SIZE AS A FUNCTION OF PORTFOLIO OPTIMIZATION

Abstract

The issue of the optimal number of securities an investor can hold to achieve optimal diversification has
remained controversial in corporate and academic cycles. Harry Markowitz model initiated a novel
explanation on the effect of number of securities on portfolio diversification. Modern portfolio theory
postulated that increasing the size of a portfolio reduces idiosyncratic risk and the investor can achieve
optimal risk-adjusted performance. Markowitz (1952) formulated the portfolio selection problem as a
comparison of mean and variance of a portfolio of assets. The number of securities to invest, the
combination of securities in a portfolio and the risk involved are vital considerations for investors.
Holding too few stocks exposes the investor to idiosyncratic risk while holding too many stocks becomes
too costly in terms of numerous transactions required to build initial portfolio and the opportunity cost to
monitoring a large diversified portfolio. It is not clear how many stocks are sufficient to achieve full
diversification.
Key words: Portfolio, Optimization, Size, Risk, Securities.