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.

*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.__”