# Model risk in mean-variance portfolio selection: an analytic solution to the worst-case approach

## TL;DR

This paper derives an analytical solution for worst-case model risk in mean-variance portfolio selection, revealing that in the minimum-variance case, model risk simplifies to estimation risk, contrasting previous numerical findings.

## Contribution

It provides the first analytical solution to the worst-case model risk problem in mean-variance portfolio selection, improving understanding of risk reduction.

## Key findings

- Analytical solution differs from previous numerical results.
- In minimum-variance case, model risk reduces to estimation risk.
- Numerical example illustrates the theoretical findings.

## Abstract

In this paper we consider the worst-case model risk approach described in Glasserman and Xu (2014). Portfolio selection with model risk can be a challenging operational research problem. In particular, it presents an additional optimisation compared to the classical one. We find the analytical solution for the optimal mean-variance portfolio selection in the worst-case scenario approach. In the minimum-variance case, we prove that the analytical solution is significantly different from the one found numerically by Glasserman and Xu (2014) and that model risk reduces to an estimation risk. A detailed numerical example is provided.