Portfolio Evaluation with the Vector Distance Based on Portfolio Composition

We propose a novel portfolio evaluation method, a distance-based approach, which directly evaluates the portfolio composition rather than portfolio returns. In this approach, we consider a portfolio as an estimator for an in-sample tangency portfolio, which we define as the optimal reference portfolio. We then evaluate the portfolio by computing its vector distance to the optimal reference portfolio. In search of the proper distance-based performance measure, we choose four representative vector distances and compare their suitability as a new portfolio performance measure. Through extensive statistical analysis, we find that the Euclidean distance is the most proper distance-based performance measure of the four representative vector distances. We further verify that a portfolio with a large Euclidean distance is not desirable because not only does it provide a low utility implied by the first four moments of portfolio returns, but also it is not likely to maintain its long-term performance. Hence, the Euclidean distance can complement the return-based performance measures by confirming the reliability of a portfolio in its investment performance.