OVERVIEW
Objective
¾
To understand the Capital Asset Pricing Model and its uses in financial management.BETA FACTORS
USES OF THE CAPM
¾ Measurement ¾ Calculation ¾ Interpretation
¾ Formula
¾ Security Market Line
¾ Well-diversified investor ¾ Companies
¾ Asset betas ¾ Equity betas
¾ Use of the equity beta
ASSUMPTIONS AND LIMITATIONS CAPITAL ASSET
PRICING MODEL
DEGEARING AND REGEARING BETA
¾ Project appraisal in a new industry
¾ MM and betas
¾ Assumptions ¾ Limitations SYSTEMATIC AND
UNSYSTEMATIC RISK
¾ Definitions
1
SYSTEMATIC AND UNSYSTEMATIC RISK
1.1
Definitions
¾
Risk, the variability of returns, can be split into two elements:unsystematic risk − These are the risks that are unique to each company’s shares;
− It is the element of risk that can be potentially eliminated by shareholders building a diversified portfolio.
− It is also known as unique or industry-specific risk
systematic risk − These are the risks that affect the market as a whole rather than specific company shares;
− This cannot be diversified away;
− Therefore systematic risk still remains even in a well-diversified portfolio;
− This is also known as market risk.
1.2
Measurement of systematic risk
¾
A well-diversified portfolio of shares still has some degree of risk or variability. This is due to the fact that all shares are affected by systematic risk i.e. to macro-economic changes.¾
Systematic risk will affect the shares of all companies although some will be affected to a greater or lesser degree than others.¾
This sensitivity to systematic risk is measured by a beta factor.2
BETA FACTORS
2.1
Measurement
¾
Beta factors for quoted shares are measured using historic data and published in”beta books”. They are determined by comparing changes in a share’s returns to changes in the stock market returns over a period of many years (5 years data should be used at least)¾
This can be illustrated by the Security Characteristic Line which gives an indication of the share’s sensitivity to market changes.(Ri- Rf) Security characteristic line
Intercept = α
Slope = β
(Rm - Rf)
Where (Ri − Rf) = the excess return of the share over the risk free return
(Rm − Rf) = the excess return of the stock market over the risk free return Rf = the return on a risk-free investment
¾
The Security Characteristic Line should in the long run pass through the point where the two axes meet.¾
However in the short run this may not always be the case and any short term difference, or abnormal return, is known as the alpha factor.2.2
Calculation
¾
A beta factor for a share “i” can also be calculated using linear regression:Bi =
returns s
market' the
of Variance
market the
with i of Covariance
Or
Correlation of the share with the market × standard deviation of the share‘s returns Standard deviation of the market’s returns
Example 1
A share has a standard deviation of 15% and a correlation coefficient with the market returns of 0.72. The standard deviation of the market is 21%.
What is the share’s beta factor?
2.3
Interpretation
¾
A beta factor therefore simply describes a share’s degree of sensitivity to changes in the market’s returns, caused by systematic risk.Beta factor of 1 − this indicates that the share is as sensitive as the market to systematic risk
Beta factor > 1 − this means that the share is more sensitive than the market. Therefore if the market in general rises by 10% then the returns from this share are likely to be more than 10%.
Beta factor < 1 − the share is less sensitive than the market and is likely to rise and fall in value less than the market in general.
3
CAPITAL ASSET PRICING MODEL
3.1
Formula
¾
If the shareholders of a company hold well-diversified portfolios then they are concerned only with systematic risk.¾
The return these shareholders require therefore is only a return to cover the systematic risk of an investment.¾
Systematic risk is measured by a beta factor - therefore the required return from an investment must be related to the beta factor of that investment.¾
This is brought together in the Capital Asset Pricing Model which is a formula that relates required returns to beta factors as measures of systematic risk.¾
The CAPM formula is : E(ri) = Rf + βi(E(rm)–Rf)E(ri) = expected/required return from an investment
Rf = risk free return
E(rm) = expected return from the “market portfolio”
βι = beta of the investment
The Market Portfolio is a portfolio containing every share on the stock market.
3.2
Security Market Line
¾
The Security Market Line is a graph that indicates the required return from anyinvestment given its beta factor. Forecast returns from investments can be compared to the figure from the security market line to indicate whether that investment is under or over valued.
Return
Rm
Rf
x Ra
x Rb
Security market line
Beta
0 Ba 1 Bb
Where Ra = the forecast return from investment A
¾
The required return of an investment with a beta of zero (risk free) will be the risk free return.¾
The required return of an investment with a beta of 1 will be the market return.¾
Consider investment A - it is forecast to earn higher returns than the CAPM would predict given its beta. It is therefore temporarily under-priced. This is referred to as a “positive alpha” investment.¾
Consider investment B - it would appear to be temporarily over priced – a “negative alpha” investment.4
USES OF THE CAPM
4.1
Well-diversified investors
¾
If an investor already holds a well-diversified portfolio then that investor will be concerned only with systematic risk. The CAPM is therefore relevant.¾
The investor will be satisfied only if a potential investment gives a high enough return given its sensitivity to market risk as measured by its beta factor.Example 2
An investment has an forecast return over the next year of 12%. The beta of the investment is estimated at 0.9. The risk free rate is 5% and the market return is 15%.
Should a well-diversified investor buy this investment?
Solution
4.2
Companies
¾
Companies should not diversify their activities simply to reduce the risk of their shareholders. Shareholders can diversify their shareholdings much more easily than a company can diversify its activities.¾
If shareholders are already well-diversified then the company should concern itself, on behalf of the shareholders, simply with the systematic risk of potential projects.¾
Therefore the aim of a company, with well-diversified shareholders, should be to determine the required return from its investment projects and then compare this to the forecast return.¾
If the project is the same risk as that of the existing activities of the company then the existing WACC can be used.4.3
Asset betas
¾
Any company is made up of its assets or activities. These assets will have a certain amount of risk depending upon their nature. These assets will have a beta factor that recognises the sensitivity of such assets to systematic risk.¾
This beta factor is the asset beta and measures the systematic business risk of the company.¾
It can also be referred to as an ungeared beta factor4.4
Equity betas
¾
The equity beta measures the sensitivity to systematic risk of the returns to the equity shareholders in a company.¾
In an all-equity financed company, or ungeared company, the only risk that is incurred is business risk.¾
Therefore in an ungeared company the asset beta and the equity beta are the same.¾
However in a geared company the equity shareholders face not only business risk, measured by the asset beta, but also a degree of financial risk.¾
Therefore in a geared company the equity beta > the asset beta.¾
Equity betas can also be called geared betas.4.5
Use of the equity beta
¾
The equity beta measures the sensitivity to market risks of the equity shareholders’ returns. If the equity beta is used in the CAPM this gives the required return for the equity shareholders.¾
The required return of shareholders = the cost of equity geared (Keg)¾
The CAPM can therefore be used as an alternative to the Dividend Valuation Model for estimating the cost of equity of a company.Example 3
The equity beta of a company is estimated to be 1.2. The risk free return is 7% and the return from the market is 15%.
Estimate the cost of equity of the company?
5
DEGEARING AND REGEARING BETA
5.1
Project appraisal in a new industry
¾
It has already been noted that a company’s existing WACC is only a relevant discount rate for a project with the same level of business risk as existing activities..¾
If the project is in a different industry (or country) then a discount rate to reflect the business risk of that industry is required.¾
A company in a similar industry can be found and its beta discovered. If that company is geared then its equity beta will contain both business risk and financial risk.However that company will probably have a different level of gearing compared to our company.
¾
This requires us to first “degear” the beta to find the asset beta, and then “regear” to reflect our company’s level of financial risk5.2
MM and betas
¾
The following formula (based on Modigliani and Miller’s models) can be used to convert an equity beta to an asset beta (and vice-versa):
Example 4
A plc produces electronic components but is considering venturing into the manufacture of computers. A plc is ungeared with an equity beta of 0.8. The average equity beta of computer manufacturers is 1.4 and the average gearing ratio is 1:4.
The risk free return is 5%, the market return 12% and the rate of Corporation Tax 33%.
If A plc is to remain an equity financed company what discount rate should it use to appraise a computer manufacture project?
Solution
Example 5
Suppose that A plc from the previous example has a gearing ratio of 1:2. It still wishes to enter into the same computer manufacturing project.
What is the discount rate that should be used for A plc for a computer manufacturing project?
6
ASSUMPTIONS AND LIMITATIONS OF THE CAPM
6.1
Assumptions
¾
total risk can be split between systematic risk and unsystematic risk;¾
unsystematic risk can be completely diversified away;¾
all of a company’s shareholders hold well-diversified portfolios¾
a risk-free security exists;¾
perfect capital markets.6.2
Limitations
¾
it is a single period model;¾
it is a single index model - beta being the only variable to explain different required returns on different investments.¾
Lack of data for the model – particularly in developing markets¾
CAPM tends to over-state the required return on very high risk companies and under-state the returns on very low risk companies.¾
Many of the assumptions do not hold in real lifeKey points
³
CAPM is an alternative to the Dividend Valuation Model (DVM) for estimating a company’s cost of equity.³
Beta factors measure systematic risk and therefore CAPM should only be used if the company’s shareholders have themselves used portfolio theory to diversify way unsystematic risk³
Despite its assumptions and limitations CAPM is a more flexible model than DVM as it allows the estimation of project-specific discount ratesFOCUS
You should now be able to:
EXAMPLE SOLUTIONS
Therefore the investor should not invest.
Solution 3
Ke = 7 + 1.2 × (15 − 7)
= 16.6%
Solution 4
Using MM formula find the asset beta of the computer industry:
βa =
(
(
)
)
As A plc is ungeared then this asset beta is the appropriate beta for use in the CAPM in order to determine the discount rate that A plc should use for a computer manufacture project:
Required return = 5 + 1.2(12 − 5)
Solution 5
Using MM formula find the asset beta of the computer industry:
βa =
(
(
)
)
In order to find the discount rate for A plc this asset beta must be converted into an equity beta appropriate to A plc:
1.2 = Be
The discount rate that A plc must use is the WACC that it would have if its Ke were 16.2%. In the absence of any other information assume Kd is 5% (risk free rate).
Discount rate = 16.2% × ⅔ + 5 (1 – 0.33) × ⅓
