11.0
Chapter
11
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Risk and
Return
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11.1
11.1 Expected Returns and Variances
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11.2
Remember from the Prior Chapter:
 We
calculated average returns and variances
using historical data
 We now begin to discuss how to analyze
returns and variances when the information we
have concerns future possible returns and
their probabilities.
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11.3
Expected Returns
 Expected
Return: return on a risky asset
“expected” in the future.
based on the probabilities of possible outcomes
 in this context, “expected” means average if the
process is repeated many times

 The

expected return is equal to:
The sum of:


the possible returns multiplied by their probabilities
Simply multiply the possibilities by the probabilities and
n
add up the results:
E ( R)   pi Ri
i 1
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11.4
Variance and Standard Deviation
 In
Chapter 10 we were examining actual
historical returns
 We estimated the average return and variance
based on actual events
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11.5
Remember This Example from the Previous Chapter
Historical Variance and Standard Deviation
Year
Actual
Return
Average
Return
Deviation from the
Mean (Average)
Squared
Deviation
1
.15
.105
.045
.002025
2
.09
.105
-.015
.000225
3
.06
.105
-.045
.002025
4
.12
.105
.015
.000225
Totals
.42 / 4 =
.105
.000
.0045
(2) Variance = .0045 / (4-1) = .0015
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Companies
Reserved
(
) Standard Deviation ©2001
= .03873
(Positive Square
RootAll
of Rights
the Variance)
11.6
Variance and Standard Deviation
 Now
we’ll “project” future returns and their
associated probabilities

Variance and standard deviation still measure the
volatility of returns
 Therefore,
we’ll calculate “expected returns”
and variances somewhat different from the
previous chapter
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11.7
Variance and Standard Deviation

Calculating Expected Return, Variance, and
Standard Deviation for an individual stock – go to:




www.uta.edu/faculty/tjearp
Chap 11 Self Test Problem
Click on: Individual Stocks tab
Demonstrates Calculations for:

Individual Stock 


Expected Return
Variance
Standard Deviation
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11.8
11.2 Portfolios
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11.9
Portfolios
A
portfolio is a group of assets such as stocks
and bonds held by an investor
 An asset’s risk and return is important in how it
affects the risk and return of the portfolio
 The risk-return trade-off for a portfolio is
measured by the portfolio expected return and
standard deviation, just as with individual
assets
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11.10
Portfolio Expected Returns
 The
expected return of a portfolio is the
weighted average of the expected returns for
each asset in the portfolio
m
E ( RP )   w j E ( R j )
j 1
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11.11
Portfolios

Calculating Portfolio Expected Return, Variance, and
Standard Deviation – go to:




www.uta.edu/faculty/tjearp
Chap 11 Self Test Problem
Click on: Portfolio tab
Demonstrates Calculations for:

Portfolio




Weights
Expected Return
Variance
Standard Deviation
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11.12
11.3 Announcements, Surprises,
and Expected Returns
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11.13
Expected versus Unexpected Returns
Realized returns are generally not = to expected
returns
 There’s the expected component and the unexpected
component
 Total return = Expected return + Unexpected return
 The unexpected return comes about because of
unanticipated events.


The risk from investing stems from the possibility of an
unanticipated event.
 (i.e. a sudden unexpected change in interest rates)
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11.14
Announcements and News
 Announcements
and news contain both an
expected component and a surprise component
 It’s the surprise component that affects a
stock’s price and therefore its return
 This is very obvious when we watch how stock
prices move when an unexpected
announcement is made or earnings are different
than anticipated
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11.15
Efficient Markets
 We
assume that relevant information known
today is already reflected in the expected return
That is the current stock price reflects relevant
publicly available information
 This assumes that markets are at least reasonably
efficient in the Semistrong form – all public
information is reflected in the stock price

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11.16
Efficient Markets
 Efficient
markets are a result of investors
trading on the unexpected portion of
announcements
 The easier it is to trade on surprises, the more
efficient markets should be
 Efficient markets involve random price
changes because we cannot predict surprises
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11.17
11.4
Risk: Systematic and Unsystematic
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11.18
Systematic Risk
 Systematic
Risk: a risk that affects a large
number of assets
Also known as non-diversifiable risk or market risk
 Has market-wide effects
 Economywide.
 Affects nearly all companies to some degree
 Includes such things as changes in GDP, inflation,
interest rates, etc.

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11.19
Unsystematic Risk
 Unsystematic
Risk: a risk that affects at most
a small number of assets.
Also known as unique or asset-specific risk
 Unique to individual companies or assets
 Includes such things as labor strikes, part shortages,
etc.
 Firm-Specific Example:


the stock price of a gold-mining firm drops when it’s
discovered the firm’s chairman has overstated minable gold
reserves
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11.20
Systematic and Unsystematic
Components of Return
 Total
Return = expected return + unexpected
return: R = E(R) + U
 Unexpected return = systematic portion +
unsystematic portion
 Therefore:
Total Return = expected return + systematic
portion + unsystematic portion:
 R = E(R) + Systematic portion + Unsystematic
portion
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11.21
11.5
Diversification and Portfolio Risk
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11.22
Diversification
Principle of diversification: Spreading an
investment across a number of assets will eliminate
some, but not all, of the risk.
 Portfolio diversification is the investment in several
different asset classes or sectors
 Diversification is not just holding a lot of assets
 For example: if you own 50 internet stocks, you’re
not diversified
 However: if you own 50 stocks that span 20
different industries, then you are diversified

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11.23
Diversifiable Risk
 The
risk that can be eliminated by combining
assets into a portfolio
 Often considered the same as unsystematic,
unique, or asset-specific risk
 If we hold only one asset, or assets in the same
industry, then we are exposing ourselves to risk
that we could diversify away
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11.24
The Principle of Diversification
 Diversification
can substantially reduce the
variability of returns without an equivalent
reduction in expected returns
 This reduction in risk arises because worse
than expected returns from one asset are offset
by better than expected returns from another
 However, there is a minimum level of risk that
cannot be diversified away and that is the
systematic portion – market risk!
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11.25
Total Risk

Total risk (as measured by the standard deviation of
return) = systematic risk + unsystematic risk


Systematic Risk - nondiversifiable risk or market risk
Unsystematic Risk - is diversifiable risk, unique risk, or
asset-specific risk.
The standard deviation of returns is a measure of total
risk
 For well diversified portfolios, unsystematic risk is
very small
 Consequently, the total risk for a diversified portfolio
is essentially equivalent to the systematic risk

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Table 11.7 – Std Dev declines as the number of securities increases
(3)
Ratio of Portfolio
Standard Deviation to
Standard Deviation
of a Single Stock
(1)
Number of Stocks
in Portfolio
(2)
Average Standard
Deviation of Annual
Portfolio Returns
1
49.24 %
2
37.36
.76
4
29.69
.60
6
26.64
.54
8
24.98
.51
10
23.93
.49
20
21.68
.44
30
20.87
.42
40
20.46
.42
50
20.20
.41
100
19.69
.40
200
19.42
.39
300
19.34
.39
400
19.29
.39
500
19.27
.39
1,000
19.21
.39
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11.26
1.00
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11.27
Figure 11.1
Average annual
standard deviation (%)
49.2
Diversifiable risk
23.9
19.2
Nondiversifiable
risk
1
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10
20
30
40
1,000
Number of stocks
in portfolio
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11.28
11.6 Systematic Risk and Beta
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11.29
Systematic Risk Principle
 Systematic
Risk Principle: the expected
return on a risky asset depends only on that
asset’s systematic (market) risk
There is a reward for bearing risk
 There is not a reward for bearing risk unnecessarily
 Unsystematic (firm specific) risk can be eliminated at
virtually no cost (by diversifying)

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11.30
Measuring Systematic Risk


Beta Coefficient: Amount of systematic (market) risk present
in a particular risky asset relative to that in an average risky
asset
We use the beta coefficient to measure systematic (market) risk




A beta of 1 implies the asset has the same systematic risk as the
overall market
A beta < 1 implies the asset has less systematic risk than the overall
market
A beta > 1 implies the asset has more systematic risk than the overall
market
Since assets with larger betas have greater systematic risks,
they will have greater expected returns
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11.31
Table 11.8
Company
Beta Coefficient (I)
McDonalds
.85
Gillette
.90
IBM
1.00
General Motors
1.05
Microsoft
1.10
Harley-Davidson
1.20
Dell Computer
1.35
America Online
1.75
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11.32
Portfolio Betas
Example: 11.6 – Page 323
Security Amt Inv
Exp Rtn
Stock A
$ 1,000
8%
Stock B
2,000
12
Stock C
3,000
15
Stock D
4,000
18
10,000

Weight
.10
.20
.30
.40
1.00
What is the expected return on this portfolio?


Beta
.80
.95
1.10
1.40
E(Rp) = .10(.08) + .20(.12) + .30(.15) + .40(.18) = .149 or 14.9%
What is the beta of this portfolio?

Bp = .10(.80) + .20(.95) + .30(1.10) + .40(1.40) = 1.16
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11.33
11.7 The Security Market Line
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11.34
Beta and the Risk Premium
 Remember
that the risk premium = expected
return – risk-free rate
 The higher the beta, the greater the risk
premium
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11.35
Security Market Line
 The
security market line (SML): Positively
sloped straight line displaying the relationship
between expected return and beta.

Figure 11.4, Page 330
slope of the SML is: (E(RM) – Rf) / M
 But since the beta for the market is ALWAYS
equal to one, the slope can be rewritten:
 The
E(RM) – Rf
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Example: Portfolio Expected
Returns and Betas (SML)
11.36
30%
Expected Return
25%
E(RA)
20%
15%
10%
Rf
5%
0%
0
0.5
1
1.5 A
2
2.5
3
Beta
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11.37
Capital Asset Pricing Model

Market Risk Premium: The slope of the Security
Market Line (SML), the difference between the
expected return on a market portfolio and the riskfree rate.



E(RM) - Rf
the reward for bearing an average amount of systematic
risk
Capital Asset Pricing Model (CAPM): The
equation of the SML showing the relationship
between expected return and beta:
 E(RA) = Rf
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11.38
Capital Asset Pricing Model
If we know an asset’s systematic (market) risk, we can
use the CAPM to determine its expected return
 Example:
 A stock has a beta of 1.2, the expected return on the
market is 12 percent, and the risk-free rate is 6
percent. What must the expected return on this stock
be?
 E(RA) = Rf + [E(RM) – Rf] x A
 E(RA) = .06 + (.12 - .06) x 1.2 = .132

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11.39
The CAPM shows that the expected return
for a particular asset depends on three things:

The Pure time value of money – measured by the riskfree rate


The Reward for bearing systematic risk – measured by
the market risk premium: (E(RM) – Rf)


The reward for merely waiting for your money, without
taking any risk
The reward for bearing an average amount of systematic
risk in addition to waiting.
The Amount of systematic risk – measured by beta

Market risk
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11.40
Chapter 11: Suggested Homework and Test Review
Chapter Review and Self-Test Problem 11.1 and 11.2
 Critical Thinking and Concepts Review: 1 & 4
 Questions and Problems: 5, 6, 7, 9, 10, 11, 13, 15, 25


Know how to calculate the following for individual stocks and a
portfolio:
Expected Return
 Variance
 Standard Deviation


Know how to calculate:

Portfolio Beta
CAPM Equation

Risk Premium


Know chapter theories, concepts, and definitions
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