Investment Portfolio Analysis in Financial Mathematics

Abstract

This academic article present an analysis of constructing an efficient investment portfolio based on the efficient frontier theory, which gives the relationship between allocation of weight assets in investment portfolio and the expected return and the standard deviation of the investment portfolio. To construct an efficient investment portfolio consisting of n assets, a weight hyperplane is constructed, which contain all possible combinations of allocation of weight assets in the investment portfolio, laid in the n-dimensional space. Under a linear mapping, each possible combination of this allocation of weight assetsin the weight hyperplane is mapped to the corresponding order pair of (σ, μ) tracing out a curve that has a bullet shape like parabola open to the right in plan of 2-dimensional of standard deviation and σ expected return μ of investment portfolio. The set of points (σmin, μ) that givesthe minimum risk for each expected return isthe corresponding the combination of the allocation of weight assets generated the efficient investment portfolio.