Title: Portfolio composition and critical line: a methodological approach

Authors: Agim Kukeli; Fitim Deari; Carmen Rocşoreanu

Addresses: Midwestern State University, Wichita Falls, Texas, USA ' South East European University, 1200 Tetovo, Macedonia ' University of Craiova, 200585 Craiova, Romania

Abstract: 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.

Keywords: Lagrange multiplier; Kuhn-Tucker system; return; risk.

DOI: 10.1504/IJRAM.2019.101289

International Journal of Risk Assessment and Management, 2019 Vol.22 No.2, pp.195 - 211

Accepted: 23 Dec 2018
Published online: 30 Jul 2019 *

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