Portfolio Optimization in a Multidimensional Structural-Default Model with a Focus on Private Equity
Bibliographic record
Abstract
Investments in various asset classes, such as private equity or hedge funds, are prone to default risk, which needs to be accounted for when calculating individual investment opportunities and optimal portfolio selection. The correspondent literature on portfolio optimization, however, mostly disregards default risk and accordingly skewed return distributions. This article presents a realistic and tractable framework for a portfolio optimization, including default risk, with a specific focus on private equity investments. Default events are modeled by means of a Merton- or Black–Cox structural model. On a portfolio level, the mean and covariance of the resulting return distribution can be derived analytically, allowing for a classical mean-variance optimization. To include tail risk, we additionally present a Monte-Carlo simulation for a mean conditional value-at-risk optimization. The article concludes with an application to unlisted private equity and compares the results with a model proposed by Hamada [1972], which does not explicitly consider default risk. TOPICS:Private equity, portfolio construction, VAR and use of alternative risk measures of trading risk, simulations
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 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".