| Beta and the Capital Asset Pricing Model |
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| Possibly one of the biggest practical issues facing finance professionals, and especially portfolio managers, is to develop a means of assessing the risk-return trade-off for a security, or a portfolio as a whole. |
By James Ryan
Possibly one of the biggest practical issues facing finance professionals, and especially portfolio managers, is to develop a means of assessing the risk-return trade-off for a security, or a portfolio as a whole. One of the most commonly used means of measuring the riskiness of a security, is 'beta'. Beta can be used within the Capital Asset Pricing Model (CAPM) to quantify expected returns.
The beauty of the CAPM lies in its simplicity and the variety of pragmatic real-world situations to which it can be applied. Its widespread use can be seen by the fact that beta has become part of the everyday parlance of the investment community. Perhaps the only other contribution of financial researchers to match it in terms of practical importance is the Black-Scholes option pricing formula.
While the CAPM can be applied to any security, the commonest application is in evaluating shares. A cornerstone of modern portfolio theory is that high-risk assets must compensate investors by offering higher returns and the theory attempts to model this trade-off. The risk of any share consists of specific (or unique) risk, and systematic risk, which is the risk relating to the market as a whole. It is possible to eliminate the risk that is unique to a company by holding a portfolio that is carefully diversified across different market sectors. In fact it has been shown that a portfolio of as little as 20 shares can eliminate virtually all the unique risk. This illustrates how the key to the benefit from successful diversification does not lie in the number of shares in the portfolio but instead arises from combining shares with low levels of correlation.
Investors are still faced with systematic risk, as the general factors that effect the market index will tend to effect all shares within the market. Accordingly, the attention switches to this type of risk, as it is generally accepted that an efficient, competitive market will not offer a free lunch to investors by rewarding them for taking risks they could avoid.
This analysis has profound implications for the appropriate measure of risk for shares. A portfolio manager needs to evaluate each security's contribution to the overall risk of a portfolio. The area of concern is not the overall volatility of a share but the relationship between the variability of the share and the variability of the market.
Beta provides a simple measure of this risk. It is calculated by examining the historical relationship between the share price and movements in the market. It is easily interpreted, as by definition the overall market has a beta of 1. Therefore, for example, a beta of 2 indicates that, historically, the share is twice as volatile as the market. Similarly, shares with a beta of less than 1 are considered to be less risky than the market as a whole. Risk-free assets, such as government paper, have a beta of zero.
Share returns should reflect the requirement for higher-than-average returns on shares with higher betas and the CAPM is a model of how we might use beta to calculate the predicted future return. The CAPM is formulated as follows:
Expected return = Risk-free return + beta (return on the market - risk-free return)
Thus, the expected return consists of the risk-free rate plus a premium for the market related risk. Consequently, the higher the beta the higher the expected future return.
For example, suppose the beta of a share has been estimated as 1.5, the current risk-free rate of return is 4% and the equity market is expected to return 12%. From this information, we can calculate that the expected return for the share as 16%. This return consists of the risk-free return plus a premium for risk dependent on the beta of the company. As the risk of the share is 1.5 times the market risk the appropriate premium for holding the share is 1.5 times the premium (8%) attaching to the market. Thus, it is only the systematic risk, as measured by beta, which is rewarded
While beta/CAPM can be used in a wide variety of circumstances, some of the more widespread applications are worthy of note. Firstly, they can be used by portfolio managers as a means of constructing portfolios that reflect the risk tolerance of their investors. With a goal of high risk/high return, shares with high betas should be selected. Conversely, a low risk/low return objective can be achieved by choosing low beta shares. Secondly, the CAPM has a valuable role to play in providing a benchmark for monitoring portfolio performance. The focus of assessment for any portfolio should be on the returns relative to the risk taken rather than the total realised returns. For example, while a portfolio with a high level of beta risk might yield a seemingly high level of return, it is only if this return exceeds what would be expected, given the beta, that the portfolio has performed well.
Furthermore, the usefulness of CAPM stretches beyond portfolio management, it is also commonly used to estimate the cost of equity capital for corporate financial management purposes. This use has become more important and prevalent as firms increasingly focus on techniques of shareholder value maximisation, which normally employ the cost of capital as an integral component.
In conclusion, a cautionary note is required. It should not be taken for granted that CAPM provides a panacea for all of the difficulties associated with quantifying the risk-return trade-off for a security. In reality, the model is not without its drawbacks and indeed some controversy surrounds the issue of whether beta alone explains the total return of a security.
Despite this, beta along with the CAPM does provide one intuitively logical and quantifiable measure of a share's risk and therefore expected return. Consequently, and given the usefulness of the model, its adaptability, its simplicity and the variety of practical uses to which it can be put, it is likely that the CAPM will be an essential component of investment analysis for the foreseeable future. |
James Ryan is a lecturer in finance at Dublin City University Business School
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| Article appeared in the March 2000 issue.
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