On the number of securities which constitute an efficient portfolio

The purpose of this paper is to discuss the relationship between the number of securities which constitute an efficient portfolio as defined by the standard mean-variance portfolio selection model and the number of periods used to compute the efficient portfolio. It is shown that the number of data gives the upper bound of the number of securities which constitute an efficient portfolio, when each efficient portfolio is unique for a given expected return. Empirical tests based on actual return data show that this upper bound is very tight when the number of data is small. However, when more data are used, the upper bound becomes looser. This result is incompatible with the market efficiency. These empirical tests also indicate that a very tight upper bound often causes a degenerate case ensuring zero-variance portfolios.