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| Type | Master's Thesis |
| Scope | Discipline-based scholarship |
| Title | On the Merits of the Black-Litterman Model: A Detailed Analysis |
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| Institution | University of Zurich |
| Faculty | Faculty of Business, Economics and Informatics |
| Number of Pages | 64 |
| Date | 2016 |
| Zusammenfassung | The Black-Litterman (BL) model is a quantitative framework designed to overcome the practical issues of applying Mean-Variance (MV) optimisation. It features a benchmark, or a market portfolio, which serves as the basis for the resulting optimal portfolio weights. In addition, investors can express subjective views on the expected returns of single assets, or combinations thereof, which lead to weight deviations from the given benchmark. Because of the inclusion of these exogenous views, the results obtained from the model are to a large extent dependent on them, which is a well recognised fact in the literature on that matter. This makes it harder to draw conclusions about the value added by the model. Although there is a large amount of research work on the BL model and its practical applications, it does not provide a clear answer to the stated problem. The objective of this master thesis is to thoroughly analyse the merits of the model by isolating the question about the quality of the views. In addition, it shall shed light on the practical application of the model, its combination with an active investment strategy and the arising challenges in doing so. Two approaches are chosen in order to answer the stated question, for which the Swiss stock market represented by the Swiss Market Index (SMI) is the selected investment uni- verse. In the rst one, it is assumed that the investor has perfect foresight and knows exactly what the realised returns in the next period will be. This is clearly an unrealistic scenario with an intentional forward-looking bias embedded in it. However, by guaran- teeing 100% correctness of the subjective views, an analysis framework is achieved, where the question about the quality of the exogenous return beliefs is irrelevant. As shown by other researches, going this way allows one to avoid joint tests on the qualities of the model, on the one hand, and the precision of the views, on the other hand. As a way of robustness testing and making the scenario a bit more realistic, a separate quasi-perfect foresight case is introduced. Here, random errors are embedded in the otherwise perfect beliefs, re ecting a very skilful investor, whose estimated future returns are on average correct. In the second approach, the assumption about perfect foresight is revoked and an in- vestment strategy is combined with the BL model. The role of the investment strategy is to provide the exogenous views required by the model. This realistic scenario is comple- mentary to the perfect foresight and shall provide additional insights for the conclusions to be drawn. Moreover, the implementation of a realistic investment strategy merged with the model is illustrative of the model workings and some of the challenges faced with I II regard to its calibration. Some of the parameters of the model, which ultimately determine the deviations from the benchmark portfolio, are hard to set and the guidance from the literature is either limited, or very divergent. An easily implementable method is introduced in this thesis, which allows to control these deviations by providing a target level for the sum of the total absolute deviations. This method reduces the parameter sensitivity of the results obtained by the BL model and also allows for a reasonable comparison against alternative naive methods of incorporating return beliefs. The obtained results from the perfect foresight demonstrate superiority of the BL model in comparison to a number of other methods, which also incorporate the investor views. Although these try to replicate the e ects that the model has on the nal portfolio weights, it is clear that the mixing method of BL is a more ecient. As it can be expected, markets are hard to beat and nding an investment strategy, which exhibits signi cant and convincing results is a challenging endeavour. The tested low beta strategy, which aims to exploit the low beta anomaly observed in some markets, provides slightly better results than the passive market portfolio. This small outperform- ance is however not statistically signi cant. Thus, it could be argued that the outper- formance obtained, in terms of risk-adjusted performance measures, is just a historical realisation of asset returns, and not a signi cant and persistent market anomaly within the SMI universe. This would speak against a recommendation to follow this strategy for the future. Nevertheless, the positive realisation of historical events is useful to demon- strate how the strategy combination with the BL model behaves. It is illustrated that the combination leads to better results than those achieved by the market with a much lower tracking error in comparison to the pure low beta strategy. This could be very attractive to less speculative investors who would like to measure their risk in terms of return deviations from a given benchmark. |
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