Portfolio Optimization for Binary Options Based on Relative Entropy
Bibliographic record
Abstract
The portfolio optimization problem generally refers to creating an investment portfolio or asset allocation that achieves an optimal balance of expected risk and return. These portfolio returns are traditionally assumed to be continuous random variables. In An Entropy-Based Approach to Portfolio Optimization, we introduced a novel non-parametric optimization method based on Shannon entropy, called return-entropy portfolio optimization (REPO), which offers a simple and fast optimization algorithm for assets with continuous returns. Here, in this paper, we would like to extend the REPO approach to the optimization problem for assets with discrete distributed returns, such as those from a Bernoulli distribution like binary options. Under a discrete probability distribution, portfolios of binary options can be viewed as repeated short-term investments with an optimal buy/sell strategy or general betting strategy. Upon the outcome of each contract, the portfolio incurs a profit (success) or loss (failure). This is similar to a series of gambling wagers. Portfolio selection under this setting can be formulated as a new optimization problem called discrete entropic portfolio optimization (DEPO). DEPO creates optimal portfolios for discrete return assets based on expected growth rate and relative entropy. We show how a portfolio of binary options provides an ideal general setting for this kind of portfolio selection. As an example we apply DEPO to a portfolio of short-term foreign exchange currency pair binary options from the NADEX exchange platform and show how it outperforms leading Kelly criterion strategies. We also provide an additional example of a gambling application using a portfolio of sports bets over the course of an NFL season and present the advantages of DEPO over competing Kelly criterion strategies.
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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 | 0.000 | 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) | 0.004 | 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".