Correspondence: Kwok Wai Yu, Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, PR China. Tel: +852 27664368; E-mail: carisa.yu@polyu.edu.hk

¹is a PhD student at The Hong Kong Polytechnic University. Her research interests focus on asset management, risk management and financial modelling.

²received his PhD from The University of New South Wales in 1994, and now is a professor in the Department of Applied Mathematics, The Hong Kong Polytechnic University. His research interests include nonsmooth analysis, vector optimisation and financial optimisation. He is a co-author of three research monographs, has over 140 publications and is a co-editor of three books. He is the recipient of ISI Citation Classic 2000 and an associate editor for several international journals, including Journal of Optimization Theory and Applications.

³is an associate professor of the Department of Applied Mathematics, The Hong Kong Polytechnic University. He received his PhD in statistics from the University of Hong Kong. He has published in journals such as Biometrika, Journal of Hydrology, Journal of Multivariate Analysis, Annals of the Institute of Statistical Mathematics, Canadian Journal of Statistics, Computational Statistics and Data Analysis, and European Journal of Operational Research. His current research areas include time series analysis, forecasting, statistical computations and financial statistics.

Received 29 March 2007; Revised 29 March 2007.

Abstract

This paper discusses the applications of the Sharpe rule in portfolio measurement and management. It proposes that a portion of the portfolio value should be invested in some other assets for portfolio improvement. By applying the Sharpe rule, it can be determined that new stocks are worthy of adding to the old portfolio if they satisfy a condition, in which the average return rate of these stocks is greater than the return rate of the old portfolio multiplied by the sum of the elasticity of the Value at Risk and 1. One attraction of our approach is diversification. A numerical example in the Hong Kong stock market is presented for illustration. Consideration is also given to the 'optimal' number of new assets to be added in two specific cases (ie, arithmetic series and geometric series regarding the sequences of expected returns and standard deviations). Some interesting simulation results show that a new portfolio with the 'highest' Sharpe ratio can be obtained by adding only a few new assets.