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.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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 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".