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A Portfolio of Two Securities

  • Peter Brusov
  • Tatiana Filatova
  • Natali Orekhova
  • Mukhadin Eskindarov
Chapter

Abstract

The main objective of any investor is to ensure the maximum return on investment. During the realization of this goal, at least two major problems appear: the first is in which of the available assets and in what proportions an investor should invest. The second problem is related to the fact that, in practice, as is well known, a higher level of profitability is associated with a higher risk. Therefore, an investor can select an asset with a high yield and high risk or a more or less guaranteed low yield. These two selection problems constitute a problem of investment portfolio formation, the decision which is given by portfolio theory, described in this chapter. We study in detail the portfolio of the two securities (Brusov and Filatova, Financial mathematics for masters, KNORUS, Moscow, 2014, p. 480; Brusov et al., Financial mathematics for bachelor, KNORUS, Moscow, 2010, p. 224, Tasks on financial mathematics for bachelor. KNORUS, Moscow, 2012, p. 285), which represents a more simple case, containing, however, all the main features of more common Markowitz and Tobin portfolios. It appears that when selecting anticorrelated or noncorrelated securities, you can create a portfolio with the risk lower than the risk of any of the securities of portfolio, or even zero-risk portfolio (for anticorrelated securities).

Keywords

Lagrange function Portfolio theory Maximum return Portfolio risk Minimal boundary 

References

  1. Brusov P, Filatova T (2014) Financial mathematics for masters. KNORUS, Moscow, p 480Google Scholar
  2. Brusov P, Brusov PP, Orehova N, Skorodulina S (2010) Financial mathematics for bachelor. KNORUS, Moscow, p 224Google Scholar
  3. Brusov P, Brusov PP, Orehova N, Skorodulina S (2012) Tasks on financial mathematics for bachelor. KNORUS, Moscow, p 285Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Peter Brusov
    • 1
  • Tatiana Filatova
    • 1
  • Natali Orekhova
    • 2
  • Mukhadin Eskindarov
    • 1
  1. 1.Financial University under the Government of Russian FederationMoscowRussia
  2. 2.Center of Corporate Finance, Investment, Taxation and RatingsThe Research Consortium of Universities of the South of RussiaRostov-on-DonRussia

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