Download Capital Asset Pricing Model

Chapter 9
Asset Pricing
Chapter 9 Outline
9.1 The Efficient
Frontier
•The role of risk
•The efficient
frontier with riskfree borrowing
and lending
•Risk-free
investing
•Risk-free
borrowing
2
9.2 The Capital
Asset Pricing
Model
•The market
portfolio and
the capital
market line
•Risk-adjusted
performance
and the
Sharpe ratio
9.3 The CAPM
and Market Risk
•The security
market line
•Estimating
long-term
discount rates
9.4 Alternative
Asset Pricing
Models
•Fama and
French Model
•Arbitrage
Pricing Theory
9.5 Market
Efficiency
•Efficient
market
hypothesis
•Forms of
market
efficiency
•Efficient
market
assumptions
•Anomalies
and wacky
indicators
9.6 Behavioral
Finance and
Financial
Management
•Behavioral
finance
•Cognitive
bias
9.1 The Efficient Frontier
 The
efficient frontier, which is the set of assets
that offer the best opportunities in terms of risk
and return.
 If someone turns down a fair gamble, he or she is
likely risk averse.


3
A risk-averse person prefers the risk-free situation—that
is, not gambling on a risky situation where there is an
equal probability of winning or losing the same amount
of money.
We assume that investors are risk averse when choosing
among different investments: Investors are not willing to
undertake fair gambles.
The Role of Risk
 The corollary to turning down a fair gamble is
that the risk-averse person requires a risk
premium to enter into a risky situation.
 Generally, investor behavior is consistent with
risk aversion and the existence of risk
premiums to induce individuals to bear risk.
 We represent this risk aversion by the
required risk premium, with higher risk
premiums indicating greater risk aversion.
4
The Role of Risk
 We can
also reverse the situation and put
the individual in a risky situation and ask
how much he or she is willing to pay to get
out of the risky situation.
 The payment to get out of a risky situation
as an insurance premium.
5
The Efficient Frontier with Risk-Free
Borrowing and Lending


The existence of insurance markets indicates how risk
aversion creates a demand to remove risk, whereas
the existence of capital markets indicates how risk
aversion generates risk premiums required to induce
people to bear risk.
We assume the following:
1.
2.
3.
6
Investors are risk averse, that is, they require a risk
premium to bear risk
The more risk averse an investor, the higher the risk
premium the investor requires
We can represent risk by the standard deviation of the
return on the portfolio
The Efficient Frontier with Risk-Free
Borrowing and Lending
These assumptions lead to the result that investors
choose only portfolios on the efficient frontier. The
efficient frontier represents all portfolios of risky
assets that have better risk-return situations than
other portfolios of risky assets, which we represent
below:
7
Risk aversion, cont.
A very risk-averse individual may choose portfolio A,
and a less risk-averse individual may choose
portfolio B. Why do we know that the investor
choosing A is more risk averse than the investor
choosing B?
8
Risk-Free Investing
The expected return on a portfolio is always a weighted
average of the expected returns on the individual
assets, so we can estimate the expected return on this
portfolio as:
𝐸 𝑟𝑝 = 𝑟𝑓 + 𝑤 𝐸 𝑟𝑥 − 𝑟𝑓
where E(rP) is the expected return on the portfolio,
rf is the expected return on the risk free asset,
E(rX) is the expected return on the risky portfolio X, and
w is the proportion of the portfolio invested in the risk
portfolio.
9
Risk-Free Investing
Example:
Suppose an investor begins with a 100%
investment in the risk-free asset; that is, w = 0.
w = proportion of the portfolio in the risky asset
As the investor shifts the portfolio, adding more
of the risky asset, w increases, so the investor
increases the expected return on the portfolio,
E(rP), at the cost of reducing the investment in
the risk-free asset.
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Expected return
Risk-free & risk investing
C
D
rf
Standard deviation
11
Risk-free + risky investing
 If the return on the risk-free asset is 3% and
the return on the risky portfolio X is 11%, a
portfolio consisting only of the risk-free asset
has an expected return of 3%, whereas a
portfolio consisting of only the risky portfolio
X has an expected return of 11%.
 However, a portfolio consisting of equal parts
of the risk-free and risky portfolio X has an
expected return of:
12
Calculating Risk


13
We estimate the standard deviation on the portfolio in as:
where σ2X and σ2Y are the standard deviations of the returns
on assets X and Y, respectively, wX and wY are the proportions
invested in X and Y, respectively, and ρXY is the correlation of
returns between X and Y.
If we replace portfolio Y with the risk-free security and (1 – w)
for wY, we arrive at the following:
Calculating Risk



14
We know exactly what we are going to get from the
risk-free asset, so the standard deviation of its return is
zero; that is, σrf = 0 = 0. Because the return does not
vary, the correlation between the return on the riskfree asset and that on the risky portfolio X is also zero.
Therefore, the standard deviation with σrf = 0 and ρXrf =
0 reduces to:
Taking the square root of the final terms leaves us
with:
Calculating Risk
 In other words, portfolio risk increases in
direct proportion to the amount invested in
the risky asset, w.
 Therefore, the higher the proportion of the
portfolio allocated to the risky asset, the
higher the portfolio risk.
 If the standard deviation of the returns on
risky portfolio X is 20%, a portfolio comprising
equal parts of the risk-free asset and the risky
portfolio X will have a standard deviation of:
15
Risk-Free Borrowing
Consider an investor who invests $10,000 in a
portfolio of risky assets, portfolio V.
Portfolio V has an expected return of 12% and a
standard deviation of returns of 25%. If, in addition,
the investor borrows $5,000 at the risk-free rate of
3% and invests it in portfolio V, the total invested in
portfolio V increases to $15,000. What is the
expected return on this investment?
The expected return calculation requires us to first calculate
the weights: w = $15,000 ÷ $10,000 = 1.5
16
Risk-Free Borrowing

In other words, there is a short position, borrowing at
the risk-free rate. The expected return on the portfolio
is therefore:

The standard deviation of the investor’s investment,
considering both the investment in the risky portfolio
V and the borrowing, is the weight invested in the risky
portfolio (150%, in this example), multiplied by the
standard deviation of the returns on the risky asset
(the 25%):
17
9.2 The Capital Asset Pricing Model
The Capital Asset Pricing Model (CAPM) is a
model that describes expected returns in
terms of the risk-free rate of interest and a
premium for bearing market risk.
18
CAPM assumptions
 All investors have identical expectations about
expected returns, standard deviations, and correlation
coefficients for all securities.
 All investors have the same one-period time horizon.
 All investors can borrow or lend money at the risk-free
rate of return (rf).
 There are no transaction costs.
19
Assumptions, cont.
 There are no personal income taxes so that
investors are indifferent between capital gains
and dividends.
 There are many investors, and no single
investor can affect the price of a stock through
his or her buying and selling decisions.
Therefore, investors are price takers.
 Capital markets are in equilibrium.
20
Implications of the CAPM
1.
2.
The “optimal” risky portfolio is the one that
is tangent to the efficient frontier on a line
that is drawn from the risk-free rate. This
portfolio is the same for all investors.
This optimal risky portfolio is the market
portfolio that contains all risky securities.

21
The value of this portfolio is the aggregate of the
market values of all the individual assets in the
portfolio. Therefore, the weights of these assets in
the market portfolio are their proportionate weight
in its total value.
The Capital Market Line (CML)
The relationship between expected return and standard
deviation implied by the capital asset pricing model:
The Capital Market
Line
22
The Capital Market Line
The slope of the capital market line is the incremental
expected return divided by the incremental risk.
𝐸 𝑟𝑀 − 𝑟𝑓
𝑆𝑙𝑜𝑝𝑒 𝑜𝑓 𝑡ℎ𝑒 𝐶𝑀𝐿 =
𝜎𝑀
23
Market price of risk
 This
trade-off of risk and return is the market
price of risk for efficient portfolios.
 This indicates the additional expected return
that the market demands for an increase in a
portfolio’s risk. Adding the risk-free rate, rf ,
the CML is:
𝐸 𝑟𝑀 − 𝑟𝑓
𝐸 𝑟𝑝 = 𝑟𝑓 +
𝜎𝑝
𝜎𝑀
24
Risk-Adjusted Performance and the
Sharpe Ratio
 When the ideas underlying the CML are used in
this way, it leads to the Sharpe ratio, the ratio of
ex post excess returns to risks:
𝑟𝑝 − 𝑟𝑓
𝑆ℎ𝑎𝑟𝑝𝑒 𝑟𝑎𝑡𝑖𝑜 =
𝜎𝑝
 We also refer
to the Sharpe ratio as the rewardto-variability ratio or the reward-to-risk ratio
because this ratio is a comparison of the return, in
excess of the risk-free rate, to risk.
25
Example: Sharpe Ratio
Suppose a portfolio has an expected return of 5% and a
standard deviation of returns of 8%. If the risk-free rate
of interest is 3%, the Sharpe ratio is:
We have derived the Sharpe ratio in terms of “expected”
(i.e., ex ante) returns in our discussion. However, in
practice, it is a commonly used measure of ex post (i.e.,
realized) returns, where we replace expected returns
with historic realized returns.
26
9.3 The CAPM and Market Risk
 The
CML provides a method of estimating the
required return on equity assets relative to their risk,
but it applies only to efficient portfolios and not to
individual securities.
 In financial management, we are usually concerned
with the risk associated with individual firms and the
required return for investing in them.
27
The CAPM and Market Risk
Portfolio Risk
and
Diversification
The figure shows the average risk of an individual
security, where the curve gets very close to the
vertical axis, that is, a one-stock portfolio.
28
The Security Market Line
A result of the capital asset pricing model is that investors
should be compensated for market risk, as measured by
beta.
The security market line (SML):
where E(ri) is the expected return on the asset (or
portfolio) i. The term E(rM) - rf is the expected market risk
premium and is also a function of market conditions.
29
Examples of Beta
Company
Ticker
Beta
IBM
IBM
0.72
Microsoft
MSFT
0.80
Apple Computer
AAPL
0.58
FB
30
2.10
Johnson & Johnson
JNJ
0.49
General Electric
GE
1.22
Example: SML
Suppose the risk-free rate is 3% and the
expected return on the market is 9%.


If an asset’s beta is 1.2, the expected return on this
asset is 9.2%:
E(ri) = 0.03 + [(0.09-0.03) × 1.2] = 9.2%
The market risk premium in this case is 6%, and the
risk premium for this asset is 7.2%.
The SML is the most widely used contribution of
the CAPM.
31
What risk-free rate?
 Generally,
we use a risk-free security with a
maturity that mimics investors’ typical
holding period.
 Example: 10-year U.S. Treasury
 As of 10/29/13, 2.5%
32
Using the SML to Estimate LongTerm Discount Rates
Estimated Market Risk Premiums
33
9.4 Alternative Pricing Models
Fama and French Model – a pricing model
that uses three factors to relate expected
returns to risk:
 A market factor
 The
market value of a firm’s common equity
 The ratio of a firm’s book equity value to its
market value of equity)
34
Alternative Asset Pricing Models
The Arbitrage Pricing Theory (APT) is a
pricing model that uses multiple factors to
relate expected returns to risk by assuming
that asset returns are linearly related to a set
of indexes, which are proxy risk factors that
influence asset returns.
 Arbitrage is the
process of taking advantage of
different pricing for the same item in different
markets.
35
9.5 Market Efficiency
 An efficient market is one in which the
prices of
all assets accurately reflect all relevant and
available information about the assets. This
definition implies that asset prices in efficient
capital markets are “correct.”
 The efficient market hypothesis (EMH) formalized
the concept of an efficient market into a theory
that markets are efficient, and therefore, in its
strictest sense, it implies that prices accurately
reflect all information at any point in time.
36
Efficient Market Hypothesis
Weak form of market efficiency


37
Asset prices fully reflect all market data, which
refers to all past price and volume trading
information.
Historical trading data is already reflected in current
prices and should be of no value in predicting future
price changes.
 It is not possible to generate an abnormal profit,
a profit in excess of that expected for the asset’s
level of risk on a consistent basis.
Efficient Market Hypothesis
Semi-strong form of market efficiency
 Asset prices reflect all publicly known
38
and
available information.
 For stock markets this includes information
about earnings, dividends, corporate
investments, management changes, and so on.
This also includes market data, which are
publicly available.
 This version of the EMH encompasses the weak
form. In other words, if a market is semi-strong
efficient, then it must also be weak form
efficient.
Efficient Market Hypothesis
Strong form of market efficiency
 Asset prices fully reflect all information, which
includes both public and private information.
 Public information is any information that is
readily available to investors, whereas private
information is any information not available,
which we generally think of as inside
information.
39
Efficient Market Assumptions


40
A large number of rational, profit-maximizing investors
exist, who actively participate in the market by
analyzing, valuing, and trading assets. The markets are
assumed to be competitive, which means that no one
investor can significantly affect the price of an asset.
Information is costless and widely available to market
participants at the same time.
Assumptions, cont.


41
Information arrives randomly, and therefore
announcements are not related to one another.
Investors react quickly and fully to the new
information, which is reflected in stock prices.
Anomalies
 Researchers
have documented numerous
anomalies in security pricing over the past
few decades.
 An anomaly is a mispricing of an asset
such that the pricing of the asset is not
consistent with efficient markets. In other
words, the pricing of an asset is not
associated with relevant information about
the asset that is known to all market
participants.
42
Examples of anomalies
 The size effect - small capitalization stocks outperform
large capitalization stocks, which indicates that the
market is not weak-form efficient.
 The January effect - returns in January are higher than
the rest of the year. This indicates that the market is not
weak-form efficient.
 The earnings surprise anomaly - when earnings are
released by a company and there is an unexpected
portion, the market not only reacts immediately, but
also continues to react for some days following the
earnings announcement. This is evidence against semistrong market efficiency.
43
Anomalies, cont.
 The value anomaly - value stocks (that is, low
market/book ratios) outperform other securities,
which would indicate that the market is not semistrong-form efficient.
44
Wacky Indicators




45
Super Bowl winners - if a former member of the
American Football League wins, the stock market will
experience a down year.
Butter production in Bangladesh - the return on the
S&P Index will be twice that of the change in butter
production in Bangladesh.
Hemlines of women’s dresses - there is a positive
relationship between movement in the market and
hemlines: if hemlines get shorter, prices go up, and
vice versa.
Sports Illustrated Swimsuit Model - the market does
well when the swimsuit model chosen for the cover is
of U.S. nationality.
9.6 Behavioral Finance and Financial
Management

Behavioral finance - the study of how human behavior
affects economic decision making.


Cognitive bias - a mistake in decision making that
results from one’s own preferences and beliefs.


46
While we devise theories that depend on rational, riskaverse investors, there is always the possibility that financial
managers do not act this way and, in fact, make decisions
that are biased.
These biases result in decisions that are not consistent with
pure scientific or statistical reasoning.
The many sources of bias include overconfidence, loss
aversion, the disposition effect, representativeness,
anchoring, framing, and mental accounting.
Examples of Cognitive Bias

Overconfidence - there are many ways that this becomes
apparent when we observe behavior.



Loss aversion - the willingness to avoid losses that is
disproportionate to the willingness to seek similar-sized gains.
Disposition effect - the behavior of individuals in which they
avoid realizing any paper losses, but tend to realize paper gains.


47
For example, a decision maker who has a good understanding of
the role of diversification may nevertheless choose an
investment portfolio without adequate diversification because of
overconfidence in his or her ability to select investments.
In other words, people tend to hang onto losers longer than they
should.
Closely related to loss aversion.
Examples of Cognitive Bias

Representativeness - the tendency for people to judge
something, such as an investment, by the degree to which this
something resembles something else in the person’s experience.


Anchoring - the tendency to use inappropriate or irrelevant
factors in decision making.



48
In other words, an individual will overweight most recent events,
giving less weight to long-term averages.
Closely related to representativeness
Framing - the manner in which something is presented, which
may influence how someone feels about this something.
Mental accounting - the process of investors separating money
into different accounts in their thought process, which affects
decision making.
Chapter Summary




49
The efficient frontier is the set of portfolios that provides the best
return for a given level of risk (or, similarly, the lowest risk for a
given level of return). If we combine borrowing or lending at the
risk-free rate of interest, the set of investment opportunities
improves.
The capital market line depicts the required return for efficient
portfolios based on their standard deviations, whereas the security
market line depicts the relation between the required return and
market risk, as measured by beta.
An efficient market is a market in which asset prices reflect
available information quickly and accurately. The EMH is commonly
broken down into three forms that are based on the extent to
which prices reflect different types of available information.
The weak-form EMH states that security prices reflect all market
data; the semi-strong form states that prices reflect all publicly
known and available information; and the strong form states that
prices reflect all public and private information.
Chapter Summary

An implication of the capital asset pricing model for financial
decision making is that return on an investment is consistent
with the amount of market risk of the investment, not on
the investment’s total or stand-alone risk.


Behavioral finance is an area of study that examines how
human behaviors can enter into decision making.

50
The implications of market efficiency for financial decision making
include:
 The inability to time security offerings
 The expectation of returns commensurate with market risk
Cognitive biases can enter into decision making, resulting in
decisions that are not in the best interest of owners.