It's evident from the previous posts that parameter stability is an issue, at least when estimating a securities exposure to the market. This particular factor exposure is pretty much like market beta - maybe just like market beta (?). Providers of beta make a lot of adjustments. I don't know if any of this is appropriate in a factor model (anyone who knows about this please comment), but I thought I'd link to some of the related literature: On Estimating the Beta Coefficient, D. Bradfield; Periodic Return Time-Series, Capitalization Adjustments, and Beta Estimation, E. Jarnecic, M. McCorry & R. Winn; Capturing Market Risk in a Volatile World, MSCI Barra Research Bulletin.
Walt French, a quantitative fund manager, made some comments regarding parameter stability and multi-factor models that are interesting enough to be included (with his permission) in the body of the blog:
Let me propose a simple thought experiment. Consider a market in which stocks are affected by two common factors: future GDP and interest rates -- both of which drive a DDM-type price model -- and an idiosyncratic factor affecting mostly individual firms' market share. News about GDP and interest rates arrives at irregular intervals, as does idiosyncratic data on firms.
During the 60 months ending in December, 2005, GDP was the big story. The Fed just kept nodding its head, saying all was well. Stock prices reacted mostly to changes in the GDP outlook; "high beta" stocks were growth stocks most dependent on future expansion. But in the 24 months ending January, 2008, news from the Fed dominated the average stock's response. "Value" stocks were the big (down!) movers as changes in credit, as well as Fed intervention in credit, drove some stocks wild. The previously high-beta stocks didn't respond so much to the market average.
I think the multi-factor story is important in interpreting that beta coefficients should change over time, because we get a different mix of news. The Rosenberg and Guy paper highlights company changes as the basis for changing betas, but the macro-environmental changes also need to be understood as moving betas around, perhaps radically. From my perspective, this is more important than the noise of any single stock, since such noise cancels out, by definition, in larger portfolios, while the macro effects, being common factors, only become more obvious with portfolio diversification.
So forecasting beta requires a forecast over one's target time horizon of (1) each source of market variance and (2) various portfolios' sensitivities to those sources. Lots of papers have gone into the estimation errors when there is a single source of market variance, but modern practice -- and the multi-factor models that underly this blog's approach -- have to consider their variance forecasts as more important. In a diversified portfolio, these may be the greater source of beta uncertainty.
I found a link to the Rosenberg and Guy paper Walt referred to. Surprisingly, not everyone has heard of Barr Rosenberg. Barr is to Beta as Buddha is to Buddhism. Here, in addition, is a link to the Berkeley Research Program in Finance Working Papers, worth the cost of admission by themselves.
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Let me propose a simple thought experiment: in this world, stocks are affected by two common factors: future GDP and interest rates (both of which drive a DDM-type price model) and an idiosyncratic factor, mostly affecting market share. News about GDP and interest rates arrives at irregular intervals, as does idiosyncratic data on firms. During the 60 months ending in December, 2005, GDP was the big story. The Fed just kept nodding its head, saying all was well. Stock prices reacted mostly to changes in the GDP outlook; "high beta" stocks were growth stocks most dependent on future expansion. But in the 24 months ending January, 2008, news from the Fed dominated the average stock's response. "Value" stocks were the big movers as changes in credit, as well as Fed intervention in credit, drove some stocks wild. The previously high-beta stocks didn't respond so much to the market average. I think the multi-factor story is important in interpreting that beta coefficients should change over time, because we get a different mix of news. The Rosenberg & Guy paper highlights company changes, but the macro changes also need to be understood as moving betas around, perhaps radically. From my perspective, this is more important than the noise of any single stock, since such noise cancels out, by definition, in larger portfolios, while the macro effects, being common factors, only become more obvious with stock diversification.
So beta accuracy is a joint effort, relying on:
- good forecasting of the variance of the multiple factors in the model
- good insight as to stocks' sensitivity to the factors, and
- having a relevant set of factors that explain the macro factors -- it wouldn't be helpful in my example world to only have a GDP-derived factor, for example, no matter how well you did with it.
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