A Review: “Two Centuries of Trend Following”, from Victor Niederhoffer

April 29, 2014 |

The paper "Two Centuries of Trend Following" by Lemperiere, Derenble, Seager, et al of Capital Fund Management purports to show that trend following has been profitable, over a wide range of markets, consistently over 200 years. It deserves to be reviewed as it represents a case study of the statistical practices, and armchair explanations that are sometimes used to justify a system that in the most recent five year period has lost its mojo. Rocky has asked me to review it.

The amazing thing is that the authors seem to know how to compute hyperbolic tangent regressions, and compute the duration of a drawdown given a sharpe ratio, yet they seem completely unaware of the problem of multicollinearity, overlapping observations, and lack of independent observations.

In a nutshell, they compute hundreds of thousands of means, and they combine them and measure how far away from randomness they are. Recall that the average of two random observations is about 0.7 times as variable as one observations. The average of 100,000 observations is about 1/320 as variable as 1 observation.

They report t statistics of 5 to show that their results are non-random. But, but, but. If you have say an expectation of 1 with a standard deviation of 10, ( lets say 1% for a typical market ), and you divide 10 by 320 (i.e. sigma/sqrt of n), you come up with a t of 32… none of the markets they cover are independent. For example, they use 7 and 10 year interest markets, and 7 stock index markets, and apparently treat each observation as independent. Instead of dividing by the square root of thousands, they should be dividing by the square root of tens depending on the years they consider, and the overlap of the running 5 month values of the independent variable.

Their results, as biased as they are are not meaningful in any practical or economic sense. When they look for the effect of subsequent profits of trend following on past result, they come up with a slope of 0.04. What does that mean economically. If the profits of trend following in the last month was 1%, then the profits predicted in the next month would be 0.03%. The variability presumably is 330 times as great as the expectation.

The authors note that over all markets over the last 5 years, trend following has been flat. Considering that the market likes to give you a profit from a system on a market like lean hogs that trades 1/1000 as much as stock indexes in order to lure you in, the fact that it hasn't made money is very negative. Also, the performance of trend following funds tracked by all the services shows that in practice the trend followers have worse results than the averages.

Even though trend following doesn't work in the real world, the authors have several paragraphs on why it should work. They talk about the slow response to Fed actions, and the tendency of heuristics to follow what works in the past. These are arm chair explanations out of the bush with no statistical support, although their ideas that Fed qualitative actions show momentum is a valid one. The authors might benefit from reviewing Bacon on ever changing cycles or being behind the form. Perhaps I am missing some nuggets of gold in the above paper, and I am open to any corrections in my analysis, or areas that favor trend following that I have overlooked.

To hear Mr. Simonder defending the performance of trend following funds which are apparently down 4% from 2008, versus 130% up for S&P as of May 2013.

Boris Simonder writes:

A more objective description would be that I'm defending against sweeping comments that trend following "doesn't work in real practice" or "in practice the trend followers have worse results than the averages". Now you seem to have backtracked a bit by admitting the fact that there are advisers who have performed better and made money, now and in the past.

As for the percent performance of S&P, 130% as of May, 2013, this seems to be taken straight from the article you posted, although, I only see 86% between 2009 - May, 2013. (Cash index). For what it's worth, here are some TF's with better results than the averages (equities) and in real practice.

Name

Email

Website

1. Ronald on April 28, 2014 4:47 pm

Hi, Of what little i know, trend followings edge is in the money management, not the signals themselves. Perhaps theres someone here that has run tests with different allocation models to see to what extent that changes the bottom line.

I am not skeptical of trend following, nor am i skeptical of moon phases - if it works for someone and he/she makes consistent profits year after year then i take my hat off, i mean, there are smart people out there who manage a lot of money via tf and have been doing so for decades - how could it be all wrong?

Hope i did not ask anything too stupid,
No disrespect to anyone, or anyones method
Thanks

2. John B on April 28, 2014 9:37 pm

I must note that there quite a few TFs out there who have made a substantial fortune, including your old friend George Soros who has been a macro-trend follower for most of his life, as well as others such as Louis Bacon if I recall correctly. It just so happens to be my philosophy as well, that is, to find a market with a movement so obvious that it cannot help but become true, and take the trend with so much pressure on it that it just has to move.

I’ll note the two easiest trends and one developing trend

Back around 7 months ago, I was all about interest rates. They had to move up, and the more the news and media talks about it, the more self-fulfilling the prophecy seems to become. But nonetheless, I always take the easy, probable, and almost certain trend over.

Before interest rates, I was all about Nat Gas, the down trend was coming to an obvious end, and was so cheap that everyone was buying futures. Surely you can’t argue that once NG reversed and started moving in, it became flooded with TFs who saw that more and more people were looking to relieve themselves from the constant threat of rising crude prices and subsequent rises in refined products. Nat gas offered an alternative to some significant fraction of the market who were willing to make the switch (and they did), so we TFs just…you know, followed along.

The developing trend (I think, but it is not definite that it will continue much more) would have to be with emerging markets, over the last few months people were just draining emerging markets ETFs, preferring to store that capital in US stocks, and without capital, EM will fall into a vicious cycle of capital shortage, then underinvestment, then falling growth…to be continued. I believe EM is unfortunately in a downward trend, which breaks my heart because I know it should not be, but i know better than to defy the trend.

3. Slav D on April 29, 2014 12:10 am

Hi Victor,
Do you think that occasional parabolic rises and drops that occur in commodity markets aren’t frequent, and of a high enough magnitude to compensate for all the commission, slippage and stopped out trades that a trend following break out system employed on a 100+ futures portfolio would incur?
Didin’t even Mr. Soros say that once he identifies the so called bubble he buys and rides it as it inflates, stating that very large profits are to be extracted from these extended runs.

Even though I have tested various simpleton trend following break out systems on large futures portfolios and more often than not they have tested well,(if you don’t mind hair pulling drawdowns that accompany sizeable CAGR) I don’t understand how large funds that move \$billions can seek diversification in illiquid markets like hogs as you have stated above. Perhaps liquidity risks and volume oughta be incorporated into these studies as Malaysian Palm oil isn’t going to be able to absorb large \$ order without running the market away from yourself? Yet in most portfolios trendfollowers treat ES with same position weight as say Coal contracts.
Having said that do you believe that a smaller player with \$10mil or under AUM could potentially benefit from diversification in trading these illiquid markets as his impact is significantly smaller?
Another observation is perhaps ever since the turtles, covel, and others started employing/promoting trendfollowing systems even reaching people like me at retail level and attracting Billions of \$ at institutional levels perhaps they are killing each other off racing for the same entry and exit signals overcrowding the space and money is to be made FADING them?

Slav

4. Slav D on April 30, 2014 1:03 am

Soo much confusion:

Just read this interview with Richard Dennis from 2004 Stocks and Commodities October edition.
“Why do systems work and what market characteristics do they exploit?

Richard: ” Historically systems have worked because of serial correlation.There was an implication that the price would continue to move in the same direction. …
A clever trend following system just tries to overlap these momentum segments, so each of these signals reinforce the others, so that you get a prediction with more force.”

Didn’t the chair explicitly state that negative serial correlation is precisely why trend-following systems don’t work!

In addition Richard was admittedly starting to employ counter trend filters to his trend-following systems.

5. vicasdfasdf on April 30, 2014 12:16 pm

some markets have positive serial correlation like fixed incomes. also probably the grains during the active periods. The main reason trend following doesnt work aside from the rake and the bad fills is something that the authors cover. It shouldnt work because prices are moved away and predicted to move away from the previous price, which presmuably was a homoestatic or equilibrium one. the things that move prices are ephemeral in the main. so going with the ephemeral moves and exacerbating them shouldnt work in pracite. the authors claim it did work in practice. doubltless it worked during ceretain markets, certain periods, certain times especaily when there were no futures and the Fisher effect crested the illusury gains. and doubtless it works to lure people into putting big money in like the sports owner and the Large man who made money with small bucks, and then lured big public funds in where they were able to give bak to the market so much more. The fact that some people make money, e/g in the stock market, and the prices were moving consistently in a direction is not a supporter of trend following. many people think they follow trends and make money, but that deosnt mean that on a systematic non-random-non anecdotal basis that the trend following works. usually i say, with wiswell that ” a system , even a bad system is better than no system at all. “. however, i dont think that applies to trend following systems as it exacerbates the bad for all the above reasons. vic chair

6. Manuel on May 28, 2014 11:49 am

Oh, if only JP was around to debate you….one of theeee coolest operators in the business and also outside of it.
RIP JP

7. JP Bouchaud on June 19, 2014 8:54 am

Dear Victor

We discovered your review of our paper and just wanted to address a few of the points you raise and correct some erroneous statements.

a) We do not stitch our time series together, but simulate a standalone P&L equally allocated between the various instruments. The correlations between markets are indeed present but irrelevant to the estimate of the t-stat which is simply estimated using the daily returns of the strategy i.e. signal*next day (or next month) returns,
which are for all intents and purposes uncorrelated (even if the signals themselves are obviously not). The resulting t-stat measurement we feel is made more robust by the fact that t-stats are also significant for all sub-periods and all individual asset classes. We therefore don’t understand your comments about overlapping 5 month windows or the correlations between tickers.

b) Your interpretation of our regression results seems strange. We are simply looking how much the market moves on the subsequent day (on average of course), conditional to a certain value of the signal (the normalised five month trend). We find that when the signal is 1 at one sigma (not one percent!), the next day return is three times bigger than its long term average, i.e. the return of the long only strategy. We find difficult not to see this as “economically significant”; besides,
the trend following industry has certainly made very significant profits in the last thirty years.

c) Our “armchair explanations” are proposed as possible (plausible) explanations for which we do not have direct statistical evidence. Still, we refer to recent, well documented academic papers based on surveys that pretty convincingly show that most people have “extrapolative expectations”, i.e. they tend to follow trends. See Shiller, Menkhoff, Hommes, Greenwood & Schleifer, etc.

Looking forward, we believe that long term trends will persist, albeit delivering a strategy with a low Sharpe ratio.
There is however only our best guess based in part on the results of our paper that shows that trend following has delivered a highly significant Sharpe over a long history.

Sincerely yours — the authors of “Two centuries of trend following”