1. Investment Analysis and Portfolio Management
Lecture 7
Gareth Myles

2. 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?

3. 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

4. Assumptions The CAPM is built on a set of assumptions
Individual investors
Investors evaluate portfolios by the mean and variance of returns over a one period horizon
Preferences satisfy non-satiation
Investors are risk averse
Trading conditions
Assets are infinitely divisible
Borrowing and lending can be undertaken at the risk-free rate of return
There are no taxes or transactions costs

5. Assumptions The set of investors
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

6. Assumptions The first six assumptions are the Markowitz model
The seventh and eighth assumptions add a perfect capital market and perfect information
The final two assumptions make all investors identical except for their degree of risk aversion

7. Direct Implications
All investors face the same efficient set of portfolios

8. 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 of risky assets

9. 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

10. Equilibrium 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

11. 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

12. The Capital Market Line
All efficient portfolios must lie on this line
Slope =
Equation of the line

13. Interpretation 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

14. 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

15. 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 is M

16. Security Market Line Define The equation of the line becomes
This is the security market line (SML)

17. Security Market Line
There is a linear trade-off between risk measured by and return
In equilibrium all assets and portfolios must have risk-return combinations that lie on this line

18. Market Model and CAPM Market model uses CAPM 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

19. Market Model and CAPM In addition: There is a difference between these
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

20. Estimation of CAPM Use the regression equation Take the expected value
The security market line implies
It also shows

21. CAPM and Pricing CAPM also implies the equilibrium asset prices
The security market line is
But
where pi(0) is the value of the asset at time 0 and pi(1) is the value at time 1

22. CAPM and Pricing So the security market line gives
This can be rearranged to find
The price today is related to the expected value at the end of the holding period

23. 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

24. CAPM and Project Appraisal
If both p(0) and p(1) are certain then the risk-free interest rate is used to discount
The PDV is
The decision is to accept project if

25. 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

26. 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