Generalizing the Sharpe Ratio and Infinite Divisibility in Financial Markets
Bibliographic record
Abstract
Investments with high Sharpe ratios tend to be fixed income investments, particularly short-term bonds. Such securities dominate income investment, but not growth investment. We generalize the Sharpe ratio to interpolate smoothly between risk-averse and risk-seeking behaviors, with the traditional Sharpe ratio as a special case. The generalized ratios may be used to optimize portfolios within a lifestyle strategy or a lifecycle strategy. We demonstrate that the Sharpe ratio has an interpretation connected to value at risk (VaR), if returns are normally distributed. We study broad market indices and indicators for US stocks, US corporate bonds, gold, and Japanese stocks. Using monthly data obtained from FRED, we show that these datasets are neither normal, nor log-normal, nor stable. We argue that none of these distributions is appropriate for market data. We argue instead for using infinitely divisible distributions, and fit Pearson distributions to the data.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.007 | 0.051 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.000 | 0.004 |
| Scholarly communication | 0.003 | 0.009 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 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".