The GARCH-EVT-Copula Approach to Investigating Dependence and Quantifying Risk in a Portfolio of Bitcoin and the South African Rand
Bibliographic record
Abstract
This study uses a hybrid model of the exponential generalised auto-regressive conditional heteroscedasticity (eGARCH)-extreme value theory (EVT)-Gumbel copula model to investigate the dependence structure between Bitcoin and the South African Rand, and quantify the portfolio risk of an equally weighted portfolio. The Gumbel copula, an extreme value copula, is preferred due to its versatile ability to capture various tail dependence structures. To model marginals, firstly, the eGARCH(1, 1) model is fitted to the growth rate data. Secondly, a mixture model featuring the generalised Pareto distribution (GPD) and the Gaussian kernel is fitted to the standardised residuals from an eGARCH(1, 1) model. The GPD is fitted to the tails while the Gaussian kernel is used in the central parts of the data set. The Gumbel copula parameter is estimated to be α=1.007, implying that the two currencies are independent. At 90%, 95%, and 99% levels of confidence, the portfolio’s diversification effects (DE) quantities using value at risk (VaR) and expected shortfall (ES) show that there is evidence of a reduction in losses (diversification benefits) in the portfolio compared to the risk of the simple sum of single assets. These results can be used by fund managers, risk practitioners, and investors to decide on diversification strategies that reduce their risk exposure.
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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 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".