2. PRESENTATION INTRODUCTION
• What is CAPM? Background to model derivation, purposes
and issues that CAPM aims to address
• Statistical workings and pre-requisites of in-depth
understanding of CAPM (Modern Portfolio Theory)
• CAPM weaknesses and applications in financial management
• Issues of presentation to the UG cohort. Pedagogic advice
stemming from the threshold concepts paradigm
3. CAPM INVENTION
• Capital AssetPricing Model was developed as an attempt to
predict capital markets’ behaviour under the condition of risk
• CAPM is based on equilibrium assumption and used to
estimate a risk-adjusted return on asset (‘cost of equity’)
• Anacademic paper that presented CAPM is Sharpe (1964).
Capital Asset Prices: A theory of market equilibrium under
conditions of risk, Journal of Finance, 19 (3), 425-442
4. Optimization and Application to Portfolio Selection” for more details);;
e–Capital Asset Pricing Model (CAPM)predict asset prices;
Is an equilibrium model: it can be used to
– Can be factor to any in which portfolio;
Is a linear appliedmodel,security orthe factor is the market return;
– Is expressed FORMULATION USING
CAPM in from the mean-variance analysis (see “Fundam
Is derived directlyterms of expectations.
Optimization and Application to Portfolio Selection” for more detail
EXPECTATIONS ALGEBRA
Foran equilibrium model: it can be used to predict asset prices;
Is an investment I, It takes the form
Can be applied to any r R portfolio; R
E security or I E rM
I
Is • This reads as “expected excess return on Individual asset equals beta
expressed in terms of expectations.
or, alternatively excess return on Market”
times expected
an investment I, ItEtakes R E r R
rI return r form M free rate R. Excess
• Excess return is historical the minus risk
I
is r R E r R
return on market E regarded as ‘the market price of risk’
I I M
• Most of textbooks present a re-arranged expression as follows:
alternatively
E rI R I E rM R
5. THE STRUCTURE OF CAPM
This kind of explanation is typical for a US classroom. Being
difficult to comprehend, it shows a complex structure
6. WHAT IS BETA OF AN ASSET?
• Betais a parameter that gives information about individual
stock and its specific (idiosyncratic) risk
• Betais calculated as the slope of the simple linear regression
(You can remember ‘beta’ from regression formulae before!)
• What is an independent variable in the regression? (Excess
return on the market or market price of risk)
8. BETA ILLUSTRATIONS
Two examples: beta is similar for a conservative mutual fund and
Internet video streaming service. Betas for different industries
9. HOW EQUILIBRIUM WORKS
• Sincethe optimal policy is to invest a fraction of wealth into
the tangency portfolio, ultimately every investor will hold the
tangency portfolio
• Asa consequence, equilibrium will be achieved and the
market value of each risky asset will become proportional to
their weights in the tangency portfolio
• Another
formulation: expected returns and variances will
become equal to ones of the tangency portfolio
10. TANGENCY PORTFOLIO?? TOPIC
REQUIRES SOME MPT KNOWLEDGE
The tangency portfolio
Line parametrized by wt:
Return wt t 1 wt R R wt t R
wt t
t CAPM
A Tangency portfolio
B
R
B A t Risk
41
It is a portfolio of risky assets (equity, commodity) allocated in such a way
that it provides ‘the same’ return as a risk free asset (cash, bond) portfolio
Bonds are not strictly risk-free: they have interest rate and credit risks
11. CAPM IS A MODEL
Love based on outer beauty--of the elegant CAPM formulation,
of course--can be a good start but only love based on deep
understanding and acceptance of weakness endures
12. WHAT CAPM PREDICTS
• CAPM is an equilibrium model and is based on expectations.
That means that its use for prediction is theoretically justified
• It follows from the CAPM expectations formulation that the
risk premium (excess return) of an individual asset in linear
relationship with the risk premium of the market (times beta).
The principle is scaleable to a portfolio of assets
• Hence a conclusion that, on average, the market will only
compensate for taking on the systematic risk (adjusted by beta
that reflects non-systematic risk but as a constant parameter)
13. PRACTICAL FORMULATION OF
CAPM FOR MANAGEMENT
This formulation is used when
estimating ‘cost of equity’ for the
firm’s capital structure
Risk free rate can be found
using the yield curve of US
Advice: use input from Treasuries (Bloomberg website)
financial markets for corporate
budgeting and investment Market rate of return is
planning but trading requires averaged return on a market
more sophisticated tools index (e.g., Dow Jones or DAX)
14. PEDAGOGIC ISSUES
• An introduction to undergraduate students warrants step-by-
step explanation and guidance through mathematics
• Itis important make students accustomed to ‘the tools of the
trade’ and generate linkages to the underlining knowledge
while avoiding the fitting of CAPM to too many theories
• Important opportunity to do an application of the simple
regression model and give understanding of ‘mechanics’
• Justification with equilibrium and MPT rather than utility
15. THRESHOLD CONCEPT ISSUES
APPLIED TO CAPM PRESENTATION
• “Thethreshold concept approach is concerned with how
students can be helped to acquire integrating ideas.” (Davies &
Mangan 2007b)
• Flashingthe CAPM formula on a slide and then doing some
cost of capital examples would be the exactly wrong approach
• Itis better of focus on intricacies of WACC and exercise
practice closer to the time of examination, as a revision.
However, past exam papers are to be released at the start
16. THRESHOLD CONCEPT ISSUES
APPLIED TO CAPM PRESENTATION
To stimulate open mindset and memory retention:
• Demonstrate
the workings of the model (statistics).
Opaqueness will lead to rote learning of symbols’ definitions
• Show where the inputs can practically come from--the short-
term part of US Treasury yield curve--stimulate informed
guess and recognition based on prior knowledge
• Behonest about the model’s weaknesses and application of
the outputs. Provide the idea of where the model was coming
from and for what purposes it was derived and is used
