The Low-Risk Anomaly: A Decomposition Into Micro And Macro Effects by Malcolm Baker, Brendan Bradley, and Ryan Taliaferro, CFA Institute


Low-risk stocks have offered a combination of relatively low risk and high returns. We decomposed the low-risk anomaly into micro and macro components. The micro component comes from the selection of low-beta stocks. The macro component comes from the selection of low-beta countries or industries. Both parts contribute to the anomaly, with important implications for the construction of managed-volatility portfolios.

The Low-Risk Anomaly: A Decomposition Into Micro And Macro Effects – Introduction

In an efficient market, investors earn higher returns only to the extent that they bear higher risk. Despite the intuitive appeal of a positive risk–return relationship, this pattern has been surprisingly hard to find in the data, dating at least to Black (1972). For example, sorting stocks by using measures of market beta or volatility shows just the opposite. Panel A of Figure 1 shows that from 1968 through 2012 in the US equity market, portfolios of low-risk stocks delivered on the promise of lower risk as expected but had surprisingly higher average returns. A dollar invested in the lowest-risk portfolio grew to $81.66, whereas a dollar invested in the highest-risk portfolio grew to only $9.76.

A similar inverse relationship between risk and return from 1989 through 2012 in a sample of up to 31 developed equity markets can be seen in Panel B of Figure 1. A dollar invested in the lowest-risk portfolio of global equities grew to $7.23; a dollar invested in the highest-risk portfolio grew to only $1.20. This so-called low-risk anomaly suggests a very basic form of market inefficiency.

Shiller (2001) credited Paul Samuelson with the idea of separating market efficiency into two types. Micro efficiency concerns the relative pricing of individual stocks, whereas macro efficiency refers to the pricing of the market as a whole. Broadly speaking, inefficiencies can be examined at different levels of aggregation: at the individual stock level, at the industry level, at the country level, or, in some cases, at the global level.

Samuelson (1998) conjectured that capital markets have “come a long way, baby, in 200 years toward micro efficiency of markets: Black–Scholes option pricing, indexing of portfolio diversification, and so forth. But, there is no persuasive evidence, either from economic history or avant-garde theorizing, that macro market inefficiency is trending toward extinction” (p. 36). At the heart of the difference is the fact that individual securities often have close substitutes. As Scholes (1972) showed, the availability of close substitutes facilitates low-risk micro arbitrage and pins down relative prices—if there are no practical limits on arbitrage. Industry and country portfolios have fewer close substitutes, and the equity market as a whole has none. So, individual stocks, in this view, are priced more efficiently relative to each other than they are in absolute terms. Of course, limits to arbitrage are real and substitutes are never perfect, so even Samuelson’s hypothesis is one of relative, not absolute, efficiency.

In the context of the low-risk anomaly, Baker, Bradley, and Wurgler (2011) emphasized the important constraint that long-only, fixed-benchmark mandates impose on micro arbitrage. Many institutional investors are judged not by total return relative to total risk but instead by active return relative to active risk, or benchmark tracking error. Such benchmark-oriented mandates discourage investment in low-risk stocks. Despite their low risk, these stocks become attractive relative to the tracking error they create only when their anticipated return exceeds the benchmark return in absolute terms.

Low-Risk Anomaly

There are also limits on macro arbitrage. Market aggregates do not have close substitutes, and so macro arbitrage—in the usual sense of simultaneously buying low and selling fundamentally similar securities high—is largely infeasible. Standard institutional mandates and risk management practices also play a role here, typically limiting the size of benchmark-relative country or industry exposures or eliminating them entirely through narrow mandates that identify a single-country index as the benchmark return. French and Poterba (1991) and Ahearne, Griever, and Warnock (2004) documented a home bias, for example, showing that individuals often do not invest across borders.

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