Monte Carlo Portfolio Optimization for Risk and Return Targets
Summary
The document explains how to explore portfolio allocations by repeatedly assigning random weights to four U.S. financial-sector stocks, calculating each portfolio’s annualized return and standard deviation, and comparing the results. It defines three selection goals: maximize the Sharpe ratio, minimize volatility, or seek the highest return near a chosen risk level. A worked example uses one year of historical prices, daily returns, a covariance matrix, and 10,000 simulated allocations to illustrate the process and show example weights for each objective.
The approach is a simple search over randomly sampled weights whose sum is one; increasing the number of draws may improve the chance of finding a strong candidate but requires more computation. The article’s output depends on the chosen assets, historical period, return estimates, and risk assumptions. It does not establish that the selected allocation will perform well out of sample, and the simulation can miss better allocations between sampled points. Its results are illustrative rather than evidence of future performance.
Key ideas
- Portfolio optimization can target maximum Sharpe ratio, minimum variance, or maximum return near a specified risk level.
- Monte Carlo simulation samples feasible asset weights and records the return and risk associated with each allocation.
- Daily mean returns and covariance estimates are used to calculate portfolio return and standard deviation.
- More random trials can improve the search but increase computation and do not guarantee a global optimum.
- Historical sample results depend on the selected assets and period and do not establish future performance.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.