In order to use the CAPM, investors need to have values for the variables contained in the model.

### The risk-free rate of return

In the real world, there is no such thing as a risk-free asset. Short-term government debt is a relatively safe investment, however, and in practice, it can be used as an acceptable substitute for the risk-free asset.

To ensure consistency of data, the yield on UK treasury bills is used as a substitute for the risk-free rate of return when applying the CAPM to shares that are traded on the UK capital market. Note that it is the yield on treasury bills which is used here, rather than the interest rate on treasury bills. The yield on treasury bills (sometimes called the yield to maturity) is the cost of debt of the treasury bills.

Because the CAPM is applied within a given financial system, the risk-free rate of return (the yield on short-term government debt) will change depending on which country’s capital market is being considered. The risk-free rate of return is also not fixed, but will change with changing economic circumstances.

### The equity risk premium

Rather than finding the average return on the capital market, E(rm), research has concentrated on finding an appropriate value for (E(rm) – Rf), which is the difference between the average return on the capital market and the risk-free rate of return. This difference is called the equity risk premium, since it represents the additional return required for investing in equity (shares on the capital market as a whole) rather than investing in risk-free assets.

In the short term, share prices can fall as well as increase, so the average capital market return can be negative rather than positive. To smooth out short-term changes in the equity risk premium, a time-smoothed moving average analysis can be carried out over longer periods of time, often several decades. In the UK, when applying the CAPM to shares that are traded on the UK capital market, an equity risk premium of between 3.5% and 4.8% appears reasonable at the current time (Watson, D. and Head, A. (2016) Corporate Finance: Principles and Practice, 7th edition, Pearson Education Limited, Harlow p266).

### Beta

Beta is an indirect measure which compares the systematic risk associated with a company’s shares with the systematic risk of the capital market as a whole. If the beta value of a company’s shares is 1, the systematic risk associated with the shares is the same as the systematic risk of the capital market as a whole.

Beta can also be described as ‘an index of responsiveness of the returns on a company’s shares compared to the returns on the market as a whole’. For example, if a share has a beta value of 1, the return on the share will increase by 10% if the return on the capital market as a whole increases by 10%. If a share has a beta value of 0.5, the return on the share will increase by 5% if the return on the capital market increases by 10%, and so on.

Beta values are found by using regression analysis to compare the returns on a share with the returns on the capital market. When applying the CAPM to shares that are traded on the UK capital market, beta values for UK companies can readily be found on the Internet, on Datastream, and from the London Business School Risk Management Service.

**EXAMPLE 1**

**Calculating the cost of equity using the CAPM**

Although the concepts of the CAPM can appear complex, the application of the model is straightforward. Consider the following information:

Risk-free rate of return = 4%

Equity risk premium = 5%

Beta value of Ram Co = 1.2

Using the CAPM:

E(ri) = Rf + βi (E(rm) – Rf) = 4 + (1.2 x 5) = 10%

The CAPM predicts that the cost of equity of Ram Co is 10%. The same answer would have been found if the information had given the return on the market as 9%, rather than giving the equity risk premium as 5%.

### Asset betas, equity betas and debt betas

If a company has no debt, it has no financial risk and its beta value reflects business risk alone. The beta value of a company’s business operations as a whole is called the ‘asset beta’. As long as a company’s business operations, and hence its business risk, do not change, its asset beta remains constant.

When a company takes on debt, its gearing increases and financial risk is added to its business risk. The ordinary shareholders of the company face an increasing level of risk as gearing increases and the return they require from the company increases to compensate for the increasing risk. This means that the beta of the company’s shares, called the equity beta, increases as gearing increases (Watson, D. and Head, A. (2016) Corporate Finance: Principles and Practice, 7th edition, Pearson Education Limited, Harlow pp289-90).

However, if a company has no debt, its equity beta is the same as its asset beta. As a company gears up, the asset beta remains constant, even though the equity beta is increasing, because the asset beta is the weighted average of the equity beta and the beta of the company’s debt. The asset beta formula, which is included in the formulae sheet, is as follows: