# 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.