Expected return and portfolio risk in case of a risk-free loan - Investments

Expected return and portfolio risk in case of a risk-free loan

Taking into account the above analysis, it is easy to show in the same way that if an investor composes a composition portfolio by purchasing securities from any effective portfolio ( A , B, T etc.), using borrowed funds borrowed under the risk-free percentage , the effective portfolios in this case will be the segments , , , etc. (see Figure 3.4). Such composite loan portfolios have a share , so formulas for calculating expected returns and standard deviation of such portfolios (for example, portfolio G, formed on the basis of securities of an effective portfolio A by attracting additional money borrowed at a percentage r f) will take the form

If , increasing the share of borrowed funds, the investor is able to continuously increase the expected return on the portfolio while increasing the risk of investing in similar portfolios.

Portfolio composition T. Let's return to Fig. 3.4. By choosing different portfolios A, T, B , etc., which lie on the border of effective portfolios, and the acquisition of risk-free securities/the investor is able to form various loan portfolios, which will correspond to the line segments etc. Suppose that the investor considers the level of risk to be optimal. As it follows from the figure, this level of risk corresponds to the different loan portfolios C 1 , C 2 and C. According to assumption 2, in this case the investor will prefer the loan portfolio C, which provides the highest yield. But this loan portfolio is obtained by combining the risk-free means f with an effective portfolio T, for which the segment is the tangent to the boundary curve effective portfolios.

Similarly, it can be shown that even in the formation of loan portfolios with the same level of risk the investor will prefer a portfolio lying on the continuation of the segment .

Since the investor can prefer any level of risk, then an important conclusion follows: if an investor has the ability to lend or borrow money at the same risk-free interest rate , then as a risk component any portfolio (loan or loan), he will take the portfolio T. This portfolio corresponds to the point T on the border of effective portfolios, where the line passing through the points and T, is a tangent to the curve of the effective portfolios boundary.

Mathematically, the point T corresponds to such an efficient portfolio for which the value takes the maximum value.

An important conclusion of the CAPM model is that in the portfolio T absolutely all securities having circulation on the financial markets should be present. Indeed, the absence of any j-th securities in the portfolio T means that the demand for all the investors was too low. But the lack of proper demand for the j -th security will lead to the fact that its price will begin to fall, and the expected profitability to grow. At some point, it will again become attractive to investors, and they will start buying it. Therefore, in the conditions of equilibrium of financial markets (and the equilibrium of these markets is one of the assumptions of the CAPM model), the portfolio T should contain all securities of the financial market. Such a portfolio is called a market portfolio, and we will designate it as a portfolio M.

So, taking into account assumptions 1-10 in the CAPM model, it is assumed that in the equilibrium of financial markets, all investors will endeavor to make such an investment decision (in what proportions W i acquire risk securities), which provides each of them forming a market portfolio M. The weight W i of each i th security in the market portfolio equals the ratio of market value i - th securities to the total market value of all securities in the market portfolio M :

Therefore, CAPM is a model where the expected returns of all securities are set so that the supply of money intended for investment (purchase of securities) equals the demand for securities from investors.

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