Portfolio optimization: 63270

Extrait / Introduction

Extrait / Introduction :

At the beginning of the internship, it was quite a shift to start thinking in banking terms, where I was used to reason in a pure mathematical context. But as with most things in life, with a lot of curiosity, patience and perseverance a nice result can be made. I have learned a lot during the internship. It was surprising for me how much of the four-year mathematical studies I was able to use in the banking world. Optimizing, statistics, linear algebra, second order cone programming and the use of MATLAB are just a few subjects I used during the last seven months.

Plan

Plan :

The portfolio theory of Markowitz 5 2.1 Ecient frontier . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Minimum variance portfolio . . . . . . . . . . . . . . . . . . . . . 8 2.3 Tangency portfolio . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4 Optimal portfolio . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.5 Adding a risk-free asset . . . . . . . . . . . . . . . . . . . . . . . 14 2.5.1 Capital market line & market portfolio . . . . . . . . . . . 14 2.5.2 Optimal portfolio . . . . . . . . . . . . . . . . . . . . . . . 16 2.6 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.7 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.7.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.7.2 Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.8 References . . . . . . . . .

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