Investment analysis and portfolio management

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Investment Analysis and Portfolio Management

Lecture 7

Gareth Myles

The Capital Asset Pricing Model

(CAPM)

The CAPM is a model of equilibrium in the market for securities.

Previous lectures have addressed the

question of how investors should choose assets given the observed structure of

returns.

Now the question is changed to:

If investors follow these strategies, how will returns be determined in equilibrium?

The Capital Asset Pricing Model

(CAPM)

 The simplest and most fundamental model of equilibrium in the security market

 Builds on the Markowitz model of portfolio choice

 Aggregates the choices of individual investors

 Trading ensures an equilibrium where returns adjust so that the demand and supply of

assets are equal

 Many modifications/extensions can be made

 But basic insights always extend

 The CAPM is built on a set of assumptions

 Individual investors

variance of returns over a one period horizon

 Trading conditions

risk-free rate of return

The risk-free rate is the same for all

Information flows perfectly

The set of investors

All investors have the same time horizon

Investors have identical expectations

Direct Implications

 All investors face the

same efficient set of

Direct Implications

 All investors choose

a location on the

efficient frontier

 The location depends

on the degree of risk

aversion

 The chosen portfolio

mixes the risk-free

asset and portfolio M

More risk averse

M

Separation Theorem

 The optimal combination of risky assets is

determined without knowledge of preferences

 All choose portfolio M

 This is the Separation Theorem

 M must be the market portfolio of risky assets

 All investors hold it to a greater or lesser extent

 No other portfolio of risky assets is held

 There is a question about the interpretation of this portfolio

 The only assets that need to be marketed are:

 The risk-free asset

 A mutual fund representing the market portfolio

 No other assets are required

 In equilibrium there can be no short sales of the risky assets

 All investors buy the same risky assets

 No-one can be short since all would be short

 If all are short the market is not in equilibrium

 Equilibrium occurs when the demand for assets matches the supply

 This also applies to the risk-free

 Borrowing must equal lending

 This is achieved by the adjustment of asset

prices

 As prices change so do the returns on the assets

 This process generates an equilibrium structure

of returns

The Capital Market Line

 All efficient portfolios

must lie on this line

f

M f

p

r

r r

rf is the reward for "time"

Patience is rewarded

Investment delays consumption

 is the reward for accepting "risk"

The market price of risk

Judged to be equilibrium reward

Obtained by matching demand to supply

Security Market Line

Now consider the implications for

individual assets

Graph covariance against return

The risk on the market portfolio is

The covariance of the risk-free asset is zero

The covariance of the market with the market is

Security Market Line

 Can mix M and the

risk-free asset along the line

 If there was a portfolio above the line all

investors would buy it

 No investor would hold one below

 The equation of the line

f

M f

i

r

r r

Security Market Line

Define

The equation of the line becomes

This is the security market line (SML)

2

M

iM iM





 M f  iM f

Security Market Line

assets and portfolios

must have risk-return

combinations that lie

Market Model and CAPM

Market model uses

 is derived from an assumption about

the determination of returns

it is derived from a statistical model

the index is chosen not specified by any underlying analysis

 is derived from an equilibrium theory

Market Model and CAPM

In addition:

I is usually assumed to be the market index,

but in principal could be any index

M is always the market portfolio

There is a difference between these

But they are often used interchangeably

The market index is taken as an

approximation of the market portfolio

Estimation of CAPM

Use the regression equation

Take the expected value

The security market line implies

It also shows

iM iM

CAPM and Pricing

 CAPM also implies the equilibrium asset prices

 The security market line is

 But

where p i(0) is the value of the asset at time 0

and p i(1) is the value at time 1

i

i

i i

p

p p

CAPM and Pricing

value at the end of the holding period

iM f

i i

r r

r

p p

CAPM and Project Appraisal

Consider an investment project

It requires an investment of p(0) today

It provides a payment of p(1) in a year

Should the project be undertaken?

The answer is yes if the present

discounted value (PDV) of the project is

positive

CAPM and Project Appraisal

If both p(0) and p(1) are certain then the

risk-free interest rate is used to discount

f

r

p p



 1

1 0

CAPM and Project Appraisal

Now assume p(1) is uncertain

Cannot simply discount at risk-free rate if investors are risk averse

For example using

will over-value the project

With risk aversion the project is worth less than its expected return

f r

p p

)) 1 ( ( ))

1 (

CAPM and Project Appraisal

One method to obtain the correct value

is to adjust the rate of discount to reflect risk

But by how much?

The CAPM pricing rule gives the answer

The correct PDV of the project is

] [

1

) 1

( )

0

(

f M

p

r

p p