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Monday 3 March 2014

Low Risk, High Rewards: The Low Volatility Anomaly

Axiomatic Memes

It’s an axiom of standard economics that you don’t get above average returns without taking above average risks. No risk, no reward.  It’s an appealing idea, an extension of the entrepreneur's creed: you don't become successful without taking chances.  It’s a meme that’s gone viral, an idea that permeates discussions about investment, drives hard headed analysis and leads us to celebrate the risk taking achievers in society.

And of course it’s a bucketload of hogwash. In fact, lower risk portfolios will tend to outperform higher risk ones.  High risk stocks are dangerous rubbish, and offer not excess returns but excess losses.  They’re a one way ticket to the seedy side of the market.

Doffing the CAPM

The idea that you only get excess returns by taking excess risks is a prediction of the Capital Asset Pricing Model – the default model of asset pricing in traditional economics (see Alpha and Beta - Beware Gift-Bearing Greeks).  CAPM is the overt expression of the Efficient Markets Hypothesis, the idea that the right price for a security is the current price, because the markets will price in all known information about the security, and weight this against all other securities.

Mostly, serious economists no longer believe in the strong version of the Efficient Markets Hypothesis for the very good reason that markets consistently refuse to behave in even a vaguely efficient way.  There are lots of arguments about how efficient markets actually are, but a rough summary is that they’re roughly efficient most of the time, and occasionally completely barking mad.  Although “occasionally” is a moot term, given the frequent and violent violations of efficiency.


The idea that risk and reward are related springs from CAPM, because in the model risk is equated with volatility, the jitteriness of a stock’s price.  A stock that rarely jumps about in price has low volatility and considered to be low risk.  One that does the opposite is high risk.  Volatility is measured by something called beta, which tells us how volatile a stock is compared to the rest of the market, and beta is often related to risk: higher beta stocks are higher risk. 

We should treat that last statement with a certain amount of caution.  If beta measures risk it does so only in the short term – after all, if a high tech stock goes ex-growth its beta will fall, so beta tells us little about changes in fundamentals.  It also only measures systemic risk – it can’t take account of so-called idiosyncratic risk, such as where the company’s assets turn out to be figments of the corporate imagination. 

So although CAPM predicts that high risk stocks will, in aggregate, lead to higher returns: no risk, no reward, only a fool would regard this as being the basis upon which to construct an investment approach.  Memes being what they are, though, and people being the inveterate lovers of mental short-cuts that they are, though, it’s entirely to be expected that these nuances will be glossed over.

Unanchored Memes

The “no risk, no reward” mantra has become unanchored from its dubious parentage and has assumed a life of its own: most people who quote this have no idea that they’re spouting some dubious discredited dogma, even as they seek out dangerously dodgy investments.  At the extreme the high risk, high return mantra leads to people searching for stocks with high idiosyncratic risk.  After all, the reasoning goes (well, I assume this is the way it works), we’re looking for very risky stocks, because even if only a few of these do well we’ll make a lot of money. 

However, as Andrew Ang, Robert Hodrick, Yuhang Xing and Xiaoyan Zhang state in The Cross-Section of Volatility and Expected Returns:
“Stocks with high idiosyncratic volatility have abysmally low returns”
The problem is that idiosyncratic risk is unmeasurable, it lies in the cloudy domain of uncertainty.  But, as Malcolm Baker, Brendan Bradley and Jeffrey Wurgler point out in Benchmarks as Limits to Arbitrage, the scale of the underperformance of high volatility stocks is stunning:
“… a dollar invested in the highest risk portfolio in January 1968 would be worth $0.61 at the end of December 2008, assuming no transaction costs. A dollar invested in the lowest risk portfolio would be worth $56.38. The path to that higher dollar value is also considerably smoother.” 

In addition, this paper argues that not only do people pay a premium for high volatility stocks but they tend to fail at exactly the points you’d like them not to: during significant market downturns.  This is a trend we’ve seen before: the creation of wondrous models that work perfectly during stable times but which fail utterly when they’re really needed.

The researchers theorize that investors’ attraction to high volatility stocks is a manifestation of behavioral bias (there, you knew I’d get there eventually …), linked to technical limits to the ability of markets to arbitrage away the anomaly.  After all, if high volatility stocks are overpriced then there ought to be money to be made, but the suggestion is that the security industry’s dedication to benchmarking will tend to discourage investments in low volatility stocks.

Over the period in which the low volatility anomaly has gained traction the paper points out that institutional management in the US has doubled, to 60%.  However, many institutions are benchmarked against a measure called the information ratio, and the effect of this, as the paper explains, is to underweight low volatility stocks and overweight high volatility ones. 

Lottery Tickets

Meanwhile irrational investors are busily attaching themselves to higher volatility stocks.  Central to this is humanity’s love of a lottery because although we’re fundamentally loss averse we’re very attracted to low priced lottery tickets with a small chance of a huge payout – we lose very little, but stand to make enormous amounts, and this is linked to Hersh Shefrin and Meir Statman’s two level portfolio model I discussed in Behavioral Portfolios: we separate low and high risk investments, and regard the latter as a gamble we’re willing to lose: so high volatility stocks, especially ones with low prices, are viewed as lottery tickets. 

Secondly, there’s the representative heuristic – the Linda problem (see Behavioral Finance's Smoking Gun or The Zeitgeist Investor).  Behaviorally compromised investors spend their days looking for the next Apple or Microsoft and ignore the base rate, the huge rate of failure of early stage innovative companies.  And thirdly, there’s overconfidence, people are simply too optimistic about the likelihood of the success of high growth companies. 

I’d add another bias to that mix – once investors have committed themselves to some high risk piece of junk they become extremely averse to changing their mind about it.  This is confirmation bias, and it’s a nasty, pervasive little mindworm.  Don’t bother arguing with someone committed to their investments, you might as well tell them that their children are ugly and stupid for all the success you’ll have changing their minds.

Time to Sleep

Of course, low volatility stocks will never make you outrageously rich, and everyone just knows that their latest micro-cap, hi-tech, go-go growth stock is bound to multi-bag.  And it’ll probably do it next week rather taking years. 

Most anomalies end up being arbitraged away by specialists, as we’ve seen with momentum and accrual effects, so it requires some kind of structural asymmetry to allow one to flourish.  This looks like just such an opportunity.  High volatility stocks appeal to the gambler in the illogical investor, and behavioral bias drives them the rest of the way.  Meantime low volatility stocks offer more certain returns and less sleepless nights along the way.


  1. Nice article, very clear. I'm reminded of Buffett's quote about the Washington Post in 1973:

    "The Washington Post Company in 1973 was selling for $80 million in the market. At the time, that day, you could have sold the assets to any one of ten buyers for not less than $400 million … Now, if the stock had declined even further to a price that made the valuation $40 million instead of $80 million, its beta would have been greater. And to people who think beta measures risk, the cheaper price would have made it look riskier."

    Truly, Alice in Wonderland-style thinking!

  2. Higher volatility means you're more likely to hit zero boundary, which in a stock market is absobing. Well, since we don't hit 0 that often, I'd really say "in a leveraged environment, high vol means somoene is more likely to hit their margin call, which is loss-realizing and creates a positive downward feedback". Simples.
    So, while statistically higher vol gives you higher top percentile, but lowers your expected return.