CAPM-like formulae and good deal absence with ambiguous setting and coherent risk measure
Bibliographic record
Abstract
Risk measures beyond the variance have shown theoretical \nadvantages when addressing some classical problems of Financial Economics, at \nleast if asymmetries and/or heavy tails are involved. Nevertheless, in portfolio \nselection they have provoked several caveats such as the existence of good deals \nin most of the arbitrage free pricing models. In other words, models such as \nBlack and Scholes or Heston allow investors to build sequences of strategies \nwhose expected return tends to in nite and whose risk remains bounded or \ntends to minus in nite. This paper studies whether this drawback still holds if \nthe investor is facing the presence of multiple priors, as well as the properties \nof optimal portfolios in a good deal free ambiguous framework. \nWith respect to the rst objective, we show that there are four possible \nresults. If the investor uncertainty is too high he/she has no incentives to buy \nrisky assets. As the uncertainty (set of priors) decreases the interest in risky \nsecurities increases. If her/his uncertainty becomes too low then two types of \ngood deal may arise. Consequently, there is a very important di¤erence between \nthe ambiguous and the non ambiguous setting. Under ambiguity the investor \nuncertainty may increase in such a manner that the model becomes good deal \nfree and presents a market price of risk as close as possible to that re ected by \nthe investor empirical evidence. Hence, ambiguity may help to overcome some \nmeaningless ndings in asset pricing. \nWith respect to our second objective, good deal free ambiguous models \nimply the existence of a benchmark generating a robust capital market line. \nThe robust (worst-case) risk of every strategy may be divided into systemic \nand speci c, and no robust return is paid by the speci c robust risk. A couple \nof betas may be associated with every strategy, and extensions of the CAPM \nmost important formulas will be proved.
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How this classification was reachedexpand
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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".