Chapter 13
CAPM and APT
Investments
© K. Cuthbertson and D. Nitzsche
Quiz
 RA = 11.2%
βA=.82
 RB = 17.6% βB=1.46
 What is the risk free rate?
 What is the return on the market?
What is the Market Risk Premium?
© K. Cuthbertson and D. Nitzsche
Learning Objectives
 Link between CAPM and mean-variance portfolio
theory
 Beta as a measure of undiversifiable risk
 Linear relationship between expected returns and
beta of stocks- SML
 Use of CAPM for portfolio construction; for market
risk in a portfolio; for estimation of discount factor in
DFCF valuation methods, for market timing
strategies
© K. Cuthbertson and D. Nitzsche
Capital Market Theory: An Overview
 Capital market theory extends portfolio theory and
develops a model for pricing all risky assets, while
capital asset pricing model (CAPM) will allow you to
determine the required rate of return for any risky
asset based on the systematic risk in the asset
i 
COV ( Ri , Rm )
 m2
where Rm  return on the market index
 m2  variance of the market returns
Ri  return on Security i
CAPM
 CAPM states that the expected excess return on a
stock is defined by the stock’s market risk beta and
by the expected excess return on the market:

(ER-r)=β(ERm –r)
© K. Cuthbertson and D. Nitzsche
or ER=r+β(ERm –r)
Systematic Risk
6
 Risk factors that affect a large number of assets
 Also known as non-diversifiable risk or market
risk
 Examples: changes in GDP, inflation, interest rates,
general economic conditions
Portfolio Diversification (1)
7
Portfolio Diversification (2)
8
Measuring Systematic Risk
9
 Beta (β) is a measure of systematic risk
 Interpreting beta:
 β = 1 implies the asset has the same systematic risk as the
overall market
βm=Cov(Rm; Rm)/σm2

but Cov(Rm; Rm)=σm2
 β < 1 implies the asset has less systematic risk than the overall
market
 β > 1 implies the asset has more systematic risk than the
overall market
High and Low Betas
10
Portfolio Betas
11
 Consider the previous example with the following
four securities
 Security
A
B
C
D
Weight
.133
.2
.267
.4
 What is the portfolio beta? 1.773
Beta
3.69
0.64
1.64
1.79
CAPM and SIM
 SIM is statistical relationship (regression of excess
returns of a stock and a benchmark)
 The intercept of the regression line of SIM is a
performance measure Jensen’s alpha
© K. Cuthbertson and D. Nitzsche
Market Index in the SIM
0.5
0.4
Excess Return on BA Shares
0.3
0.2
0.1
0
-0.12
-0.1
-0.08
-0.06
-0.04
-0.02
0
-0.1
-0.2
-0.3
-0.4
-0.5
Excess Return on Market
0.02
0.04
0.06
0.08
Security Market Line
 CAPM is an asset pricing equation that explains the
systematic risk and the role of diversification

E(Ri) = Rf + βi(Rm-Rf)
 Rearrange CAPM in terms of market risk
 Calculate beta on historical stock returns or from
financial information vendor
 Return averages from historical data serve as
estimates of expected returns
© K. Cuthbertson and D. Nitzsche
Figure 1 : Security market line (SML)
Expected/Average
Returns
SML/CAPM
return, ERP
Average historic
return for S
14%
13%
9%
SML
Q (buy)
M
P
T (sell)
r = 5%
4%
S (sell)
0.5
1
1.2
Beta, βi
The larger is βi, the larger is the CAPM expected return ERi
© K. Cuthbertson and D. Nitzsche
Matrix
 Specific elements of a matrix are often denoted by a
variable with two subscripts. For instance, a2,1
represents the element at the second row and first
column
© K. Cuthbertson and D. Nitzsche
Applications of CAPM
 Market timing
 Portfolio construction
 Value at risk
 Performance measure
 Treynor measure for excess return (uses market risk β)
 Sharpe measure (uses total risk σ)
 Jansen’s α
© K. Cuthbertson and D. Nitzsche
Two Fund Separation and CML
© K. Cuthbertson and D. Nitzsche
Return and Risk of Two Fund Portfolio
 Return is weighted average of Risk free rate and
market return; portfolio weights sum to one
 Rp= wRf (Rf) + (1- wRf )(Rm)
 Risk on this portfolio is also weighted average
(covariance zero; σRf =0
 σRp = wRf (σRf ) + (1- wRf )(σ Rm )
© K. Cuthbertson and D. Nitzsche
Using the CML to Invest: An Example
• How much to invest in the riskless security?
11.5%= wRF (4%) + (1-wRF )(9%)
wRF= -0.5
• The investment strategy is to borrow 50% and
invest 150% of equity in the market portfolio
Background to Capital Market Theory
 Assumptions:
 All investors are Markowitz efficient investors who want
to target points on the efficient frontier
 Investors can borrow or lend any amount of money at the
risk-free rate of return (RFR)
 All investors have homogeneous expectations; that is,
they estimate identical probability distributions for future
rates of return
 All investors have the same one-period time horizon such
as one-month, six months, or one year
Continued…
Background to Capital Market Theory
 Assumptions:
 All investments are infinitely divisible, which means that
it is possible to buy or sell fractional shares of any asset
or portfolio
 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, implying that all
investments are properly priced in line with their risk
levels
Background to Capital Market Theory
 Development of the Theory
 The major factor that allowed portfolio theory to develop into
capital market theory is the concept of a risk-free asset

An asset with zero standard deviation

Zero correlation with all other risky assets

Provides the risk-free rate of return (RFR)

Will lie on the vertical axis of a portfolio graph
Risk-Return Possibilities
 One can attain a higher expected return than is available at point M
 One can invest along the efficient frontier beyond point M, such as point
D
Risk-Return Possibilities
 With the risk-free asset, one can add leverage to the portfolio by borrowing money at
the risk-free rate and investing in the risky portfolio at point M to achieve a point like
E
 Point E dominates point D
 One can reduce the investment risk by lending money at the risk-free asset to reach
points like C
Risk, Diversification & the Market Portfolio:
The Market Portfolio
 Because portfolio M lies at the point of tangency, it has the highest
portfolio possibility line
 Everybody will want to invest in Portfolio M and borrow or lend to be
somewhere on the CML
 It must include ALL RISKY ASSETS
Risk, Diversification & the Market Portfolio:
The Market Portfolio
 Since the market is in equilibrium, all assets in this portfolio are in
proportion to their market values
 Because it contains all risky assets, it is a completely diversified portfolio,
which means that all the unique risk of individual assets (unsystematic
risk) is diversified away
Risk, Diversification & the Market Portfolio
 Systematic Risk
 Only systematic risk remains in the market portfolio
 Variability in all risky assets caused by macroeconomic
variables




Variability in growth of money supply
Interest rate volatility
Variability in factors like (1) industrial production (2) corporate earnings
(3) cash flow
Can be measured by standard deviation of returns and can
change over time
Risk, Diversification & the Market Portfolio
 How to Measure Diversification
All portfolios on the CML are perfectly positively
correlated with each other and with the completely
diversified market Portfolio M
 A completely diversified portfolio would have a
correlation with the market portfolio of +1.00
 Complete risk diversification means the elimination of all
the unsystematic or unique risk and the systematic risk
correlates perfectly with the market portfolio

Risk, Diversification & the Market Portfolio:
Eliminating Unsystematic Risk
 The purpose of diversification is to reduce the standard deviation of the
total portfolio
 This assumes that imperfect correlations exist among securities
Risk, Diversification & the Market Portfolio
 The CML & the Separation Theorem
The CML leads all investors to invest in the M portfolio
 Individual investors should differ in position on the CML
depending on risk preferences
 How an investor gets to a point on the CML is based on
financing decisions

Risk, Diversification & the Market Portfolio
 The CML & the Separation Theorem
Risk averse investors will lend at the risk-free rate while
investors preferring more risk might borrow funds at the
RFR and invest in the market portfolio
 The investment decision of choosing the point on CML is
separate from the financing decision of reaching there
through either lending or borrowing

Risk, Diversification & the Market Portfolio
 A Risk Measure for the CML
 The Markowitz portfolio model considers the average
covariance with all other assets
 The only important consideration is the asset’s covariance with
the market portfolio