Comparing Equal-Weight and Minimum-Variance Portfolios

Summary

The document describes a simulation comparing equal-weight portfolios with portfolios whose weights are chosen to minimize variance. In each iteration, it selects one asset from each of several groups, uses two years of daily returns to set the optimized weights, and compares annualized portfolio volatility. The author asks whether the equal-weight approach can outperform or whether the result could reflect a calculation or labeling error.

The document provides no results table, implementation details, or resolution to the question, so it does not establish which method performs better. It does, however, identify a useful evaluation problem: minimum variance measured on the same historical data used to choose weights is an in-sample objective, and its apparent advantage may not carry over to future returns. The comparison also depends on constraints, covariance estimates, and consistent return aggregation, none of which are specified. The evidence is therefore insufficient to diagnose the simulation or draw a performance conclusion.

Key ideas

• The simulation compares equal weights with weights optimized to minimize historical portfolio variance.
• Each iteration samples one asset from every group and uses daily returns from a two-year period.
• Annualized portfolio volatility is the stated comparison measure.
• The document asks whether equal weighting can outperform but provides no results or answer.
• In-sample optimization alone cannot establish how either approach will perform out of sample.

Tags

# Can simple risk management outperform portfolio optimization like this, or is there most likely an error?


# Can simple risk management outperform portfolio optimization like this, or is there most likely an error?












I am using a simulation approach to compare the performances achievable by simple risk management and portfolio optimization for portfolio selection. My problem is that my results indicate that simple risk management outperforms portfolio optimization. Is this possible or is there most likely an error in my simulation?

My simulation approach is as follows. Assume there are N different assets in the universe, each of which is assigned to one of K groups, based on some properties. For each of these assets I have daily returns data for a two-year period. Each iteration in the simulation randomly selects one asset from each of the groups. I.e., K assets are selected and will be assigned a weight in $[0, 1]$ Then, each asset is assigned a weight. The mean-variance approach calculates the optimal weights based on the daily returns data. The naive approach simply assigns the weight $1/M$ to each of the assets in the portfolio. This gives the portfolio returns, from which I calculate annualized portfolio volatility. The results are shown in the table below. Could these results be feasible or could it be that I made a mistake somewhere (e.g., mixed up the column names, incorrectly multiplied returns with weights, etc.)?

Edit: the optimal portfolio is the one with minimal variance over all returns.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.