An Application of the Black Litterman model in Borsa İstanbul using analysts’ forecasts as views

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2016
Adaş, Cansu
The optimal number of stocks to include in a portfolio in order to achieve the maximum diversification benefit has been one of the issues in which investors have focused on since Markowitz introduced fundamentals of the Modern Portfolio Theory. Each stock included in an investor's portfolio decreases the portfolio risk, while increasing the transaction costs incurred by the investor to create this portfolio. In this thesis, the size of a well-diversified portfolio consisting of stocks included consistently in the Borsa İstanbul-50 (BIST-50) Index during every calendar year from 2005 to 2015 are determined. Due to the differences in the number of stocks consistently included in the BIST-50 index and the correlation between these stocks from one year to another, the range for the optimal number of stocks varies between 8-10 to 16-18 stocks for the years in the sample period analyzed. The results in this thesis indicate that the average size of the portfolio for the years examined in this thesis is between 11 and 13 stocks. The same analysis is repeated by using posterior variance-covariance matrix derived from Black-Litterman (B-L) portfolio optimization model, which is another subject of this thesis. When the results derived from both the prior and the posterior variance-covariance matrices are compared, no remarkable differences are observed. Another issue that investors have been interested in is the allocation of funds across stocks included in a portfolio to earn the maximum return. Although Markowitz made a significant contribution to portfolio optimization in theory, he was criticized in practice for his model's high sensitivity to inputs and disregard to investors' views. To resolve some of the problems with Markowitz Model, B-L, developed a model which uses the market returns derived from the Capital Asset Pricing Model (CAPM) as its first estimate, and updates this first estimate with investors' views. In this thesis, market returns of each stock included consistently in the BIST-50 Index during the whole one year are combined with average return expectations of Bloomberg financial analysts for the corresponding stock to incorporate investor views. It is observed that the weights of stocks on which Bloomberg analysts did not state any opinion do not change that much from their market capitalization weights. It is observed that the posterior weights of some stocks on which Bloomberg analysts specified views do not change in the same direction as the views expressed on them. For example, it is possible to observe a negative change in the weight of a stock when the analysts express a positive view on this stock or vice versa. Possible reasons for these counterintuitive changes in the weights of stocks are the covariance structure of the stocks and the way the analyst views are defined. These explanations are shown to be instrumental by using an example of a portfolio with 3 stocks. Furthermore, first the budget constraint and then the short selling constraint in addition to the budget constraint are imposed on B-L portfolio optimization, and the results are analyzed. Finally, optimal B-L portfolios obtained by incorporating average views of Bloomberg analysts and the portfolios constructed from the CAPM are compared in terms of the Sharpe ratio and efficient frontier. As a result of these comparisons, it is seen that under certain conditions the portfolios based on the B-L Model perform better than the portfolios based on the CAPM. However, under some other conditions the portfolios based on the CAPM perform better than the portfolios based on the B-L Model.