Typical returns of a trend following strategy carry features of a “long vol” position and have positive convexity. Typical returns of long only strategies, such as risk parity, rather exhibit a “short vol” profile and negative convexity. This makes trend following a useful complement of long-only portfolios, by mitigating tail risks that manifest as escalating trends. Options are naturally a cleaner hedge for tail risk, but have over the past two decades been prohibitively expensive.

Dao, Tung-Lam, Trung-Tu Nguyen, Cyril Deremble, Yves Lemperiere, Jean-Philippe Bouchaud, Marc Potters – CFM (2016), “Tail Protection for Long Investors: Trend Convexity at Work”. 

The below are excerpts from the paper. Headings, links and cursive text have been added.

Comparing trend following fund returns to hedge fund returns

“Since a majority of investors have a long exposure to stock markets, a strategy that allows one to mitigate losses when the market goes down sounds like a very useful idea, and, if available, should be highly valued by those investors. As has already been pointed out several times, trend following strategies appear to offer such a downside protection.

“.. if one plots the monthly performance of a global hedge fund index… as a function of the contemporaneous market return, as we do in Figure 1, one sees not only a strong positive correlation between the two (ie. when the market goes down, so do hedge fund returns), but also a negative convexity. [the hedge fund index loses more when the S&P plunges than it gains when the S&P soars.]”


“One interesting exception is the trend following strategies followed by CTAs…We illustrate these conclusions in [the figure below]… The aim of this paper is to understand the mechanism at work behind the convex behaviour of CTAs’ performance, and to find a better way to quantify it, such that we can be sure that this property is not a statistical fluke.”


The importance of long term and short term variance

“In practice, most trend following funds use a combination of exponential moving averages to compute their trending signals… the trend following performance, once averaged over a suitable period of time… can be rewritten as a difference between a long term volatility (the square of the exponential moving average of past returns) and a short term volatility (the exponential moving average of the square of daily returns).”

“…the performance of a trend following strategy…can be thought of as the difference between a long-term and a short-term variance.”

Convexity at work on CTA indices

“We will consider the SG CTA Index, and show that our simple trend strategy allows us to reproduce its main features… provided an appropriate value of the effective time horizon… is chosen.”


“The natural idea is not to take S&P500 Index as a reference, but rather a long-only risk managed diversified portfolio, and show that a diversified trend following strategy is convex with respect to this product… CTAs do provide a very significant protection against the potential large moves of our proxy Risk Parity portfolio


Trend following versus option strategies

“The premium paid on option markets is however too high in the sense that long vol portfolio have consistently lost money over the past 2 decades (barring the 2008 crisis), while trend following strategies have actually posted positive performance. So even if options provide a better hedge, trend following is a cheaper way to hedge long-only exposures.

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Saeed Amen is the founder of Cuemacro. He has a decade of experience creating and successfully running systematic trading models at Lehman Brothers, Nomura, the Thalesians and now at Cuemacro. Independently, he runs a systematic trading model with proprietary capital. He is the author of Trading Thalesians – What the ancient world can teach us about trading today (Palgrave Macmillan). He graduated with a first class honours master’s degree from Imperial College in Mathematics & Computer Science. He is also the co-founder of the Thalesians.