    What is the Capital Asset Pricing Model?

# What is the Capital Asset Pricing Model?

In any given CII R02 paper, there’ll almost certainly be at least one question relating to the Capital Asset Pricing Model or, as it’s more commonly referred to as, CAPM. CAPM can also appear in J10, J12, and AF4. What we don’t know for certain is which element of CAPM will be tested – the formula itself, the assumptions behind the model, or its limitations. In this blog post, we look at all three.

## What is CAPM?

CAPM is a model that is used to describe the relationship between the expected return of an investment and its risk. It is based on the assumption that investors will require a higher return (a risk premium) than the risk-free rate when taking on a riskier investment (in other words an investor is asking of the model ‘how will I be rewarded for holding this share or fund?’).

## CAPM Formula

The CAPM formula calculates the expected return from an investment as follows:

The risk-free rate of return + Beta x (The expected market return – the risk-free rate of return).

The expected market return less the risk-free rate is the risk premium.

The CAPM formula is expressed as follows:

E(Ri) = Rf + βi[E(Rm) – Rf]

Where:

E(Ri) = Expected return of investment

Rf = Risk-free return

E(Rm) = Expected market return

β = Sensitivity to market

## CAPM Example

Let’s take a look at an example.

The current yield on UK Treasury Bills is 1%. Company X, which is listed on the FTSE 100, has a Beta of 1.10.  The expected market return of the FTSE 100 is 5.4%. Given this information, what is the expected return of Company X?

If we plug the numbers into the formula we get:

E(Ri) = 1.00 + 1.10[5.4 – 1.00]

We work out the numbers in the brackets first, i.e. 5.4 – 1.00:

E(Ri) = 1.00 + 1.10[4.4]

Then multiply the answer (4.4) by the company’s beta of 1.10, i.e. 4.4 x 1.10:

E(Ri) = 1.00 + 4.84

Then add the final two figures together to give the expected return of Company X.

E(Ri) = 5.84

From this, we can see that the expected return of Company X is slightly above that of the market as a whole. This makes sense because it has a beta of 1.10. This means that it is more volatile than the average share in the market (i.e. there is more systematic risk) and its expected return is therefore higher.

If its beta had been below 1, then it would have less systematic risk (it is less volatile) than the average security in the market and the expected return would therefore be lower than the 5.4% expected from the market as a whole.

## Assumptions

CAPM is based on two main assumptions. Firstly, that the securities market is very competitive and efficient and, secondly, that the markets are dominated by rational, risk-averse investors whose goals are to maximise the returns from their investments.

These overriding assumptions can be broken down further (as they are in the CII’s study text) as follows:

• investors make rational decisions based on risk and return alone;
• all investors have the same holding period;
• no single investor can affect the market price;
• there are no taxes, transaction costs, or restrictions on short-selling;
• information is free and available to all investors at the same time;
• investors can lend and borrow unlimited funds at the risk-free rate; and
• the liquidity of an asset can be ignored.

Many of these assumptions are open to challenge. For example, we know from behavioural finance that investors don’t always make rational decisions, and very few investors will have the same time frame for their investment.

## Limitations

In addition to limitations relating to the validity of the assumptions, there are a number of further limitations to consider, including:

1. Finding a totally risk-free return – in the UK, Treasury Bills are commonly used to represent this, and while there is almost no risk involved, that’s not quite the same as saying there is no risk at all. In addition, the yield on Treasury Bills changes daily, making it a volatile measure.
2. Finding the correct market portfolio – again, in the UK, the FTSE 100 or FTSE All-share are commonly used. Care should be taken to select the most appropriate market as the beta for each are different.
3. Beta suitability – betas are based on historic data; they may therefore be unreliable. The relationship between beta and the risk-free rate has been called into question.

## Conclusion

Despite its limitations, CAPM is widely used. This is primarily down to the fact it is fairly easy to use and understand, but also because it is felt to provide a better steer than the available alternatives.

## Grab the resources you need!

If you’re studying for your CII R02 exam, and your confidence is a bit deflated, grab our free taster to try out one of Brand Financial Training’s resources for yourself.  Click the link to download the R02 calculation workbook now! Alternatively, you can download the calculation workbook taster for J10, J12, or AF4 if one of those exams is stressing you out.