Evaluating the impact of inequality constraints and parameter uncertainty on optimal portfolio choice

We present new analytical results for the impact of portfolio weight constraints on an investor’s optimal portfolio when parameter uncertainty is taken into account. While it is well known that parameter uncertainty and imposing weight constraints results in reduced certainty equivalent returns, in the general case, there are no analytical results. In a special case, commonly used in the funds management literature, we derive analytical expression for the certainty equivalent loss that does not depend on the risk aversion parameter. We illustrate our theoretical results using hedge fund data, from the perspective of a fund-of-fund manager. Our contribution is to formalize the framework to investigate this problem, as well as providing tractable analytical solutions that can be implemented using either simulated or asset manager returns.