Testing Markowitz Portfolio Sensitivity to Uncertain Expected Returns

Summary

The document describes a portfolio robustness exercise using a Markowitz model. The author estimates expected returns and covariances from historical monthly stock data, finds portfolios associated with minimum and maximum expected returns, and then perturbs the expected-return estimates by randomly generating alternative vectors within a narrow range around the original values. They solve the portfolio problem for the original and perturbed estimates at a specified target return.

The author asks whether to compare the average perturbed portfolio weights with the original portfolio, for example using a distance measure, and what such a comparison would reveal. This frames a useful question about how sensitive optimized allocations are to estimation error in expected returns. However, the document provides no results or resolution, and it does not specify constraints, a distance metric, or how to interpret the chosen target return. The random perturbations are illustrative assumptions, not evidence that the tested range or distribution matches real forecasting uncertainty.

Key ideas

• Markowitz portfolio weights can change when expected-return estimates are perturbed.
• The described exercise compares an original optimized portfolio with portfolios based on alternative return vectors.
• A distance between average perturbed weights and original weights is one possible sensitivity measure.
• The document poses, but does not answer, how to interpret such a comparison.
• The perturbation range and random distribution are assumptions whose realism is not assessed.

Tags

# Markowitz models with uncertain returns


# Markowitz models with uncertain returns












I am analyzing the Markowitz models with uncertain returns as follows: after calculating the expected returns and the covariances of 30 monthly historical series of 30 stocks, I resolve the Markowitz model to determine the minimum and maximum expected returns. After randomly generating with uniform distribution five vectors of random returns with values ​​in the intervals $ [0.95 R_i, 1.05 R_i] $. For the original expected yield vector and for each yield vector generated, I resolve the Markowitz model with the required yield of $ R = 1/2 (R_ {max} -R_ {min})$ thus obtaining the exact portfolio and five perturbed portfolios .

I am asked to calculate the average of the disrupted portfolios and to compare it with the exact portfolio, for example by calculating the distance from the average portfolio to the exact one

By average portfolios do you mean the average odds found by solving the exact model? What should I expect? What do you think is the reason to analyze these perturbed portfolios?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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