The Capital Asset Pricing Model

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1 Introduction

In the previous chapter on Portfolio Theory we looked at the nature of risk in share investments, and described what is meant by a well-diversified portfolio. In this chapter we will look at the importance of the systematic risk in relation to the return given by quoted shares and then discuss its relevance to project appraisal.

2 The return from quoted shares

Shareholders (as a whole) can get whatever return they require from a quoted share because they determine the market value of the share. The market value is determined by the expected future dividends and the investors’ required rate of return.

We assume that the shareholders in a large quoted company are overall well-diversified (partly because there are many shareholders, but also because many of the shareholders will be pension funds and unit trusts that will have large portfolios).

If the shareholders’ are well-diversified, then they will have diversified away all the unsystematic risk (portfolio theory) and will therefore only be concerned with the level of systematic risk. It is therefore the level of systematic risk that will determine the return that they require (and hence the return actually given) from the share.

Instead of measuring the systematic risk in isolation as a %, we normally measure it relative to the risk of the market as a whole (i.e. the stock exchange as whole). We call this the β of the share.

Since it is the level of the systematic risk in a share that determines the return required, we would expect that the higher the β the higher the required return (and the lower the β, the lower the required return!).

The most important formula of all in CAPM is the formula expressing the required return, which is as follows:

E(r_i) = R_f + β_i[E(r_m) – R_f]

3 Calculating β in practice

In practice, it is assumed that CAPM ‘works’ and that therefore the return given by a share is determined by its β. It is therefore possible to calculate a β by working backwards (as in example 2 above).

However, even assuming that CAPM does work, it would be too perfect to assume that the formula works exactly from day-to-day – market imperfections will mean that on any one day the actual return may be slightly ‘wrong’. In practice therefore the returns from a share are compared with those from the market over a long period and a β calculated in this way.

You will not be expected to do this in the examination.

4 Combining investments

If an investment is made in a combination of several shares with different levels of systematic risk, then the overall β will be the weighted average of the individual share β’s.

5 Alpha values

We have already stated that even assuming that CAPM ‘works’ in practice, it would be unrealistic in the real world to expect that it works precisely at each moment in time. Even if it does work overall, it will not be surprising if some days the actual return is a little higher than it should be, and some days a little lower.

The alpha value is simply the difference between the actual return and the theoretical return (using CAPM).

6 Ungearing B’s

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Until now, we have been ignoring gearing and assuming that the companies in our examples have been all equity financed. In this case the risk of a share is determined solely by the risk of the actual business.

If, however, a company is geared, then a share in that company becomes more risky due to the gearing effect.

If, therefore, we are given the β of a share in a geared company, then the gearing in that company will have made the β higher than it would have been had there been no gearing. The β of a share measures not simply the riskiness of the actual business but also includes the gearing effect.

We therefore need to be careful when comparing the β’s of shares in different companies. A higher β certainly means that the share is more risky, but it may be due to the fact that the company is more highly geared, or due to the fact that the business is inherently more risky, or a combination of the two!

The formula for removing the gearing effect is given in the examination and is:

Note that although you are given this formula in full in the examination, we normally assume that debt is risk free and that therefore βd = 0, which makes the formula much shorter! In every relevant examination question so far we have been expected to make this assumption.

7 The implications of CAPM for project appraisal

If the shareholders of a company are well-diversified, then their shares in this company are just part of their overall portfolio.

If the company is to invest the shareholders money in a new project, then the project should be appraised in the same way as the shareholders themselves would appraise the investment if they were invested their money in it directly.

If they were investing directly, then they would base their required return simply on the β of that investment (not on how it related to any particular other investment in their portfolio).

Therefore, when the company is appraising a new project they should calculate the β of the project, determine the required return for that β, and appraise the project at that required return.

How to calculate the β of a project? Find a similar quoted company and use the β of that company (ungeared if relevant).

We will illustrate the above with a full example:

Do note, however, that when there is a major change in gearing (as in the example) it is far better to take an Adjusted Present Value (APV) approach. This is commonly asked in the exam and will be explained in a later chapter.