ANALYSIS OF ARBITRARILY SMALL RISK PORTFOLIO

Abstract

In the paper there have been given formulae for risk and return of market portfolio, and, consequently, the range of risk and return variation of any portfolio from the capital market line. There have also been given formulae for composition, risk, and return of such a portfolio, depending on the level of risk aversion, or, as an equivalent, on the level of expectations of an adequate return. Unfortunately, it is impossible to apply the new results to multi-element portfolios. However, such a possibility arises after the introduction of a notion of an arbitrarily small risk portfolio in this paper. Initially, the arbitrary decrease of risk refers to a minimum risk stock portfolio, with a possibility of considering a portfolio with an arbitrary number of stocks. After the inclusion of bonds, the portfolio’s risk may fall even to zero. Due to the short sale, it is also possible (at least, theoretically) to obtain arbitrarily big return.