Abstract
It is commonly thought that a poorly conditioned covariance matrix causes the sensitivity of mean-variance optimised portfolios to deviations in expected return forecasts. In this research, we question this explanation and show that it does not necessarily hold when a budget constraint is included in the optimisation problem. Our research is centred on the analytical results derived by Best and Grauer (1991) that describes the maximum amount by which a portfolio and its performance can change due to changes in the mean vector. Our empirical analysis shows that these derived bounds can overstate the actual corresponding maximums by several orders of magnitude. We explain these results with reference to the original derivations. In conclusion, we find that these bounds, and the condition number, in particular, are unable to characterise portfolio sensitivity.
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