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.


  • 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.