The Low Volatility, Low Beta Anomaly

by: Erik van Dijk

Are Investors Really Awarded for Extra Risk?[1]


Financial markets theory states that higher risks should be rewarded with higher returns. The well-known Capital Asset Pricing Model (CAPM) tells us that the expected return on a financial security or portfolio is linearly linked to the so-called systematic risk of such a security or portfolio. Systematic risk is defined as the relative sensitivity of that security or portfolio to fluctuations in the so-called market portfolio of all available securities. If we concentrate for the time being on an equity mandate, that would imply that the relevant market portfolio is some broad-based index like for instance the S&P 500 (NYSEARCA:SPY) [US portfolios] or the MSCI World [global, developed markets equity portfolios] or the MSCI Emerging Markets [global, emerging markets equity portfolios]. The systematic risk indicator – beta – is defined as:

Beta(i) = cor.coefficient(i,m) x (VOLA(i) / VOLA(m))

With Beta(i) representing the systematic risk of security or portfolio i, VOLA(i) the total risk or volatility of the security or portfolio i (the numerator) and VOLA(m) the volatility of the market portfolio / relevant index m (the denominator). In normal English: a higher correlation with the market index translates into more ‘risk’ and this is logical because that would reduce the diversification opportunities of that security or portfolio vis-a-vis other options that we have at our disposal. Lower correlations are an item of ‘value’. But higher systematic risk is not just related to the correlation of a security or portfolio with the market index: it is also linear to its relative total risk. Above average volatility translates into higher betas, unless there is a more than proportional compensation in the form of lower correlations.

The CAPM has long been an often used model in academic research and quantitative asset managers have used it as their basic model as well. And even with the new research it is shown that there is nothing wrong with using it this way when looking at multi-asset-class portfolios. The problems arise when it is used in smaller samples and especially those concentrated within one asset class like for instance stock portfolios. The CAPM states that:

E(R(i)) = Rf + Beta(i) x E(R(m)-Rf)

With E representing the expectations indicator, R the returns on the security or portfolio (i), the risk-free asset (f) and the market index (m) respectively. The level of Beta determines the excess return of the security or portfolio vis-à-vis the risk-free asset (with the latter of course having a beta of zero).

In other words: what we would expect is that higher betas translate into higher returns. And since the distribution of correlation coefficients is in practice a much tighter one than the one of volatilities of various securities, the same would hold for volatility: higher betas and higher volatilities do very often go hand-in-hand.

Academic as well as practitioner research seems to indicate that the CAPM is – at best – flawed. The link between beta and return seems to be flatter than suggested by the model, and lately studies do even seem to suggest that the relationship is inverted! What is going on? Does less risk translate into higher returns and more risk into lower returns? The Baker, Bradley & Wurgler (BBW)study in the Jan/Feb 2011 edition of the Financial Analysts Journal sheds some new light on the amazing low risk anomaly, linking it to both behavioral factors and to investment behavior by professional investors. We thought that this paper was of so much interest that we decided to write this note about it, adding into it some of LMG’s own research insights.

Is there really no free lunch in financial markets?

Is there really no free lunch?

Risk and Behavioral Biases

When looking at the loss aversion theorem within Behavioral Finance one would expect that investors – if anything – are very wary of risk. When presented with a betting opportunity with a 50 percent chance of a negative return of $ 100 and a 50 percent chance of a positive return of $ 110, most people would refrain from participating albeit that the expected pay-off is equal to +$5 (0.5 x -100 + 0.5 x 110). But the strange thing is that when we play around a bit with the skewness of the probability distribution so as to create a ‘lottery style’ bet with a 0.0001 percent chance of winning $ 6 million and otherwise a zero payment, most people would find it an interesting gamble for which they wouldn’t mind buying a $1 ticket. When we look at the expected pay-off we see that it is once again +$5 (0.000001 x 6,000,000 – 1)! This fondness of right-skewed distributions leads to excess popularity for high volatility and risk, and also ‘growth’ stories vis-à-vis value.

But there is more. Most people are not just struggling with this standard application of probability theory as a result of which similar expected returns translate into different (and actually illogical!) levels of popularity with ‘investors’. Investors do also struggle with representativeness issues. They have difficulties differentiating between ‘great investments’ and ‘great stories.’ That is why stocks with fantastic growth characteristics in ‘hot’ sectors do always attract a lot of investors who expect the ‘sky to be the limit’ (which in turn represents a direct link to the above ‘lottery bias’). But investors operate in a market environment. ‘Great investments’ and ‘great growth stories’ are not necessarily positively correlated things: it is not unlikely that - when the majority of people love ‘great growth stories’ – stock prices of this type of security will be too high. And that will of course translate into relatively disappointing results in the future. The other way round: ‘not so great or actually even poor firm stories’ do not change the fact that publicly listed stocks of these firms do also have to be traded at an exchange.

Result: so as to at least trigger some demand for these ‘neglected’, impopular stocks’ prices have to be lower than what they should be in a fair value environment with only rationally trading investors. And that does then translate into higher expected returns!

Of course all this is not new. Behavioral Finance has attracted dozens of scholars as well as the popular press, but still the bias remains. Why? Well, there is also a third behavioral flaw at work, and that is overconfidence. When people are asked the question ‘Do you think that you are an above-average driver?’ far more than 50 percent reply with a firm and confident ‘YES.’ Translated into investment activity it leads to a situation in which the bulk of investors think that it is particularly true for their neighbor or ‘less experienced’ colleagues that they should refrain from high volatility, high beta riskier growth stories. But alas, reality is different.

Overconfidence Bias

Using a US stock market dataset with 41 years of data (1968-2008) BBW conclude that quintiles with the highest beta or volatility stocks underperformed those with the lowest beta or volatility by an enormous margin. Table 1 (All Stocks) and Table 2 (Top-1000 stocks) summarize some of their results:






Excess Return Rp-Rf















Tracking Error





Sharpe Ratio





Information Ratio





TABLE 1 – Highest versus Lowest Risk Quintiles (All Stocks); US Equities 1968-2009

From the first row in the table we can deduct that the lowest risk stocks outperform the highest risk ones by an annualized margin of almost 7 percent (classification based on beta) to more than 11 percent (classification based on volatility). And not just that, the returns on the highest risk stocks were far below the risk-free rate!






Excess Return Rp-Rf















Tracking Error





Sharpe Ratio





Information Ratio





TABLE 2 – Highest versus Lowest Risk Quintiles (Top 1000 Stocks); US Equities 1968-2009

Table 2 indicates that things are a little bit less extreme when we limit ourselves to the largest 1,000 stocks but the low risk anomaly remains. The excess returns are even in the case of those more solid, larger and more liquid stocks of an order of magnitude of 5-7 percent per annum.

An intermediate conclusion: What this implies for Penny Stocks

BBW do not pay special attention to the phenomenon because they proceed to focus on peculiarities of institutional investor, i.e. ‘smart money’ behavior. We will get to that in the next paragraph. But, when comparing table 1 and 2 we can conclude that the popular ‘Penny Stocks’ strategies of small investors are basically nothing more or less than an application of the behavioral lottery bias explained above. Great investment stories of very ‘cheap’ stocks are presented with great confidence and investors who do not understand that even with a stock price of $ 0.05 a drop to $0.01 represents an 80 percent negative return are betting on ‘the sky is the limit’ kind of return expectations. In the meantime brokers or specialized Penny Stock Investment Magazines, Websites etc., benefit in a similar fashion as casino owners do.

What about the professional, ‘smart money’ investors?

When analyzing the results we can understand why institutional, ‘smart money’ investors do not arbitrage away mispricing in the smallest and penny stocks. Answer: they simply can’t. But what about the mispricing in table 2, where we limit ourselves to the largest 1,000 highly liquid stocks within the US universe? BBW address this question in great detail and present convincing evidence that ‘benchmarking to an index’ might explain things to quite some extent. Institutional investors do normally – often even obliged to do so by law – benchmark their performance by comparing it with a relevant index. In-and-of-itself that is not such a bad thing. Institutional mandates are large, and overall portfolios of pension plans and endowments are often subdivided into specialist mandates categorized by asset class and / or geographical region. In such a situation benchmarking will enable better control and that is important because the overall portfolio of the institutional investors has to be in line with optimal strategic allocation requirements based on a so-called Asset Liability Model. But the thing is that to ensure that the overall portfolio’s returns do not deviate too much from expectations is not the same as saying that this should then one-on-one translate into a similar approach at the individual specialist manager level!

An example: suppose that an endowment believes that it will – on average – generate a 4% annualized return on its fixed income strategy and an 8% annualized return on its equity strategy. If the target is to achieve a 6% overall portfolio return, the strategic weights will be 50 percent in fixed income and 50 percent in equities. Whenever equities are expected to go through a bad period, fixed income allocations will be increased and vice-versa when fixed income is expected to do less well. If we assume that the average beta of the equity portfolio is 1.0 and that of the fixed income portfolio 0.0, things will translate into an expected beta for this strategy of 0.5. Within the equity portfolio this focus on a 1.0 beta does imply that the hired, external asset manager – when faced with the mandate constraints – will be wary to deviate his portfolio beta too far from 1.0. In other words: the overall portfolio management constraints of the asset owner might make it less interesting for the asset manager to arbitrage away the low risk anomaly! This is especially so when taking into account the existence of short constraints and limitations whereby he would be able to reach a 1.0 average beta even when expanding the portfolio weight of low risk stocks.

Unfortunately for the asset owner there was another opportunity to lock in the low risk, positive alpha anomaly: if the equity manager wants to use that opportunity by overweighting the low risk (low beta, low volatility) stocks in his portfolio, the equity beta would drop to let’s say 0.8. And based on what we derived in table 1 and 2 it is not unlikely that this might lead to a portfolio return of 10 percent instead of the 8 percent for the beta=1.0 equity portfolio. If we still insist on an overall risk profile with a beta of 0.5, we could follow one of a few possibilities (see Table 3):

Equity Beta

Exp Equity Return

Exp Fixed Income Return

Equity Weight

Fixed Income Weight

Exp Portfolio Return

Portfolio Beta








0.8 – TAA change







0.8 – Re-allocate Fixed Income


4% + x



7% + 0.5x


Table 3 – Exploiting the Low Risk Anomaly within an Institutional Portfolio

Table 3 shows two alternative strategies that allow the equity manager to exploit the Low Risk Anomaly. In the second row, the lower beta of the equity strategy is compensated for by rebalancing the overall portfolio. The equity weight will go up to 62.5 percent, the overall portfolio beta will remain 0.5 and the institutional end investor locks in a 1.75 percent higher expected return. Another alternative is presented in the third row: if trustees argue that this is all very neat, but to a large extent related to the persistence of the Low Risk anomaly and the relatively good performance of equities vis-à-vis bonds – something that is of course not 100 percent certain – they might want to keep the equity weight at a 50 percent maximum. Even in that case we can at the overall allocation level ensure that the equity manager is still stimulated to arbitrage away the Low Risk anomaly. How? We could do that by changing the composition of the fixed income mandate. Assuming that the beta of 0.0 for the Fixed Income strategy was the result of a pure focus on developed market, triple AAA government bonds we could add some corporate and high yield bonds, credits, emerging market debt etc.

That would then increase the expected return (and risk) of the fixed income portfolio and still allow the equity manager to lock in the potential alpha gain in Low Risk. And there are more opportunities: in case the end investor would not like to change the manager composition within Fixed Income he could also increase the beta by allowing some leverage.

The conclusion of BBW in their study: ‘smart money’ could arbitrage away the anomaly to some extent but the way benchmarking is structured inhibits them very often from having a sufficiently large incentive to do so. Their performance is judged on the basis of a tracking-error-related risk adjustment and this will penalize against over-allocation in the lowest risk quintiles who have above average tracking errors. And even when shorting would be allowed it is questionable if that would change a lot. The highest risk quintile – which would in that case be the ‘ideal’ short-selling group – has relatively high tracking errors as well, thereby making it unlikely that a good long/short strategy will ‘solve’ the issue.

Will the anomaly remain?

The anomaly is likely to persist. Not just because the evidence given by BBW above is pervasive, but also because in the end boards of trustees of smart money investors consist to a large extent of non-specialists.

Boards of Trustees: Can they really steer smart money in a smart way?

In other words: exactly those groups of people that formed the basis below the behavioral aspects of the bias! Knowing that this is the case, a ‘smart money’ investment professional will not only take into consideration the excess return opportunities by going for a deviant (vis-à-vis the index) strategy, but he/she will also incorporate that his performance will be judged by non-specialists. Suppose that markets go through a period of exuberance. Enthusiasm rules and optimism translates into very good stock market returns. BBW show that in those kind of periods higher beta stocks do actually outperform the lower beta ones, albeit that these periods do normally not last very long. And taking into account the linkage between high beta, high volatility and ‘great growth stories’ the asset manager will think like this:

I could allocate a larger portion of my portfolio to low risk, low volatility stocks that are basically neglected by other market participants. Taking into account the exuberance in the market I do of course know that I might be penalized in case the enthusiasm and optimism continue for some time. But hey, wait a minute! If I look at the exact composition of the low beta, low volatility group I sense that it is the kind of ‘lousy or at best boring’ stories that people don’t want to hear at the moment. So, in case the optimism continues and I do have to show my performance in quarterly meetings all will think that I am an idiot for buying ‘this crap’. On the other hand: if the market climate switches back to normal or even worse, I could always get away with lousy performance of the high beta, high volatility, great-story group of stocks since no one would really penalize me for holding the Google’s (NASDAQ:GOOG), Microsofts (NASDAQ:MSFT) and other great growth stocks of my universe!

An Emerging Markets and a US Application

And that is why we believe that the Low Risk Anomaly might continue to prevail. Not just in the United States, but also elsewhere. And in an international setting it will also be of extreme interest to Emerging Markets investors. They could and should translate these lessons into a larger interest in:

* Small and Mid-Cap Stocks with relatively lower betas and volatilities

* Countries within the MSCI Emerging and Frontier Markets spectrum with relatively lower betas and volatilities

* Next-11 and Frontier Markets instead of BRIC

The Power Shares S&P Emerging Markets Low Volatility ETF (NYSEARCA:EELV) could be a nice way to benefit from the above when you are interested in expanding your Emerging Markets allocation.

In case you want to use the phenomenon within the US component of your portfolio you can use the Russell 1000 Low Volatility ETF (NYSEARCA:LVOL) or the Power Shares S&P 500 Low Volatility ETF (NYSEARCA:SPLV), while at the same time staying far from the Russell 1000 High Volatility ETF.

[1] LMG Note based on the Financial Analysts Journal article ‘Benchmarks as Limits to Arbitrage: Understanding the Low Volatility Anomaly’ by Baker, Bradley and Wurgler (FAJ, Jan/Feb 2011). The authors are associated to Acadian Asset Management. Although we do focus especially on Equity Investments in our Note, the results do also apply to other asset classes.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

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