bias is affecting an asset’s price and understand why large pools of capital aren’t exploiting this biased behavior (in this case the large pools of capital are increasing the bias!).

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About the Author

Wesley R. Gray, Ph.D.

After serving as a Captain in the United States Marine Corps, Dr. Gray received a PhD, and was a finance professor at Drexel University. Dr. Gray’s interest in entrepreneurship and behavioral finance led him to found Alpha Architect. Dr. Gray has published three books: EMBEDDED: A Marine Corps Adviser Inside the Iraqi Army, QUANTITATIVE VALUE: A Practitioner’s Guide to Automating Intelligent Investment and Eliminating Behavioral Errors, and DIY FINANCIAL ADVISOR: A Simple Solution to Build and Protect Your Wealth. His numerous published works has been highlighted on CBNC, CNN, NPR, Motley Fool, WSJ Market Watch, CFA Institute, Institutional Investor, and CBS News. 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.

  • Fascinating as usual. Eyeballing the chart, I wonder: how consistent is the low-vol anomaly across the bottom four quintiles? How do they look for different starting points (looks to me ? What does the chart look like if you graph the quintiles on a relative basis (i.e. quintile level divided by market level)? I don’t have the CRSP data.

    Looking at the MSCI AC World Min Vol compared to the main index, it looks to me as if min vol is long vol — it flatlines on a relative basis but outperforms in “jumps” in general market declines. Nice feature! Would an optimiser adore it as much as systematic trend following?

  • Trollmen

    Hello AlphaArchitect,
    Could you please explain why investment managers will not overweight until alpha > 2.5%? And why 2.5%?


  • Jack Vogel, PhD

    The paper claims this is due to limits of arbitrage: “An institutional investor with a fixed benchmark is surprisingly unlikely to exploit such mispricings. In fact, in empirically relevant cases, the manager’s incentive is to exacerbate them.”

  • Trollmen

    Thank you.