Friday, July 10, 2015

A tale of two asset pricing models


A while ago I talked about the fact that DSGE macro models haven't seen industry applications, and that this means people don't yet trust them to give a good conditional forecast of the effect of economic policy changes on macro variables. How about asset pricing models from the finance literature? How do these pass the market test?

There are basically three things you might use an asset pricing model for in the real world. The first is to measure risk. The second is to beat the market, if you believe that the model represents a long-term equilibrium from which assets will only deviate for a short time. The third is to arrive at a fair starting price when brokering deals between two parties.

There are two main classes of asset pricing models in the finance literature. The first class is equilibrium models. These are basically economic models that treat asset prices as solutions to consumers' utility maximization problem (and, sometimes, firms' profit maximization problem). The most famous of these is the CCAPM. Modern extensions of that include Bansal and Yaron's long-run risk model, Campbell and Cochrane's habit formation model, and various models based on "rare disasters." Though these days these models are usually pitched as solutions to time-series puzzles like the equity premium, excess volatility, and volatility clustering puzzles, they are models of risk and of the cross-section of expected returns. 

The second main class of models is factor models, such as the Fama-French 3-factor model, the Carhart 4-factor model, and various macroeconomic factor models. These models are based not on any behavioral assumptions like utility or profit maximization. They only require no-arbitrage conditions, and some assumptions about the structure of the market. Though they may be motivated by economics, they are not economic models, in the modern sense of the neoclassical, maximization-based econ that we are all used to. 

Factor models can end up looking a lot like equilibrium models - factor models give you factor betas and equilibrium models give you consumption betas and stuff like that. But the methods they use to derive the betas are much different, and the substance of the conclusions is almost always very different. 

I don't have a comprehensive data set of the finance industry, so don't regard my info as complete, but I've talked to a fairly large number of industry people, and they all say the same thing. Factor models are very common, even ubiquitous, in the industry. Equilibrium models are essentially never used by anybody.

The most obvious reason for this is that equilibrium models are harder to make. You have to make a bunch of assumptions, solve an optimization problem, then estimate the thing to see how well it works. With factor models you just skip the first two steps, slap down some factors, and estimate it. As you might expect, the ease of generating factor models leads to a lot of false positives in the academic literature. But in the finance industry, a lot of effort goes into exhaustive backtesting and robustness-checking of factor models, which cuts down massively on false positives (though overfitting is of course still a danger). You have companies that exist just to make, test, and sell factor models.

So is the disuse of equilibrium asset-pricing models just a function of the effort that goes into making them? Maybe. But you'd think that eventually, academics - who are more than willing to put in that effort, and who in fact make oodles of such models - would come up with a really good one that industry would adopt. It's no harder to use an equilibrium model than it is to use a factor model.

But they don't. No one I've talked to or heard about uses consumption betas of any kind, including ones based on habit formation or Epstein-Zin preferences. Despite decades of high-powered research, equilibrium models are not yet passing the market test. 

I assume that this is because when you test these things, factor models come out ahead. I hope that someone is using information criteria or some other defense against overfitting when these comparisons are made. If they are, then what it means is that the best factor models are more empirically successful than the best equilibrium models. Which in turn implies that equilibrium asset-pricing models are, basically, misspecified. 

Why would equilibrium models be misspecified? They might be focusing on fitting time-series facts and neglecting the cross-section. Or there might simply be something very wrong with the workhorse assumptions economists use to describe consumer behavior at the aggregate level - something so deep that modifications like Epstein-Zin or habit formation can't fix it. Tests of the basic consumption Euler equation make me suspect that that is the case. If economists find that wrong thing and fix it, it could reap big dividends not just for asset pricing models, but for macroeconomics as well.


Updates

Two caveats to this post! First of all, the story isn't over yet. New models are coming out all the time - for example, a commenter points me to this model from 2014, which is a hybrid of a typical factor model and a production-based theory of firm investment behavior. Looking over it, it looks pretty good. It also agrees with my prior that firm behavior is a lot more important and a lot easier to explain than consumer behavior. But the main point is that industry could start using equilibrium models - even consumption-based equilibrium models - at any time.

The second caveat is that the notion of what it means to "use" a model is a lot more subtle than I'm making it out to be. For example, you could find factors by data mining, then use an equilibrium model to convince yourself that the factors will be stable in the future (in fact, that's exactly how you might use the model I linked to above). To my knowledge this kind of use is very rare so far, and I've heard stories of people in industry trying and failing to do just this. But if people do start doing it, it won't look like people ditching factor models for equilibrium models. It will look like people using equilibrium models to check their factor models. Another way you could use equilibrium models is to search for new ideas for factors. But since the set of available macro variables is too limited, it's highly likely that data-mining will find the factors long before equilibrium modelers do.

19 comments:

  1. possibly a dumb question, but doesn't an equilibrium model reduce to a factor model after you solve it, like CAPM -> beta? it has to have some systematic indicators of value and risk, i.e. factors, and everything else is assumed to be uncorrelated so it cancels out in a diversified portfolio?

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    1. Correct. The factors will just be different things, related to stuff like consumption growth.

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    2. Since the factor model is intuitively understandable to MBAs, seems like it makes sense to reduce the equilibrium model to a factor model and sell / teach that!

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  2. Noah, why are you treating financial industry use of model x or y as a test of the optimality of method x or y? The information production industry (of which finance and private sector econ consultancies are in some sense special cases) is plagued by pervasive assymetric info and moral hazard ,since almost by definition info production industry exists because some people have better info/info processing ability than others -> the buyers of the service are disadvantaged in terms of assessing the quality of the service -> private sector service is not the optimal benchmark relative to academic or government service (e.g private sector macro analysis versus IMF or central bank). The public certainly seems to think a lot that private sector finance industry is highly suboptimal in terms of honesty and providing the best info on things like the state of financial institutions' health, investment advice etc...This is maybe more related to your "market test" of academic macro models usage, but it might also apply to your current discussion. The issues are a bit different because, forecasting asset prices is much harder than things like gdp growth, and asset pricing equilibrium models are behind the best equilibrium macro models (equilibrium macro has moved beyond the representative agent endowment economies that you cite, but the state of the art models have only been rarely examined in their non-linear form that allows you to analyse asset pricing issues like risk premia).

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    1. Anonymous7:35 PM

      But this probably doesn't apply to what Noah's saying here since the industry people he's referring to are presumably from hedge funds etc and they just want models that make good predictions about returns. If a consumption model could do better than a factor model in this sense, why wouldn't they use it?

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    2. So daniels, your idea is basically "The financial market has lots of market failures, so the market test is not a good test". That's certainly possible. But I see tons of finance companies hiring tons of very smart people to make models that are just a tiny bit better than the competition. So a lot of effort goes into information production, even if that information is not widely shared after it is produced.

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    3. And the academic or policy institutions sectors probably have even smarter people, who are motivated by other non financial motives in their info production. Only formal analysis I'm aware of is here,
      https://ideas.repec.org/p/qed/wpaper/1198.html
      .
      As for hedge funds (formal ones or financial institutions like GS or DB), it's still not clear if they really produce reliable alpha and if they do a good job at managing their investors' different beta risks. e.g
      http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1910719
      .
      But yeah, if the goal is to arbitrage some short term deviations from efficient pricing (which I think is what most trading is about), then reduced form statistical methods are simpler to use and more reliable than equilibrium models. I don't think you need to take into account general equilibrium complexities to benefit from momentum effects.
      .

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    4. Even if hedge funds as an asset class don't produce reliable alpha, it's certainly possible - in fact, statistically almost certain, given serial correlations - that some hedge funds do produce reliable alpha.

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    5. I'm not so sure. By definition there will always be some better than risk adjusted market average hedge fund performance out there in the tails of the distribution, as well as some significantly worse than average hedge funds. But it's not clear to me outperformance is stable across time. For mutual funds and macro forecasting I think it's not, except maybe for bad performance. In any case, you can appear to make good alpha even if you exploit the unconditional average excess returns on some factors, then report alpha against models omitting that factor. Macro modeling would help you by giving you a better understanding of the dynamics of those factors across time. My impression is that this is still not well developed, or at least the private sector examples I've run into it seem a bit too simple to me, e.g
      http://www.pimco.com/EN/Insights/Pages/Asset-Allocation-Does-Macro-Matter-Part-II-.aspx

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    6. Daniels,

      Your comments are really entertaining. Yes, academic and policy institutions have definitely smarter people. How do you know? Because they talk to each other. The model quality is obviously better since, you know, they talk to each other.

      The models clearly produce great information. The information is so good that you could produce reliable alpha yourself with all the extra smarts. I am just a tiny bit perplexed what you are waiting for. Julian Simmons billions are waiting for you.

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    7. Daniels,

      Your comments are really entertaining. Yes, academic and policy institutions have definitely smarter people. How do you know? Because they talk to each other. The model quality is obviously better since, you know, they talk to each other.

      The models clearly produce great information. The information is so good that you could produce reliable alpha yourself with all the extra smarts. I am just a tiny bit perplexed what you are waiting for. Julian Simmons billions are waiting for you.

      Delete
  3. I'm not too well versed in this area, but isn't the paradoxical negative correlation between consumption and interest rates in the Euler model due to putting the cart before the horse? I mean if everyone wants to consume more, consumption will go up as will the desire for money to finance consumption, thus creditors can charge to borrowers higher rates and must offer higher rates to savers as well. Why isn't expected utility taken as a given and the interest rate derived from that?

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  4. Thank you for sharing! What about behavioral models, as markets become more and more influenced (if not dictated) by agent-based actions like inflation targeting, dual mandates, ECB/FED QE programs etc.. (not to forget consumer behavior).

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    1. I'm going to do another post on this...

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  5. Anonymous11:50 AM

    You might find the q-factor model to be of some interest. It's a factor model with some equilibrium logic...

    http://rfs.oxfordjournals.org/content/28/3/650.full.pdf+html

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  6. Robert Flood4:48 PM

    May have something to do with different conditioning information. Finance models - factor models in particular - take the market return as an exogenous variable and model deviations. Macro models explain the market return with specific assumptions about the SDF.

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    1. Yep, exactly right. That's why I suspect that if we had equilibrium macro models that worked well, we'd be able to predict a lot more about market movements than we currently can.

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  7. do models price the market or do markets price the model? it's probably both . I've seen derivations from models in regard to option pricing, but there is often a specific reason why

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