M.Sc Student | Eran Raanan |
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Subject | Financial Modeling Portfolio Optimization - Equilibrium Approach |

Department | Department of Industrial Engineering and Management |

Supervisor | Professor Haim Reisman |

Full Thesis text |

The equilibrium approach provides the solution to many problems raised by former optimization models introduced to investors in the capital market. The equilibrium approach builds at first a very diverse market portfolio, then allows the investor to experience his views in relation to different stocks yield, degree of confidence in his views and market state: Bearish or Bullish. Finally the equilibrium approach model makes sure to maintain reasonable weight distribution results. Such a model composed of two parts. First, the model extracts from the market all relevant information in order to build well define market portfolio. We can assume that market portfolio, or in other words: investor's benchmark, is a well-diversified portfolio built by different weights allocation. We can either observed all daily weights from the stock exchange web-site, or from various models that come to our assistant in defining market portfolio, such as: Markowitz Mean - Variance, Capital asset pricing model: 'CAPM' or its extension: three factors model of the CAPM'.

The next step is providing the investor tools to incorporate his personal opinions on any assets in the benchmark. Since most of the assets are correlated between themselves, even single change in one asset return will affect all the other weights in the portfolio and therefore build an entirely new portfolio.

This is where the main challenge of the equilibrium model stands. The model needs to adjust the market portfolio (i.e. benchmark) with any investor's views and maintain reasonable output results. Furthermore, we compel the model to allow the investor pointing his confidence level in each view to allow the optimization process to tilt across the entire range between market portfolio and portfolio which built based on the investor opinions alone.

After formulating such a mathematical model, I evaluate empirically its benefits using MATLAB algorithm which allows me to test the model with more than thousands simulations using several types of investors, different levels of confidence and different types of benchmark portfolios, and finally draw conclusions about how well equilibrium approach model takes the challenge.