Principio de calidad

Contents Page

Introduction 190

A. Risk, Return and CAPM 190

Systematic and Unsystematic Risk 190

Measuring Systematic Risk 191

Market Risk and Return 192

The Beta Factor and Market Risk 193

The Capital Asset Pricing Model Formula 195

Alpha Values 195

The CAPM and Share Prices 195

The CAPM and Gearing 196

B. Calculation of Betas 196

C. Validity of the CAPM 197

CAPM Assumptions 197

Limitations of CAPM 198

D. Practical Applications of CAPM 199

CAPM and Portfolio Management 199

CAPM and Capital Investment Decisions 200

E. The Arbitrage Pricing Model 200

Answers to Practice Question 202

INTRODUCTION

In the last study unit we discussed portfolio theory and said that it underpins the Capital Asset Pricing Model (CAPM). CAPM was developed in the 1960s by Sharpe and Litner building on the work of Markowitz and portfolio theory. The model at its simplest brings together aspects of share valuations, the cost of capital, and gearing, and thus has important implications in financial management.

For our purposes, we can make the assumption that there are two basic functions associated with the CAPM:

 Attempting to establish the "correct" equilibrium market value of a company's shares.

 Calculating the cost of a firm's equity (and thus the weighted average cost of capital), as an alternative approach to the dividend valuation model which we considered in a previous unit.

The model also implies equilibrium between risk and the expected return for each security and can be used by the financial manager in the assessment of risk in either individual company shares or a portfolio of securities.

A. RISK, RETURN AND CAPM

There is risk associated with investment in any security, and we said in the last study unit that the greater the risk, the greater the required return from the investment. However, one type of stock which has a low risk, and which is assumed in portfolio theory to be risk-free, is Treasury bills (because, as we have already seen, the Government is unlikely to renege on its commitments to pay the returns agreed on the bills). The difference between a higher return and that achieved at the risk-free rate is known as the excess return, and it will differ between securities depending on the market's perception of the relative risk of each.

The only way for an investor to avoid risk altogether is to invest solely in government securities, but in doing so the investor will trade off risk for a lower return than might otherwise have been made.

Systematic and Unsystematic Risk

We showed in the last study unit that risk comprises financial and business risk. We also saw that investors tend to diversify their portfolios to reduce their risk whilst maintaining their return. The risk which can be diversified away is known as unsystematic risk, and is unique to a particular company. It is independent of political and economic factors, and may arise, for example, as a result of bad labour relations causing strikes, the emergence of improved competitor products or adverse press reports. It is diversified away because the factors causing it are different for different companies and cancel each other out.

The risk related to the market, however, cannot be diversified away (if it could then the return on the market would not be higher than the risk-free rate), and is known as systematic or market risk. Systematic risk is unavoidable risk. Systematic risk may also vary between projects. Such risk may arise as a result of government legislation, from adverse trends in the economy or from other external factors over which the company has no control.

The two types of risk are significant, because in building a portfolio of shares the investor will want to minimise unsystematic risk.

We noted earlier that research has found that if a portfolio has between 15 and 20 shares selected at random then the unsystematic risk in the portfolio should be eliminated.

Increasing the size of the portfolio up to this level will certainly reduce the level of unsystematic risk (see Figure 8.1).

Figure 8.1: Systematic and systematic risk

Although by definition unavoidable, the degree of systematic risk will be a variable factor between different industries – shares in different companies will have systematic risk characteristics which are different from the market average because the market considers some investments to be riskier than others (for example, food retailers are lower risk than those in the fashion industry). When an investor holds a portfolio which is balanced

throughout with all available stocks and shares, or a unit trust which mirrors the market, he will incur systematic risk which is equal to the average systematic risk in the market as a whole.

We can also see that individual investments will have their own levels of systematic or market risk.

Measuring Systematic Risk

The CAPM is principally concerned with:

 How systematic risk is measured.

 How systematic risk affects the required returns and share price.

In order to measure systematic risk, we use the beta factor ().

The CAPM also includes some fundamental assumptions which we can summarise as follows:

(a) Investors in shares (as opposed to risk-free investments, which are generally government securities) require a return which is in excess of the risk-free rate as a form of compensation for taking the systematic risk of the investment.

(b) Investors should not require a premium for unsystematic risk as this may be diversified and removed from the portfolio (as discussed earlier).

(c) As the systematic risk is higher for some companies (as measured by their factor) the investor will expect a greater return and will continue to do so as the gets larger.

(d) Investors are rational and want to maximise their return.

(e) All information is feely available to investors and they are competent in interpreting that information.

(f) Investors are able to borrow and lend at the risk free rate.

(g) Capital markets are perfectly competitive with a large number of buyers and sellers, no monopolies, no taxes or transaction costs, and no entry or exit barriers to the market.

The financial manager may, incidentally, adopt a similar approach to investment in one or more new projects. When a company is considering an investment in a new project, there will be a degree of risk involved. The greater the perception of risk in the venture, the greater will be the expected return (assuming, of course, that the directors are willing to sanction the investment in the first place).

Market Risk and Return

The CAPM was formulated principally to evaluate investments in stocks and shares ("the market") as opposed to investment projects under consideration by companies. The model is based on the comparison of systematic risk within individual investments and shares, with that in the market as a whole (hence systematic risk also being described as market risk).

Market risk, in its simplest form, is the average return of the market.

Market risk is, of course, something which is almost impossible to determine with any degree of accuracy, as it is based on the total expected market return. As the components of the market fluctuate consistently, so the systematic risk attached to shares will also change.

Therefore CAPM must make one major and fundamental assumption – that there is a linear relationship between the return obtained from one single investment and the market average.

Let's look at an example.

Our aim is to demonstrate at a basic level how the return from one investment compares with the market:

Company A Whole Market

Price at start of period 110 490

Price at end of period 130 510

Dividend paid 6.5 40.1

The return on Company A's shares (R_s) and the return on the general market portfolio of shares (R_m) may now be calculated as follows:

period

Statistical analysis of "historical" returns from Company A and from the "average" market may suggest that a linear relationship exists. Thus, the linear relationship can be demonstrated through collecting comparative figures from Company A and average market returns (say on a month by month basis). The results can then be plotted on to a scatter diagram and a line of best fit can then be drawn with linear regression (see Figure 8.2).

Figure 8.2: Relationship of returns between one company and the market

This approach to analysis could bring out three important issues, namely:

 The return from Company A (R_s) and the return from the market (R_m) will tend to rise or fall together.

 The return from R_smay be higher or lower than R_mbecause the systematic risk of an individual security differs from that of the whole market. Company A is an illustration of an investment which provides generally higher returns than the market and is therefore considered more risky than the average.

 The graph may not always produce a line of good fit. This typically happens when there is insufficient data to be plotted, and the data available is being affected by both unsystematic and systematic risk.

Negative returns may also be possible, which may happen when share prices drop suddenly.

This will then amount to a capital gains loss, thereby equating to a negative return.

Our example demonstrates the relationship between an individual company's systematic risk and that of the market fairly predictably. The measure of the relationship between the returns of the company and those of the market can then be developed in the beta factor () for that company. The line of best fit, also known as the characteristic line, will dictate the beta factor – the steeper the line, the greater will be the beta factor.

The Beta Factor and Market Risk

The beta factor is a measure of a share's volatility in terms of market risk.

We can identify three possibilities for that measurement:

 Where > 1, the shares would be described as aggressive, i.e. they would outperform the Stock Market whichever way the general trend in prices was moving.

 Where  1, the shares would be described as neutral, i.e. they would follow the general trend of the Stock Market.

Return from company A’s shares (R_s)

Return from whole market (R_m) Line of best fit

 Where < 1, the shares would be described as defensive, i.e. they would be less risky than the market generally.

As you will see, the market as a whole is assigned the value of "1". If a company's beta factor is 2, this would indicate that it would return twice as much as the market generally.

Therefore, it would be expected that, if the market return (R_m) rose by 5%, then the return in a company (R_s) with a beta factor of 2 would rise by 10%. Variations in the company's return (R_s) outside this would be specifically due to the impact of its own unsystematic risk, which is unique to that company.

We should remember that another essential characteristic of the CAPM is that unsystematic risk can be cancelled out by diversification of the portfolio. In a simple example, Company Y's shares do worse than the average market returns and Company Z's do better (as

originally predicted by the beta factor). The net effect will be self-cancelling and therefore the unsystematic risk has been removed from this hypothetical portfolio.

In such circumstances, the average return on the portfolio will be dependent upon:

 Changes in the average market return, and

 The beta factors of the shares which make up the portfolio.

We will now look at a further example to highlight these points.

Example Suppose that:

(a) The return on government stock is 10%.

(b) The average market return is 15%.

(The difference of 5% is therefore the excess return as we described earlier.)

The difference between the risk-free return and the expected return on an individual investment can be measured as the excess return for the market as a whole, multiplied by the beta factor of the investment.

Now suppose that we take the example of a company with a of 1.4, the risk-free return is 9%, and the expected market return is 13%. The expected return on the company's shares would exceed the expected market return by:

1.4(13 9)%, or 5.6%

(The total expected return would be 14.6% (9 5.6).)

If the market as a whole fell by an average of 3%, to 10%, then the total expected return on the company would also fall as follows:

9% 1.4(10  9)  10.4%.

(The fall is represented by 1.4 3%  4.2%)