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The paradox of low volatility

In college finance courses we are taught about the risk-return trade-off where expected return rises with increased risk. This insight is formalised in the Capital Asset Pricing Model (CAPM), which specifies the amount of compensation an investor needs for taking on additional risk.

In college finance courses we are taught about the risk-return trade-off where expected return rises with increased risk. This insight is formalised in the Capital Asset Pricing Model (CAPM), which specifies the amount of compensation an investor needs for taking on additional risk.

Although the CAPM is a beautiful and elegant theory there are many issues with its application in the real world.

Although the CAPM is a beautiful and elegant theory there are many issues with its application in the real world. One fascinating anomaly Quants observe is that low volatility, less risky stocks appear to outperform high volatility stocks over the long term on a risk-adjusted basis.

Let’s replicate this anomaly ourselves in a backtest and discuss the results.

The methodology employed here is simple by design. The investment universe comprises all stocks in the FTSE World index from January 1994 to March 2016 (22 years & 3 months). At the start of every month, the volatility of every stock is calculated where volatility is defined as the annualised standard deviation of the percentage price changes over the last 24 months. All stocks are then ranked from low to high volatility and split into deciles, with 10% of the market capitalisation of FTSE World in each decile. The returns of each decile over the month are then determined. This process is repeated at the start of every month and the return and volatility for each decile calculated for the entire period.

The striking results of the backtest are shown in Fig. 1. As we move from left to right, from the lower volatility deciles to the higher volatility deciles, the returns seem to decline. But what is particularly noticeable is the almost monotonic decrease in Sharpe ratios, a measure of excess return per unit of risk.

Low volatility stocks have positive alpha, while high volatility stocks have negative alpha.

Another way of displaying the backtest results is to plot the return against beta (the volatility of the stock compared to the market) of each decile. If the CAPM held true then all the deciles would lie close to the Security Market Line (SML) meaning excess return is a linear function of beta. Clearly this is not the case – if anything the deciles seem to form a line perpendicular to the SML! Low volatility stocks lie above the SML and hence have postive alpha, while high volatility stocks have negative alpha.

Academics have shown that this anomaly goes back to 1963 in the US, and it occurs in both developed and emerging markets.

Explanations for low volatility outperformance

There are several plausible explanations for this anomaly.

One rationale might be due to fund manager compensation where the manager is paid a bonus if performance is sufficiently high. More volatile portfolios increase the expected value of the bonus.

Another explanation is that fund managers favour newsworthy stocks, for which they can make a compelling investment case. But because of the relatively intense newsflow surrounding these stocks, their returns are often volatile. Baker & Haugen (2012) say agency issues such as the two just described create excess demand for highly volatile stocks which boost prices and depress future expected returns.

A recent paper by academics at the London School of Economics suggests the anomaly could be related to the so called “Curse of the Benchmark.” If the price of a stock doubles and a manager has a half-weight relative to the benchmark then the active bet doubles. On the other hand if the price halves then the negative active bet halves also. Hence volatile stocks have the greatest potential to cause underperformance meaning managers have an incentive to buy such stocks and neutralise positions relative to their benchmark.

Whatever the true explanation for this observed anomaly the simple backtest described above provides powerful empirical evidence of the risk-adjusted outperformance of low volatility stocks.

References

Ang, Andrew (2014) Asset Management Oxford University Press

Baker, Nardin & Haugen, Robert (April 2012) Low Risk Stocks Outperform within All Observable Markets of the World  LowVolatilityStocks.com

Blitz, David & van Vliet, Pim (April 2007) The volatility effect: lower risk without lower return Robeco Asset Management

Vayanos, Dimitri & Woolley, Paul (March 2016) Curse of the Benchmarks London School of Economics

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