Asset Allocation; Construction Problem; Forecasts; Confidence Levels; Performance and Stability Analysis
In an asset allocation task an investor seeks the optimal combination of assets that best suits his needs in an uncertain environment. The most popular approach to asset allocation is the mean variance model by Markowitz. However, using the Markowitz optimization will lead to portfolio weights that tend to be extreme, instable and poorly diversified. This is because the traditional Markowitz approach treats the inputs as if they were known with 100% certainty. An alternative approach is the Black-Litterman model. The Black-Litterman model uses the market portfolio as a neutral starting point that initially requires zero certainty about the inputs. The market returns implied in the market portfolio can then be tilted in accordance with the investors views by using a Bayesian approach. The Black-Litterman model extended by Meucci's weighting approach gives the opportunity to valuate this certainty/uncertainty by using confidence in subjective views. In this context, the following questions are particularly of interest: a. In how far affect different levels of confidence in subjective views the asset allocation? b. How do different levels of confidence in subjective views concern the portfolio's performance? c. And how do different levels of confidence in subjective views affect the portfolio's stability and risk? A detailed analysis of these questions unveils interesting asymmetries in the risk-return profile that an investor may take advantage of. In addition, the finalizing outlook suggests new fields of application for the Meucci Black-Litterman model and Bayesian approaches in general, such as a decision making/investment tool in corporate finance as well as a new method to bring in subjective views on the second moment of the return distribution with regard to stress events.