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The Taming Of The Skew

Campbell White Paper Series

Investors are often concerned about the negative skewness, or left-tail asymmetry, of equity returns. In response, they seek risk-mitigating strategies to provide offsetting returns when equity markets fall. Due to their association with positive skewness, trend-following strategies are popular candidates for risk-mitigation or crisis-offset. This paper explores how a trend-following portfolio can achieve positive skewness, and finds that time variation in risk is the primary factor. In fact, any portfolio with a positive Sharpe ratio can achieve positive skewness simply by varying the level of risk taken through time.

To illustrate this point, three different approaches to risk management are applied to trend-following: constant risk targeting (CRT) achieves zero skewness, signal risk targeting (SRT) achieves positive skewness by chance, and equity risk targeting (ERT) achieves positive skewness by design. Each risk targeting approach is studied from 1990 to 2016. The key features are summarised in Fig.1.

Finally, the paper turns to investor objectives and discusses the distinction between a diversifier and a complement. A diversifier is an investment strategy which has accretive portfolio benefits with the goal to increase the overall long run Sharpe ratio of a relatively diversified portfolio. A complement is an investment strategy which is designed to best improve a concentrated portfolio by exploiting conditional correlation. In this study, the CRT was found to have the best stand-alone performance and was therefore the best diversifier. The ERT portfolio provided the best equity protection with the highest risk-adjusted return during crisis periods. The SRT portfolio achieves the highest skewness, but with less crisis alpha than the ERT and a lower Sharpe ratio than the CRT. This highlights the fact that positive skewness alone is not enough for risk mitigation; timing matters.

Skewness is simply an outcome; the ultimate decision of whether or not to vary risk over time depends on the investor’s objective: to diversify or to complement?

Fig.1
Source: Campbell & Company

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