Portfolio Selection with Parameter and Model Uncertainty: A Multi-Prior Approach
Bibliographic record
Abstract
In this paper, we show how an investor can incorporate uncertainty about expected returns when choosing a mean-variance optimal portfolio. In contrast to the Bayesian approach to estimation error, where there is only a single prior and the investor is neutral to uncertainty, we consider the case where the investor has multiple priors and is averse to uncertainty. We characterize the multiple priors with a confidence interval around the estimated value of expected returns and we model aversion to uncertainty via a minimization over the set of priors. The multi-prior model has several attractive features: One, just like the Bayesian model, it is firmly grounded in decision theory. Two, it is flexible enough to allow for different degrees of uncertainty about expected returns for different subsets of assets, and also about the underlying asset-pricing model generating returns. Three, for several formulations of the multi-prior model we obtain closed-form expressions for the optimal portfolio, and in one special case we prove that the portfolio from the multi-prior model is equivalent to a ‘shrinkage’ portfolio based on the mean-variance and minimum-variance portfolios, which allows for a transparent comparison with Bayesian portfolios. Finally, we illustrate how to implement the multi-prior model for a fund manager allocating wealth across eight international equity indices; our empirical analysis suggests that allowing for parameter and model uncertainty reduces the fluctuation of portfolio weights over time and improves the out-of sample performance relative to the mean-variance and Bayesian models.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.009 | 0.026 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".