Centred expected shortfall (CES): a traditional asset manager’s view on decomposing downside investment risk
Bibliographic record
Abstract
Risk driver contributions are key to understanding portfolio risk. Often, this is done by decomposing portfolio ‘volatility’. This is problematic in the presence of non-elliptical distributions. Some asset managers propose switching to value-at-risk (VaR) or expected shortfall (ES) as risk measures. Often the latter is preferred as it deals better with risk in sub-portfolios. However, we argue that the traditional asset management industry should, as a rule, ‘not’ apply ES directly. Instead, expected portfolio return should be first subtracted from it; this ‘Centred Expected Shortfall (CES)’ forms a natural extension of volatility. The ‘relative’ breakdowns of both are identical if the underlying multivariate distribution is elliptical. From a practical perspective, we show how to correctly decompose CES and how ES can be misleading. Moreover, we recommend plotting so-called ‘alpha-CES/volatility profiles’. These work with distribution-free risk estimates and give a bird’s eye view on the downside impacts of any non-ellipticalities as a function of the portfolio’s left tail size (alpha). Conveniently, these profiles also describe upside tail (surplus) risks. We end with two practical illustrations: A simple assets-only example based on historical data with assets as risk drivers; and a more complex Liability-Driven Investing (LDI) simulation example with factors as drivers. Notes: A) This version is the “authors’ original manuscript (AOM)” of an article published by Taylor & Francis in Quantitative Finance on 01 December 2023, available online: https://doi.org/10.1080/14697688.2023.2269992. B) The link in A) also shows a "Supplemental" section where you can download a freely available excel template which produces for your own dataset the CES decomposition results. Alternatively, you can directly download the template via its own URL: https://www.tandfonline.com/action/downloadSupplement?doi=10.1080%2F14697688.2023.2269992&file=rquf_a_2269992_sm5937.xlsm.
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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 | 0.005 | 0.010 |
| Meta-epidemiology (narrow) | 0.002 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".