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Risk diversification on the Polish capital market.

Article Excerpt
Abstract

The basics of portfolio management theory and methods of efficient selection of assets and their financing have been created by Markowitz and Sharpe. They propose that risk diversification consists, generally speaking, of the increase in the number of securities in a portfolio. So, authors try to answer the question of how many securities have to be bought on a given market to assure a well-diversified portfolio, where the increase in the number of securities does not lead to a significant decrease in portfolio risk. To evaluate such a purpose on the Polish capital market, 20 companies were surveyed that are included in the WIG20 index in the period January 2-October 10, 2001. The returns were estimated on a weekly basis. The research shows that a portfolio of securities constructed, according to the Sharpe Model, has a wide application to the Polish capital market. (JEL C10)

Introduction

The basics of portfolio management theory and methods of efficient selection of assets and their financing have been created by [Markowitz, 1952; 1959]. According to his works, when constructing a portfolio of securities, it is the qualitative benefits yielded by diversification of investment in securities that gets the most attention. Risk diversification, i.e., risk reduction, proposed by Markowitz, consists, generally speaking, of the increase in the number of securities in a portfolio.

Given a portfolio comprised of N shares, where all variances and covariances are exactly the same, variance is greater than covariance, and the shares of securities in the portfolio are equal. Variance of such a portfolio [S.sub.p.sup.2] is given by the following formula [Tarczynski, 1997, p. 77]:

[S.sub.p.sup.2] = [N.summation over (i=1)][1/[N.sup.2]] x [S.sup.2] + [N-1.summation over (i=1)][N.summation over (j=i+1)][1/[N.sup.2]] x cov = [1/N] x [S.sup.2] + (1 - [1/N]) x cov, (1)

where 1/N is the share of each of N shares in the portfolio, [S.sup.2] is the variance for each of N shares in the portfolio, and cov is the covariance between all the pairs of shares in portfolio, which is the same for every pair.

Formula (1) implies that portfolio variance is a weighted arithmetic mean of variance and covariance of individual securities comprising portfolio. It is obvious that if the number of securities in portfolio N tends to infinity, portfolio variance decreases to the level of covariance:

[lim.[N[right arrow][infinity]]] [S.sub.p.sup.2] = cov. (2)

It proves that portfolio diversification (increase in the number of securities comprising portfolio) allows decreasing the share of individual security variances in total portfolio risk to zero. On the other hand, total portfolio risk, the lowest possible, cannot be lower than covariance, whose share in total risk cannot be decreased.

Evans and Archer [1968] proved that a random selection of securities to a portfolio would eliminate most of specific risk if the number of securities in the portfolio remained within the limits of 10-15. On the other hand, Wagner and Lau's research carried out in 1971 proved that investment in 16-20 securities reduced approximately 80% of a specific risk. Investment in one security implies exposure to more risk than necessary. Increase in the number of securities in portfolio leads to a significant risk reduction. It is important since the investment process on capital market is governed by the rule: The greater the level...

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