ACCA paper f9 financial management study materials F9FM session12 d08

1 SYSTEMATIC AND UNSYSTEMATIC RISK 1.1 Definitions Ü Risk, the variability of returns, can be split into two elements: unsystematic risk − These are the risks that are unique to each co

OVERVIEW

Objective

Ü To understand the Capital Asset Pricing Model and its uses in financial management

BETA FACTORS

USES OF THE

CAPM

Ü Measurement

Ü Calculation

Ü Interpretation

Ü Formula

Ü Security Market Line

Ü Well-diversified investor

Ü Companies

Ü Asset betas

Ü Equity betas

Ü Use of the equity beta

ASSUMPTIONS AND LIMITATIONS

CAPITAL ASSET PRICING MODEL

DEGEARING AND REGEARING BETA

Ü Project appraisal in a new

industry

Ü MM and betas

Ü Assumptions

Ü Limitations

SYSTEMATIC AND UNSYSTEMATIC RISK

Ü Definitions

Ü Measurement of systematic risk

1 SYSTEMATIC AND UNSYSTEMATIC RISK

1.1 Definitions

Ü 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

Ü 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

Ü Systematic risk will affect the shares of all companies although some will be affected to

a greater or lesser degree than others

Ü This sensitivity to systematic risk is measured by a beta factor

Ü 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)

Ü This can be illustrated by the Security Characteristic Line which gives an indication of the share’s sensitivity to market changes

Ü The beta factor is estimated from these observations by determining the gradient or slope of the “line of best fit” through the observed points The steeper the slope the

(Ri - R f ) Security characteristic line

Intercept = α

Slope = β

(R m - R f )

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

Ü The Security Characteristic Line should in the long run pass through the point where the two axes meet

Ü 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

Ü 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

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?

Solution

2.3 Interpretation

Ü 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

3.1 Formula

Ü If the shareholders of a company hold well-diversified portfolios then they are

concerned only with systematic risk

Ü The return these shareholders require therefore is only a return to cover the systematic risk of an investment

Ü 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

Ü 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

Ü The CAPM formula is :

E(ri) = Rf + i(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

Ü CAPM is the equation of the Security Market Line

3.2 Security Market Line

Ü The Security Market Line is a graph that indicates the required return from any

investment 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

Where Ra = the forecast return from investment A

Ü The required return of an investment with a beta of zero (risk free) will be the risk free return

Ü The required return of an investment with a beta of 1 will be the market return

Ü 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

Ü Consider investment B - it would appear to be temporarily over priced – a “negative alpha” investment

Ü In the long run market forces should ensure that all investments do give the returns predicted by the Security Market Line

4 USES OF THE CAPM

4.1 Well-diversified investors

Ü If an investor already holds a well-diversified portfolio then that investor will be

concerned only with systematic risk The CAPM is therefore relevant

Ü 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

Ü 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

Ü 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

Ü 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

Ü If the project is the same risk as that of the existing activities of the company then the existing WACC can be used

Ü However if the project is of a different risk type to the existing activities then the

existing WACC will not be appropriate In these instances a tailor-made discount rate for that type of project must be determined using the CAPM

4.3 Asset betas

Ü 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

Ü This beta factor is the asset beta and measures the systematic business risk of the

company

Ü It can also be referred to as an ungeared beta factor

4.4 Equity betas

Ü The equity beta measures the sensitivity to systematic risk of the returns to the equity shareholders in a company

Ü In an all-equity financed company, or ungeared company, the only risk that is incurred

is business risk

Ü Therefore in an ungeared company the asset beta and the equity beta are the same

Ü 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

Ü Therefore in a geared company the equity beta > the asset beta

Ü Equity betas can also be called geared betas

4.5 Use of the equity beta

Ü 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

Ü The required return of shareholders = the cost of equity geared (Keg)

Ü 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?

Solution

5 DEGEARING AND REGEARING BETA

5.1 Project appraisal in a new industry

Ü 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

Ü If the project is in a different industry (or country) then a discount rate to reflect the business risk of that industry is required

Ü 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

Ü This requires us to first “degear” the beta to find the asset beta, and then “regear” to

reflect our company’s level of financial risk

Ü 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):

a = ( + ( − ) ) e

T 1 Vd Ve







− +

−

d T 1 Vd Ve

T 1 Vd

where βa = asset beta

βe = equity beta

βd = beta of corporate debt

Ve = market value of equity Vd= market value of debt

T = corporation tax rate

Ü If the exam question does not give a beta factor for debt then assume that debt is risk free i.e βd = 0

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?

Solution

6 ASSUMPTIONS AND LIMITATIONS OF THE CAPM 6.1 Assumptions

Ü total risk can be split between systematic risk and unsystematic risk;

Ü unsystematic risk can be completely diversified away;

Ü all of a company’s shareholders hold well-diversified portfolios

Ü a risk-free security exists;

Ü perfect capital markets

6.2 Limitations

Ü it is a single period model;

Ü it is a single index model - beta being the only variable to explain different required returns on different investments

Ü Lack of data for the model – particularly in developing markets

Ü CAPM tends to over-state the required return on very high risk companies and under-state the returns on very low risk companies

Ü Many of the assumptions do not hold in real life

Key points

ÐCAPM is an alternative to the Dividend Valuation Model (DVM) for

estimating a company’s cost of equity

ÐBeta 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 risk

ÐDespite its assumptions and limitations CAPM is a more flexible model

than DVM as it allows the estimation of project-specific discount rates

FOCUS

You should now be able to:

Ü understand the meaning and significance of systematic and unsystematic risk;

Ü appreciate the uses of the CAPM for financial management;

EXAMPLE SOLUTIONS

Solution 1

Beta factor =

21

15 72

Solution 2

Required return = 5 + 0.9 × (15 − 5)

Expected return = 12%

Therefore the investor should not invest

Solution 3

Solution 4

Using MM formula find the asset beta of the computer industry:

a = ( + ( − ) ) e

T 1 Vd Ve







− +

−

d T 1 Vd Ve

T 1 Vd

) 67 0 1 ( 4

4

× +

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:

a = ( + ( − ) ) e

T 1 Vd Ve







− +

−

d T 1 Vd Ve

T 1 Vd

) 67 0 1 ( 4

4

× +

In order to find the discount rate for A plc this asset beta must be converted into an equity beta appropriate to A plc:

0.67) 1 ( 2

2

× + 1.2 = 0.749 × Be

Ke of A plc if in computer manufacture = 5 + 1.6 (12 – 5)

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% × + 5 (1 – 0.33) ×