Assessing the level of systematic risk
Characteristic straight line of a security
To assess the level of systematic risk of an individual stock, it is enough to compare its expected return with the expected return on the market portfolio. Researchers, in doing so, operate with yields that exceed the risk-free interest rate, i.е. with values representing additional returns calculated as the difference between the expected and risk-free rate of return (Figure 3.14).
Fig. 3.14. The ratio between the additional stock returns and the market portfolio
The characteristic straight line represented by the figure is constructed, as a rule, on the basis of statistical observations. Each point corresponds to the additional stock returns (the y-axis) and the market portfolio (the abscissa axis) for a certain period of time (for example, a month).
The spread of points around the characteristic line reflects the level of specific (non-systematic) equity risk. In particular, the farther away the points from the straight line, the more unsystematic the risk of shares. For a portfolio of 25-30 carefully selected stocks, the points will be grouped close to the characteristic straight line.
It is easy to verify that the analysis of the angular coefficient of the characteristic line, called in the international financial management beta coefficient (β), allows to obtain exhaustive information about the level of systematic risk of a particular share (Figure 3.15). In particular, if β = 1, this means that the additional yield of the stock changes in an exact (strict) correspondence with changes in the yield of the market portfolio. In other words, such an action is characterized by the same level of systematic risk as the entire stock market as a whole.
Fig. 3.15. Coefficient β and the level of systematic share risk
In the case where β & gt; 1, the additional yield of the stock grows faster than the additional yield of the market portfolio. Naturally, with a decrease in the additional yield of the stock market as a whole, the decrease in the yield of such a stock will be more significant, this is the risk. Considering the above, this type of stock is called aggressive. The value of β & lt; 1 means a corresponding lag in the growth of the additional yield of the stock from the increase in the additional yield of the market portfolio. Therefore, in the price model of the capital market, the beta coefficient reflects the sensitivity of the stock's yield to the change in the yield of the market portfolio, thus being the coefficient of the systematic risk of a particular security .
So the β-coefficient of the i-th stock (β,) can be calculated as follows:
where σ/ <5f - the standard deviation of the yield, respectively i - th share and market; ky - the correlation coefficient between the yield of r-i shares and the market's profitability as a whole.
In many countries β-coefficients are calculated centrally. In the US, for example, such well-known companies as Merrill Lynch and Value Line find β-coefficients for many hundreds companies. For most shares, β-coefficients fluctuate from 0.5 to 1.5, and their average value for all shares by definition is equal to one.
β-coefficient of the portfolio
By definition β-coefficient of the market investment portfolio . As for an arbitrary investment portfolio, its β-coefficient can be found as the weighted-average value of β-coefficients that make up this portfolio of securities (shares):
The weighting factors /, are equal to the share of the market value of the portfolio, which corresponds to one or another share. For example, if an investor holds a portfolio consisting of 10 shares with a coefficient β = 0.8 for a total of $ 100,000, and $ 10,000 is invested in each share, then = 0, 8. Suppose that one share of the portfolio is sold, and another is purchased with β = 2. It is easy to see that this will increase the risk of the portfolio under analysis to < >
Thus, β -the security ratio is its contribution to the risk of a diversified portfolio of shares, which can be reduced by including in the portfolio of shares having a low β-factor .
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