The Black-Litterman Model: An Investigation of Confidence
Abstract: This paper examines Idzorek’s extension of the Black-Litterman model with respect to confidence levels and makes a general comparison with the Canonical Reference Model. To test Idzorek’s method a global equities portfolio is constructed using assets representing nine different countries consisting in total of 80.9% of the global equities market. Two views are specified, one absolute view and one relative view. A sensitivity analysis of the weights is then performed by altering the investors’ confidence in each view based on an interval from 0% to 100%. The portfolio weights are also derived using the Canonical Reference Model without altering the investors’ confidence. Monthly return data is used spanning a 5-year period from May 2016 to April 2021, totaling 60 observations. Bayes-Stein shrinkage estimation is applied to derive the historical covariance matrix of excess returns. This paper shows that there can be both a linear and a non-linear relationship between the weight of the views and the level of confidence. And that this relationship can differ within the same portfolio. Because the relationship can be non-linear it is concluded that the marginal effect of the level of confidence can vary within the view itself. This means that the sensitivity of the views with respect to confidence will fluctuate between different levels of confidence. The results also show that the weights derived using the Canonical Reference Model are comparable to roughly 50% confidence when using Idzorek’s approach. And finally, that the sensitivity of the weights involved in the views is also dependent on their market capitalization weight(s) as well the specified excess return.
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