Portfolio Optimization in a Multidimensional Structural-Default Model with a Focus on Private Equity
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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. <b>TOPICS:</b>Private equity, portfolio construction, VAR and use of alternative risk measures of trading risk, simulations
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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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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 it