THE EFFECT OF PORTFOLIO SIZE ON PORTFOLIO PERFORMANCE: AN EMPIRICAL ANALYSIS*

Abstract

TWO FACTORS determine the risk-return performance of a portfolio. They are the individual securities held and the diversification strategy of the portfolio. Diversification strategy can be divided into two parts, the number of securities held and the proportion of funds invested in each. This research focuses on the effect of portfolio size on portfolio performance where size is measured by the number of different securities held. Portfolio performance is measured in two dimensions, return and risk. The objective of this research is to strengthen the existing empirical knowledge regarding the relationship between portfolio size and portfolio return and between portfolio size and portfolio risk. In addition, the intent of this research is to determine an optimal portfolio size for common stock portfolios. A number of research studies have attempted to determine the effect of portfolio size on portfolio performance. To date, the basic empirical research has been done with random portfolios. Random selection of securities has two limitations. First, random selection of securities for investment portfolios is practiced only by academicians, not practitioners. Second, while the random selection procedure provides the effect of portfolio size on portfolio risk, it precludes the determination of the effect of portfolio size on portfolio return. The return on a portfolio of common stocks selected randomly from a feasible set of common stocks is an unbiased and consistent estimator of the mean return on that feasible set. Hence, the effect of portfolio size on portfolio return is lost when random selection is employed. Consequently, only one dimension, risk, has been considered in determining the effect of portfolio size on portfolio performance. This research represents an initial attempt to employ nonrandom portfolios in determining the effect of portfolio size on portfolio performance. Due to the employment of nonrandom portfolios, both dimensions of portfolio performance, return and risk, are investigated to determine the effect of portfolio size. The year-end portfolios (1967-1970) of eight randomly selected growth-income mutual funds provided thirty-two nonrandom portfolios. In order to measure the effect of portfolio size on portfolio return, portfolio risk and overall portfolio performance, it was necessary to simulate the portfolio building process. This was accomplished by ranking the securities within each mutual fund portfolio in order of portfolio inclusion, where the market value of the mutual fund's investment in each security was used as a proxy for the portfolio manager's ranking for portfolio inclusion. Furthermore, to permit the measurement of the effect of portfolio size on the various portfolio parameters, this research abstracted from the funds allocation decision and assumed the equal allocation of investment funds. The simulation of the nonrandom portfolios of increasing size led to statistical dependence among the parameter measurements on the simulated portfolios.