Transcript Chapter 8

Chapter 8
Risk and Return
© 2000 South-Western College Publishing
PORTFOLIO THEORY
The Relationship Between Risk and Return
Inherent in Investing in Securities
Especially Stocks
WHY STUDY RISK AND RETURN?
Over a Long Period of Time, Stocks returned about 9%,
Debt returned about 3%
But
Returns on stocks could be very low (or high) over shorter periods.
Look for a way to capture the high average returns of equity
while avoiding as much risk as possible.
In General, Investments With High Returns Also Have High risk.
We need a way to measure risk and relate it to return so we can choose among
investment opportunities.
TM 8-1
THE RETURN ON ONE-YEAR
INVESTMENTS
DEBT
Interest paid divided by the loan principal
k
int erest paid
loan amount
EQUITY
What the investor receives divided by what was invested
k
D1  ( P1  P0 )
P0
TM 8-2 Slide 1 of 2
The Expected Return
Based on general knowledge about the stock
The Required Return
Based on perceived risk
Substantial investment in a stock will take place only if
the generally expected return exceeds most people's
required return.
TM 8-2 Slide 2 of 2
RISK - A PRELIMINARY DEFINITION
The chance (probability) that the return
on an investment will turn out to be less
than expected when the investment is made
Note: Includes earning slightly less
as well as losing money
TM 8-3 Slide 1 of 2
RISK AVERSION
People have negative feelings about bearing risk in investments.
They prefer lower risk if the expected return is about the same.
E.g., most prefer an 8% bank account to a stock with an
expected return of 8%.
However there's a trade-off.
If the choice is between the 8% bank account and a
10% stock, many will choose the stock.
Risk aversion doesn't mean risk is to be avoided at all cost.
It is a negative that can be
compensated with more expected return.
TM 8-3 Slide 2 of 2
RANDOM VARIABLES
A random variable is the outcome of a chance process.
Discrete random variables take on only specific values.
Continuous random variables take on values over a range.
Example of a Discrete Random Variable
Toss a coin four times, call the number of heads X.
X is a random variable which can take on any of five discrete values.
The probability distribution of X is:
X
P(X)
0
.0625
1
.2500
2
.3750
3
.2500
4
.0625
1.0000
TM 8-4 Slide 1 of 3
OR
P(X)
.3750
.2500
.0625
0
1
2
3
4
Figure 8-1 Discrete Probability Distribution
TM 8-4 Slide 2 of 3
The most likely value is the mean or expected value
The weighted average of all possible outcomes where each
is weighted by its probability.
X
0
1
2
3
4
P(X)
.0625
.2500
.3750
.2500
.0625
1.0000
X * P(X)
0.00
0.25
0.75
0.75
0.25
X = 2.00
TM 8-4 Slide 3 of 3
CONTINUOUS RANDOM VARIABLES
Can take on any numerical value over some range.
E.g. people's heights
P(H)
4’10”
5’8”
6’6”
Figure 8-2 Probability Distribution for a Continuous Random Variable
TM 8-5 Slide 1 of 2
CONTINUOUS RANDOM VARIABLES
(continued)
The probability of an actual outcome is expressed within a
range rather than as an exact amount.
For example, the probability of being exactly 5'2" isn't meaningful,
but being between 5' 1 7/8" and 5' 2 1/8" is.
Probability is represented by the area under the curve.
When the distribution is symmetrical and has only
one peak, the mean is found under that peak.
TM 8-5 Slide 2 of 2
PORTFOLIO THEORY
The Return on an Investment in Stock is Represented as a
Continuous Random Variable
D1  ( P1  P0 )
P0
D1 and P1 are subject to a large number of uncertain factors.
Therefore, k has the characteristics of a random variable.
k
P(kX)
Variance (  2 )
kX
Expected return
8.0
8.5
kX
Return
Figure 8-3 The Probability Distribution of the Return on an Investment in Stock X
TM 8-6 Slide 1 of 2
PORTFOLIO THEORY
Portfolio theory assumes the investment community's knowledge
about a stock is reflected in the probability distribution of returns.
The mean or expected value is the statistical representation of the
average investor's expected return.
The variance (  ) shows how likely a return is to be some distance
away from the expected value.
2
The diagram shows the variance conceptually as the width of the
distribution.
TM 8-6 Slide 2of 2
VARIANCE
Think of variance as variability in successive annual returns
The bigger the variance, the more different successive returns
are likely to be
P(kX)
Small Variance
(low risk)
Large Variance
(high risk)
kX
kX
Expected Return
Return
Figure 8-4 Probability Distributions with Large and Small Variances
TM 8-7 Slide 1of 2
VARIANCE
(continued)
The large variance distribution has more area under the
curve further away from the mean
When the variance is large:
More returns are likely to fall far away from the mean
Returns will be more different or more variable
from year to year
TM 8-7 Slide 2of 2
RISK: REDEFINED AS VARIANCE
In portfolio theory, risk is defined as variability.
A risky stock's return is likely to be significantly different from one
year to the next
A risky stock has a large probability of producing a return that's
substantially away from the mean of its distribution
Hence a large probability of a big loss (or a big gain)
But this is exactly the idea of variance so:
In Portfolio Theory, a stock investment's risk is defined as the
variance of the probability distribution of its return
TM 8-8 Slide 1 of 2
Seems inconsistent with earlier definition that risk is the probability
that return is less than expected - the left side of the distribution
This definition includes better outcomes than expected
Done for mathematical convenience understanding that most
distributions are symmetrical
Hence there are two definitions of risk that are both correct:
In practical terms, risk is the probability that return
will be less than expected.
In financial theory, risk is the variance of the probability
distribution of returns.
TM 8-8 Slide 2 of 2
AN ALTERNATE VIEW
Risk as Variability of Return Over Time
Return
kX
A - High risk
kX
B - Low Risk
Time
Figure 8-5 Investment Risk Viewed as Variability of Return Over Time
TM 8-9
RISK AVERSION
A More Precise Definition
People prefer investments with less risk to those with more risk if the
expected returns are equal
Otherwise, individual preferences vary
P(k)
P(k)
Neither preferred
Preferred
with certainty
k
k
k
kA
(a)
kB
(b)
Figure 8-6 Risk Aversion
TM 8-10
DECOMPOSING RISK INTO COMPONENTS
SYSTEMATIC (MARKET) RISK AND
UNSYSTEMATIC (BUSINESS-SPECIFIC) RISK
Returns on stock investments move up and
down in response to stimuli which may affect
all stocks or only specific businesses
News of politics and economics tends to affect all stocks
A labor dispute affects only firms in one
industry
TM 8-11 Slide 1 of 2
Market Risk
Movement in return in response to stimuli which affect all stocks is
known as systematic risk or market risk.
In general, most stock's returns move together.
Hence, market risk is the degree to which a stock's
return moves with the (average) return on the
market.
Business-specific Risk
Whatever movement in a stock's return is left over after market risk
is removed is known as unsystematic risk or business-specific risk.
TM 8-11 Slide 2 of 2
PORTFOLIOS
Investors generally hold the stocks of several companies.
An investor's total stock holding is a portfolio.
Risk and Return for a Portfolio
The return on a portfolio is the average return of the stocks in it,
weighted by the dollars invested in each stock.
The portfolio's return has a probability distribution
with a mean and variance.
These are the portfolio's expected return and risk.
The expected return is the weighted average of the stock's expected
returns. The variance depends on the stock's variances,
but in a complex way.
TM 8-12 Slide 1 of 2
The Goal of the Investor/Portfolio Owner
To capture the high average returns of equities while avoiding
as much risk as possible
Done by constructing diversified portfolios of securities
with minimum variation in return
Portfolio Theory Assumes:
Investors care only about portfolio performance,
not about individual stock performance.
A stock's risk can appear different in and out of a portfolio.
TM 8-12 Slide 2 of 2
DIVERSIFICATION
HOW RISK IS AFFECTED WHEN STOCKS
ARE ADDED TO A PORTFOLIO
Business-specific (Unsystematic) Risk
Stimuli are random events that push the returns
on individual stocks up or down.
Over a large number of different (diverse) stocks
the pluses and minuses wash out and
Business-specific Risk is Diversified Away
TM 8-13
DIVERSIFICATION
Systematic (Market) Risk
A more difficult concept since returns on
most stocks tend to move together
The Portfolio
Assume portfolio mirrors the makeup of the stock market
so its risk is the market's risk
Consider the impact on the portfolio's risk of adding a
little of either of two new stocks
TM 8-14 Slide 1 of 3
Return, k
A
C
C
A
P
kp
k
B
B
Time
Figure 8-7 Risk In and Out of a Portfolio
A adds risk to the portfolio (perfectly positively correlated with market)
B reduces the portfolio's risk (perfectly negatively correlated with market)
BUT outside the portfolio A and B are equally risky
TM 8-14 Slide 2 of 3
Portfolio risk depends on the timing
of the variation of return
There are very few stocks like B (gold mines)
Variation in portfolio return can be reduced, but not
eliminated, with stocks like C (not perfectly positively
correlated with market)
They bring a little of the "personality" of B along
TM 8-14 Slide 3 of 3
The Importance of Market Risk
In Portfolio Theory
The risk attributes of stocks change when we assume investors
focus on portfolios
Only market risk counts because business-specific risk
is diversified away
This is a dangerous result
Not applicable to small investors with limited portfolios in which a
business-specific event can cause a major loss
Nevertheless
The central risk concept in portfolio theory is market risk
The variation in a stock's return that accompanies variation in the
market's return
Business-specific risk is ignored
TM 8-15
MEASURING MARKET RISK
THE CONCEPT OF BETA
A stock's beta coefficient captures the historical variation
in a stock's return that accompanies variation
in the market's return.
Developing Beta
Plot historical values for kX against kM
Fit a regression line to the data
Known as the characteristic line for the stock
TM 8-16 Slide 1 of 2
kX
.
. Characteristic
. . . . Line
. .
.
.
.
.
.
.
.
. . .
.
.
.
. .
. . .
.
.
.
.
. Values of
. (kM, kX)
.
.
kM
{
 kX{
.
 kM
Slope 
k X
k M
 b X  Beta
Figure 8-8 The Determination of Beta
Represents the average relationship between the stock's return
and the market's return.
The slope indicates on the average how much of a change in kX
comes with a change in kM.
This is exactly the notion of market risk.
TM 8-16 Slide 2 of 2
UNDERSTANDING BETA
Example 8-1 - Projecting Returns with Beta
Conroy Corp. has a beta of 1.8 and returns 14%. The stock market is
reacting negatively to a new Middle East crisis which threatens world
oil supplies and limited war. Experts estimate the return on an
average stock will drop from 12% to 8%. Estimate Conroy's new
return.
Solution:
b Conroy 
1.8 
k Conroy
k M
k Conroy
4%
k Conroy  7.2%
k Conroy  14%  7.2%  6.8%
TM 8-17 Slide 1of 2
Example 8-2 - Business-specific effects
Would the estimate of return be valid if Conroy was a defense
contractor?
Solution:
Probably not because of a positive business-specific effect from the
threat of war
Beta Over Time
Use of a stock's beta implicitly assumes it will remain what it has been
in the past
Example 8-3
Consider Conroy as a defense contractor in the early 1990's with the
Cold War ending and military spending declining. Would a
projection using beta have been valid?
Solution:
The changing conditions make it unlikely that the historical beta
would be good in the future.
TM 8-17 Slide 2of 2
Beta Measures Volatility
With Respect To Market Changes
Beta = 1.0
The stock's return moves on average as much as the market's return.
Beta > 1.0
Return moves more than the market's
Beta < 1.0
Return moves with the market but less.
Beta < 0
Return moves against the market
(Stock B - gold mines)
TM 8-18 Slide 1of 2
Beta in Practice
Widely used to discuss risk
However,
Many people probably forget the definition
as market risk only.
Beta for a Portfolio
Weighted average of betas of individual stocks
Weights are dollars invested in each stock
TM 8-18 Slide 2of 2
THE CAPITAL ASSET PRICING MODEL
(CAPM)
A theory explaining how the market sets the prices of financial
(capital) assets
Explains how required rates of return (k) are determined, which in
turn implies price
One year return
D1  P1
P0 
(1  k )
Gordon model
D0 (1  g )
P0 
kg
TM 8-19 Slide 1of 3
The Security Market Line (SML)
Required rates of return are determined by:
Stock’s
Risk
Premium
k X  k RF  ( k M  k RF )b X
Market
Risk
Premium
where:
kX is the required return on Stock X
kRF is the risk free rate
kM is the return on the market, and
bX is Stock X's beta coefficient
TM 8-19 Slide 2 of 3
The Market Risk Premium
Reflects investors' tolerance for risk
Indicative of the degree of risk aversion in the investing community.
The Risk Premium for Stock X
"Average" risk premium multiplied by stock X's beta,
the measure of its market risk
The only thing related specifically to company X is bX,
the measure of X's market risk
Implication: only market risk counts.
Business-specific risk doesn't enter the equation
Investors are rewarded with extra return only for bearing market risk, not
for bearing business-specific risk which is diversified
away for portfolio investors.
TM 8-19 Slide 3 of 3
THE SML AS A PORTRAYAL OF THE
SECURITIES MARKET
kX
Security Market Line
k X  k RF  ( k M  k RF )b X
kA
* B Disequilibrium
ke<kB
kRF
bA
bB
bX
Figure 8-9 The Security Market Line
TM 8-20
VALUATION USING CAPM AND THE SML
Two Step Process:
Find required return with SML
Use in Gordon model
Example 8-4
The Kelvin's last annual dividend was $1.50. The firm is expected to
grow at 7% indefinitely. Short term treasury bills yield 6%. An
average stock yields 10%. Kelvin stock is relatively volatile; its return
moves twice as much as the average in response to political and
economic changes. For what should the Kelvins sell?
TM 8-21 Slide 1 of 3
Solution:
kRF = treasury bill rate = 6%
kM = "average" return = 10%
bKelvin = 2.0
SML:
k Kelvin  k RF  ( k M  k RF )bKelvin
k Kelvin  6  (10  6 ) 2.0  14%
Gordon model:
P0 

D0 (1  g )
kg
$1.50(1.07)
 $22.93
.14.07
TM 8-21 Slide 2 of 3
Making Decisions Based On Stock Price
Example 8-5
A new venture at Kelvin will: Increase growth rate from 7% to 9%
Raise beta from 2.0 to 2.3
Should Kelvin undertake the new project?
Solution:
Changes move stock price in opposite directions
More growth - good, more risk - bad
Evaluate and choose option with highest stock price
k Kelvin  6  (10  6 ) 2.3  15.2%
P0 
D0 (1  g ) $1.50(1.09 )

 $26.37
kg
.152.09
The higher price implies the venture is a good idea.
TM 8-21 Slide 3 of 3
ADJUSTMENTS TO CHANGING MARKET CONDITIONS
Response to a Change in the Risk Free Rate
The SML shifts up or down parallel to itself to a position
determined by the new kRF
(For the slope to remain unchanged kM must also change)
kX
kRF'
kRF
bX
Figure 8-10 A Shift in the Security Market Line to Accommodate an Increase
in the Risk Free Rate
TM 8-22 Slide 1 of 3
The Response to a Change in Risk Aversion
Changes the market risk premium, (kM - kRF) the slope of the SML
A rotation around the intercept at KRF
kX
SML2
SML1
kRF
bX
Figure 8-11
A Rotation of the Security Market Line to Accommodate a Change in Risk Aversion
TM 8-22 Slide 2 of 3
Example 8-6
Sidel Co:
bS = 1.2, kRF = 6%, kM = 10%
kS = kRF + (kM - kRF)bS
= 6 + (10 - 6)1.25 = 11.0
Calculate new required rates if:
a. kRF increases to 8%
b. kM increases to 11%
Solution:
a. kS = kRF + (kM - kRF)bS = 8 + (12 - 8)1.25 = 13.0%
b. kS = kRF + (kM - kRF)bS = 6 + (11 - 6)1.25 = 12.25%
TM 8-22 Slide 3 of 3