# On the low volatility anomaly

Low volatility investing remains very popular. According to Morningstar, the 25 US listed ETFs tracking low volatility indices managed about $35bn of assets by the end of April 2016. In the first four months of this year alone, they raised about $10bn – more than the amount raised in the whole of 2015. It appears therefore legitimate to question why investors are still adding to what appears to have become a popular and (for some) even a crowded trade.

Before reporting on our own experience and our take on the volatility anomaly, by way of introduction, I think it is important to clarify a few things.

First, low volatility investing is a general term that captures a variety of portfolio construction techniques, with the primary objective of minimising portfolio risks (not maximising returns). Hence, almost by definition, investors should not expect superior future returns from this investment style. But it is intuitive to why there is appetite for low volatility investing. Investors have had to cope with two major market corrections already this century (the tech bubble and the 2008 financial crisis), not to mention the current uncertainty over future economic growth, as well as ongoing concerns around geopolitical instability. Maybe low volatility investing is the solution to navigating through turbulent times.

Broadly speaking, low volatility investing can be achieved following either an optimisation process which requires, in its simplest form, the covariance matrix (volatilities and correlations), or following a heuristic approach which uses only the diagonal of the covariance matrix (i.e. the volatilities and assumes correlations are constant and equal to one). Both approaches come with advantages and disadvantages, but there is an incredibly large body of literature confirming that both approaches help to construct low volatility portfolios.

That investors have been adding to low volatility products, like those mentioned in the Morningstar report, is not just driven by their risk concerns. Very often, low volatility investing is referred to as the low volatility anomaly. This appears to be the greatest anomaly in finance as it flies in the face of the Capital Asset Pricing Model, which states that in order to increase returns one needs to take more risks. Empirical evidence has shown that this is not the case. Stocks with a lower historical risk profile tend to outperform stocks with a higher risk profile. But this is not just a recent finding! As early as the 1970s, Black, Jensen and Scholes (1972) discovered that high beta assets were not compensating investors for their risks as predicted by the theory. Haugen and Heins (1975) also confirmed that beta was not accurately explaining returns and Fama and French (1992) found that the relationship between risk and return, between 1963-1990, was flat or even negative. More recently, Haugen and Baker (1991, 1996, 2012), Blitz and Van Vliet (2007) confirmed that even in the most recent period this negative relationship between historical volatility and future equity returns holds.

## Our evidence in the UK market

Rather than focusing on US or global equities, which have been an object of thorough analysis by academics and practitioners, we turned to our domestic UK equity market. Our dataset includes all large-cap stocks listed on the LSE since 31 January 2001. For this test, only those stocks with a positive weight in the index at month-end are considered. Securities that are still trading but are not part of the index are excluded.

In order to prove the existence of the low volatility anomaly, we computed the volatility of each stock over the 12 month time-window using the historical returns computed on the total return times series and ranked them into quintiles at the end of each month. In the subsequent month, we measured the performance and the risk of the five portfolios, assuming stocks are weighted inversely proportionately to their volatility levels. No transaction costs are included in this simulation as we are only interested to see if the low volatility anomaly also holds among UK large-cap equities. The evidence that the low volatility anomaly holds is usually proven by showing the strongest performance achieved by the bottom quintile versus the performance of the top quintile. However, it would be encouraging to see a decreasing and gradual trend throughout the quintiles. Exhibit 1 shows the annualised average monthly return of the five quintiles.

**Exhibit 1 - UK equities, annualised historical returns**

Source: Sarasin & Partners, Bloomberg. The performance of the quintiles is derived by averaging the monthly returns achieved by weighting inversely proportionately to the volatility levels the stocks ranked by volatility within each quintile, at the end of each month. Neither transaction costs nor other fees area considered. Performance is reported in GBP and includes dividends.

Firstly, we can confirm that in the period between January 2002 and May 2016, a portfolio invested in the stocks with the lowest historical volatility, ranked in the bottom quintile and weighted inversely proportionately to their volatility levels, achieved an annualised return of +8.9% (GBP), while the riskiest stocks returned only +5.1%. Hence the volatility anomaly holds among UK equities too. Secondly, the much hoped for negative trend across the five quintiles is not observable. Both the second and third quintile, in fact, achieved higher returns than the bottom quintile.

Exhibit 2 shows the historical volatility of the five quintiles, and in this case the gradual trend is observable. Starting from the bottom quintile, the volatilities gradually increase until the 5th and most volatile quintile. From this evidence, we can certainly confirm that the stocks with the highest volatility profile have delivered the highest risk, but also the lowest returns.

But how can this be explained? Is this an arbitrage? Can investors buy companies with a lower risk profile, hold them for a period of time, and expect to get a superior return than the benchmark? Are there any other factor tilts hidden behind low volatility that could explain the excess return? Perhaps value? There is enough support for the fact that the low volatility anomaly is not an arbitrage opportunity, and it has been explained over time using behavioural arguments and through factor tilts.

**Exhibit 2 - UK equities, realised volatility**

Source: Sarasin & Partners, Bloomberg. The chart plots the historical volatility of the entire time series of the total returns of the five quintiles as reported in Exhibit 1.

Blitz (2016) reported that low volatility strategies show a performance not explainable by the Fama-French HML value factor. Nevertheless, historically there were times when there was an overlap with the value factor, for example during the tech bubble, when low volatility strategies were invested in value stocks.

But maybe there is a simpler explanation. Maybe the low volatility anomaly could be explained just by the “volatility-drag”. Volatility is a cost which negatively affects compounded returns. When invested, investors care about geometric returns rather than arithmetic returns, as returns compound. For instance an investment that returned -20%, regardless of the period in question, requires a return of +25% to return to break-even. It is possible to prove that the larger the volatility, the larger the drag. Cooper (2010) linked the geometric return (𝜇_{g}) to the arithmetic return (𝜇_{a}), through a Taylor series expansion:

In other words, in presence of risk, compounded returns will always be lower than simple arithmetic returns. Maybe this can help to reveal what lies beneath the success of the low volatility anomaly. Low volatility stocks are not in themselves generating superior returns, which also seems to be widely supported by academics, who refer to this phenomenon as an ‘anomaly’ rather than a ‘risk-premium’. Through our simulation we were also able to find out that the second and third quintiles were even more profitable than the bottom one. Hence low volatility stocks are not the necessarily the most profitable stocks, but given the lower realised volatility they have a much lower drag which enhances the compounded effect.

**Exhibit 3 – Cumulative returns of the bottom and top quintile**

Source: Sarasin & Partners, Bloomberg. The chart plots the cumulative returns of the bottom and top quintile. It assumes monthly rebalancing and neither transaction costs nor other fees are considered.

Even though Exhibit 1 shows a relatively narrow gap between the returns of the bottom and top quintile (3.8%), having accounted for the volatility levels, the gap increases substantially. Exhibit 3 clearly shows the substantial outperformance of the bottom volatility quintile. After 173 months, the bottom quintile portfolio outperformed the top quintile by 189% or 7.6% per annum which is very close to the difference of the two geometric returns, as estimated using the formula described above.

## Concluding remarks

Trying to be a bit provocative, maybe the anomaly – though well documented and supported by analysis using techniques that go beyond those adopted within this note – is not an anomaly as such. Maybe the low volatility anomaly should be simply understood as the advantageous compounding effect derived by avoiding risky stocks. In fact, low volatility strategies underperform the market cap remarkably during sharp market rallies, indicating that it is the return associated with the risk taken that counts, and not just the simple risk metric.

Therefore, I do not believe there is an arbitrage available for investors. I don’t believe there is an anomaly as such, but I believe investors need to be aware of the volatility drag when investing. However, they should not exclude riskier investments than those suggested, for instance, by a minimum variance portfolio, provided that those higher risks are accompanied by superior expected returns. Hence I believe that in order to exploit the great benefits of low volatility investing, an investor should combine this investment approach with other factors like momentum, for example, as it is important to minimise the risks around a steep trend. Buying companies that move sideways with low variability may be a safer investment, but certainly not a profitable one.

## References

Baker N. and Haugen R., “Low Risk Stocks Outperform within All Observable Markets of the World”, SSRN working paper, No.2055431, 2012.

Baker M., Bradley B. and Wurgler J., “Benchmarks as Limits to Arbitrage: Understanding the Low-Volatility Anomaly”, Financial Analysts Journal, 67 (2011), pp. 40-54.

Black F., Jensen M. and Scholes M., “The Capital Asset Pricing Model: Some Empirical Tests.” Studies in the Theory of Capital Markets, Jensen, M.C. (Ed.), Praeger, 1972.

Blitz D., Falkenstein E. and Van Vliet P., “Explanations for the Volatility Effect: An Overview Based on the CAPM Assumptions” Journal of Portfolio Management, 40 (2014), pp. 61-76.

Blitz D. and Van Vliet P., “The Volatility Effect: Lower Risk Without Lower Return” Journal of Portfolio Management, 34 (2007), pp. 102-113.

Blitz D., “The Value of Low Volatility”, SSRN working paper, No.2730557, 2016.

Cooper T., “Alpha Generation and Risk Smoothing using Managed Volatility”, SSRN working paper, No.1664823, 2010.

Clarke R., de Silva H. and Thorley S., “Know Your VMS Exposure” Journal of Portfolio Management, 36 (2010), pp. 52-59.

Fama E. and MacBeth J., “Risk, Return and Equilibrium: Empirical Tests” Journal of Political Economy, 81 (1973), pp. 607-636.

Haugen R. and Baker N. “The Efficient Market Inefficiency of Capitalization-Weighted Stock Portfolios” Journal of Portfolio Management, 17 (1991), pp. 35-40.

Hsu J. “Value Investing: Smart Beta versus Style Indices” Journal of Index Investing, 5 (2014), pp. 121-126.