Transcript Chapter 8

Chapter 8
Risk and Return
Slides developed by:
Pamela L. Hall, Western Washington University
Why Study Risk and Return?

Returns to equity investments (stock) have
historically been much higher than the return to
debt investments

Equity returns averaged more than 10% while debt
returns average between 3% and 4%
• Inflation also averaged about 3% during the same time
period

Returns on equity investments are much more
volatile than the returns on debt instruments in
the short-run
2
Why Study Risk and Return?

Since equity earns a much higher return but with
higher risk, it would be nice if we could invest
and earn a high return but reduce the risk
associated with such investments

Investing in portfolios of securities can help manage
risk
• A portfolio is a collection of financial assets by investors

We wish to capture the high average returns of
equity investing while limiting the associated risk
as much as possible
3
The General Relationship
Between Risk and Return

Risk in finance is defined as the probability of
losing some or all of the money invested in a
deal


Generally investments that offer higher returns
involve higher risks
Suppose you could invest in a stock that would
either return you 15% or a loss of everything (100%)


Also, suppose the chance of losing everything is 1%
and the chance of earning 15% is 99%
The risk associated with this investment is the 1%
chance of losing everything
4
The General Relationship
Between Risk and Return



Investors more or less expect to receive a
positive return but they realize that there is risk
associated with these investments and the
chance that they can lose their money
Stocks offering a higher likely return also have
higher probabilities of total loss
It is difficult to determine how much risk is
associated with a given level of return

Need to define risk in a measurable way
• The definition has to include all the probabilities of loss

Have to relate that measurement to return
5
Portfolio Theory—Modern
Thinking about Risk and Return
Portfolio theory defines investment risk in
a measurable way and relates it to the
expected level of return from an
investment
 Has had major impact on practical
investing activities

6
The Return on an Investment


The rate of return allows an investment's return
to be compared with other investments
One-Year Investments

The return on a debt investment is
• K = interest paid  loan amount
• A return is what the investor receives divided by what is
invested

The return on a stock investment is
• K = D1 + (P1 – P0)  P0
7
Returns, Expected and
Required

The expected return on a stock is the
return investors feel is most likely to occur
based on currently available information
Anticipated return based on the dividends
expected as well as the future expected price
 No rational person makes any investment
without some expectation of return

8
Returns, Expected and
Required

The required return on a stock is the minimum
rate at which investors will purchase or hold a
stock based on their perceptions of its risk

People will only invest in an asset if they believe the
expected return is at least equal to the required
return
• Different people have different levels of both expected and
required return
• Significant investment in a stock occurs only if the expected
return exceeds the required return for a substantial number of
investors
9
Risk—A Preliminary Definition

A preliminary definition of investment risk is the
probability that return will be less than expected


This definition includes both positive and negative returns that
are lower than expected
Feelings About Risk




Most people have negative feelings about bearing risk
Risk averse investors prefer lower risk when expected returns
are equal
Most people see a trade-off between risk and return
However risk isn't to be avoided, but higher risk investments
must offer a higher expect return to encourage investment
10
Portfolio Theory

Review of the Concept of a Random
Variable
In statistics a random variable is the outcome
of a chance process and has a probability
distribution
 Discrete variables can take only specific
variables
 Continuous variables can take any value
within a specified range

11
Review of the Concept of a
Random Variable

The Mean or Expected Value

The most likely outcome for the random
variable
For symmetrical probability distributions
the mean is the center of the distribution
 Statistically it is the weighted average of
all possible outcomes

X =  XiP  Xi 
n
i=1
12
Portfolio Theory

Variance and Standard Deviation

Variability relates to how far a typical observation of
the variable is likely to deviate from the mean
• There's is a great deal of difference in variability around the
mean for different distributions
• Telephone poles don't vary much in height from pole to pole—
actual pole heights are closely clustered around the mean
• Office buildings do vary a great deal in terms of height—widely
dispersed around the mean
• The standard deviation gives an indication of how far from
the mean a typical observation is likely to fall
13
Portfolio Theory

Variance and Standard Deviation

Variance Formula


2

Var X     Xi  X  P  Xi 


i=1 
2
x
n
• Variance is the average squared deviation from
the mean

Standard deviation formula
SDX


2

  x   Xi  X  P  Xi 


i=1 
n
14
Portfolio Theory—Example
Example
Q:If you toss a coin four times what is the chance of
receiving heads (x)?
X
P(X)
0
0.0625
1
0.2500
2
0.3750
3
0.2500
4
0.0625
The mean of this
distribution is 2, since it is
a symmetrical distribution.
1.0000
15
Portfolio Theory—Example
Example
A: The Variance and Standard Deviation of the
distribution is:
Xi
(Xi – )
(Xi – )2
P(Xi)
(Xi –X)2 x P(Xi)
0
-2
4
0.0625
0.25
1
-1
1
0.2500
0.25
2
0
0
0.3750
0.00
3
1
1
0.2500
0.25
4
2
4
0.0625
0.25
Var X =
1.00
SD X =
1.00
Since the variance
is 1.0, the
standard deviation
is also 1.0.
16
Review of the Concept of a
Random Variable

The Coefficient of Variation

A relative measure of variation—the ratio of the
standard deviation of a distribution to its mean
• CV = Standard Deviation  Mean
• For example, if the CV = 0.5, then the typical variation is
50% the size of the mean, or ½

Continuous Random Variable


Can take on any numerical value within some range
We talk about the probability of an actual outcome
being within a range of values rather than being an
exact amount
17
The Return on a Stock Investment
as a Random Variable

In financial theory, the return on a stock investment is
considered a random variable

Return is influenced by the future price of the stock and the
expected dividends
• There is an element of uncertainty in both of these variables



Return is a continuous random variable with a low value
of -100% but no limit to the high value
The mean of the distribution of returns is the stock's
expected return
The variance and standard deviation show how likely it
is that an actual return will be some distance from the
expected value

Actual return in a distribution with a large variance is likely to be
different from the mean
18
Figure 8.4: Probability Distributions
With Large and Small Variances
19
Risk Redefined as Variability


In financial theory risk is defined as variability in
return
A risky stock has a high probability of earning a
return that significantly differs from the mean of
the distribution


While a low-risk stock is more like to earn a return
similar to the expected return
In practical terms risk is the probability that
return will be less than expected
20
Figure 8.5: Investment Risk Viewed
as Variability of Return Over Time
While both stocks have the
same expected return, the
high risk stock has a
greater variability in
returns.
21
Risk Aversion
Risk aversion means investors prefer
lower risk when expected returns are
equal
 When expected returns are not equal the
choice of investment depends on the
investor's tolerance for risk

22
Figure 8.6: Risk Aversion
23
Portfolio Theory—Example
Example
Q: Harold MacGregor is considering buying stocks for the first time
and is looking for a single company in which he'll make a major
investment. He's narrowed his search to two firms, Evanston
Water Inc. (a public utility) and Astro Tech Corp. (a new hightech company).


Public utilities are low-risk stocks because they are regulated
monopolies
High tech firms are high-risk because new technical ideas can
succeed tremendously, fail completely or end up in-between
Harold has studied the history and prospects of both firms and
their industries, and with the help of his broker has made a
discrete estimate of the probability distribution of returns for
each stock as follows:
24
Portfolio Theory—Example
Example
Evanston
Water
Astro
Tech
kE
P(kE)
kA
P(kA)
6%
0.05
-100%
0.15
8
0.15
0
0.20
10
0.60
15
0.30
12
0.15
30
0.20
14
0.05
130
0.15
Evaluate Harold's options in terms of statistical concepts of risk and
return.
25
Portfolio Theory—Example
A: First calculate the expected return for each stock--the mean for each
distribution.
Example
Evanston Water
Astro Tech
kE
P(kE)
kE* P(kE)
kA
P(kA)
kA* P(kA)
6%
0.05
0.3%
-100%
0.15
-15.0%
8
0.15
1.2
0
0.20
0.0
10
0.60
6.0
15
0.30
4.5
12
0.15
1.8
30
0.20
6.0
14
0.05
0.7
130
0.15
19.5
10.0%
15.0%
26
Portfolio Theory—Example
A: Next, calculate the variance and standard deviation of the stocks'
returns.
Example
kE
(kE – kE) (kE – kE )2
P(kE)
(kE – kE )2 x P(kE)
6%
-4%
16
0.05
0.8
8
-2
4
0.15
0.6
10
0
0
0.60
0.0
12
2
4
0.15
0.6
14
4
16
0.05
0.8
Var kE =
2.8
SD kE =
1.7%
27
Example
Portfolio Theory—Example
kA
(kA – k A)
(kA – k A)2
-100%
-115%
13,225
0.15
1,984
0
-15
225
0.20
45
15
0
0
0.30
0
30
15
225
0.20
45
130
115
13,225
0.15
1,984
Var kA =
4,058
SD kA =
63.7
P(kA)
(kA – k A )2 x P(kA)
A: Finally, calculate the coefficient of variation for each stock's return.
σ
σ
1.7
63.7
CVE = E =
= 0.17 CVA = A =
= 4.25
10.0
15.0
kE
kA
28
Portfolio Theory—Example
Example
A: If Harold only considers expected return, he’ll certainly choose Astro.
However, with Evanston his investment is relatively safe while with
Astro there is a substantial chance he’ll lose everything.
No one but Harold can make the decision as to which investment he
should choose. It depends on his degree of risk aversion.
29
Decomposing Risk—Systematic (Market)
and Unsystematic (Business-Specific) Risk

Fundamental truth of the investment world

The returns on securities tend to move up and down
together
• Not exactly together or proportionately

Events and Conditions Causing Movement in
Returns

Some things influence all stocks (market risk)
• Political news, inflation, interest rates, war, etc.

Some things influence only particular firms (businessspecific risk)
• Earnings reports, unexpected death of key executive, etc.

Some things affect all companies within an industry
• A labor dispute, shortage of a raw material
30
Decomposing Risk—Systematic (Market)
and Unsystematic (Business-Specific) Risk
Date
IBM
Boeing
10/10/2001
9/10/2001
8/10/2001
7/10/2001
6/10/2001
5/10/2001
4/10/2001
3/10/2001
2/10/2001
1/10/2001
12/10/2000
Index Value
1600
1400
1200
1000
800
600
400
200
0
11/10/2000
140
120
100
80
60
40
20
0
10/10/2000
Stock Price
Comparison of IBM, Boeing and the S&P500
Market
reopens after
World Trade
Center
collapses.
S&P500
31
Decomposing Risk—Systematic (Market)
and Unsystematic (Business-Specific) Risk

Movement in Return as Risk


The total movement in a stock's return is the total risk
inherent in the stock
Separating Movement/Risk into Two Parts

A stock's risk can be separated into systematic or
market risk and unsystematic or business-specific
risk
32
Portfolios


A portfolio is an investor's total stock holding
Risk and Return for a Portfolio


Each stock in a portfolio has its own expected return
and its own risk
Portfolios have their own risks and returns
• The return on a portfolio is a weighted average of the returns
of the individual stocks in the portfolio
• The risk is the variance or standard deviation of the
probability distribution of the portfolio's return
• Not the same as the weighted average of the standard
deviations or variances of the individual stocks within the
portfolio
33
Portfolios

The Goal of the Investor/Portfolio Owner

Goal of investors: to capture the high
average returns of equities while avoiding as
much risk as possible
• Generally done by constructing diversified
portfolios to minimize portfolio risk for a given
return

Investors are concerned with how stocks
impact portfolio performance, not with the
stocks' stand-alone characteristics
34
Diversification—How Portfolio Risk Is
Affected When Stocks Are Added

Diversification means adding different (diverse)
stocks to a portfolio


Can reduce (but not eliminate) risk in a portfolio
Business-Specific Risk and Diversification

Business-specific risk is a series of essentially
random events that push the returns of individual
stocks up or down
• Their effects simply cancel when added together over a
substantial number of stocks
• Is essentially random and can be diversified away
• For this to work, the stocks within the portfolio must be from
fundamentally different industries
35
Diversification—How Portfolio Risk Is
Affected When Stocks Are Added

Systematic (Market) Risk and Diversification

If the returns of all stocks move up and down more or less
together, it's not possible to reduce risk completely
• Systematic risk can be reduced but never entirely eliminated

The Portfolio


If we have a portfolio that is as diversified as the market, its
return will move in tandem with the market
The Impact on Portfolio Risk of Adding New Stocks


If we add a stock to the portfolio which has returns perfectly
positively correlated with the portfolio, it will generally add risk to
the diversified portfolio
If we add a stock that is perfectly negatively correlated with the
portfolio, it will decrease the risk of the portfolio
36
Diversification—How Portfolio Risk Is
Affected When Stocks Are Added

The Risk of the New Additions By Themselves and in
Portfolios



Stocks with equal stand-alone risk can have opposite risk
impacts on a portfolio because of the timing of the variation in
their returns
A stock's risk in a portfolio sense is its market risk
Choosing Stocks to Diversify for Market Risk

How do we diversify to reduce market risk in a portfolio
• Theoretically it's simple: just add stocks that move counter
cyclically with the market
• Unfortunately it's difficult to find stocks that move in that direction
• However numerous stocks exist that have returns that are less than
positively correlated with the market
• Adding these stocks to the portfolio will generally reduce risk
somewhat, but will not eliminate it
37
Diversification—How Portfolio Risk Is
Affected When Stocks Are Added

The Importance of Market Risk

Modern portfolio theory is based on the
assumption that investors focus on portfolios
rather than on individual stocks
• How stocks affect portfolios depends only on
market risk

For the small investor with a limited portfolio,
these concepts do not apply
38
Measuring Market Risk—The
Concept of Beta


Market risk is a crucial concept in investing, so we need
a way to measure it for individual stocks
A stock's beta measures its market risk


It measures the variation of a stock's return which accompanies
the market's variation in return
Developing Beta

Beta is developed by determining the historical relationship
between a stock's return and the return on a market index, such
as the S&P500
• The stock's characteristic line reflects the average relationship
between its return and the market
• Beta is the slope of the characteristic line

Projecting Returns with Beta

Knowing a stock's beta enables us to estimate changes in its
return given changes in the market's return
39
Measuring Market Risk—The
Concept of Beta
Characteristic Line for IBM
0.15
Return on IBM
0.1
0.05
0
-0.06
-0.04
-0.02 -0.05 0
0.02
0.04
0.06
-0.1
-0.15
-0.2
Characteristic line
determined using
data from Slide 31.
Return on S&P500
y = 1.3037x + 0.0009
IBM’s
beta
40
Measuring Market Risk—The
Concept of Beta
Example
Q: Conroy Corp. has a beta of 1.8 and is currently earning its owners a
return of 14%. The stock market in general is reacting negatively to a
new crisis in the Middle East that threatens world oil supplies. Experts
estimate that the return on an average stock will drop from 12% to 8%
because of investor concerns over the economic impact of a potential
oil shortage as well as the threat of a limited war. Estimate the change
in the return on Conroy shares and its new price.
A: Beta represents the past average change in Conroy’s return relative to
changes in the market’s return.
bConroy 
k Conroy
kM
or 1.8 
k Conroy
4%
k Conroy = 7.2%
The new return can be estimated as
kConroy = 14% - 7.2% = 6.8%
41
Measuring Market Risk—The
Concept of Beta

Betas are developed from historical data




Small investors should remember that beta doesn't
measure total risk
A beta > (<) 1.0 implies the stock moves more (less)
than the market
Beta < 0 means the stock tends to move against the
market


May not be accurate if a fundamental change in the business
environment occurs
Stocks in gold mining companies are a real-world example of
negative beta stocks
Beta for a Portfolio

Beta for a portfolio is the weighted average of the betas of the
individual stocks within the portfolio
42
Using Beta—The Capital Asset
Pricing Model (CAPM)

The CAPM helps us determine how stock prices
are set in the market


Developed in 1950s and 1960s by Harry Markowitz
and William Sharpe
The CAPM's Approach


People won't invest unless a stock's expected return
is at least equal to their required return
The CAPM attempts to explain how investors'
required returns are determined
43
Using Beta—The Capital Asset
Pricing Model (CAPM)

Rates of Return, The Risk-Free Rate and Risk
Premiums

The risk-free rate (kRF) is a rate for which there is no
chance of receiving less than what is expected
• Returns on federally insured bank accounts and short-term
Treasury debt are examples of risk-free investments

Investing in any other investment is a risky venture;
thus investors will require a return greater than the
risk-free rate
• Investors want to be compensated for the extra risk taken via
a rate known as the risk premium (KRP)
• The CAPM purports to explain how the risk premium in
required rates of return are formed
• The Security Market Line (SML) is the heart of the CAPM
44
The Security Market Line
(SML)

The SML proposes that required rates of return
are determined by:
k X  kRF   kM  k RF  b X
Market Risk
Premium
Stock X's Risk Premium

The Market Risk Premium
• Is a reflection of the investment community's level of risk aversion
• It is the risk premium for an investment in the market as a whole

The Risk Premium for Stock X
• The beta for Stock X times the risk premium of the market
• Says that the risk premium for a stock is determined only by the
stock's relationship with the market as measured by beta
45
The Security Market Line
(SML)

The SML as a Portrayal of the Securities Market

The standard equation of a straight line is
• y = mx + b
• Where: y is the vertical axis variable; x is the horizontal axis
variable; m is the slope of the line and b is the y intercept

The SML can be viewed as a straight line:
k X  k RF   k M  k RF  b X
y=
b+
m
x
• The slope of the SML plotted in risk-return space reflects
the general level of risk aversion
• The vertical intercept of the SML represents investment in
short-term government securities
46
The Security Market Line
(SML)

The SML as a Line of Market Equilibrium


If, for every stock, its expected return equals its
required return, the SML represents equilibrium
Suppose that a stock's expected return now becomes
less than its required return
• Investors would no longer desire that stock and owners of
the stock would sell while potential buyers would no longer
be interested
• The stock price would drop because supply would exceed
demand
• Since the stock price is dropping, its expected return is
increasing, driving it back toward equilibrium
• The SML represents a condition of stable equilibrium
47
The Security Market Line
(SML)

Valuation Using Risk-Return Concepts



The SML allows us to calculate the minimum required
rate of return for a stock
This return can then be used in the Gordon model to
determine an intrinsic value for a stock
The Impact of Management Decisions on Stock
Prices

Since managers can influence a stock's beta and
future growth rates, management's decisions impact
the price of the stock
48
The Security Market Line
(SML)—Example
Example
Q: The Kelvin Company paid an annual dividend of $1.50 recently, and is
expected to grow at 7% into the indefinite future. Short-term treasury
bills are currently yielding 6%, and an average stock yields its owner
10%. Kelvin stock is relatively volatile. Its return tends to move in
response to political and economic changes about twice as much as
does the return on the average stock. What should Kelvin sell for
today?
A: The required rate of return using the SML is:
kKelvin = 6 + (10 – 6)2.0 = 14%
Plugging this required rate of return along with the growth rate of 7%
into the Gordon model gives us the estimated price:
P0 
D0 1  g
kg

$1.5 1.07 
.14  .07
 $22.93
49
Example
The Security Market Line
(SML)—Example
Q: The Kelvin Company has an exciting new opportunity. The firm has
identified a new field into which it can expand using technology it
already possesses. The venture promises to increase the firm's growth
rate to 9% from the current 7%. However, the project is new and
unproven, so there's a chance it will fail and cause a considerable loss.
As a result, there's some concern that the stock market won't react
favorably to the additional risk. Management estimates that
undertaking the venture will raise the firm's beta to 2.3 from its current
level of 2.0. Should Kelvin undertake the new project if the firm’s
current stock price is $22.93?
A: The objective of the firm’s management should be to maximize
shareholder wealth. If growth is expected to increase, this will have a
positive impact on stock price; however, if an increase in beta is
expected, stockholders will demand a higher rate of return which will
cause an offsetting drop in the stock price. The expected price of the
stock given both the increase in the growth rate and the increase in the
firm’s beta must be calculated.
50
The Security Market Line
(SML)—Example
Example
The new required rate of return will be:
kKelvin = 6 + (10 – 6)2.3 = 15.2%
Plugging this new required rate of return along with the higher growth
rate of 9% into the Gordon model gives us the new estimated price:
P0 
D0 1  g
kg

$1.5 1.09 
.152  .09
 $26.37
Thus, the venture looks like a good idea.
51
The Security Market Line

Adjustments to Changing Market Conditions

The response to a change in the risk-free rate
• If all else remains the same, a change in the risk-free rate
causes a parallel shift in the SML
• The slope of the SML remains the same which means KM
must increase by the amount of the change in kRF

The response to a change in risk aversion
• Changes in attitudes toward risk are reflected by rotations of
the SML around its vertical intercept
52
The Validity and Acceptance of
the CAPM and SML

CAPM is an abstraction of reality designed to
help make predictions

Its simplicity has lead to its popularity
• It relates risk and return in an easy-to-understand concept

However, CAPM is not universally accepted

Continuing debate exists as to its relevance and
usefulness
• Fama and French found no historical relationship between
the returns on stocks and their betas
53