Investment Appraisal, Part V: Capital Asset Pricing Model [CAPM]

Investing is not only about taking on particular projects with a finite useful life from a company’s perspective, but can also be undertaken by individuals. When an individual or company invests capital in another company, they take an investment risk and as such require to be rewarded by the company or this risk. This reward comes as an excess return on their investment i.e. making a profit, through either dividends or capital gains (for more information on dividend policy and the relationship with shareholder wealth click here) depending on the company’s policies and shareholder requirements. This additional level of risk is called the ‘risk premium’.


Systematic Risk

Systematic risk is the risk relating to the market, and therefore affects all securities to a greater or lesser extent. It is not possible to reduce this risk as it is entirely dependent on uncontrollable factors such as inflation rates, taxation, general economic conditions etc.

Systematic risk is measured by Beta (β) – this measures how sensitive the security is to movements in the market as a whole (the greater the beta, the more sensitive the security). Market beta is always 1 as it is a relative figure to the market, however shares may have betas of more or less than 1.

Unsystematic Risk

Unsystematic risk is the risk that is unique to individual companies i.e. it affects that company and no other – this is why this risk can be reduced through diversification. It must be pointed out, however, that the risk does not disappear – it is simply offset by other securities in the portfolio.

[Un]Systematic Risk

It is possible to reduce risk through diversification i.e. investing in an array of different types of company within different industries. Investors can reduce their risk by holding a ‘diversified portfolio’. An investor is usually considered to have a diversified portfolio if they have shares in 10 – 15 different companies from different industries. The amount of risk that an investor suffers is reduced rapidly at first by having a diversified portfolio, however, as with most things there is only so much this risk can be reduced by.

A well diversified portfolio only contains systematic risk, thus the return earned compensates for this type of risk only. Shares earn a risk premium over and above the risk free rate – the size of this premium depends on the amount of risk (beta).

Market Return and Capital Asset Pricing Model (CAPM)

The expected return on the market E(Rm) or RM is the average return of all securities, hence it is the return that a share of average risk should expect to earn.


Capital Asset Pricing Model

Every investor earns the risk-free rate of interest, but taking a risk earns a premium on top of this. The premium for the market as a whole is E(Rm) – rf (or RM – RF).

The expected return on any individual security (E(Ri) or RE) is the risk free rate + a certain amount of risk premium. The amount of risk premium depends on the amount of risk (beta).

The CAPM formula is as follows:

E(Ri) = rf + [E(Rm) – rfi                        OR                   RE = RF + β[RE – RF]

Example. 1 – Calculating expected return on a single share

Company X has a CAPM-beta value of 1.3, the risk free rate of return is 8% and the historic risk premium for shares over the risk free rate of return has been 5%. Calculate the return expected on shares in X assuming CAPM applies.

RE  = ?  |    RF = 8%   |     RM = 13% (premium 5%)    |   β = 1.3

RE = RF + β(RM – RF)

? = 8% + 1.3(13% – 8%)   = 14.5%

Example. 2 – Calculating the risk premium on a single share (rearranging the equation)

The risk free return is 9%, Company J has a beta of 1.5 and an expected return of 20%. Calculate the risk premium for the market index over the risk free rate assuming J is on the security market line.

RE = RF + β(RM – RF)

RE  = 20%  |    RF = 9%   |     RM = ? (premium ?)    |   β = 1.35

Rearrange equation:        RE = RF + βRM – βRF   –>    (RE – RF + βRF) / β   = RM

RM = [20% – 9% + 1.5(9%)] / 1.5     =  16.33%

Premium = (RM – RF) = 16.33% – 9% = 7.33%

Securities Market Line

All securities should lie on the security market line, but at any point in time, shares could lie above or below the line – this abnormal return is called the ‘alpha value’. However, over time the alpha value will average out at zero, and will always be zero on a well-diversified portfolio.


If a security was above the line i.e. earning more than it should, investors would buy it, the price would rise and the return would thus fall. If a security was below the line i.e. earning less than it should, investors would sell it, the price would fall and the return would thus rise.

Beta Calculation

Beta is calculated as:

β = σiσmρim / σm2

σ = standard deviation  (σi = of a share, σm = of the market)  |  ρim = correlation coefficient

This is the covariance of the share and the market compared to the variance of the market. The beta required by CAPM is the future beta, however, in practice beta is calculated using returns from the previous 60 months.

A beta for an entire portfolio can be calculated – it is the average of the individual betas, weighted based on the value they each contribute.

Worked Example: Beta calculation for a share portfolio

A client has shares in four companies and wants to know if each of these is still a good investment, or if they should consider selling some of their shares. The following data is available:

Example Question Table

The risk free rate of interest is currently 6.3% and the average risk premium of equities is 5%.

a) Calculate:

i) the current return and beta of the portfolio, and the return required according to CAPM. Also show the amount of excess return that the portfolio is earning.

ii) the excess return being earned by each share.

b) Give reasoned advice to your client on which shares in the portfolio should be sold and, of which, more should be bought

For the answer to the worked example click here.

For more information on the Capital Asset Pricing Model click here.

Featured image courtesy of×403.jpeg



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