Bibliographic record
Abstract
There is much discussion in the academic and practitioner literature about the appropriate number of stocks that make up a well diversified investment portfolio. Likewise, there has been a lively dialogue on the topic of multi-period diversification and the perception that a longer time horizon decreases the riskiness of an investment. However, there is little, if any, research on the inter-relationship and trade-off between the two possible dimensions of diversification; namely, the number of stocks in a portfolio (which we call space), and time. In this brief paper we will quantify the link between the two dimensions by examining the effect of both space and time on the shortfall risk of an investment portfolio. The shortfall risk, originally introduced into finance by A. D. Roy (Econometrica, 1952), and employed by many others since, is defined equal to the probability that a portfolio will under-perform the return from the risk-free asset. This risk framework allows us to compute the marginal benefit of one more investment asset versus one more investment year. We obtain the somewhat paradoxical result that although, in aggregate, space diversification is preferred to time diversification for reducing shortfall risk, on the margin, it may be better to increase the holding period as opposed to the size of the portfolio.
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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 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.007 | 0.016 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 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".