Calculating The Beta of a Share

Calculating The Beta of a Share The idea of systematic risk is central to CAPM. An asset whose systematic risk, i.e. its ß, is larger than 1 will be expected to earn a greater 'excess' return than that offered by the market portfolio. For example, a share such as S, in Figure 6.8 has a ß of 1.25. From equation 6.10, its expected risk premium is 1.25 (rm - rr) i.e. 1.25 (25% - 5%)=25 per cent. The expected return on S, will be the risk-free rate, 5 per cent, plus its individual risk premium, 25 per cent, i.e. 30 per cent. If the actual return on the market portfolio in a particular period were only 10 per cent, i.e. the market risk premium was reduced to 5 per cent (10%-5%), then the expected return on S, would be r, + B (E(rm) - r;) = 5% + 1.25 (10% -5%) = 11.25 per cent. An estimate of the ß of an individual share, i, can be made by plotting the excess return earned on security i, (r-rr), against the excess return earned by investing in the market portfolio (rm - Ir). The slope of the regression line through the plotted points gives an estimate of the share's B. Figure 6.10 shows three regression lines for three shares - A, B and C. Such lines are known as 'security characteristic lines' (SCLs). In Figure 6.10 the three SCLs are shown as passing through the origin. This indicates that, when markets are in equilibrium, a zero excess return on the market portfolio will lead to a zero excess return on other shares in the market; In reality, when data for actual shares are plotted against the axes of Figure 6.10, the SCL rarely passes through the origin. The distance between the origin and the point at which the regression line cuts the vertical axis is known as the security's alpha value (a). Interpretation of a values is difficult. It may be argued that they are not inconsistent with CAPM. CAPM is based on expected return, but the SCL is derived from actual data. This may explain the existence of a values, while not invalidating CAPM. Alternatively, if CAPM fails to consider items which are important to investors when making investment decisions in the real world, the long-term existence of a values may well be caused by these ignored factors. Obviously, such an explanation would undermine CAPM as a model of reality. CAPM as an Economic Model At this point it may be useful to consider whether CAPM is a 'good' economic model. A good economic model is one which can be used to explain and predict economic events. It is not necessary for the assumptions of the model to be realistic. The ultimate test of any model is its capacity to explain and predict events. The basic premise of CAPM is that the expected return on any risky asset is proportional to its B. Is this consistent with observed facts? Unfortunately, it is not possible to give a simple answer to this question, as CAPM is a very difficult model to test. The testing difficulties arise from two main sources. First, as noted above, CAPM is a model of expected returns, but only actual returns can be observed. Second, the market portfolio should contain all risky assets. As there is no quoted portfolio containing all such assets, a surrogate for the market portfolio, such as the FTSE index, must be used. For these reasons, some researchers have argued that CAPM is a theory which cannot be tested (Roll, 1977). However, notwithstanding the methodological problems, others have tried to test CAPM, to ascertain whether the risk/return trade-off for all risky assets does actually lie along the security market line. Some studies, such as the famous Black, Jensen, Scholes paper 1972), appear to vindicate CAPM. But other studies have found CAPM to be a much more approximate representation of reality (e.g. Fama and Macbeth 1973, and Banz 1981), indicating that the model might well omit factors which are important in setting the price of risky assets. Nevertheless, despite evidence that CAPM does not include all the factors relevant to setting share prices, research suggests that systematic risk is an important factor. We may conclude that CAPM represents the truth, but not the whole truth. Future developments in finance theory, such as arbitrage pricing, may advance our understanding of the problem. But for the moment CAPM, provides a simple and useful model for looking at risk and return.