Equities with lower than average volatility have delivered superior returns, both absolute and risk-adjusted, over a period spanning many decades. Investors should consider an allocation to strategies that take advantage of the so-called low-volatility anomaly.
Low-volatility stocks — those with less price variability than the average stock in the market — deliver higher returns than other stocks. This is an empirical fact, at least insofar as the last 90 years or so are concerned. And it is one of the most surprising market anomalies (a result not predicted by theory) ever found. It’s surprising because, as almost everyone believes, return is supposed to be related to risk so that higher-risk stocks should deliver higher returns and lower-risk stocks should deliver lower returns. The low-volatility anomaly stands this sensible theory on its head and, if it persists in the future, may provide a remarkable opportunity to make outsize returns.
Before getting into the history of the low-volatility anomaly and how we apply it in today’s markets, let’s briefly review the data behind this surprising finding. While low-volatility pioneers Nardin Baker and Robert Haugen (2012) have shown that the low-volatility anomaly holds in every country’s equity market for which data can be collected, we focus on the United States. Figure 1 shows the raw (not risk adjusted) returns on quintiles of stocks sorted by volatility over the period 1970–2011. The relationship that emerges is the opposite of what common sense and financial theory would lead us to expect: low-volatility stocks outperformed even before adjusting for risk. Other researchers have shown that this finding is consistent over longer periods.
Risk-adjusted returns follow an even more dramatic pattern. Figure 2 shows the Capital Asset Pricing Model (CAPM) alphas (returns after adjusting for each stock’s beta or “market” risk) for each quintile.
The alpha of more than 5% of the lowest volatility quintile (a reasonably well-diversified strategy of 200 large-cap stocks) is extraordinary. Even more striking is the 12.6% spread between the performance of the first and the last quintile. Because beta does not capture all of the risk in a portfolio, we confirm these results by calculating the Sharpe ratio (total return divided by volatility as measured by standard deviation) as shown in Figure 3.
When portrayed as Sharpe ratios, returns are still monotonically decreasing as risk increases, and the size of the effect is still substantial — despite the theory that financial markets should reward investors for taking risk predicts the opposite.
How can this be?
The prehistory of low-volatility
The possibility of a low-volatility effect has been known since the work of the near-Nobel Prize-winning economist Fischer Black as far back as 19721. Black (1972) pointed out that if investors want to take more risk than the market, they can leverage up the market portfolio. But if leverage is unavailable or costly, they may choose to buy high-risk (high-volatility) stocks instead, leaving low-volatility stocks undersubscribed and underpriced. Black expressed this concept by saying that the CAPM line should appear flatter under conditions of restricted leverage than it would be otherwise.
Let’s examine this statement, reviewing the basic principles of the CAPM as needed to indicate what Black was talking about. The CAPM posits a relationship between market risk and expected return shown as the CAPM dotted line in Figure 4. Market risk, measured by beta, is that part of a security’s overall risk or volatility that is due to correlation with a capitalization-weighted market benchmark. The beta measure is scaled such that “cash” has a beta of zero and the cap-weighted benchmark (of the stock market in this case) has a beta of 1.
The solid line shows the relationship predicted by Fischer Black if borrowing is restricted. Excess demand for high-beta stocks pushes their price up (expected return down) until demand and supply are equated. Because low-beta stocks then face insufficient demand at their CAPM price, their price is pushed down (expected return up).
Traditional finance says that if conditions in the market make it possible for arbitrageurs to earn a large riskless profit (larger than the cost of executing the arbitrage), the condition will disappear. In the case of Black’s solid line, arbitrageurs would short high-beta stocks and buy low-beta stocks in such proportions that the overall beta of the arbitrage portfolio would be zero, but with a large positive expected return. Arbitrageurs would thus push the solid line back toward the CAPM dashed line and the superior risk-adjusted return of low-beta stocks would disappear.
In practice it seems that few people are engaging in this arbitrage. First, it is far from riskless; while the arbitrage portfolio would have a beta equal to that of cash, i.e., zero, its return would have a very large standard deviation (in other words, beta does not capture the true risk of the arbitrage portfolio) and it discourages arbitrageurs. Second, many potential arbitrageurs may not know that the arbitrage opportunity exists, or do not believe it will persist over the time horizon with which they are concerned. At any rate, the low-volatility anomaly has persisted for decades despite the possibility of it being arbitraged away.
The market, then, is inefficient and contains surprisingly large and persistent anomalies or profit opportunities. This fact relies on the widespread violation of the no-arbitrage condition (the idea that if a profit opportunity exists, it would be quickly arbitraged away) and has spawned a large “limits to arbitrage” literature.2 Jay Ritter, a pioneer of behavioral finance, notes that market inefficiency depends on two conditions being simultaneously met: (1) at least some degree of investor irrationality, and (2) arbitrage being limited.3 Our theoretical justification for low-volatility investing depends on Ritter’s two conditions.
Was Black’s conjecture of a flatter CAPM line already confirmed by data available at the time he wrote his 1972 article? His article notes that Shannon Pratt, studying U.S. stocks over 1926–1960, found that “high-risk stocks do not give the extra returns that the theory predicts they should give.”4 Black, Jensen, and Scholes (1972) also obtain this result, as did a number of subsequent scholars whose work was motivated by Black’s conjecture. So the low-volatility anomaly was in force even then. But the discovery of the effect in the 1960s and 1970s is just the beginning of the low-volatility story — these results were not used to build portfolios and earn alpha.5
We are beginning to see why low-volatility stocks might earn a positive alpha (not a higher raw return, but a higher risk-adjusted return). Borrowing really is restricted; only a few hedge funds and banks can make leveraged investments in equities. The rest of us must be content with unleveraged investments, and if we want to take more risk, we’ll buy riskier securities. But this logic only explains an empirical CAPM line that is flatter than the theoretical or pure CAPM line, not one that’s sharply inverted as we saw in Figure 1 on page 2. The empirical data show higher returns — much higher returns — for lower-volatility portfolios, something that cries out for a better explanation.
Low-volatility investing emerges
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