Elementary Derivation of Efficient Frontier Based on the Efficiency Function

Abstract

This paper provides the derivation of the index stock price as a quadratic curve between standard deviation and return values. The curve is known as the efficient frontier in the Portfolio Theory. Parameters in the parabolic curve are determined by a polynomial interpolation. The efficiency function is defined based on the efficient frontier obtained by interpolation of the given data. The efficient frontier is separated into two conditions : pessimistic condition and optimistic condition. The efficiency function is then renewed based on these two conditions. The analysis agrees with the Markowitz expectation that the chosen portfolio should be in the pessimistic condition