Autocorrelation Of Trend-Following Returns: Illusion And Reality by Winton Global Investment Management
In the five years prior to 2014 managed futures trend-following strategies experienced a long run of weak performance, leading to speculation that the strategy might be ‘dead’. The last six months of 2014 saw a reversal of these bad fortunes, with trend-following funds producing surprisingly strong returns. Prompted by these variations in performance, we ask: can we conclude from a series of good years that the environment is good for trend-following, so that high returns are likely to continue? Or is the opposite true? We give reasons to be skeptical, examine the evidence, and conclude that the case for either positive or negative effects is weak.
Good and bad periods for managed futures
The chart below shows how difficult recent years have been for trend-following strategies. It shows the BarclayHedge CTA index back to 1980. This is an independently-produced index which averages the performance of real funds. It includes systematic and discretionary traders, but is dominated by the performance of funds with a large trend-following component. Since 2011 this index had been in its longest ever drawdown, until the performance spurt that we saw at the end of 2014.
If last year was good, should we expect this year to be good too?
The question we address here is related to a previous client research paper, where we showed evidence that faster trend-following strategies have seen declining performance. These were changes in average performance over long periods of decades or more, whereas in this brief we are looking for short-term structure. Is a good year likely to be followed by another good year, and a poor year by another poor one?
To answer this question, we will look at the correlation between the previous and forthcoming years’ returns for each calendar year (1980 to 2014). This is called the “lag-autocorrelation” of annual returns. We can also calculate a correlation coefficient for quarterly or monthly returns. In all cases we are looking for evidence of a relationship between past and future performance.
The use of control groups: deciding on the significance of results
The raw numbers for annual, quarterly and monthly autocorrelations do not tell the full story. As we have noted before, there is a strong analogy between testing for “real effects” in financial data and the testing of medical treatments. In both cases, it is important to compare the results of any test with a control group (or placebo) where we know the effect that we are looking for is not present.
Control group 1: the influence of performance fees
We use two different types of control in order to be more confident in our conclusions. The first is a randomly generated track record with similar performance to the BarclayHedge index, but no correlation at all between successive returns. These simulated returns are generated by a random walk with drift and variance chosen so that after fees are subtracted, the mean and variance of returns is the same as the BarclayHedge index. We apply a two per cent management fee each year, and a 20% performance fee.
This simulation has an important advantage over real history: we can run it for as long as we like, generating enough data to calculate long-term averages accurately. By simulating ten thousand years3 of trading for our fictional CTA, we show that the autocorrelations on the three timescales are all negative, with values given in the table below.
This means that a “good” year is more likely to be followed by a “bad” one, and vice-versa. The same is true, to a lesser extent, for quarters and months. We refer to negative autocorrelation as ‘mean reversion’, because it implies that excursions away from a long-term mean tend to be followed by movements back towards the mean.
Performance fees cause mean reversion
We created a random fund with no correlation between successive gross returns, and then discovered mean reversion in its net performance. Why? The reason, of course, is in the difference between gross and net; the fees. Performance fees are charged only on the part of the profit that exceeds the previous “high-water mark”, and this has induced the mean reversion.
Profits which are made after a similar or larger loss do not incur a performance fee. The net returns from these profits are therefore higher than those from other profits. It is this structure in the data that induces the apparent mean reversion.
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