Min-Max robust and CVaR robust mean-variance portfolios
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Bibliographic record
Abstract
ABSTRACT This paper investigates robust optimization methods for mean-variance portfolio selection problems under the estimation risk in mean returns. We show that with an ellipsoidal uncertainty set based on the statistics of the sample mean estimates, the portfolio from the min-max robust mean-variance model equals the portfolio from the standard mean-variance model based on the nominal mean estimates but with a larger risk aversion parameter. We demonstrate that the min-max robust portfolios can vary significantly with the initial data used to generate uncertainty sets. In addition, min-max robust portfolios can be too conservative and unable to achieve a high return. Adjustment of the conservatism in the min-max robust model can be achieved only by excluding poor mean-return scenarios, which runs counter to the principle of min-max robustness. We propose a conditional value-at-risk (CVaR) robust portfolio optimization model to address estimation risk.We show that using CVaR to quantify the estimation risk in mean return, the conservatism level of the portfolios can be more naturally adjusted by gradually including better scenarios; the confidence level β can be interpreted as an estimation risk aversion parameter. We compare min-max robust portfolios with an interval uncertainty set and CVaR robust portfolios in terms of actual frontier variation, efficiency and asset diversification. We illustrate that the maximum worst-case mean return portfolio from the min-max robust model typically consists of a single asset, no matter how an interval uncertainty set is selected. In contrast, the maximum CVaR mean return portfolio typically consists of multiple assets. In addition, we illustrate that for the CVaR robust model, the distance between the actual mean-variance frontiers and the true efficient frontier is relatively insensitive for different confidence levels, as well as different sampling techniques.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.006 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it