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

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.


An Analysis of momentum and mean reversion effects on equity indices
Özbilge, Armağan; Yolcu Okur, Yeliz; Nazlıben, Kamil Korhan; Department of Financial Mathematics (2015)
Momentum and mean-reversion effects have become very popular in finance literature for the last two decades since their presence can generate abnormal profit patterns by applying either relative strength or contrarian trading strategy accordingly. Even though there are some common factor explanations for return reversals, they might not provide the full picture for return persistence. In our theoretical framework, we analyse some of the well-known discrete time momentum studies including the initial one and...
An Examination of betas for Borsa İstanbul
Koca, Onur; Oran, Adil; Department of Business Administration (2016)
This study aims to investigate the Betas, which is called as systematic risk and introduced by Capital Asset Pricing Model (CAPM), of stocks traded in Borsa Istanbul (BIST). Issues about Beta have been examined for many years and mainly focus on its estimation and stability. These topics set up the core of this thesis. The closing prices of 203 eligible stocks between 2005 and 2015 are used in the work and data is collected from Thomson Reuters. The estimation of Beta is performed in four different methods,...
Application of stochastic volatility models with jumps to BIST options
Rahiminejat, Monireh; Sezer, Ali Devin; Department of Financial Mathematics (2017)
This thesis gives a derivation of call and put option pricing formulas under stochastic volatility models with jumps; the precise model is a combination of Merton and Heston models. The derivation is based on the computation of the characteristic function of the underlying process. We use the derived formulas to fit the model to options written on two stocks in the BIST30 index covering the first two months of 2017. The fit is done by minimizing a weighted $L_2$ distance between the observed prices and the ...
Investor attention and IPO performance
Akgün, Başak Elif; Danışoğlu, Seza; Department of Business Administration (2016)
This study examines the influence of pre-IPO investor attention on short- and long-run IPO returns and post-IPO stock liquidity in an emerging market. Individual investor attention is proxied by both passive and active measures. Passive attention is proxied by a traditional media coverage whereas active attention is proxied by a measure that is constructed from Google search volume (GSV) data. Findings imply that, unlike U.S. market findings, investor attention prior to the IPO date does not have an influen...
A Comparison of constant and stochastic volatility in Merton’s portfolio optimization problem
Öztürk, Ozan; Sezer, Ali Devin; Department of Financial Mathematics (2018)
Merton's Portfolio Problem is a dynamic portfolio choice problem, which assumes asset returns and covariances are constant. There is well documented evidence that, stock returns and volatilities are correlated. Therefore, stochastic volatility models in dynamic portfolio problems can give better results. The work [J. Liu, Portfolio selection in stochastic environments, Review of Financial Studies, 20(1), 2007] developed a general dynamic portfolio model that allows the parameters of the model to depend on a...
Citation Formats
C. Adaş, “An Application of the Black Litterman model in Borsa İstanbul using analysts’ forecasts as views,” M.S. - Master of Science, Middle East Technical University, 2016.