Momentum strategies

Momentum is an age-old feature of financial markets. It is perhaps the simplest and also the most puzzling of the “anomalies” discovered.  It is simply the tendency for assets (for example shares of some company) that did well (or poorly) in the past to continue to do so for a time in the future. It has been extensively examined in academia and has been found to be present in virtually all markets and going as far back as we have data. It has even persisted some decades after being extensively investigated for the first time. And still, it seems, we do not understand it very well. In today’s post I just want to highlight some different momentum strategies and their uses.

A property and a strategy

Momentum is a property of asset prices in markets and momentum strategies try to benefit from this property. One way of understanding momentum is to consider different momentum strategies and the profits they make, which gives an indirect means of understanding how asset prices work. For investors, of course, this is perhaps the most convenient way to study momentum as they are inherently interested in the strategies. They only care about momentum as a property if they can exploit it. The distinction between momentum as a property and as a strategy is not always clear because academics have not yet, I think, deemed it important to make the distinction explicit and thus both are simply called momentum. 

How to construct a momentum strategy

Momentum strategies come in all shapes and forms. Basically all of technical analysis is some kind of momentum strategy. A very general way of thinking about constructing a momentum strategy is depicted in the picture below. One starts by identifying some kind of trend (or signal) for each of the assets you are considering. This gives the direction of the momentum for the asset (for instance up or down). One can then assign a strength (or score) to this signal, which can be related to the magnitude of the momentum or the confidence you place in it. Then based on the signal and strength one makes an allocation decision – you decide how to bet in order (hopefully) to profit.

Time-series and cross-sectional momentum

Momentum strategies come in two main forms (though they are related). The first is to consider momentum for individual assets – the tendency for an asset’s price to go up if it went up in the past.  Here the signal and strength are evaluated for assets in isolation. This is time-series momentum. This form of momentum can be contrasted with cross-sectional momentum, which considers the momentum of assets relative to each other, e.g. the tendency of one asset to perform better than other assets if it also did so in the past, for instance. Here the signal and strength depends on how assets compare to each other.

Time-series momentum (strategy) tends to do well if an asset’s return is related positively related to its own past (property), for instance in what is called an AR(1) process:

Thus a higher return in the past predicts a higher return in the future.

Cross-sectional momentum (strategy) tends to do well if one asset’s return is negatively related to the past return of another asset (property), for instance if (numbering the assets 1 and 2)

This means that a high return on the one asset predicts a lower return for the other asset in the future.

Some simple strategies

Here are some simple strategies, based on a simple taxonomy:

Signed time-series momentum: buy any asset that went up in the past; sell any asset that went down.

Signed cross-sectional momentum: this is analogous to the above, but now invest in deviations from the average return or the market return. For instance the deviation of asset i’s return from the average is

If the asset did better than the average, buy the asset and sell the market and do the opposite if it did worse. This is a bet that assets that had above average performance in the future will continue to do so in the future.

Linear time-series strategy: again buy any asset that went up and sell any asset that went down, but invest more in assets with larger returns (invest proportionally to the asset’s past return)

Linear cross-sectional strategy: the same as above, but for deviations from the average (or market) return.

Quantile cross-sectional strategy: buy, for instance, the top third of assets and sell the bottom third.

In practice only the signed time-series and quantile cross-sectional strategies are used. The other strategies are, however, useful in formulating theory. For instance the linear strategies are easier to cope with mathematically, but amplify volatility too much to make them useful in practice.

Some references

My thesis:

• Du Plessis, J. (2013). Demystifying momentum: time-series and cross-sectional momentum, volatility and dispersion. University of Amsterdam. Retrieved from http://www.johandp.com/downloads/johandp_momentum_final.pdf?attredirects=0

Some empirical articles looking at momentum strategies:

• Jegadeesh, N., & Titman, S. (1993). Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency. The Journal of Finance, 48(1), 65–91. doi:10.1111/j.1540-6261.1993.tb04702.x
• Lewellen, J. (2002). Momentum and Autocorrelation in Stock Returns. (C. H. Schiller, Ed.)Review of Financial Studies, 15(2), 533–564. doi:10.1093/rfs/15.2.533
• Moskowitz, T. J., Ooi, Y. H., & Pedersen, L. H. (2012). Time series momentum. Journal of Financial Economics, 104(2), 228–250. doi:10.1016/j.jfineco.2011.11.003

Review: Models. Behaving. Badly

This book was written by the famous quant “Emanuel Derman”, whom I mentioned in one of my blog posts before when I commented on the Financial Modeller’s Manifesto.  I was expecting a lot from this book, I admit. And I was disappointed. That is not to say that the book did not contain valuable insight, but I was hoping for more. For a book inspired by the financial crisis, it has precious little to say about it.

Not really about finance: The very long preamble

If you were hoping to read a book about finance (or at least financial models) with some references to other material for diversion (as I was) you will be disappointed.  Most of the book hardly even mentions finance. Instead it deals with the Emanuel’s (admittedly not uninteresting) view of models in physics,  society (such as during the apartheid era) and Spinozan philosophy. The point of this, I think, was to illustrate in a more general setting the idea of a model or a theory. But given that the book is portrayed as being firstly about “Wall Street” it feels a bit like fluff.

There are some autobiographical passages about Dermans life in South Africa. I found these very interesting, but they added little value to the goal of the book. The point Derman was trying to make (that the models used in apartheid South Africa failed) could have been made in much less space.  But then the book would have been even shorter than it already is. I hardly think anyone who buys the book would be truly interested in reading about Spinoza’s theory of emotions (as interesting it might be philosophically). I certainly hoped the financial stuff would come soon.

One would have expected to get at least a good explanation of how models were used during the financial crisis and how they failed. Instead, the links that Derman makes with his descriptions of some basic financial models and the financial crisis are superficial at best. If you want insight into this part of the financial crisis, you must go elsewhere.  Early on in the book Derman laments what had happened during the crisis and before it: “decline of manufacturing; the ballooning of the financial sector; that sector’s capture of the regulatory system; ceaseless stimulus whenever the economy has waivered; tax-payer-funded bailouts…” It’s a very long list and not one item on it is treated in the book. We are told that model failure was the cause – we are never given any more insight than that.

The value of commonsense

I have been quite critical thus far, but the book does add value. There is a distinction between models used in physics, which are accurate, and those used in finance which are, at best, sometimes useful. The latter often treat people as if they are just particles or objects, which they are not. Derman calls this “pragmamorphism”. Financial models always leave out something important. The admonition to always use common sense is valid. However, I was hoping to come away with more insight than that. Perhaps that’s all there is, really.

Models and theories and facts – Derman does the unforgivable

Central to the book is the distinction between “models”, which are based on analogy, and
“theories” which attempt to describe the real world without analogy. Essentially, physics works with theories (mostly) and finance works exclusively with models. This is a useful distinction – though I am not convinced that the two categories are not instead two extremes of a continuum of models. However, as far as thinking about modelling goes, I believe it is very valuable.

Dr Derman goes one step further though, doing something I find unforgivable.  He claims that a “correct” theory becomes a fact. Physics models that say there are electrons and that they behave in certain ways are the truth. I do not think Dr Derman actually thinks this – because to do so would be to disavow even the possibility of a theory being overturned, replaced by something better. And we have seen it done: Newton’s laws, “confirmed” to be accurate for hundreds of years turned out to be a poor description of reality once you started looking at things moving near the speed of light.

Physics uses mathematics and mathematics is not and will never be the real world – though it is the most useful tool we have for describing the world. In science (all of science, including physics) we can only ever say this: IF my model or theory is correct then we would expect certain observations in the real world.

Science can never confirm a theory to be correct. Theories that are considered “facts” are just the ones that have not yet been proven to be wrong. I think that a better theory than general relativity or quantum electrodynamics may come along – it may only bring incremental changes or it may bring a revolution in the way we think about the world. But it is the way we think about the world that changes, not the world.

Verdict

I must, if I am kind, conclude that Derman’s book tries to do a little too much (or, if I am unkind, that it tries to do too little and pads it with fluff): it wants to be philosophy, biography, essay and social commentary. It does none of these particularly well. 

Reference

Derman, E., 2012. Models.Behaving.Badly.: Why Confusing Illusion with Reality Can Lead to Disaster, on Wall Street and in Life, Free Press. Available at: http://www.amazon.com/Models-Behaving-Badly-Confusing-Illusion-Reality-Disaster/dp/1439164991 [Accessed January 27, 2013].

The Financial Modellers' Manifesto

Paul Wilmott and Emanuel Derman, both quant gurus, wrote and signed what they call The Financial Modeller’s Manifesto in 2009. It is modelled after The Communist Manifesto written by Marx, which I find quite ironic.

About the authors

Before we get onto the manifesto, I want to mention some things about the people behind it. Derman started off in South Africa, studying at the university of Cape Town, just as I did (although he got a PhD in theoretical physics). In a sense, therefore, he is a role model for me.

Wilmott started the Certificate in Quantitative Finance, a six month course. He is editor-in-chief of Wilmott magazine and has a quantitative finance forum and recruitment organisation run under his name (some hubris here?).

Both warned against the risk of misusing mathematical models long before the crisis (though I know quotes have a way of being taken out of context).

What I like about the manifesto

1. It is honest. 
2. It is written in a colloquial style, making it more accessible and emotive. 
3. The oath will always be relevant as it contains timeless principles. 
4. It is a call to action.
5. It draws the crucial distinction between physics and financial mathematics.

What I dislike

1.   There are too many specifics. CDOs might not exist in twenty years, making the manifesto applicable mostly to the present (with the exception of the oath).
2. There is too much jargon.
3.  The authors claim no responsibility. They are reacting to everyone else’s mess.
4.  It is too informal, making it harder to take seriously.
5.  It does not advise on how to fulfil its demands.
6.  Discussions about whether the Black-scholes model is good or not are not really relevant.
7.  It was written after everything it says had already become obvious.

What we need

We need clear guidance for future quants and a way to hold them accountable. The manifesto points in the right direction. It gives a useful oath, and by adjusting the first line to make it more formal (perhaps, “I know the world of finance does not function according to exact mathematical laws”) it could become something quants can put on plaques and recite as they get their qualifications.

But we need more. We need a code of ethics or a code of conduct for quants. Not a one page document that reads more as an article than anything else, but something substantial with a gravity that weighs on your conscience. More than that, though, we need people to ascribe to this code. That is, we need a professional body for quants that police their behaviour and set best practices. I find myself wondering whether actuaries can do this. We already have professional conduct standards (lacking only in specifics that will apply to quants). The creation of a quantitative finance specialisation for actuaries would allow quants to practice as actuaries and thus they would be held to these standards.

The problem is actuarial training is ill-suited to providing the kind of (highly mathematical) skills that quants need (I know this from unfortunate experience). The alternative is to create a professional body for quants alone, but this may involve a lot more work and may take years to be accepted. The public would appreciate it, I think. Throughout the financial crisis they have heard only horror stories of quants and such a large step would certainly help assuage fears, and, I think, result in more responsible practices.

Some references:

Wikipedia:

• Wikipedia, 2011a. Emanuel Derman. Wikipedia. Available at: http://en.wikipedia.org/wiki/Emanuel_Derman [Accessed January 22, 2011].
• Wikipedia, 2011b. Financial Modelers’ Manifestor. Wikipedia. Available at: http://en.wikipedia.org/wiki/Financial_Modelers’_Manifesto [Accessed January 22, 2011].
• Wikipedia, 2011c. Paul Wilmott. Wikipedia. Available at: http://en.wikipedia.org/wiki/Paul_Wilmott [Accessed January 22, 2011]

The actual manifesto:

• Wilmott, P. & Derman, E., 2009. Financial Modelers’ Manifesto. Paul Wilmott’s Blog. Available at: http://www.wilmott.com/blogs/paul/index.cfm/2009/1/8/Financial-Modelers-Manifesto [Accessed January 23, 2011].

The professional conduct standards of the Institute of Actuaries in the UK:

• Professional Affairs Board. (2007). Professional conduct standards. Retrieved from http://www.actuaries.org.uk/sites/all/files/documents/pdf/PCSV3-0.pdf.