Training and Development
DEPARTMENT OF ECONOMICS Uppsala University Thesis Work Economics D Author: Jonathan Mårtensson Tutor: Lennart Berg Term and Year: Autumn 2005
Portfolio optimisation
- improved risk-adjusted return?
Abstract
In this thesis, portfolio optimisation is used to evaluate if a specific sample of portfolios have a higher risk level or lower expected return, compared to what may be obtained through optimisation. It also compares the return of optimised portfolios with the return of the original portfolios. The risk analysis software Aegis Portfolio Manager developed by Barra is used for the optimisations. With the expected return and risk level used in this thesis, all portfolios can obtain a higher expected return and a lower risk. Over a six-month period, the optimised portfolios do not consistently outperform the original portfolios and therefore it seems as though the optimisation do not improve the return of the portfolios. This might be due to the uncertainty of the expected returns used in this thesis.
Keywords: Efficient frontier, mean-variance optimisation, portfolio optimisation, Sharpe ratio
1
Table of contents
1 INTRODUCTION 3 1.1 BACKGROUND .............................................................................................................................................. 3 1.2 PURPOSE OF STUDY .................................................................................................................................... 4 1.3 LIMITATIONS ................................................................................................................................................. 4
2 THEORY
5
2.1 RETURN ....................................................................................................................................................... 5 2.2 RISK .............................................................................................................................................................
Portfolio optimisation
- improved risk-adjusted return?
Abstract
In this thesis, portfolio optimisation is used to evaluate if a specific sample of portfolios have a higher risk level or lower expected return, compared to what may be obtained through optimisation. It also compares the return of optimised portfolios with the return of the original portfolios. The risk analysis software Aegis Portfolio Manager developed by Barra is used for the optimisations. With the expected return and risk level used in this thesis, all portfolios can obtain a higher expected return and a lower risk. Over a six-month period, the optimised portfolios do not consistently outperform the original portfolios and therefore it seems as though the optimisation do not improve the return of the portfolios. This might be due to the uncertainty of the expected returns used in this thesis.
Keywords: Efficient frontier, mean-variance optimisation, portfolio optimisation, Sharpe ratio
1
Table of contents
1 INTRODUCTION 3 1.1 BACKGROUND .............................................................................................................................................. 3 1.2 PURPOSE OF STUDY .................................................................................................................................... 4 1.3 LIMITATIONS ................................................................................................................................................. 4
2 THEORY
5
2.1 RETURN ....................................................................................................................................................... 5 2.2 RISK .............................................................................................................................................................
References: Articles Black, F (1994), “Estimating Expected Return” Financial Analysts Journal, Jan/Feb 1995, Volume 51, Issue 1, p Web documents Avanza Vikingen AB, “Vikingen Option” http://www.avanzavikingen.se/templates/Product.aspx?PageID=247 (2005-12-04) Barra Inc, (2002-04-01). “Portfolio Management and Risk Control” http://www.barra.com/products/pdfs/AegisDataPortManRiskControl.pdf (2005-11-16) Barra Inc, (2002-04-01) Schwartz, T, (2000-03-15). “How to Beat the S&P 500 with Portfolio Optimization” http://www.departments.bucknell.edu/management/apfa/Dundee%20Papers/27Schwartz.pdf (2005-11-18) 22