We have all heard the timeless adage **“Cut your losses, let your winners run”**, which forms the central tenet of Trend Following.

Proverbs travel through generations and their origins get lost, so I was quite interested when I found out about an 1838 book, The Great Metropolis, Vol II by James Grant, tracing back the saying to eighteenth century British economist and trader **David Ricardo** (I actually thought that this legendary trading maxim was introduced by Jesse Livermore in Reminiscences of a Stock Operator).

The actual wording was:

“Cut short your losses,” – Let your profits run on”

and further description can be found in the book:

It does seem that smart traders were already using trend following principles as far back as a few centuries ago.

I did find out about this book thanks to a very interesting paper by Stig Ostgaard: On the Nature and Origins of Trend Following, which retraces the early history of trend following, from Ricardo all the way to trend following pioneer Richard Donchian. Well worth a read in my opinion.

### More History, and Correlation

Another very good and interesting document I came across recently is a presentation by Trend Following Wizard Liz Cheval, which can be found on her EMC Capital CTA website.

The presentation is called “Let’s get negative: Correlation and the case for Managed Futures” and is divided in two parts.

The first part is also historical. First using the Nasdaq as an example, it describes market manias (a.k.a. supersized trends) and why they are bound to repeat (**Investment Psychology**). The main concepts are:

**Chrono-centricity**: Each generation believes they are on the cusp of history and what is happening to them is so important that it will impact the world deeply and permanently and that this is the beginning of a new era (as experienced during the internet boom, which actually generated very similar reactions to the telegraph, as per the book The Victorian Internet).

**Short financial memory**: In A short history of financial euphoria, John K. Galbraith explains that non-stop cycles of boom and bust are bound to repeat due to the brevity of financial collective memory: every 20 years, we collectively forget what has happened in the last 20 years.

**Inability to predict**: using after-the-fact “funny” examples of prediction quotes, Cheval shows that we cannot rely on experts and analysts to make reliable forecasts. One such is, then IBM Chairman, Thomas J. Watson declaring in 1943: “I think there is world market for about five computers”

The presentation then moves on to second part: **mathematics of correlation/diversification**.

There is nothing revolutionary new: talking about Markowitz and the Modern Portfolio Theory, Cheval shows that you can put a more risky asset in a portfolio and improve its risk-adjusted return. The following chart taken from the presentation, shows how adding the blue “ugly curve” to the green “beautiful” one does improve its return and eliminate its volatility as per the orange curve (the two equity curves were engineered and do not represent actual assets).

The interesting point is that it is possible to improve performance by adding curve “blue”, an asset with negative geometric average return (but with positive arithmetic return). Intuitively, most people would tend to think that curve “blue” is a “dud” and can in no way improve performance. Cheval likens this curve to Managed Futures, which she compares to the “investment ugly sister” (high drawdowns, volatility, etc.) that can actually greatly improve an investor’s diversified portfolio, thanks to their low to negative correlation and positive returns.

The discussion and clarification on correlation is interesting. Everybody (myself included) must be falling prey to some misconceptions/mis-uses of correlation in everyday language. Common language has it that two things are correlated if they “move together” and anti-correlated if they “move opposite to each other”.

As such most investors would probably think that the “ideal” asset would be one negatively correlated during an equity bear market and positively correlated during a bull market (ie the best of both worlds). Not quite.

As Liz Cheval puts it – in plain simple English but correct definition:

Correlation is a numerical measure of the tendency for two assets to concurrently under-perform or over-perform their average returns by the same number of standard deviations.

So, not “moving together, or opposite to each other”, but rather away from their averages in the same, or opposite direction (in their respective magnitude).

Meaning that an asset can be strongly negatively correlated (even perfectly at -1) to another one, with both being in a bull market as illustrated by this plot of two equity curves, which concludes this article:

Correlation of assets « 4pi Logic// Apr 11, 2011 at 3:40 pm[...] via Eighteenth Century Trend Following and More History | Au.Tra.Sy blog – Automated trading Syste…. [...]

Monday links: learn to survive Abnormal Returns// Apr 11, 2011 at 5:30 pm[...] The tenets behind trend following are old. (Au.Tra.Sy Blog) [...]

George// Apr 12, 2011 at 10:38 amHi Jez,

Thanks for the post. Intriguing. I like Liz’s voice. :) My 3 cents:

1.

After watching Liz, the problem (to me) is the 25%/75% allocation should be maintained daily. That is the essence. Without it, it doesn’t work. However, take into account the daily rebalancing costs, friction…

2.

Looking at Asset A (the ugly sister). Liz says it has positive average return. I guess many readers shake their heads on it, but she is right. And it beautifully reveals the difference between the arithmetic and geometric mean. And this is almost everyone in the blogosphere tends to forget. Asset A has negative arithmetic mean return, but positive geometric mean return (as Liz says correctly). Please blog authors, put the geometric mean too into your performance metric.

3.

As a very good, enjoyable, not too long, simple-English-language book about combining assets for decreasing volatility and increasing profit and about the importance of correlations (not daily rebalancing), I would happily suggest The Intelligent Asset Allocator by Bernstein.

http://www.amazon.com/exec/obidos/ASIN/0071362363/autotradblog-20

Jez Liberty// Apr 12, 2011 at 11:24 amGeorge, Not too be pedantic (but this is important distinction), but I believe this is the other way around: geometric mean return is negative but arithmetic mean return (which is what is used in the MPT by Markowitz – which he is sometimes criticized for it) is positive. I have not done any calculation on it but since end equity of curve blue is less than starting equity, it has to be a negative… And since she is saying the average return is positive, I take it she means the arithmetic average return.

Actually, the geometric return can never be higher than the arithmetic return, because of the “variance drain”. Ralph Vince describes this as the Pythagorean Theorem (in his LSPM book):

But I agree with your main point, geometric average return is important in general.

Thans for the book suggestion. I’ll check it out!

George// Apr 12, 2011 at 11:52 am” I believe this is the other way around: geometric mean return is negative but arithmetic mean return”,

Exactly, Jez. You are right. It is the other way around.

Rick// Apr 12, 2011 at 12:21 pmHello again,

A high school kid knows that the geometric mean applies only to positive numbers. As soon as an asset produces negative returns the use of the geometric mean makes no sense.

Then, on hindsight, one can match exactly series that produce perfect correlations, like in he presentation. The presenter though implicitly assumed a monthly correlation of returns. If one considers a yearly rolling correlation then the assets are perfectly correlated. Thus, the particular example she presented does not eliminate risk but only smoothes the equity curve. Actually, she confuses the two. It’s a pity she does. Anti-correlation aims primarily in diversification, not smoothening of returns. If you try to smooth returns, you are essentially correlated. You don’t believe me? See what happened to many funds in 2008.

I argue as a conclusion that the presentation mixed up equity smoothening with diversification.

Jez Liberty// Apr 12, 2011 at 1:09 pmA high school kid could probably also run a quick google query to find out that the geometric mean return is calculated using the return multiplicators (ie 0.95 for -5%, 1.2 for 20%) and not the actual percentage returns, thereby avoiding the “negative” numbers issue…

Cheval does not “confuse” risk and equity curve smoothness, she merely presents correlation and diversification using the MPT framework, which DOES equate risk with volatility (which many critics have criticized, but this is beyond the point of the presentation). and Cheval simply stays with this nomenclature.

This “variance=risk” relationship is still used by many investors, fund allocators, traders, etc. so to reach out to them, it does make sense from a marketing point of view to “speak their language”.

Moreover, the presentation nicely puts Markowitz’s theory into historical context. It is easy to find its flaws decades later, but the overall concept was still groundbreaking at the time.

Regarding your other point, I think you have it backwards, It is diversification which aims at adding low to negative correlations to the portfolio (not the other way around), a consequence of which would be reduced volatility (ie smoothening of returns). Of course, correlations being what they are (non-stationary), one cannot rely too much on historical values for optimization/risk management.

And by the way, I am sure 2008 was an excellent year for Liz Cheval and her fund (and many other trend following funds, which very likely adhere to the concepts laid out in her presentation)

PS: it seems that you did not take RiskCog’s “hint” in from the last post – would be great if you did..

Rick// Apr 12, 2011 at 1:34 pm“A high school kid could probably also run a quick google query to find out that the geometric mean return is calculated using the return multiplicators (ie 0.95 for -5%, 1.2 for 20%) and not the actual percentage returns, thereby avoiding the “negative” numbers issue…”

So you are telling us here that the geometric mean of -5% and 7% is equal to the geometric mean of 0.95 and 1.07.

Are you kidding us? The former is an imaginary number.

The return multiplicator tell you how much money you have left in your account as a percentage of equity. Not your return. They can not be used to study return correlations. Go back to school before you blog. You are not behaving yourself with the visitors to your naive blog who are trying to help you.

Bye-bye…

Jez Liberty// Apr 12, 2011 at 2:27 pmGeometric Mean Return for Dummies

Eventhorizon// Apr 12, 2011 at 3:23 pmRick,

In your example, geometric return = squareroot(0.95 x 1.07) – 1

arithmetic return = (0.95 + 1.07) / 2 – 1

So why is the geometric return of -0.05 and 0.07 even germane to the discussion?

For a correlation study, you can correlate the r% series or the (1+r%) series since the series are centered as part of the correlation calculation i.e. x – avg(x), y – avg(y) -> adding 1 to both series makes no difference. What you cannot do is correlate the price series (e.g. prices of asset 1 vs prices of asset 2, or the daily deltas in prices).

Now, I am guessing you know this, so perhaps you are just not expressing yourself well. Help us out!

Eventhorizon// Apr 12, 2011 at 3:36 pmEdit above: So why is the geometric return of -0.05 and 0.07 even germane to the discussion?

should read …

So why is the geometric MEAN of -0.05 and 0.07 even germane to the discussion?

Rick// Apr 12, 2011 at 3:50 pmEventhorizon,

(1) They talked specifically about “geometric mean returns”. A return is a return. Get it now, it is not a return multiplicator. That was my dispute.

(2) The geometric return is the annualized rate of return for yearly returns or the time-weighted rate of return in general. It has nothing to do with the mean return.

You can play all sorts of math games with numbers. The issue is what these numbers really mean taken in CONTEXT.

Unfortunately, Jez does not understand context. This is why he is using ratio adjusted data with futures, a true blunter, never includes commission and slippage and never presents results for individual contracts, only averages, without stating minimum capital required for achieving the results.

Bye

Pretorian// Apr 12, 2011 at 4:18 pmI have a few comments to make:

1. As Jez points out correlations are not stationary, correlation between 2 assets has absolutely no meaning if those assets returns are non normally distributed.

2. As a consequence of non normally distributed returns, using variance as a measure of risk sounds absurd to me.

3. I wonder if Trend Followers change their discourse when the approach traditional allocators (it comes to my mind a presentation I saw from Bill Dunn). Personally I don’t believe Trend Following should be used as a diversification tool for traditional assets, I think it is the most robust approach to investing/trading and I intend to use it as the core of my portfolio.

Thanks

Eventhorizon// Apr 12, 2011 at 4:38 pmI agree context is paramount.

I believe that, in this field (i.e. in THIS context), “geometric return” is interpreted to mean the rate at which your capital grows i.e. compounds.

So are you simply being pedantic stating that the compounded annual rate of growth of capital is not strictly “geometric mean of annual returns” but is the “(nth root of the product of (1+annual returns)) – 1″? Or do you have a more subtle point that I am missing?

RiskCog// Apr 13, 2011 at 5:00 amI agree with Pretorian that using the variance is a bad idea because it doesn’t penalize large drawdowns nearly enough. I actually proposed a replacement algorithm for portfolio diversification that does not rely on variance or correlations. There is a free eponymous optimizer online actually http://www.riskcog.com

I also agree that trend following done well is more robust than an MPT portfolio done well, which in turn is more robust than a traditional stock heavy portfolio done well. That is no reason to forgot about the tool of diversification though. Anytime I see an even-weighted allocation used by trend followers or anyone else, I see money left on the ground!

Trendfollowing in the 1800s – World Beta – Engineering Targeted Returns and Risk// Apr 18, 2011 at 5:54 pm[...] Nice post here that traces the phrase ““Cut short your losses,” – Let your profits run on”: [...]

David Ricardo’s Golden Rules « Systematic Relative Strength// Apr 20, 2011 at 8:39 pm[...] tip to the World Beta blog and the Au.Tra.Sy blog for pointing me in the direction of this fantastic [...]

Liz Cheval// Aug 23, 2012 at 8:15 pmVery flattered to see the lively discussion and perfect defense of my presentation. And yes, EMC was up 46% in 2008. Cheers!

Jez Liberty// Aug 24, 2012 at 9:49 amI will return the compliment in saying that I am very flattered and honoured that you drop by to read and comment on the blog!

I would have one question to you regarding the correlation presentation video: it does not seem to be available publicly any more (on your website) and I was wondering if you could let me/us know if it is available in some other place? (that would be great as it is a very good video).

Thanks,

Jez

Cameron// Feb 16, 2013 at 7:36 amHey everyone,

Apologies to come in late, I’m looking for a copy of Liz’s Let’s Get Negative presentation could anyone pass it on?