Chapter 7
Portfolio Theory and
Asset Pricing
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–1
Learning Objectives
•
Understand how ‘risk’ and ‘return’ are defined
and measured.
•
Understand the concept of risk-aversion by
investors.
•
Explain how diversification reduces risk.
•
Understand the importance of covariance
between returns on assets in determining
the risk of a portfolio.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–2
Learning Objectives (cont.)
•
Explain the concept of efficient portfolios.
•
Explain the distinction between systematic
and unsystematic risk.
•
Explain why systematic risk is important to
investors.
•
Explain the relationship between returns and
risk proposed by the capital asset pricing model.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–3
Learning Objectives (cont.)
•
Understand the relationship between the
capital asset pricing model and the arbitrage
pricing model.
•
Explain the development of the Fama–French
three-factor model.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–4
Return
•
There is uncertainty associated with returns
from shares.
•
Assume we can assign probabilities to the possible
returns — given an assumed set of circumstances,
the expected return is given by:
E R  
n
R P
i i
i 1
where:
Ri  return in event or case i
Pi  probability of event or case i
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–5
Expected Return Calculation
•
Distribution of returns for security
Percentage
Return, Ri
Probability,
Pi
9
0.1
10
0.2
11
0.4
12
0.2
13
0.1
Expected Return = (0.09 × 0.1) + (0.10 × 0.2) + (0.11 × 0.4)
+ (0.12 × 0.2) + (0.13 × 0.1)
= 0.11 or 11.0%
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–6
Risk
•
Risk is present whenever investors are not certain
about the outcome an investment will produce.
•
Risk is measured in terms of how much a
particular return deviates from an expected
return, measured by variance:

2

n
2




R

E
R
Pi
 i
i 1
•
We often use standard deviation to measure risk.
This is simply the square root of the variance.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–7
Risk Calculation
• Continuing with the previous example,
risk is given by:
Variance:
 2 =  0.09-0.11  0.1   0.10-0.11  0.2 
2
2
  0.11-0.11  0.4    0.12-0.11  0.2 
2
2
  0.13-0.11  0.1
2
= 0.000 12
Standard Deviation:  = 0.000 12  0.01095 1.095% 
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–8
Risk Attitudes
•
Risk-neutral investor:
–
•
Risk-averse investor:
–
•
One whose utility is unaffected by risk and hence, when
choosing an investment, focuses only on expected return.
One who demands compensation in the form of higher
expected returns in order to be induced into taking on
more risk.
Risk-seeking investor:
–
One who derives utility from being exposed to risk, and
hence may be willing to give up some expected return
in order to be exposed to additional risk.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–9
Risk Attitudes (cont.)
•
The standard assumption in finance theory is
risk-aversion.
–
This does not mean an investor will refuse to bear
any risk at all.
–
Rather, an investor regards risk as something
undesirable, but which may be worth tolerating
if compensated with sufficient return.
–
That is, there is a trade-off between risk and return.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–10
Utility to Wealth Functions
Utility U(W )
riskseeking
risk-neutral
risk-averse
Wealth (W )
Figure 7.3
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–11
Investors’ Risk Preferences
•
Indifference curve
–
Curve which represents those combinations of expected
return and risk that result in a fixed level of expected
utility for an investor.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–12
Indifference Curves
(for a risk-averse investor)
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–13
Risk of Assets and Portfolios
•
We now know that the risk of an individual asset
is summarised by standard deviation (or variance)
of returns.
•
Investors usually invest in a number of assets
(a portfolio) and will be concerned about the risk
of their overall portfolio.
•
Now concerned about how these individual risks
will interact to provide us with overall portfolio risk.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–14
Portfolio Theory
•
Assumptions
–
Investors perceive investment opportunities in terms
of a probability distribution defined by expected return
and risk.
–
Investors’ expected utility is an increasing function of
return and a decreasing function of risk (risk-aversion).
–
Investors are rational.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–15
Measuring Return for a Portfolio
•
Portfolio return (Rp) is a weighted average of
all the expected returns of the assets held in
the portfolio:
   w j E R j 
n
E Rp 
j 1
where:
w j = the proportion of the portfolio
invested in asset j
n = the number of securities in the portfolio
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–16
Portfolio Return Calculation
•
•
•
Assume 60% of the portfolio is invested in
security 1 and 40% in security 2.
The expected returns of the securities are
0.08 and 0.12 respectively.
The Rp can be calculated as follows:
E  Rp  
w E R 

 0.6  0.08
n
j 1
j
j

 0.4  0.12 
 0.096 or 9.6%
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–17
Portfolio Risk
• Portfolio risk depends on:
–
The proportion of funds invested in each asset held
in the portfolio (w).
–
The riskiness of the individual assets comprising
the portfolio (2).
–
The relationship between each asset in the portfolio
with respect to risk, correlation  .
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–18
Measurement of Portfolio Risk
•
For a two-asset portfolio, the variance is:
 2p  w12 12  w22 22  2w1w2 1,2 1 2
where:
wi = the proportion of the portfolio
invested in asset i
 i = the standard deviation of asset i
ij  correlation between asset i and j returns
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–19
Portfolio Risk Calculation
• Given the variances of security 1 and security 2
are 0.0016 and 0.0036, respectively, and
the correlation (1,2) is –0.5:
 p2  w12 12  w22 22  2 w1w2 1,2 1 2



 0.6  0.6  0.0016 
 0.4  0.4  0.0036 
2  0.6  0.4  0.5  0.04  0.06 
 0.000576  p  0.024 
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–20
Relationship Measures
•
Covariance
– Statistic describing the relationship between
two variables.
–
If positive, when one of the variables takes on
a value above its expected value, the other
has a propensity to do the same.
–
If the covariance is negative, the deviations
tend to be of an opposite sign.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–21
Relationship Measures (cont.)
•
Correlation coefficient is another measure of the
strength of a relationship between two variables.
•
The correlation is equal to the covariance divided
by the product of the asset’s standard deviations.
 xy 
•
covx, y 
 x y
It is simply a standardisation of the covariance and
for this reason is bounded by the range +1 to –1.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–22
Gains from Diversification
•
The gain from diversifying is closely related to
the value of the correlation coefficient.
•
The degree of risk reduction increases as
the correlation between the rates of return
on two securities decreases.
•
Combining two securities whose returns are
perfectly positively correlated results only in
risk averaging, and does not provide any
risk reduction.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–23
Gains from Diversification (cont.)
•
Risk reduction occurs by combining
securities whose returns are less than
perfectly positively correlated.
•
When the correlation coefficient is less than one,
the third term in the portfolio variance equation is
reduced, reducing portfolio risk.
•
If the correlation coefficient is negative, risk is
reduced even more, but this is not a necessary
prerequisite for diversification gains.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–24
Diversification with Multiple Assets
•
These diversification benefits are greater, the more
assets we incorporate into the portfolio.
•
The key is the correlation between each pair of assets
in the portfolio.
• With n assets, there will be a n × n covariance matrix.
• The properties of the variance–covariance matrix are:
• It will contain n2 terms.
• The two covariance terms for each pair of assets are identical.
• It is symmetrical about the main diagonal which contains
n variance terms.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–25
Diversification with Multiple Assets
(cont.)
•
For a diversified portfolio, the variance of the
individual assets contributes little to the risk of
the portfolio.
–
•
For example, in a 50-asset portfolio there are 50 (n)
variance terms and 2450 (n2 − n) covariance terms.
The risk depends largely on the covariances
between the returns on the assets.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–26
Systematic and Unsystematic Risk
•
Intuitively, we should think of risk as comprising:
Total Risk = Systematic Risk + Unsystematic Risk
•
Systematic risk (market-related risk or non-diversifiable
risk):
–
•
That component of total risk that is due to economy-wide
factors.
Unsystematic risk (diversifiable risk):
–
That component of total risk that is unique to the firm and
may be eliminated by diversification.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–27
Systematic and Unsystematic Risk
(cont.)
•
Unsystematic risk is removed by holding a
well-diversified portfolio.
•
The returns on a well-diversified portfolio will
vary due to the effects of market-wide or
economy-wide factors.
•
Systematic risk of a security or portfolio will
depend on its sensitivity to the effects of these
market-wide factors.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–28
Risk of an Individual Asset
•
The risk contribution of an asset to a portfolio is
largely determined by the covariance between the
return on that asset and the return on the holder’s
existing portfolio:


Cov Ri , R p  i, p i p
•
Well-diversified portfolios will be representative of
the market as a whole, thus the relevant measure
of risk is the covariance between the return on the
asset and the return on the market:
CovRi , RM 
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–29
Beta
 Beta is a measure of a security’s systematic risk,
describing the amount of risk contributed by the
security to the market portfolio.
 Cov(Ri , RM) can be scaled by dividing it by the
variance of the return on the market. This is the
asset’s beta (i):
i 
Cov  Ri , RM 
 M2
where:
RM = return on the market portfolio
Ri = return on the particular asset
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–30
Construction of a Portfolio
• The opportunity set:
• The set of all feasible portfolios that can be
constructed from a given set of risky assets.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–31
Construction of a Portfolio (cont.)
•
•
The efficient frontier
–
Given risk-aversion, each investor will try to secure
a portfolio on the efficient frontier.
–
The efficient frontier is determined on the basis
of dominance.
A portfolio is efficient if:
–
No other portfolio has a higher return for the same risk, or
–
No other portfolio has a lower risk for the same return.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–32
Construction of a Portfolio (cont.)
•
Investors are a diverse group and, therefore,
each investor may prefer a different point along
the efficient frontier.
•
Investor risk preferences will determine the
preferred portfolio on the efficient frontier.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–33
Value at Risk
•
A relatively new measure of the riskiness of an asset
or portfolio.
•
Defined as ‘the worst loss that is possible under normal
market conditions during a given time period’.
•
Requires the standard deviation of the return on the asset
or portfolio.
•
Typically assumes returns are normally distributed.
•
Using the normal distribution and the standard deviation,
can calculate a worst-case scenario.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–34
Value at Risk (cont.)
•
Investment of $10m in Curzon has an estimated return
of zero and a standard deviation of 20% ($2m).
•
Assume returns are normally distributed and bad market
conditions expected 5% of the time.
•
Worst outcome under normal conditions is a loss of 1.645
(from normal tables) multiplied by standard deviation of $2m.
•
Worst outcome is loss of $3.29m or an investment value
of $6.71m.
•
VaR was not used effectively used by NAB in the foreign
exchange scandal — poor implementation and execution.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–35
The Pricing of Risky Assets
•
What determines the expected rate of return on
an individual asset?
•
Risky assets will be priced such that there is a
relationship between returns and systematic risk.
•
Investors need to be sufficiently compensated for
taking on the risks associated with the investment.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–36
The Capital Market Line
•
Combining the efficient frontier with preferences,
investors choose an optimal portfolio.
•
This can be enhanced by introducing a risk-free
asset:
–
•
The opportunity set for investors is expanded and results
in a new efficient frontier — Capital Market Line (CML).
The CML represents the efficient set of all
portfolios that provides the investor with the
best possible investment opportunities when
a risk-free asset is available.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–37
The Capital Market Line (cont.)
•
The CML links the risk-free asset with the
optimal risky portfolio (M).
•
Investors can then vary the riskiness of their
portfolio investment by changing weights in the
risk-free asset and portfolio M.
•
This changes their return according to the CML:
E  Rp   R f
 E  RM   R f 
 
  p
M


Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–38
The Capital Market Line (cont.)
Copyright  2006 McGraw-Hill Australia Pty Ltd
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Prepared by Dr Buly Cardak
7–39
The CAPM and the Security Market
Line
• In equilibrium, the expected return on a risky asset i
(or an inefficient portfolio), is given by the security
market line:
 E RM   R f 
 covRi , RM 
E Ri   R f  
M


where:
E ( Ri ) = the expected return on the ith risky asset
Cov( Ri , RM ) = the covariance between returns
on ith risky asset and the market portfolio
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–40
The CAPM and the Security Market
Line (cont.)
• The covariance term is the only explanatory factor
in the equation that is specific to asset i.
• As Cov(Ri,RM) is the risk of an asset held as part
of the market portfolio, and M is the risk of the
market portfolio, beta   measures the risk of i
relative to the risk of the market as a whole.
• We can thus write the SML as the CAPM equation:
E  Ri   R f  i  E  RM   R f 
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–41
The CAPM and the Security Market
Line (cont.)
 Graphical depiction of CAPM, the security market line.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–42
Portfolio Beta
• The systematic risk (Beta) of a portfolio is
calculated as the weighted average of the
betas of the individual assets in the portfolio:
n
 p   wi  i
i 1
where:
n  number of assets in the portfolio
wi = proportion of the current market value
of portfolio p constituted by the i th asset
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–43
Risk and the CAPM
•
The capital market will only reward investors
for bearing risk that cannot be eliminated
by diversification.
•
Unsystematic risk can be diversified away,
so capital market will not reward investors for
taking this type of risk.
•
However, CAPM states the reward for
bearing systematic risk is a higher expected
return, consistent with the idea of higher risk
requires higher return.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–44
Tests of the CAPM
•
Early empirical evidence was supportive of CAPM in
explaining asset pricing.
•
Roll’s critique (1977) criticised methodology of testing
CAPM empirically.
•
Most tests of the CAPM can only determine if the market
portfolio used is efficient.
•
In response, researchers implemented methodological
refinements — CAPM seems untestable, given Roll’s
critique.
•
However, CAPM is a useful tool when thinking about
asset returns.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–45
Arbitrage Pricing Theory (APT)
•
Developed primarily as a response to
the shortcomings of the CAPM.
•
Less restrictive assumptions.
•
Empirically testable.
•
A model of asset pricing that describes the
risk premium for a risky asset as a linear
combination of various risk factors.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–46
Arbitrage Pricing Theory (APT)
(cont.)
•
The APT model is based on the following equation
describing the returns to asset i:
Ri   i   i F  E F   ei
where:
 i = a constant, specific to asset i
i = measure of sensitivity of returns on asset i to factor F
F  a risk factor which explains returns
E  F  = the expected value of F
ei = error term with an expected value of zero
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–47
Arbitrage Pricing Theory (APT)
(cont.)
•
From the previous equation, we can conclude that in the
absence of arbitrage opportunities, the expected return
on asset i:
E  Ri   l0  l1 i
where: l1 ,l2 = constants
•
Interpret l1 as the risk-free rate and l2 as the risk premium
on the risk factor F.
•
This seems like the CAPM, main point is that with APT we
have not specified the source of risk — the risk factor F.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–48
Arbitrage Pricing Theory (APT)
(cont.)
•
Another important point is that the APT can be
generalised to explain asset returns as a function
of multiple factors:
E  Ri   R f  l1 i1  l2 i 2  ...  lk ik
where:
E  Ri   expected return on asset i
R f  risk free interest rate
l j  risk premium to the jth factor
ij  sensitivity of asset i to the jth risk factor
Copyright  2006 McGraw-Hill Australia Pty Ltd
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Prepared by Dr Buly Cardak
7–49
APT: The Factors
•
What factors should be included in the model?
•
How many factors should be included in the
model?
•
It is only with retrospective factor analysis that
these questions can be addressed.
•
These questions are best answered empirically
as the theory does not explicitly specify what
the risk factor(s) are.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–50
Empirical Evidence on APT
•
Empirical work on the APT can be classified along
the following lines:
–
Do share returns appear to have an implicit factor
structure?

–
How well do sensitivities to factors explain asset
prices (returns)?

–
Evidence supportive of factor structure in Australia:
Sinclair (1984) and Faff (1988).
For Australia, Faff (1988) found three factors to be
priced and thus able to explain returns.
What factors, and how many, might there be?

For Australia, inflation and interest rate variables:
Groenewold and Fraser (1997)
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–51
Fama–French Three-Factor Model
•
Fama and French (1992) provide evidence on factors
that explain asset returns — no support for CAPM,
support for firm size, leverage, P/E, BV/MV, though
not definitive.
•
Fama and French (1995) leads to the most common
three-factor model:
E  Rit   R ft 
•
i M  E  RMt   R ft   i S E  SMB  + i h E  HML 
Includes the CAPM, market factor, a small minus
large portfolio factor (SML) and a high minus low
market to book portfolio (HML).
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–52
Fama–French Three-Factor Model (cont.)
•
This model is supported by Australian data relative
to CAPM: Gaunt (2004).
•
While the three-factor model is empirically robust, it
suffers from difficult economic interpretation — why
do company size and BV/MV explain asset returns?
•
The fact that Fama–French includes market factor,
along with ambiguity of role of other factors is
supportive of CAPM.
•
The three-factor model is now very common in
empirical research.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–53
Summary
•
Portfolio theory tells us that diversification
reduces risk.
–
•
Risk can be divided into two categories:
–
–
•
Diversification works best with negative or low
positive correlations between assets and
asset classes.
Systematic risk — cannot be diversified away.
Unsystematic risk — can be diversified away.
Systematic risk of an asset is measured by the
asset’s Beta. Risk of asset is relative to market.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–54
Summary (cont.)
•
CAPM provides the relationship between risk
and expected return for risky assets.
•
CAPM uses asset’s beta and assumes linear
relationship between expected return and risk
relative to market, measured by beta.
•
Arbitrage pricing theory is an alternative to CAPM.
–
APT assumes that asset returns are linearly related to
many factors, typically macro variables and fundamental
asset-specific factors.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–55
Summary (cont.)
•
Fama–French three-factor model is a
contemporary version of the APT
multi-factor model.
–
Key factors are the market excess return, return on
a small minus large portfolio, return on a high minus
low market to book portfolio.
Copyright  2006 McGraw-Hill Australia Pty Ltd
PPTs t/a Business Finance by Peirson, Brown, Easton, Howard and Pinder
Prepared by Dr Buly Cardak
7–56