An Investigation of the Relationship between Portfolio Sizes and Unsystematic Risk of Common Stock in Iran

The present paper deals with the relationship between portfolio sizes and unsystematic risk using diversification method introduced by Evans & Archer for monthly data in Tehran stock market during 1994-2003. The results show that there is an inverse but significant relation between the portfolio sizes and unsystematic risk. It also shows that the unsystematic risk can be eliminated by increasing the portfolio size. Specifically, we have shown that the portfolio risk reduced as the number of securities increased in an asymptotic way in which the asymptotic line will be converged to the average systematic risk of the market at a portfolio including 36 securities. In other words, the unsystematic risk reduces dramatically as securities increase and when it reaches beyond 36 securities, then the diversification effect will be reduced and / or unsystematic risk will be nearly vanished.