6_Risk_and_Return_ppt.ppt,,,,,,,,,,,,,,,,,,

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Copyright © 2001 by Harcourt, Inc. All rights reserved.
CHAPTER 6
Risk, Rates of Return,
Capital Assets Pricing Model
Stand-alone risk
Portfolio risk
Risk & return: CAPM/SML

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RETURNS ON INVESTMENTSRETURNS ON INVESTMENTS
With most investments, an individual or business
spends money today with the expectation of
earning even more money in the future.
The concept of return provides investors with a
convenient way to express the financial
performance of an investment.

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What is investment risk?What is investment risk?
Investment risk pertains to the probability
of actually earning a low or negative return.
The greater the chance of low or negative
returns, the riskier the investment.

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RISK
Risk is defined in Webster’s as “a hazard; a
peril; exposure to loss or injury.”
Thus, risk refers to the chance that some
unfavorable event will occur.
If you go skydiving, you are taking a chance
with your life—skydiving is risky. If you bet
on horse races, you are risking your money.

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STAND-ALONE RISK
An asset’s risk can be analyzed in two ways:
(1) on a stand-alone basis, where the asset is
considered in isolation, and
(2) on a portfolio basis portfolio basis, where the asset is held as one
of a number of assets in a portfolio.
Thus, an asset’s stand-alone risk is the risk an
investor would face if she held only this one asset.
Obviously, most assets are held in portfolios, but it is
necessary to understand stand-alone risk in order to
understand risk in a portfolio context.

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Probability Distributions
An event’s probability is defined as the chance
that the event will occur. For example, a
weather forecaster might state: “There is a
40% chance of rain today and a 60% chance
that it will not rain.”
If all possible events, or outcomes, are listed,
and if a probability is assigned to each event,
then the listing is called a probability
distribution.
Keep in mind that the probabilities must sum
to 1.0, or 100%.

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Investment Alternatives
(Given in the problem)
EconomyProb.T-BillHT CollUSR MP
Recession0.18.0%-22.0%28.0%10.0%-13.0%
Below avg.0.28.0-2.014.7-10.0 1.0
Average 0.48.020.00.07.0 15.0
Above avg.0.28.035.0-10.045.0 29.0
Boom 0.18.050.0-20.030.0 43.0
1.0

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Annual Total Returns,1926-1998
AverageStandard
ReturnDeviation Distribution
Small-company
stocks 17.4% 33.8%
Large-company
stocks 13.2 20.3
Long-term
corporate bonds 6.1 8.6
Long-term
government 5.7 9.2
Intermediate-term
government 5.5 5.7
U.S. Treasury
bills 3.8 3.2
Inflation 3.2 4.5
0 17.4%
0 13.2%
0 6.1%
0 5.7%
0 5.5%
0 3.8%
0 3.2%

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Why is the T-bill return independent
of the economy?
Will return the promised 8%
regardless of the economy.

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Do T-bills promise a completely
risk-free return?
No, T-bills are still exposed to the
risk of inflation.
However, not much unexpected
inflation is likely to occur over a
relatively short period.

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Do the returns of HT and Coll. move with
or counter to the economy?
HT: Moves with the economy, and has a
positive correlation. This is typical.
Coll: Is countercyclical of the economy,
and has a negative correlation. This is
unusual.

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Expected Rate of Return
If we multiply each possible outcome by its
probability of occurrence and then sum these
products, the result is a weighted average of
outcomes. The weights are the probabilities, and
the weighted average is the expected rate of
return, r
̂
, called “r-hat.”
 The expected rates of return for both Sale.com
and Basic Foods are shown in Figure 6-2 to be 15%.
This type of table is known as a payoff matrix.

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The range of probable returns for Sale.com is from -60% to +90%, with an
expected return of 15%.
The expected return for Basic Foods is also 15%, but its range is much
narrower.

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A common definition that is satisfactory for many
purposes is stated in terms of probability distributions
such as those presented in previous slides
The tighter the probability distribution of expected
future returns, the smaller the risk of a given
investment.
According to this definition, Basic Foods is less risky
than Sale.com because there is a smaller chance that
its actual return will end up far below its expected
return.
Measuring Stand-Alone Risk:
The Standard Deviation

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Calculations
Standard Deviation

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Using Historical Data to Measure Risk

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Coefficient of Variation (CV)
Standardized measure of dispersion
about the expected value:
Shows risk per unit of return.
CV = = .
Std dev 
^
r
Mean

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0
A B

A = 
B , but A is riskier because larger
probability of losses.
= CV
A > CV
B.

^
r

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Portfolio Risk and Return
Assume a two-stock portfolio with
$50,000 in HT and $50,000 in
Collections.
Calculate r
p
and 
p
.
^

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Portfolio Return, r
p
r
p is a weighted average:
r
p
= 0.5(17.4%) + 0.5(1.7%) = 9.6%.
r
p is between r
HT and r
COLL.
^
^
^
^
^ ^
^ ^
r
p = w
ir
i
n
i = 1

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CV
p = = 0.34.
3.3%
9.6%
p = = 3.3%.

12/






















(3.0 – 9.6)
2
0.10
+ (6.4 – 9.6)
2
0.20
+ (10.0 – 9.6)20.40
+ (12.5 – 9.6)
2
0.20
+ (15.0 – 9.6)
2
0.10

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
p = 3.3% is much lower than that of either
stock (20% and 13.4%).

p = 3.3% is lower than average of HT and Coll
= 16.7%.
Portfolio provides average r but lower risk.
Reason: negative correlation.
^

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General statements about risk
Most stocks are positively correlated. r
r,m
 0.65.
35% for an average stock.
Combining stocks generally lowers risk.

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Returns Distribution for Two Perfectly
Negatively Correlated Stocks (r = -1.0) and for
Portfolio WM
25
15
0
-10 -10 -10
0
0
15 15
25 25
Stock W Stock M Portfolio WM
.
..
. .
.
.
.
.
.
.....

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The reason Stocks W and M can be combined to
form a riskless portfolio is that their returns move
counter cyclically to each other—when W’s
returns fall, those of M rise, and vice versa. The
tendency of two variables to move together is
called correlation, and the correlation coefficient
measures this tendency. In statistical terms, we
say that the returns on Stocks W and M are
perfectly negatively correlated, with ρ = −1.0.
Stocks W and M

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What would happen to the
riskiness of an average 1-stock
portfolio as more randomly
selected stocks were added?

p would decrease because the added
stocks would not be perfectly correlated
but r
p
would remain relatively constant.
^

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The tendency of two variables to move together
is called correlation, and the correlation
coefficient measures this tendency.

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Large
0 15
Prob.
2
1
Even with large N, 
p 20%

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# Stocks in Portfolio
102030 40 2,000+
Company Specific Risk
Market Risk
20
0
Stand-Alone Risk, 
p

p (%)
35

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Diversifiable risk
Diversifiable risk is caused by such random
events as lawsuits, strikes, successful and
unsuccessful marketing programs, winning or
losing a major contract, and other events that are
unique to a particular firm.
Because these events are random, their effects on
a portfolio can be eliminated by diversification—
bad events in one firm will be offset by good events
in another

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Market risk
Market risk, on the other hand, stems
from factors that systematically affect
most firms: war, inflation, recessions, and
high interest rates. Because most stocks
are negatively affected by these factors,
market risk cannot be eliminated by
diversification.

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As more stocks are added, each new
stock has a smaller risk-reducing
impact.

p
falls very slowly after about 10
stocks are included, and after 40
stocks, there is little, if any, effect.
The lower limit for 
p is about 20% =

M .

43. 6 - 43
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Stand-alone Market Firm-specific
Market risk is that part of a security’s
stand-alone risk that cannot be
eliminated by diversification, and is
measured by beta.
Firm-specific risk is that part of a
security’s stand-alone risk that can be
eliminated by proper diversification.
risk risk risk
= +

44. 6 - 44
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By forming portfolios, we can eliminate
about half the riskiness of individual
stocks (35% vs. 20%).
If you chose to hold a one-stock
portfolio and thus are exposed to more
risk than diversified investors, would
you be compensated for all the risk you
bear?

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NO!
Stand-alone risk as measured by a
stock’s 
or CV is not important to a well-
diversified investor.
Rational, risk averse investors are
concerned with 
p , which is based on
market risk.

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There can only be one price, hence
market return, for a given security.
Therefore, no compensation can be
earned for the additional risk of a one-
stock portfolio.

47. 6 - 47
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Individual Stocks’ Betas
The tendency of a stock to move up and down
with the market is reflected in its beta coefficient.
An average-risk stock is defined as one with a
beta equal to 1 (b = 1.0).
Beta measures a stock’s market risk.
It shows a stock’s volatility relative to the
market.
Beta shows how risky a stock is if the stock is held
in a well-diversified portfolio.

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A portfolio of such b = 1.0 stocks will move up and
down with the broad market indexes, and it will be
just as risky as the market.
A portfolio of b = 0.5 stocks tends to move in the same
direction as the market, but to a lesser degree.
On the other hand, a portfolio of b = 2.0 stocks also
tends to move with the market, but it will have even
bigger swings than the market.

50. 6 - 50
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How are betas calculated?
Run a regression of past returns on
Stock i versus returns on the market.
Returns = D/P + g.
The slope of the regression line is
defined as the beta coefficient.

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Yearr
M
r
i

115% 18%
2 -5-10
312 16
.
.
.
r
i
_
r
M
_
-5 0 5 10 15 20
20
15
10
5
-5
-10
Illustration of beta calculation:
Regression line:
r
i
= -2.59 + 1.44 r
M
^ ^

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Portfolio Betas
Here bp is the beta of the portfolio, which shows its
tendency to move with the market; wi is the fraction of
the portfolio invested in Stock i; and bi is the beta
coefficient of Stock i.
For example, if an investor holds a $100,000 portfolio
consisting of $33,333.333 invested in each of three
stocks, and if each of the stocks has a beta of 0.70,
then the portfolio’s beta will be
bp = 0.70: bp = 0.3333(0.70) + 0.3333(0.70) + 0.3333(0.70) = 0.70
An important aspect of the CAPM is that the beta of a
portfolio is a weighted average of its individual
securities’ betas:

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If beta = 1.0, average stock.
If beta > 1.0, stock riskier than average.
If beta < 1.0, stock less risky than
average.
Most stocks have betas in the range of
0.5 to 1.5.

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List of Beta Coefficients
Stock Beta
Merrill Lynch 2.00
America Online 1.70
General Electric 1.20
Microsoft Corp. 1.10
Coca-Cola 1.05
IBM 1.05
Procter & Gamble 0.85
Heinz 0.80
Energen Corp. 0.80
Empire District Electric 0.45

55. 6 - 55
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Can a beta be negative?
Answer: Yes, if r
i, m
is negative.
Then in a “beta graph” the
regression line will slope
downward. Though, a negative
beta is highly unlikely.

56. 6 - 56
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HT
T-Bills
b = 0
r
i
_
r
M
_
-20 0 20 40
40
20
-20
b = 1.29
Coll.
b = -0.86

57. 6 - 57
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Riskier securities have higher returns,
so the rank order is OK.
HT 17.4% 1.29
Market 15.0 1.00
USR 13.8 0.68
T-bills 8.0 0.00
Coll. 1.7 -0.86
 Expected Risk
Security Return (Beta)

58. 6 - 58
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Use the SML to calculate the
required returns.
Assume r
RF
= 8%.
Note that r
M
= r
M
is 15%. (Equil.)
RP
M = r
M – r
RF = 15% – 8% = 7%.
SML: r
i
= r
RF
+ (r
M
– r
RF
)b
i
.
^
Risk premium for Stock i = RPi = (RPM)bi

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The Security Market Line (SML)
The Security Market Line (SML) equation
shows the relationship between a security’s
market risk and its required rate of return.
The return required for any security i is equal
to the risk-free rate plus the market risk
premium multiplied by the security’s beta:
 ri = rRF +(RPM)bi.

60. 6 - 60
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Required Rates of Return
r
HT = 8.0% + (15.0% – 8.0%)(1.29)
= 8.0% + (7%)(1.29)
= 8.0% + 9.0%= 17.0%.
r
M= 8.0% + (7%)(1.00)= 15.0%.
r
USR
= 8.0% + (7%)(0.68)= 12.8%.
r
T-bill= 8.0% + (7%)(0.00)= 8.0%.
r
Coll= 8.0% + (7%)(-0.86)= 2.0%.

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The Security Market Line (SML)

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HT 17.4% 17.0% Undervalued:
r > r
Market 15.0 15.0 Fairly valued
USR 13.8 12.8 Undervalued:
r > r
T-bills 8.0 8.0 Fairly valued
Coll. 1.7 2.0 Overvalued:
r < r
Expected vs. Required Returns
^
^
^
^
r r

63. 6 - 63
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.
.
Coll.
.
HT
T-bills
.
USR
SML
r
M
= 15
r
RF
= 8
-1 0 1 2
.
SML: r
i = 8% + (15% – 8%) b
i .
r
i (%)
Risr, b
i

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Calculate beta for a portfolio with 50%
HT and 50% Collections
b
p
= Weighted average
= 0.5(b
HT
) + 0.5(b
Coll
)
= 0.5(1.29) + 0.5(-0.86)
= 0.22.

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The required return on the HT/Coll.
portfolio is:
r
p
= Weighted average r
= 0.5(17%) + 0.5(2%) = 9.5%.
Or use SML:
r
p
= r
RF
+ (r
M
– r
RF
) b
p
= 8.0% + (15.0% – 8.0%)(0.22)
= 8.0% + 7%(0.22) = 9.5%.

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If investors raise inflation
expectations by 3%, what would
happen to the SML?

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SML
1
Original situation
Required Rate
of Return r (%)
SML
2
0 0.5 1.0 1.5 Risk, b
i
18
15
11
8
New SML
 I = 3%

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If inflation did not change but risk
aversion increased enough to cause
the market risk premium to increase
by 3 percentage points,
what would happen to the SML?

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r
M = 18%
r
M
= 15%
SML
1
Original situation
Required
Rate of
Return (%)
SML
2
After increase
in risk aversion
Risk, b
i
18
15
8
1.0
 RP
M = 3%

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Has the CAPM been verified through
empirical tests?
Not completely.
Those statistical tests have
problems that make verification
almost impossible.

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Investors seem to be concerned
with both market risk and total risk.
Therefore, the SML may not produce
a correct estimate of r
i:
r
i
= r
RF
+ (r
M
– r
RF
)b + ?

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Also, CAPM/SML concepts are
based on expectations, yet betas are
calculated using historical data. A
company’s historical data may not
reflect investors’ expectations about
future riskiness.

74. 6 - 74
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Capital Asset Pricing Model (CAPM)
Capital Asset Pricing Model (CAPM), an important
tool used to analyze the relationship between risk
and rates of return.
The primary conclusion of the CAPM is this: The
relevant risk of an individual stock is its contribution
to the risk of a well diversified portfolio.
A stock might be quite risky if held by itself, but—
since about half of its risk can be eliminated by
diversification—the stock’s relevant risk is its
contribution to the portfolio’s risk, which is much
smaller than its stand-alone risk.
The risk that remains after diversifying is called
market risk, the risk that is inherent in the market