Session 9: Capital Asset Pricing Model

Transport Financial Analysis

Page 42 of 43 pages. Chapter: 13: Risk Analysis

Session 9: Capital Asset Pricing Model (CAPM)

Learning Objective

Introducing to the learners to different aspects of risk associated with the business operations.

Discussing the Security market line.
Guiding the learner how to estimate the cost of equity using CAPM.

Important Terms

Weighted average cost of capital.(WACC)
Financial risk premium
Business risk premium
Risk free rate of return

Introduction

The Capital asset pricing model (CAPM) relates the risk-return trade-off of individual assets to market returns. The basic form of the CAPM is linear relationship between returns on the individual shares and the stock market returns over time. The capital asset pricing model is an attractive to the dividend valuation model and dividend growth model as a method as a model as a method of establishing the cost of equity. The uses of the capital asset pricing model (CAPM) include;

Trying to establish the ‘correct’ equilibrium market price of company’s shares.
Trying to establish the cost of a company’s equity, taking account of the risk characteristics of a company’s investments, both business and financial risk.

Systematic and Unsystematic Risk

Every investment portfolio has a risk element, which is the investor will always not be certain whether the investment will be able to generate income as per investor’s requirement. The degree of risk defers from industry to industry but also from company to company. It is not possible to eliminate the investment risk altogether but with careful diversification the risk might be minimised. Provided that the investor diversify their investments in a suitably wide portfolio, the investments which perform well and those which perform badly, should tend to cancel each other out, and much risk is diversified away.
Risks that can be reduced through diversification are referred to as unsystematic risk as they are associated with a particular company or sector of the business. Remember investors are supposed to be compensated for any risk assumed, but with unsystematic risk the investor will not be have any extra risk premium as it can be eliminated through diversification.
Some investments are by their nature more risky than others. These risks are called as systematic risk which will always remain in an investment despite holding a well diversified investment opportunities. If an investor would not take systematic risk, then should be prepared to settle for risk free return which has a lower level of return. Where an investor assumes the systematic risk, and then should expect to earn a return which is higher than a risk free rate of return. The amount of systematic risk in an investment varies between different types of investment. The systematic risk in the operating cash flows of a tourism company which is highly sensitive to consumer’s spending power might be greater than the systematic risk for a company which operates a chain of supermarkets.

CAPM theory includes the following propositions:

Investors in shares require a return in excess of the risk free rate, to compensate for the systematic risk.
Investor should not require a premium for unsystematic risk, because this can be diversified away by holding a wide portfolio of investments.
Because systematic risk varies between companies, investor will require a higher return from shares in those companies where the systematic risk is greater.

The same propositions can be applied to capital investment by the companies:

Companies will want a return on a project to exceed the risk-free rate, to compensate them for systematic risk.
Unsystematic risk can be diversified away, and so a premium for unsystematic risk should not be required.
Companies should want a bigger return on projects where systematic risk is greater.

The Beta Factor and Risk Free Rate of Return

A share’s beta factor is the measures of measure of its volatility in terms of market risk. The beta factor of the market as a whole is 1.0. Market risk makes market returns volatile and the beta factor is simply a yardstick against which the risk of other investments can be measured. Risk or uncertainty describes a situation where there is not first one possible outcome but array of potential returns. Risk is measured as the beta factor or B.

- The market as a whole has B = 1
- Risk free security has a B = 0
- A security with a B < 1 is lesser risky than average Market
- A security with a B > 1 has risk above market

Independence Curves

Investors always try to minimise their risk while trying to maximise their return.
Indifference Curve analysis draws on the concept of utility to present alternative trade off between risk and return each equally acceptable to the investors. Every individual will exhibit unique preference for risk and return hence different set of indifference curves.
Prudent investors will choose the investment portfolio where the indifferent curve is to the far left as the return is higher for the same assumed level of risk as the investment on the lower indifferent curve.

Security Market Line

The line that indicates the most efficient return and risk to an investor. An investor who is risk averse will always investment in those opportunities which are risk free. Such opportunities are very rare but the government securities are considered to be risk free as the chances of default by the government are very slim. Though this is not the case in countries of unstable political environment where coup governments may refuse to honour obligations of their predecessor governments. The investors who are risk seeker will assume extra risk in order to achieve higher return. The security market line as shown below show the most efficient risk return ratio which a prudent investor should assume.

Excess Return over Risk-free Return

The CAPM also makes use of the principal that the returns on shares in the market as a whole are expected to be higher than the return of risk free investment as out lined above on Security market line. The difference between market returns and risk-free returns is called an excess return. For example, if the return on Malawi’s Treasury bill is 20% and market returns are 28%, the excess return on the market share as whole is 8%.
The difference between the risk free return and the expected return on an individual security can be measured as the excess return for the market as a whole multiplied by the security’s beta factor. Thus, if the shares in H Ltd have a beta factor of 1.2 when the risk free return is 8% and the expected market return is 10.5%, then the expected return on H Ltd shares would exceed the risk free return by ( 10.5 – 8) 1.2% = 3%, and the total expected return on H Ltd shares would be (8 + 3)% = 11%. The risk level will always affect the rate of return which is expected, say for H Ltd if the beta factor was 1.8, then the expected return would have been 8% + (10.5 – 8)x 1.8% =

The CAPM Formula

The capital asset pricing model is a statement of principles explained above. It can be stated as follows.

The CAPM and Share Prices

The CAPM can be used not only to estimate the expected returns from securities with differing risk characteristics, but also to predict the value of shares, using the dividend valuation model.

Example

Company X and Y both pay annual dividend of 40 tambala to their shareholders and this is expected to continue in perpetuity. The risk-free rate of return is 6% and the current average market rate of return is 10%. Company X’s ß is 1.1 and for Y is 0.8. What is the expected rate of return for each company and what would the share price of each company be?

Solution

a) The expected return for X is 6% + (10%- 6%) x 1.1 = 10.4%

b) The expected return for Y is 6% + (10% - 6%) x 0.8 = 9.2%

The dividend valuation model can now be used to derive the expected share prices.

c) The predicted share value of X is 40t/0.104= 385 tambala.

d) The predicted share value of Y is 40t/0.092 = 435 tambala.

The actual share price can be lower or higher than the one predicted using CAPM. The CAPM acts as a guide in predicting the levels where share prices are expected to be.

The Usefulness and Limitation of CAPM

The expected return calculated using CAPM is an important tool in project appraisal. It can be used to compare projects of all different risk classes and is therefore superior to a Net present value (NPV) approach which uses only one discount rate for all projects, regardless of their risk.
The practical problems with the use of CAPM in investment appraisal are follows:

It is hard to estimate the risk free rate of return on projects under different economic environment.
The CAPM is really just a single period model. It is not possible to use the CAPM for projects which last for more than one year.
It may be had to estimate the risk-free rate of return.
Complications in decision-making cannot be modeled easily.

The Arbitrage Pricing Model

The CAPM was developed as a model for investment appraisal and share valuation. As stated above the CAPM is a one year model and not suitable for projects longer than one year. The arbitrage pricing model (APM) is a model that was developed out of the CAPM and considers various numbers of independent factors which may affect the share price. CAPM consider the risk in form of the beta factor. The expected rate of return using APM considers factors such as unanticipated inflation, changes in the expected level of industrial production; changes in the risk premium on bonds, and unexpected changes in term structure of interest rates.