## An Analysis of Expected Returns of Trend-Following Strategies

Author: **Nilsson**

Title: **Trend Following – Expected Returns**

Link: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2689861

Abstract:

This paper describes how to create ex-ante expectation for generalized trend-following rules. This report first study the effect of trend-following rules applied to random data with varying degrees of drift and autocorrelation. There is a positive relationship between drift, autocorrelation and the theoretically extractable Sharpe ratio for a trend following strategy. Drift is more important, since it is theoretically unbounded, but strong auto-correlation can create positive returns in the absence of long term drift. The realized Sharpe ratio of a trend strategy is proportional to the absolute drift and auto-correlation of a market above a threshold. From a practical perspective, this means that anyone engaging in trend following strategies, should expect to generate positive returns if the drift is strong enough or if there is enough autocorrelation. Conversely, when there is no drift or auto-correlation, trend-following is not profitable. There is a strong preference for slower strategies under drift and transaction costs. Returns are compared to actual markets and indices of active traders (managed futures) and a high correlation is detected to the results in this paper. Trend-following should never be applied to a single market on a stand-alone basis. That said, even portfolios of trend following strategies have low expected Sharpe, especially so when the systems generated correlated trades. In the end, trend-following does not necessarily need uncorrelated markets, but rather uncorrelated system-market returns. A nuance that is often lost.

Notable quotations from the academic research paper:

"In this report, the author has derived and verified the importance of auto-correlation and risk-adjusted drift for simple trend based strategies. After having reviewed the facts, auto-correlation for actual markets is close to zero (at least over the last 15 years) and most markets have a low drift. Thus, any return generated from medium to long-term trend following strategies is mostly due to market drift, rather than auto-correlation.

Trend-following, on a stand-alone basis, is a low Sharpe strategy, with an expected per-market Sharpe of approximately 0.15, depending on the drift of the underlying market. From there, the author performs an analysis in terms of market / system-market correlation which allows a predication of the expected Sharpe ratio for portfolios of strategies.

Trend following depends, not only on having a low market correlation, but is more dependent on having a low correlation between trading-systems. To some extent, this is one of the reasons for why trend-following is sometimes referred to as a portfolio effect. Most successful trend-following results have been recorded in diversified portfolios, rather than for single market traders.

This report rests on the assumption that it is correct to approximate the result and correlation for other trend strategies with a long term momentum strategy. This is not always the case as there are trend strategies that are not perfectly correlated to the tested strategies.

When compared to actual hedge fund results, this report finds that two (Barclay and Credit Suisse) out of three indices tested, mirrors the results of a correlation driven reduction in the realized Sharpe. Larger managers, in more concentrated indices (Newedge CTA), have managed to generate better results. As a first approximation, attributing this to higher concentration to liquid markets (equities and fixed income) as well as potentially having access to diversifying strategies seems prudent.

For traders that using trend-following strategies, it would seem prudent to continue to look for uncorrelated markets/trading systems while trying to explicitly understand why a market would have a persistent auto-correlation and/or a high risk adjusted drift.

A more extreme version would be to build a large number of uncorrelated systems and apply them to a set of markets. There, despite having a long expected Sharpe ratio for each system, it is still possible to create diversifying return streams. This may no longer be a trend-following strategy though."

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