Risk measures used by the models
| Risk measures | Models |
|---|---|
| Mean-Variance, Mean-VaR, Mean-Conditional VaR | Black–Litterman, Mean-variance |
| Below-mean absolute, semi-deviation | Multi-objective optimization |
| Variance | Robust portfolio |
| Variance and higher moments (e.g. skewness, kurtosis) | Multi-period Portfolio Selection with Fuzzy Returns |
| Volatility | Markov-switching asset allocation |
| Conditional Value-at-Risk (CVaR) | Risk Parity, Dynamic robust portfolio, robust mean-CVaR portfolio |
| Drawdown duration (average, maximum, and tail) | Portfolio model for optimizing drawdown duration |
| Robust version of variance | A robust markowitz mean-variance portfolio selection |
| Value-at-Risk (VaR) | Nonlinear portfolio selection, mean-VaR portfolio selection model |
| Semivariance | Mean-semivariance portfolio selection model |
| Beta | A multiple objective stochastic portfolio selection |
| S-shaped utility function and probability distortions | Behavioral portfolio selection |
| Liquidity risk, loss-averse utility, chance constraint | Behavioral portfolio |
| Spectral risk measure | A robust behavioral portfolio selection |
| Risk measures | Models |
|---|---|
| Mean-Variance, Mean-VaR, Mean-Conditional VaR | Black–Litterman, Mean-variance |
| Below-mean absolute, semi-deviation | Multi-objective optimization |
| Variance | Robust portfolio |
| Variance and higher moments (e.g. skewness, kurtosis) | Multi-period Portfolio Selection with Fuzzy Returns |
| Volatility | Markov-switching asset allocation |
| Conditional Value-at-Risk (CVaR) | Risk Parity, Dynamic robust portfolio, robust mean-CVaR portfolio |
| Drawdown duration (average, maximum, and tail) | Portfolio model for optimizing drawdown duration |
| Robust version of variance | A robust markowitz mean-variance portfolio selection |
| Value-at-Risk (VaR) | Nonlinear portfolio selection, mean-VaR portfolio selection model |
| Semivariance | Mean-semivariance portfolio selection model |
| Beta | A multiple objective stochastic portfolio selection |
| S-shaped utility function and probability distortions | Behavioral portfolio selection |
| Liquidity risk, loss-averse utility, chance constraint | Behavioral portfolio |
| Spectral risk measure | A robust behavioral portfolio selection |
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