Modern Portfolio Theory

2 Study of the theoretical fundamentals of the modern portfolio theory

In the first paragraph we show the crucial differences between the modern portfolio theory and pre-Markowitz one, summarize the mathematical framework of the MPT and critically evaluate the core assumptions building the MPT. This paragraph is devoted to the second stage of the portfolio selection process assuming that all input parameters of the model are true.

2.1 Definition of the modern portfolio theory

Harry Markowitz is highly regarded as a pioneer in theoretical justification of investor’s behavior and development of optimization model for portfolio selection process. In 1990, Markowitz shared a Nobel Prize for his contributions to financial economics and corporate

Yet, if we ignore market imperfections, the foregoing rule never implies that there is a diversified portfolio which is superior to all non-diversified ones. The hypothesis recommends the investor to put all his funds in the security with the greatest discounted value. If two or more securities have, the same value, then any of these or any combination of these is as good as any other. Thus, according to this logic the investor would never (strictly) prefer a diversified portfolio to all non-diversified ones. Nevertheless, in the real world most investors hold portfolios consisting of different (types of) securities. Therefore, the theory does not reflect the existing investment strategies. Markowitz summarizes this conflict between the theory and practice very precisely: “Diversification is both observed and sensible; a rule of behavior which does not imply the superiority of diversification must be rejected both as hypothesis and as a

In general, risk measure should assess the probability, essence, and intensity of a deviation from the expected value of return. Nevertheless, Markowitz portfolio selection theory states that the risk of each asset in isolation is not crucial, but the contribution of each asset to the risk of the portfolio is decisive. In context of a portfolio, the total risk of a security can be divided into two basic components: systematic risk (also known as market risk or common risk) and unsystematic risk (also known as diversifiable risk). Although, since the returns on different assets are correlated to at least some degree, unsystematic risk can never be completely eliminated regardless of how many types of assets are aggregated in a portfolio, it can be significantly reduced by the diversification of securities within a