**INTRODUCTION **

The Capital Asset Pricing Model (CAPM) is an extension of Portfolio Theory, which is concerned with the risk and return of portfolios and the process by which risk can be reduced by efficient diversification. The CAPM assumes that all investors are efficiently diversified and examines the risk and return of any capital asset. A capital asset can be a portfolio, an individual share or security, a portfolio of projects or investments made by a company or even an individual project.

The CAPM gives the required rate of return on a capital asset, based on its contribution to total portfolio risk, called systematic risk. It gives a very neat way of calculating riskadjusted discount rates.

**SYSTEMATIC AND UNSYSTEMATIC RISK **

When securities are combined in a portfolio part of each security’s total risk (its standard deviation) is eliminated. This is the basis of diversification. That part of an individual security’s total risk which can be eliminated by combining that security with an efficient portfolio is called unsystematic (or specific) risk. The balance of an individual security’s total risk (that part which cannot be eliminated by diversification) is called systematic (or market) risk.

** Unsystematic Risk** – risk which

__can__be eliminated by diversification. It is the variation in a company’s returns due to specific factors affecting that company and not the market as a whole, e.g. strikes, the breakdown of machinery, changes in fashion for that company’s products etc. This specific risk is a random fluctuation uncorrelated with the returns on the market portfolio (the market as a whole). Therefore, when a large number of shares are held these random fluctuations tend to cancel out – i.e. there is risk reduction.

** Systematic Risk **– risk which

__cannot__be eliminated by diversification. This is the fluctuation in returns due to general factors in the market affecting all companies e.g. inflation, government policy, economic conditions etc. It is that part of the fluctuations in returns which is correlated with those of the market portfolio.

When a capital asset (s) is combined with no other assets, the risk of the portfolio is simply the standard deviation of (s). When further assets are added, however, the contribution of (s) to the portfolio risk is quickly reduced – diversification is eliminating the unsystematic risk. It takes a surprisingly low number of shares in a portfolio to eliminate the majority of unsystematic risk (twenty holdings/shares in a portfolio will eliminate approximately 94% of unsystematic risk). All unsystematic risk could only be eliminated when the market portfolio is held.

Only __systematic__ risk is relevant in calculating the required return on capital assets. This is because, on the assumption that investors hold efficient portfolios, unsystematic risk is automatically eliminated when another asset is incorporated within that portfolio. The only effect an asset has on portfolio risk is through its systematic risk.

Some investments may be regarded as risk-free – such as investment in government securities (“Gilts”). Investors in risky investments should expect to earn a higher return than investors in risk-free investments, to compensate for the risks they are taking. Thus, if investors in Gilts can obtain a return of, say, 6%, an investor in a risky asset should expect a yield in excess of 6%. The Capital Asset Pricing Model uses this approach of rewarding investors in risky assets with a premium on top of the yield on risk-free assets. The CAPM is:

Rs = Rf + β (Rm – Rf )

Where: Rs = the expected return on a capital asset (s)

Rf = the risk-free rate of return

β = a measure of the systematic risk of the capital asset (the Beta factor)

** **Rm = the expected return from the market as a whole** **

This is a very important formula. Note that the expected return (Rs) is equal to the risk-free rate of return (Rf) plus an excess return or premium (Rm – Rf ) multiplied by the asset’s Beta factor. You may see different symbols in many textbooks but the same principles apply.

The Beta factor is a measure of the systematic risk of the capital asset. Thus, if shares in ABC plc tend to vary twice as much as returns from the market as a whole, so that if market returns __increase__ by, say, 3%, returns on ABC plc shares would be expected to increase by 6%. Likewise, if market returns __fall__ by 3%, returns on ABC plc shares would be expected to fall by 6%. The Beta factor of ABC plc shares would, therefore, be 2.0.

The CAPM provides a useful technique for calculating costs of capital and discount rates appropriate to capital projects based on their individual levels of risk. However, there are two drawbacks to the practical application of the CAPM. Firstly, the data necessary to calculate Beta factors and the difficulty in obtaining them. Secondly, the assumptions on which the model is based, which question the validity of the model itself. Among these assumptions are:

- Investors are rational and risk-averse – without this the whole idea of diversification becomes meaningless.
- There are no transaction costs – this is not true in practice e.g. brokers’ fees. It effectively makes the attainment of the market portfolio impossible. However, by holding only a limited number of well selected shares it should be possible to obtain a fairly close approximation to the market portfolio.
- All investors are efficiently diversified – the CAPM is based on the assumption that all investors have eliminated unsystematic risk by diversification and hence only systematic risk (measured by Beta) is relevant in determining returns.

In conclusion, although the CAPM can be criticised it is nevertheless a very useful model in dealing with the problem of risk.