Mean-variance optimization (MVO) is a widely used approach in portfolio management. It is a mathematical technique that aims to find the portfolio with the highest expected return for a given level of risk (measured as the portfolio variance).
On the other hand, mean-CVaR optimization (MCO) is a more recently developed approach that addresses some of the limitations of MVO. CVaR stands for Conditional Value at Risk, which is a risk measure that captures both the magnitude and the likelihood of extreme losses.
The main differences between MVO and MCO are:
1. Risk measure: MVO uses variance as a measure of risk, while MCO uses CVaR. CVaR is a more robust risk measure because it takes into account extreme events that can have a significant impact on the portfolio’s performance.
2. Treatment of downside risk: MVO treats downside risk symmetrically with upside risk, while MCO places more emphasis on the downside. This means that MCO portfolios are typically more conservative and have a higher allocation to safe assets.
3. Solution approach: MVO is a quadratic programming problem that can be solved analytically. MCO is a nonlinear optimization problem that is more challenging to solve, but numerical methods are available.
4. Sensitivity to input parameters: MVO is highly sensitive to the input parameters, especially the expected returns and covariance matrix. In contrast, MCO is less sensitive to these parameters and can handle more complex and uncertain scenarios.
In summary, MCO is a more advanced method that can lead to better risk-adjusted returns, especially in turbulent markets where downside risk is a concern. However, MCO requires more sophisticated modeling and computation, and may be subject to estimation errors and parameter uncertainty.