Portfolio Opt - Practical Portfolio Optimization K V...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Practical Portfolio Optimization K V Fernando NAG Ltd Wilkinson House Jordan Hill Oxford OX2 8DR United Kingdom email: vince@nag.co.uk
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
i Abstract NAG Libraries have many powerful and reliable optimizers which can be used to solve large portfolio optimization and selection problems in the Fnancial industry. These versatile routines are also suitable for academic research and teaching. Key words Markowitz, mean-variance analysis, optimal portfolios, minimum variance portfolio, portfolio selection, portfolio allocation, portfolio diversiFcation, portfolio optimization, efficient frontier, mean-variance frontier, MV efficiency
Background image of page 2
ii Contents 1 Introduction 1 2 NAG Routines for Optimization 2 2 . 1 AS e l e c t i ono fL ib ra ryR ou t in e s................. 2 2.2 Quadratic Programming with Linear Constraints . . . . . . . 3 2 . 3 N on l e a rP ro g ramm ing . .................... 3 2 . 4 R t e sf o rSpa r s eM a t r ixP rob l em s.............. 3 2 . 5 F o rw a rdandR ev e r s eCommun i c a t i on . ............ 4 2.6 Hardware, Operating Systems and Environments . . . . . . . 4 3I n t e r f a c e s t oR o u t i n e s 4 3 . 1 P o r t f o l i oW e i gh t s......................... 4 3 . 2 P r im a ryD a t a........................... 4 3 . 3 G en e lL e a rCon s t t s ................... 5 3 . 4 N l e a s t t s ...................... 6 3 . 5 Co ldandW a rmS t a r t s...................... 6 4 The Optimization Problems 6 5 Processing of Raw Data 7 5 . 1 Th eCo v a r i an c a t r ixinF a c t o r edF o rm . .......... 7 5.2 Determination of the Singular Values of the Cholesky Factors 9 5 . 3 I fth v a r i c a t r ixA l r e adyEx i s t s............ 9 5 . 4 E i g v a lu e so v a r i c a t r ix. ............. 1 0 5 . 5 M i s s ingV a e s .......................... 1 0 6 Numerical Examples: Selection of Equities 10 7 Numerical Example: Asset Allocation 15 8 Transactions Costs 15 9 An Example Program 17 10 Acknowledgements 20
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
1 1 Introduction The selection of assets or equities is not just a problem of Fnding attractive investments. Designing the correct portfolio of assets cannot be done by human intuition alone and requires modern, powerful and reliable mathe- matical programs called optimizers. The Numerical Algorithms Group Ltd (NAG) is world renowned for its work on numerical algorithms, and NAG routines for optimization are being used extensively in industry, commerce and academia. Many leading Fnancial companies and institutions employ NAG optimizers to select, diversify and rebalance their portfolios. They are also used by business and management schools for teaching and research. Any investor would like to have the highest return possible from an in- vestment. However, this has to be counterbalanced by the amount of risk the investor is able or desires to take. The expected return and the risk mea- sured by the variance (or the standard deviation, which is the square-root of the variance) are the two main characteristics of a portfolio. Unfortunately, equities with high returns usually correlate with high risk. The behaviour of a portfolio can be quite di±erent from the behaviour of individual components of the portfolio. The risk of a properly constructed portfolio from equities in leading markets could be half the sum of the risks of individual assets in the portfolio. This is due to complex correlation patterns
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 08/11/2009 for the course ENGIN 120 taught by Professor Ilan during the Summer '08 term at University of California, Berkeley.

Page1 / 24

Portfolio Opt - Practical Portfolio Optimization K V...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online