Timeline for CAPM yields very poor fit (low R-squared). Is that normal?
Current License: CC BY-SA 4.0
18 events
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| Feb 23, 2023 at 15:00 | vote | accept | Richard Hardy | ||
| Jan 31, 2023 at 13:42 | comment | added | Richard Hardy | @MatthewGunn, I have posted a couple of related questions. Given your immense expertise, I dear to notify you... (Sorry if I bother you!) | |
| Jan 30, 2023 at 20:14 | comment | added | Richard Hardy | @MatthewGunn, a slightly different question (which I may later post separately): I read Cochrane's chapters on GMM (beautifully written but still tough!) and thought I would try that out. I estimated the CAPM for multiple assets and then tested that the intercepts are jointly zero. This produced an error, likely because my data contains more assets than there are time periods ($N>T$), so a certain covariance matrix is not invertible. Cochrane mentions this can be a problem, but I did not see him offer a solution to that. Is there a way around, or must I have $T>N$ (or even $T\gg N$)? | |
| Jan 27, 2023 at 21:00 | history | tweeted | twitter.com/StackQuant/status/1619077817047588883 | ||
| Jan 27, 2023 at 17:25 | comment | added | Richard Hardy | @MatthewGunn, thank you, I will try the simpler solution that you have suggested. I have found data on SMB, HML and momentum factors for my exchange, so I will try sorting stocks into portfolios based on HML. | |
| Jan 27, 2023 at 16:38 | comment | added | Matthew Gunn | You'll have more power if you sort into portfolios based upon a characteristic (eg. B/M) that leads to a spread in average returns (one can debate of course if value is still there...). French also has portfolio returns on that page at the European level, but that may still not help if you're looking at one exchange. For portfolios, you might get more power with equal weight, but there's also a sense in value weight is more what people care about. You can also go slightly higher tech stats and run a cap weighted panel regression with clustered standard errors by date. | |
| Jan 27, 2023 at 7:36 | comment | added | Richard Hardy | @MatthewGunn, thanks, that is encouraging! Too bad I am investigating a particular stock exchange in Europe rather than NYSE, so I am not really interested in American data from Ken French. I will try building portfolios from my data and see if that helps at all, even though I indicated in my previous comment that I expect that approach to fail. | |
| S Jan 27, 2023 at 7:32 | history | edited | Richard Hardy | CC BY-SA 4.0 |
Improved formatting.
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| S Jan 27, 2023 at 7:32 | history | suggested | Alper | CC BY-SA 4.0 |
Improved formatting.
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| Jan 27, 2023 at 4:00 | review | Suggested edits | |||
| S Jan 27, 2023 at 7:32 | |||||
| Jan 27, 2023 at 3:46 | comment | added | Matthew Gunn | You can get returns for the Fama-French "25 Portfolios Formed on Size and Book-to-Market (5 x 5) " here so you could go that direction. It sounds like what you did with 100 stocks is still an instructive, interesting exercise in a slightly different way though! It may not be as high powered test of the CAPM as can be instructed, but it still may be instructive and a good pedagogical exercise. | |
| Jan 26, 2023 at 17:09 | comment | added | Richard Hardy | @MatthewGunn, on a second thought, I have under 100 stocks, so either I will have very few portfolios for the cross-sectional regression, or the portfolios will retain quite a bit of the idiosyncratic risk of their constituents. That makes me think I am stuck due to pretty fundamental reasons... | |
| Jan 26, 2023 at 15:00 | comment | added | Richard Hardy | @MatthewGunn, thank you, this was helpful! I discovered some discussion of the matter in Cochrane "Asset Pricing" (2005) Section 20.2 (see my answer). While he does not seem to mention (at least in the brief section that I read) that CAPM fails after 1980, he explains why we can get very poor fit regardless. So I guess I should try portfolios instead of individual stocks. I would then see more clearly (i.e. higher signal, lower noise) how the returns behave in relation to the betas, and thus to which extent the CAPM is a good approximation of reality (roughly speaking). | |
| Jan 26, 2023 at 12:33 | answer | added | Richard Hardy | timeline score: 6 | |
| Jan 25, 2023 at 22:06 | comment | added | Matthew Gunn | Fig I got looks like this. (Red line regression with intercept, black line regression with no intercept.) The red, estimated security market line has the wrong slope. (I recall these were 25 size B/M portfolios, but I could be remembering wrong.) | |
| Jan 25, 2023 at 22:05 | comment | added | Matthew Gunn | The CAPM doesn't work. It's been definitively refuted a long while ago by Fama French and others. A good exercise I remember from a class back in the day: using Ken French data library, (1) estimate market betas for 25 portfolios sorted on size and value and (2) run cross-sectional regressions to estimate your $\lambda$ parameter. Run this regression in two samples (a) data up to 1980 (b) full sample. At least a number of years ago, you'd see some plausibility for CAPM <1980 but a disaster in more recent times. | |
| Jan 25, 2023 at 20:49 | history | edited | Richard Hardy | CC BY-SA 4.0 |
added 469 characters in body
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| Jan 25, 2023 at 20:38 | history | asked | Richard Hardy | CC BY-SA 4.0 |