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 advantages when addressing some classical problems of Financial Economics, at least if asymmetries and/or heavy tails are involved. Nevertheless, in portfolio selection they have provoked several caveats such as the existence of good deals in most of the arbitrage free pricing models. In other words, models such as Black and Scholes or Heston allow investors to build sequences of strategies whose expected return tends to in nite and whose risk remains bounded or tends to minus in nite. This paper studies whether this drawback still holds if the investor is facing the presence of multiple priors, as well as the properties of optimal portfolios in a good deal free ambiguous framework. With respect to the rst objective, we show that there are four possible results. If the investor uncertainty is too high he/she has no incentives to buy risky assets. As the uncertainty (set of priors) decreases the interest in risky securities increases. If her/his uncertainty becomes too low then two types of good deal may arise. Consequently, there is a very important di¤erence between the ambiguous and the non ambiguous setting. Under ambiguity the investor uncertainty may increase in such a manner that the model becomes good deal free and presents a market price of risk as close as possible to that re ected by the investor empirical evidence. Hence, ambiguity may help to overcome some meaningless ndings in asset pricing. With respect to our second objective, good deal free ambiguous models imply the existence of a benchmark generating a robust capital market line. The robust (worst-case) risk of every strategy may be divided into systemic and speci c, and no robust return is paid by the speci c robust risk. A couple of betas may be associated with every strategy, and extensions of the CAPM most important formulas will be proved.
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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 | 0.003 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.008 | 0.001 |
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".