Portfolio composition and critical line: a methodological approach

The purpose of this paper is to illustrate, at least pedagogically, composition of an efficient portfolio. Principally, two scenarios are examined. In the first we intend to minimise the portfolio variance and achieve a desired level of return. To do so, we find the optimal weights using Lagrange multiplier method. Short sales of securities are allowed. This implies that negative weights can be found. In the second case, we obtain the optimal portfolio composition, considering that weights cannot be negative. This suggests that short sales of securities are not allowed, and the Kuhn-Tucker system is used. Results are examined in the light of the investor's risk tolerance, and reveal that an investor who chooses an aggressive investment is focused more on return rather than risk. Conversely, when the investor's risk tolerance decreased, funds were invested more in stocks with both lower return and risk.