CHAPTER 8
Asset Pricing Models
What are we going to learn
in this chaper?
Why are we interested in
these models?
Capital Market Theory
 Determination of the returns for risky assets
 Assumptions:
 All investors are efficient investors
(points on the efficient frontier)
(importance of utility function)
 Investors can borrow or lend any amount of money at the
risk-free rate of return (RFR)
(ease of lending, difficulty in borrowing)
 All investors have homogeneous expectations
(identical probability distributions for future returns)
Capital Market Theory
 All investors have the same one-period time horizon
 All investments are infinitely divisible, which means that it is
possible to buy or sell fractional shares of any asset or
portfolio
(investment alternatives as continuous curves)
 There are no taxes or transaction costs involved in buying or
selling assets
 There is no inflation or any change in interest rates, or
inflation is fully anticipated
 Capital markets are in equilibrium
(all investments properly priced in line with their risk levels)
Risk Free Asset
 Development of Capital Market Theory
 What would be a risk free asset?
 Why would it be considered risk free?
Risk Free Asset
 What is the formula of covariance?
 If the return for the risk free assets are certain, what
does this mean in terms of standard deviation?
 How does this affect covariance of the risk free asset
with a risky asset?
 What is the formula of correlation? The effects on
correlation?
Risk Free Asset
 What happens to the average rate of return when
you combine a risk-free asset with a portfolio of
risky assets such as those that exist on the
Markowitz efficient frontier?
 What happens to the standard deviation of returns
when you combine a risk-free asset with a portfolio
of risky assets such as those that exist on the
Markowitz efficient frontier?
Utilizing Risk Free Asset
 RFR-A
 RFR-B
 Tangent line to the efficient frontier
 Point M
Utilizing Risk Free Asset
Incorporating Leverage
 How could an investor attain a higher expected
return than is available at Point M?
 What effect would adding leverage have on the
return and risk for your portfolio if you borrow an
amount equal to 50 percent of your original wealth
at the risk-free rate?
Assume that E(RFR) = 0.06 and E(RM) = 0.12
The return on your leveraged portfolio and its risk
would be:
Incorporating Leverage
Incorporating Leverage
 New efficient frontier: the straight line from the RFR
tangent to Point M.
 Capital market line (CML)
 You either invest part of your portfolio in the risk-free asset
and the rest in the risky asset Portfolio M, or you borrow at
the risk free rate and invest these funds in the risky asset
portfolio.
 In either case, all the variability comes from the risky asset
M portfolio.
Market Portfolio
 What is special about portfolio M?
 What should be the weight of each asset in this
portfolio?
 Market portfolio
 What would be some assets included in this portfolio?
 Completely diversified portfolio
Market Portfolio
 Completely diversified portfolio: all the risk
unique to individual assets in the portfolio is
diversified away.
 Unsystematic risk
 Systematic risk
Diversification
 What is diversification?
 What is the purpose of diversification?
 How many securities must be included to arrive at a
completely diversified portfolio?
 Can reduce the overall standard deviation of the
portfolio but you cannot eliminate variability by
adding stocks to the portfolio?
Diversification
CAPM
 Capital asset pricing model (CAPM)
 What is CAPM used for?
 Security market line (SML)
SML
 The relevant risk measure for an individual
risky asset is its covariance with the market
portfolio (Covi,M)
 Slope of SML
 Restatement using Beta
SML
Beta
 What does Beta measure?
 Standardized measure of risk
 What is the beta of the market portfolio?
 What does a beta higher/lower than 1 mean?
Beta
Beta & Expected Returns
Stock
A
B
C
D
E
Beta
0.70
1.00
1.15
1.40
-0.30
RFR
0.06
0.06
0.06
0.06
0.06
RM
0.12
0.12
0.12
0.12
0.12
E(Ri)
Beta
 In equilibrium, all assets and all portfolios of assets should
plot on the SML.
 What if the estimated rate of return lies above the SML?
 What if the estimated rate of return lies below the SML?
 In an efficient market in equilibrium, you would not expect
any assets to plot off the SML because. If there are
deviations, what would be the source?
Identifying Undervalued and Overvalued Assets
 How do we identify whether a stock is under
or over valued?
 What tools to use for estimations of returns?
 Which action to take when a stock is
under/over valued?
Identifying Undervalued and Overvalued Assets
Stock
A
Cur. Price
25
Exp. Price
27
Exp. Div.
0.50
B
C
D
E
40
33
64
50
42
39
65
54
0.50
1.00
1.10
-
Stock
A
B
Beta
0.70
1.00
Req. Ret.
10.20 %
12.00 %
Est. Ret.
10 .00 %
6.20 %
C
1.15
12.90 %
21.20 %
D
E
1.40
-0.30
14.40 %
4.20 %
3.30 %
8.00 %
Diff.
Est. Fut. Ret.
Evaluation
Identifying Undervalued and Overvalued Assets
Calculating Systematic Risk
 How do we calculate the systematic risk?
 What is the characteristic line?
Calculating Systematic Risk
END OF CHAPTER