Are there any literature on selecting systematic views for Black-Litterman along with methods to specify the uncertainty parameter?

For example, rather than specifying a portfolio manager's subective belief, we perhaps scale a belief based on a historical residual return of a stock based on the market model. e.g if $\epsilon_i = r_i - (\hat{\alpha} + \hat{\beta}R_m)$ then one view can be that stock one is expected to outperform stock two by $1/K *(\frac{\bar{\epsilon_1}}{\sigma_{\epsilon_1}} - \frac{\bar{\epsilon_2}}{\sigma_{\epsilon_2}})$ where $K$ is some scaling constant to ensure that views are accounted for.

Just a crazy thought.

  • $\begingroup$ I just rephrase that I am looking for literature that talks of methods that have worked well in being an automated process within the BL View framework $\endgroup$ – Kevin Pei May 14 '15 at 2:19

Yes, you can formulate such a view. A lot of ways to formulate views are described in the literature (one can start here). However, your view is based on the assumption that CAPM works precisely for single stocks. This assumption will be wrong in most cases.

EDIT after a comment by the OP: I think now I understand. You want to replace expert's views (discretionary) by some systematic trading view. I would say: yes why not. But what is your prior? The market equilibrium? How do you choose the confidence in the view? The prior and the view are mixed proportional to the confidence. All in all if you have a systematic approach that works, why use Black-Litterman and mix the system with some prior? Furthermore market equilibrium (a possible prior) is something that works (if at all) on the long run.

  • $\begingroup$ The site is certainly useful but a lot of the papers describes the process of constructing the BL model, calibration of inputs or comparison with other author's models. I was looking for a paper that focused on just views in terms of being able to form views from a systematic process rather than from a subjective belief standpoint. Backtesting using the systematic process would also be possible this way. If i have misunderstood, please let me know. $\endgroup$ – Kevin Pei May 13 '15 at 15:57
  • $\begingroup$ I edited my answer. $\endgroup$ – Richard May 15 '15 at 7:57
  • $\begingroup$ Hi Richard, yes the market equilibrium is an issue since it may be suboptimal over a long period of time. The main reason is estimation risk in the presence of systematic approaches or its estimates of return/risk. If we were to optimize over these systematic approaches directly, it may produce concentrated portfolios. I feel like mixing with a prior of some kind can help with that issue. Confidence levels can be accounted for based on cross-validated forecast errors or something of the same nature. $\endgroup$ – Kevin Pei May 17 '15 at 1:02

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