Beta and Systematic Risk

Beta and Systematic Risk In CAPM the level of systematic risk of a financial asset is known as its 'beta' (P). The market portfolio, M, has a value of 1. Assets with more systematic risk than the market have a ß greater than 1. If an asset has less systematic risk than the market, its ß is less than 1. If an asset has the same systematic risk as the market, its ß is equal to 1. The risk premium on an asset is thus directly proportional to its ß so that, for any asset i its expected return E(ri) is given by: To understand ß intuitively, remember that when we are looking at the variation of a large portfolio of investments the covariance terms dominate our calculations. In other words, it is the covariance of the returns of portfolio assets with each other that determines the risk of a portfolio. The market's perception of the risk of an individual share is no different. It is the covariance of the returns of an individual share with the other shares in the market that determines its risk. In the capital asset pricing model, the covariance of an individual share with the market rate of return is used as a substitute for the total of all the individual covariances weighted by their relative market values. To emphasize this point we can rewrite equation 6.10 as follows: In words, the required return, E(r,) of an individual share is made up to the riskfree rate of return r, plus the market's perception of the risk of an individual share Cov (r, Im), multiplied by the price of risk per unit of variance' or In effect, this last term converts the covariance into an interest rate which is the risk premium. As CAPM postulates that the risk premium is a reward for bearing systematic risk, it follows that an individual asset having a particular level of systematic risk should offer the same expected return as a portfolio with the same systematic risk level. For example, let Figure 6.7 shows the capital market line consistent with this data. The investor can build a portfolio anywhere along the CML to suit his tastes. If he does not wish to accept the variability of returns associated with the market portiolio, M, he can move down the CML towards r,. Suppose he requires an expected return of 10 per cent. This could be achieved by investing 75 per cent of his money in the risk-free asset r, and 25 per cent of his funds in the market portfolio. The expected return on his portfolio, E(r) is given by: The standard deviation associated with this portfolio, Op, is i.e. as only 25 per cent of the portfolio is invested in risky assets, its standard deviation, at 7.5 per cent, is only 25 per cent of the market standard deviation 01 30 per cent. This portfolio is represented by point P in Figure. If an individual share has the same expected return as portfolio P, i.e. 10 per cent, its systematic risk must also be equal to that of portfolio P. In equilibrium, expected return is a function of systematic risk. If an individual share with the same expected return as P offered investors a different risk/re-turn trade-off to that offered by P, the share would be traded. It would be bought if its systematic risk were lower than P's, and sold if its systematic risk were higher. Purchases would drive the price of the share up, and hence the expected return down, to a level commensurate with its systematic risk. Similarly, sales would depress the share price, and thus increase its expected return, again to a level commensurate with its systematic risk.