Markowitz Portfolio Optimization
Report
Introduction
Markowitz (1952, 1956) pioneered the development of a quantitative method that takes the diversification benefits of portfolio allocation into account. Modern portfolio theory is the result of his work on portfolio optimization. Ideally, in a mean-variance optimization model, the complete investment opportunity set, i.e. all assets, should be considered simultaneously. However, in practice, most investors distinguish between different asset classes within their portfolio-allocation frameworks.
In our analysis, we view the process of asset allocation as a four-step exercise like Bodie, Kane and Marcus (2005). It consists of choosing the asset classes under consideration, moving forward to establishing capital market expectations, followed by deriving the efficient frontier until finding the optimal asset mix.
We take the perspective of an asset-only investor in search of the optimal portfolio. An asset-only investor does not take liabilities into account. The investment horizon is 5 - 10 years and the opportunity set consists of twelve asset classes. The investor pursues wealth maximization and no other particular investment goals are considered.
We solve the asset-allocation problem using a mean-variance optimization based on excess returns. The goal is to maximize the Sharpe ratio (risk-adjusted return) of the portfolio, bounded by the restriction that the exposure to any risky asset class is greater than or equal to zero and that the sum of the weights adds up to one. The focus is on the relative allocation to risky assets in the optimal portfolio.
In the mean-variance analysis, we use arithmetic excess returns. Geometric returns are not suitable in a mean-variance framework. The weighted average of geometric returns does not equal the geometric return of a simulated portfolio with the same composition. The observed difference can be explained by the diversification benefits of the portfolio allocation. We derive the arithmetic
Introduction
Markowitz (1952, 1956) pioneered the development of a quantitative method that takes the diversification benefits of portfolio allocation into account. Modern portfolio theory is the result of his work on portfolio optimization. Ideally, in a mean-variance optimization model, the complete investment opportunity set, i.e. all assets, should be considered simultaneously. However, in practice, most investors distinguish between different asset classes within their portfolio-allocation frameworks.
In our analysis, we view the process of asset allocation as a four-step exercise like Bodie, Kane and Marcus (2005). It consists of choosing the asset classes under consideration, moving forward to establishing capital market expectations, followed by deriving the efficient frontier until finding the optimal asset mix.
We take the perspective of an asset-only investor in search of the optimal portfolio. An asset-only investor does not take liabilities into account. The investment horizon is 5 - 10 years and the opportunity set consists of twelve asset classes. The investor pursues wealth maximization and no other particular investment goals are considered.
We solve the asset-allocation problem using a mean-variance optimization based on excess returns. The goal is to maximize the Sharpe ratio (risk-adjusted return) of the portfolio, bounded by the restriction that the exposure to any risky asset class is greater than or equal to zero and that the sum of the weights adds up to one. The focus is on the relative allocation to risky assets in the optimal portfolio.
In the mean-variance analysis, we use arithmetic excess returns. Geometric returns are not suitable in a mean-variance framework. The weighted average of geometric returns does not equal the geometric return of a simulated portfolio with the same composition. The observed difference can be explained by the diversification benefits of the portfolio allocation. We derive the arithmetic