Tuesday, December 26, 2006

Do Factor Models Work in the Short Term?

Besides pair-trading, “factor model” is the most popular workhorse of the statistical arbitrageur. In a previous article, I discussed the most well-known factor model – the Fama-French Three-Factor model, with the general market index returns, the market-cap of the stock, and the book-to-price ratio as the only three factors driving returns. However, as I explained earlier, this factor model has a very long horizon. For the quantitative trader who needs to make money every month, the natural instinct is to look for a more “sophisticated” factor that works in the short term, or even to develop some kind of model that use different factors every month in response to “market condition”. Alas, other than hearsays and second-hand gossips, I have never witnessed an actual success of this approach in a hedge fund or proprietary trading group – at least a success that lasts for more than a year.

I am of course not privy to the current performance numbers of factor models run by some of the most successful hedge funds today. However, there is a class of ETF (called “XTF”) marketed by PowerShares Capital Management that uses a similar factor approach for its stock selection criteria. According to media reports, each stock in these XTF’s is scored by 25 variables such as cash flow, earnings growth, price momentum, etc. This sounds like a classic factor model to me. This model is reportedly designed by the quantitative unit at American Stock Exchange. To find out if they have indeed discovered the holy grail of factor models, I looked at the performance of these XTF compared to their benchmarks.

Here I tabulate the XTF’s for each market cap and value category, their corresponding benchmark market index ETF’s, and finally the YTD differential returns up to December 13, 2006. (PJG and PJM have too short a history for this comparison.)

Large capPWV-IVE=4.8%PWC-IVV=-3.6%PWB-IVW=-5.0%
Mid capPWP-IJJ=0.1%PJG-IJH=N/APWJ-IJK=3.1%
Small capPWY-IJS=-0.7%PJM-IJR=N/APWT-IJT=-4.9%

The differential returns are all over the place: some positive, others negative. To me, this is symptomatic of a factor model that does not have predictive power. (After all, if the differential returns are consistently negative, we could have long the ETF, short the XTF, and make consistent profits!) At the very least, this factor model may have a horizon much longer than what most traders would be interested in – in which case, why not just use the simple Fama-French model?

This is not to say that exotic, proprietary factor models have no use: they tend to be pretty useful for risk management, as volatilities and correlations are often easier to predict than returns. But beware every time your risk management software vendor tries to sell you an alpha generator!


NA said...

good analysis as usual.

While I've never worked in a quant department I'm sure the quant guys backtest 100s of different strategies and every now and then some work.

Its an ongoing process in my view. No strategy works forever, you have to continually tweak and modify it. Even with normal investing.

The markets are always changing so are the models. I won't be surprised to hear if quants are like RnD people- Always experimenting.

JR said...

Dear Ernie

This is a very interesting post. Apologies for my very late contribution to this thread – I have been away out of the country on vacation.

To declare my allegiance up-front, I am an academic quantitative social scientist (PhD was in Economics), but currently trying my hand at building factor models with a view to trading on my own account. So, perhaps my thoughts on the merits of factor models are clouded by naive optimism. But here are my thoughts in any case.

As you mentioned in your article, the Fama-French factor model is indeed a factor model that has performed well over time. This itself is a laudable testimony to the efficacy of factor models that should not be overlooked. At the same time, it is incredulous were anyone to suggest (not that you are) that the Fama-French model is the Holy Grail. For starters, price-to-book, although a reasonable first approximation of a company’s value, is likely to be improved by other valuation metrics which take account of earnings growth, etc. Moreover, the three factors comprising the Farma French model are unlikely to be the only three significant determinants of stock returns. For instance, there is plenty of evidence to indicate that many financial series exhibit serial correlation (i.e. momentum is important).

For what it’s worth, my own take on why factor models are often unsuccessful relates to the way they are often constructed:

First, the problem of over-fitting models (which improves the fit of within-sample models but often not out-of-sample models), seems to be often overlooked by practitioners, despite the problem being well—recognised in the academic literature. Your example of the twenty-five factor model may well fall into this category. The lesson is to give more weight to parsimony.

Second, it seems to me that many models are developed and traded without being properly tested on out-of-sample data. In other words, a model is typically constructed and back-tested using the same data, when some data should be held back to test the model’s performance before trading it.

Third, many models appear to be highly rigid in that they fail to adequately adjust for changes in market conditions. Ways to achieve this would be to include relevant market factors in the model, estimate the parameters using recursive techniques (which give weight to more recent observations) or use appropriately constructed rolling windows.

Fourth, I am not convinced that many models that claim to be factor models are indeed factor models, at least not in the Fama-French vein. It seems to me that many models give equal (or an arbitrary) weight to each factor in the model (this may be the case with the twenty-five factor model you mentioned in your article). The Fama-French model is based on a multiple regression which takes account of colinearity between factors. In other words, the implicit weight of a factor should be net of the impact of other factors in the model.

In general, my impression is that many hedge funds fail to adequately invest in research and development. Of course, this is not a problem confined to the hedge fund space. I think the performance of many factor models could benefit from more rigorous R&D, but this investment is often sacrificed by hedge funds in the pressing drive for profit.

So, am I naively optimistic on the potential of factor models or unduely cynical of their use by many hedge funds? In terms of developing my own models, time will tell I guess.


Ernie Chan said...

Dear JR,

Thank you for your thoughtful comments. Actually I agree with all of your points. All the steps you mentioned in preserving the validity of factor model predictions are valid and necessary. Certainly there can be better variables than the ones chosen by Fama/French too.

However, my major contention is that though factor models can be valid and predictive in the long term (more than 6 months at least?), it is not useful in the short term (shorter than 3 months). Since market neutral hedge funds are supposed to be profitable at least every quarter, this becomes far less useful for them.

Why do I believe that factor models are not useful in the short term? Just take the case of a value factor such as price-to-book. In the long term, everyone believes excess return is inversely proportional to price-to-book. However, in late 1990’s, when the internet bubble took over, nobody cares about price-to-book. Therefore, most people trading using the traditional factor models lose money in that period. Now they may have made back their money in the 2000’s. But then, they may also have closed down shops already!

JR said...

Dear Ernie

I entirely take on board your comments. I agree that traditional factor models (such as the Fama-French model) may under-perform in the short-term, even though they may out-perform in the long-term. As you describe, this is indeed a problem for most hedge funds, given their investment horizon.

However, I think that factor models still have a role to play, both the ‘traditional’ models and other types of models:

First, there is no reason a priori why a traditional-type factor model cannot out-perform in the short-term. For example, inclusion of momentum factors with, say, monthly rebalancing will help capture short-term dynamics. So too will a flexible estimation procedure which permits parameters to be up-dated (the recursive estimation and rolling window approaches mentioned in my previous post being two possible solutions). I agree that the main strength of the traditional factor model is in the medium- to long-term, but I think that the short-term performance of many traditional factor models can be improved.

Second, the traditional factor model (e.g. the Fama-French model) is in my view just one variant of the class of factor models, some of which have been successfully implemented in the pursuit of short-term profit. Two examples spring immediately to mind, one based on predicting events, the second on predicting price movement following an event:

(i) Factor models designed to predict ‘positive’ events (typically maximum likelihood estimation procedures such as logit or probit models. The idea is to buy the stock of companies which have a high probability of experiencing a positive event. The classic example here is models used to predict takeover targets. Factors in this model might include firm characteristics (e.g. takeover targets are typically found to be smaller in size, less liquid and under-valued) as well as market conditions (e.g. a company has a higher probability of being a takeover target following a recent history of industry-specific merger activity). Many models predicting takeover targets have not performed well. However, I am inclined to think that many of these models are poorly constructed (for reasons elaborated in my previous post), given that some highly regarded firms claim to have built models of takeover targets that have consistently returned positive results. Predicting (usually positive) earnings surprises is another example of this type of factor model, and my impression is that this type of model has a fairly successful track record.

(ii) Factor models designed to identify positive returns following an event. An example here is models designed to predict positive price movements following an analyst up-grade. There is often significant short-term positive price movement following some analyst up-grades, but by no means all up-grades. So, the trick is to identify the subsample of up-grades most likely to exhibit short-term out-performance. Factors in this type of model may include the reputation/quality of the analyst and the extent of dispersion (disagreement) around consensus recommendations.

The key point behind these event-related factor models is that they are usually specifically designed to capture short-term price movement. So, a multi-strategy factor model approach should (at least in theory) contain some short-term models which would sit alongside the more traditional factor models which often (but not necessarily) have a longer investment horizon.


Ernie Chan said...

JR: First off, I agree with you that if you include factor models that predict likelihood of events, it may show much better results than traditional factor models that maintain a long-short position at all times.

However, I don't think simply adding factors such as "momentum" will make a traditional factor-model perform well in the short-term. While in an internet bubble the momentum factor will certainly save you from losing too much money on your value factor, once the market becomes value-driven again, the momentum factor will start losing money. So it is all a matter of how much weight you assign to each factor. Now most models train those weights based on the recent history, but if you were trading such a model around April 2000, recent history would have told you to put more weight on momentum, and that would have been disasterous for the next few months.

JR said...

Dear Ernie

Well, I’m glad we agree that non-traditional factor models (e.g. event-related models) may be used to capture short-term profit opportunities! I would be extremely interested to hear of your experience of this type of model.

You are right of course to point out that a factor model incorporating momentum is likely to have performed poorly in April 2000. But to the extent the model quickly adapted to changes in market volatility (e.g. through type of estimation procedure of factors in the model), the story might not have been too bad (certainly compared to many HF returns at the time). My general point is, however, that I think the short-term performance of traditional factor models can be enhanced by explicit inclusion of short-term dynamic features.

As I mentioned earlier, my impression is that many factor models (both traditional and event-related) perform poorly since they have often not been rigorously constructed and tested. I’d be interested to hear whether this is your view too or whether perhaps I’m being a little disingenuous to many in the HF community.


Hank.Terrebrood said...


I know this was many years ago, but interested to see how you progressed.

I chose risk factor modeling as my dissertation subject and wrote a model which, one day lagged, showed a better than 96% explanation of price (and thus 2 standard deviation violations of the model are excellent indicators). I did not use book value nor did I divide the securities by market value. Instead I took other variable which one would take into account on a value decision, added price momentum, volume and volatility measures and then calculated daily means for every variable by sector and for the entire market.

That model was then checked for explanatory power over many time frames from 1 month to 18 months.
The period over which was the strongest was then applied to all securities and a regression equation built for every stock in a universe of 1,200 tickers every day.

In that manner the day-to-day changes in market risk appetite, relative value, price move and volatility recreate the expected price and standard deviations.

It is a terrible amount of work to calculate all of the variables, populate the market and sector means and run the regression analysis every day, but the results are extremely satisfying.

I look forward to hearing from you either on this blog or directly.


Faisal said...

Hi Ernie,

Thanks for sharing your wisdom in your blog and books. I am currently going through your first book 'Quantitative Trading' and I am stuck in example 7.4 on Principal Components Analysis. I am not really stuck on the concept but MATLAB seems to take ages. It was on the 'Busy' state for 20 minutes and then I decided to break the loop. Is that normal?

I am also a bit confused on the issue of factor models. I thought factor models are more like risk models. The different factors are supposed to 'absorb' the excess returns. I am not sure how they are used for trading.

Ernie Chan said...

Hi Faisal,
Your Matlab may be stuck because your PC doesn't have enough memory for this problem, or its CPU is too slow.

Risks and returns are two sides of a coin. While some people use factors models to estimate their risks, we can use factors to estimate our returns as well. Admittedly, it is probably more accurate for risk estimation than returns estimation, since we don't need to know the sign of the expected returns for risk estimation.


Intraday Tips said...

With some experience I don't think simply adding factors such as "momentum" will make a traditional factor-model perform well in the short-term. While in an internet bubble the momentum factor will certainly save you from losing too much money on your value factor,