Is there any research on applying state-space or dynamic linear models to forecasting equity risk premia on a security-by-security basis with a medium term horizon (say 3 month to 12 months horizon)?

Markov Models are a special case of state-space models where the states are discrete. There's an avalanche of research on these MM's and HMM's (beginning with Ryden 1998) but it seems to me there are some advantages to taking an approach where the state is a continuous variable. I have seen papers by Johannes, Lopes, and Carvalho that focus on shorter-horizons and demonstrate the superiority of PL over MCMC methods.

Seems to me that this approach could capture the time-series dependence and cross-sectional dependencies in a way that traditional panel models cannot. Also, it seems that since history rhymes but does not repeat, a long-memory state-space model would be better than an HMM.

Before I go down this windy road I'm curious if anyone out there has already attempted this or if there is a weakness with this approach. For example, perhaps state-space or particle filtering models only work best when the forecast horizon is very short.

  • $\begingroup$ What does it mean to forecast the ERP on a single security? Do you want to forecast the expected return over the risk free rate (in which case, this is equivalent to just forecasting expected return)? $\endgroup$ – Tal Fishman Aug 26 '11 at 1:56
  • $\begingroup$ Yes - it is forecasting expected return. They are risk premia in the sense that I am regressing on risk factors (value, size, beta). $\endgroup$ – Ram Ahluwalia Aug 26 '11 at 2:34
  • $\begingroup$ Is this about dynamic regression of single security returns on risk factors (market, value, size, momentum, . .)? I see that as a 2-step process, first estimating betas for each security for each risk factor under consideration. Second; forecast expected returns to each risk factor and then use those forecasts coupled with betas to forecast expected returns to the security. $\endgroup$ – Vishal Belsare Sep 11 '12 at 21:02

I think, as with many machine learning approaches to investing decision support, it depends largely on the data. With a good selection of features, yes dynamic models like you're talking about will probably do better than a simple linear regression; but then again, with a good selection of features, linear regression will probably work reasonably well, too. On the other hand, with a poor selection of features, you can use any statistical model in the world and it won't work -- simply put, you can't learn from patterns that aren't there.

That aside, you could probably also make gains by generalizing your search a bit from the models you describe to all Bayesian dynamic models.

  • $\begingroup$ Agreed. It just seems to me that state-space representations are more faithful representations of the dynamic nature of betas (vs. static OLS betas). $\endgroup$ – Ram Ahluwalia Sep 20 '11 at 4:06
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    $\begingroup$ I was mainly using OLS as an example to illustrate the point that the data greatly overwhelms the importance of the model in the quant space. That said, I'd probably use a dynamic Bayesian model of some type as well. $\endgroup$ – William Sep 20 '11 at 14:44

Here's a paper by Dangl, Halling, and Randl (2006) that uses a dynamic linear model to forecast the equity risk premium.


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