Portfolio optimisation inputs
December 14, 2023
Expected Returns:
- Mean: The average historical return of a portfolio, serving as a basic estimate of future returns.
- Exponentially-Weighted Mean: This method gives more weight to recent returns, assuming they are more indicative of future performance.
- CAPM (Capital Asset Pricing Model): A more sophisticated approach that estimates expected returns based on a risk-free rate, the asset's beta, and the expected market return.
Risk Model (Covariance Matrix):
- Sample Covariance Matrix: Measures how different assets move in relation to each other using historical data.
- Semicovariance: Focuses only on the downside (or negative) movements, providing a view of risk that's more relevant to loss-averse investors.
- Exponential Covariance: Similar to exponentially-weighted mean, it gives more weight to recent movements in asset prices.
- Covariance Shrinkage: A technique to improve the estimation of the covariance matrix, especially when dealing with limited data.
- Minimum Covariance Determinant: An approach to identify a subset of observations that has the lowest covariance determinant, reducing the impact of outliers.
Objective Function:
- Maximum Sharpe Ratio: Aims to find the portfolio with the highest return per unit of risk.
- Minimum Volatility: Focuses on minimizing the portfolio's overall risk.
- Efficient Return: Seeks a target return with the lowest possible risk.
- Efficient Risk: Finds the highest return for a given level of risk.
- Maximum Quadratic Utility: Balances return and risk in a quadratic utility framework, allowing for more complex investor preferences.
Constraints:
- Long/Short: Allows for both buying (long) and selling (short) positions in the portfolio.
- Market Neutrality: Ensures the portfolio is not overly exposed to market movements.
- Minimum/Maximum Position Size: Sets limits on the proportion of the portfolio that can be allocated to any single asset.