Out-of-sample performance of the Black-Litterman model

Abstract

The aim of this paper is to test the out-of-sample performance of the Black Litterman (BL) model for a German stock portfolio compared to the traditional mean-variance optimized (MV) portfolio, the German stock index DAX, a reference portfolio, and an equally weighted portfolio. The BL model was developed as an alternative approach to portfolio optimization many years ago and has gained attention in practical portfolio management. However, in the literature, there are not many studies that analyze the out-of-sample performance of the model in comparison to other asset allocation strategies. The BL model combines implied returns and subjective return forecasts. In this study, for each stock, sample means of historical returns are employed as subjective return forecasts. The empirical analysis shows that the BL portfolio performs significantly better than the DAX, the reference portfolio and the equally weighted portfolio. However, overall, it is slightly outperformed by the MV portfolio. Nevertheless, the BL portfolio may be of greater interest to investors because -according to this study, where the subjective return forecasts are based on historical returns of a rather long past period of time-it could lead in most cases to lower absolute (normalized) values for the stock weights and for all stocks to smaller fluctuations in the (normalized) weights compared to the MV portfolio. JEL classification numbers: C61, G11. Keywords: Black-Litterman, Mean-variance, Portfolio optimization, Performance.