10. A Portfolio of Two Securities

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).