Foundations of Finance
Arthur J. Keown
J. William Petty
John D. Martin
David F. Scott, Jr.
Chapter 6
The Meaning and Measurement of
Risk and Return
Chapter 6
The Meaning and Measurement of Risk and Return
Learning Objectives
 Define and measure the expected
rate of return of an individual
investor.
 Define and measure the riskiness of
an individual investment.
 Compare the historical relationship
between risk and return in the capital
markets.
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Learning Objectives
 Explain how diversifying investments
affects the riskiness and expected
rate of return of a portfolio or
combination of assets.
 Explain the relationship between an
investor’s required rate of return on
an investment and the riskiness of
the investment.
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Principles Used in this Chapter
• Principle 1: The Risk-Return
Trade-off – We Won’t Take on
Additional Risk Unless We
Expect to Be Compensated with
Additional Return.
• Principle 3: Cash-Not Profits-Is
King.
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Expected Cash Flow
• Weighted Average of the possible
cash flows outcomes such that the
weights are the probabilities of the
occurrence of the various states of
the economy.
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Measuring the Expected Return
State of
Probability Cash flow
% Return (Cash
the
of the
from the
Flow/Inv. Cost)
investment
$1,000
10%
1,200
($1,000/$10,000)
12%
economy states
Economic 20%
Recovery
Moderate
30%
Economic
Growth
Strong
($1,200/$10,000)
50%
1,400
Economic
Growth
6-6
14%
($1,400/$10,000)
Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Expected Rate of Return
• Weighted average of all the
possible returns, weighted by
the probability that each return
will occur.
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
ILLUSTRATION
• State Probability Return on Return on
Stock A
Stock B
1
20%
5%
50%
2
30%
10%
30%
3
30%
15%
10%
4
20%
20%
-10%
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Studying and Understanding Risk
• What is risk?
• How do we know the amount of risk
associated with a given investment;
that is how do we measure risk?
• If we choose to diversify our
investments by owning more that one
asset, as most of us do, will such
diversification reduce the riskiness
of our combined portfolio of
investments?
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
RISK AND RETURN
Return—profit as a percentage of total
investment
Risk—uncertainty about the actual rate
of return over an investment period
Risk and Return are directly related
(investors require greater returns for
greater risk)
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Risk
• Potential variability in future
cash flows
• The wider the range of possible
events that can occur, the
greater the risk
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Standard Deviation of Return
• Square root of the weighted
average squared deviation of
each possible return from the
expected return
• Quantitative measure of an
asset’s riskiness
• Measures the volatility or
riskiness of portfolio returns
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Measuring the Expected Return
State of
Probability Cash flow
% Return (Cash
the
of the
from the
Flow/Inv. Cost)
investment
$1,000
10%
1,200
($1,000/$10,000)
12%
economy states
Economic 20%
Recovery
Moderate
30%
Economic
Growth
Strong
($1,200/$10,000)
50%
1,400
Economic
Growth
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14%
($1,400/$10,000)
Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
ILLUSTRATION
• State Probability Return on Return on
Stock A
Stock B
1
20%
5%
50%
2
30%
10%
30%
3
30%
15%
10%
4
20%
20%
-10%
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
RISK-REWARD TRADE OFF
• A balance an investor must
decide on between the desire
for the lowest possible risk for
the highest possible return.
Chapter 6
The Meaning and Measurement of Risk and Return
RISK-TRADE OFF DIAGRAM
10%
12%
13%
17%
15%
19%
16%
20%
18%
24%
Return
Expected Standard
Return
Deviation 8%
10%
Standard Deviation
Chapter 6
The Meaning and Measurement of Risk and Return
Total Risk or Variability
• Company-Unique Risk
(Unsystematic)
• Market Risk (Systematic)
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Company-Unique Risk
• Unsystematic risk
• Diversifiable -Can be diversified away
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Market Risk
•
•
•
Systematic
Non-diversifiable
Cannot be eliminated through
random diversification
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Market Risk
Events that affect market risk
Changes in the general economy,
major political events, sociological
changes
Examples:
*Interest rates
*General economic conditions
*Changes in tax legislation that
affect all companies
*War
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Measuring Market Risk
• Characteristic line
– The slope of the characteristic line
measures the average relationship
between a stock’s returns and
those of the S&P 500 Index
Returns.
– Indicates the average movement in
a stock’s price to a movement in
the S&P 500 Price Index.
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Measuring Market Returns
Monthly Holding-Period Returns of Barnes & Noble and the S&P 500
Index, December 2002 to November 2004
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Diversification
• If we diversify investments
across different securities, the
variability in the returns
declines
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Beta
• Average relationship between a
stock’s returns and the market’s
returns
• Slope of the characteristic line—or
the line that measures the average
relationship between a stock’s
returns and the market
• Measure of a firm’s market risk or
systematic risk that remains for a
company even after diversified our
portfolio.
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Beta
• A stock with a Beta of 0 has no
systematic risk
• A stock with a Beta of 1 has
systematic risk equal to the “typical”
stock in the marketplace
• A stock with a Beta exceeding 1 has
systematic risk greater than the
“typical” stock
• Most stocks have betas between .60
and 1.60
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Portfolio Beta
• Weighted average of the individual
securities’ betas, with the weights
being equal to the proportion of the
portfolio invested in each security
• Portfolio beta indicates the
percentage change on average of the
portfolio for every 1 percent change
in the general market
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Portfolio Beta
Holding-Period Returns: High- and Low-Beta Portfolios and the
S&P 500 Index
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Risk and Diversification
• The market rewards
diversification
• We can lower risk without
sacrificing expected returns
• We can increase expected
returns without having to
assume more risk
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Asset Allocation
• Diversification among different
kinds of asset types:
T Bills
Long-Term Government Bonds
Common Stocks
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Required Rate of Return
• Minimum rate of return
necessary to attract an investor
to purchase or hold a security
• Considers the opportunity cost
of funds
– The next best investment
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Real Average Annual Rate of
Return
• Nominal rate of return less the
inflation rate
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Required Rate of Return
k=kfr + krp
Where:
k = required rate of return
kfr = Risk-Free Rate
krp = Risk Premium
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Risk-Free Rate
• Required rate of return or
discount rate for risk-less
investments
• Typically measured by U.S.
Treasury Bill Rate
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Measuring the Required Rate
of Return
• Systematic risk is the only
relevant risk-the rest can be
diversified away
• The required rate of return, k,
equals the risk free rate, krf,
plus a risk premium, krp
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Measuring the Required Rate
of Return
Risk Premium = Required Return –
Risk-Free rate
krp = k - kfr
How much is the risk
premium if the
Where:
required rate of
k = required rate of return
return
is
12%
and
the
k Risk-Free Rate
risk free rate is 5%?
k Risk Premium
fr =
=
6rp
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
Capital Asset Pricing Model
• Equation that equates the expected
rate of return on a stock to the riskfree rate plus a risk premium for the
systematic risk.
• CAPM provides for an intuitive
approach for thinking about the
return that an investor should require
on an investment, given the asset’s
systematic or market risk.
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
CAPM
If required return is 15% and the
risk-free rate
is 5%,
How
muchthen
is thethe
risk
risk premium
is 10%.
premium
for the
If the requiredmarket
rate of
return
for
if the
required
the market portfolio
km is 12%,
return for market
and the krf isportfolio
5%, the
is risk
14% and
premium krp the
forrisk
thefree
market
rate is
would be 7%.
5%?
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
CAPM
This 7% risk premium would
apply to any security having
systematic (nondiversifiable)
risk equivalent to the general
market, or beta of 1.
In the same market, a security
with Beta of 2 would provide a
risk premium of 14%.
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
CAPM
• CAPM suggests that Beta is
a factor in required returns
kj = krf + B(market rate – risk-free rate)
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
CAPM
Example:
Market risk = 12%
Risk-free rate = 5%
5% + B(12% - 5%)
If B = 0
Required rate = 5%
If B = 1
Required rate = 12%
If B = 2
Required rate = 19%
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
The Security Market Line
• Graphic representation of the
CAPM, where the line shows the
appropriate required rate of
return for a given stock’s
systematic risk.
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Foundations of Finance
Pearson Prentice Hall
Chapter 6
The Meaning and Measurement of Risk and Return
The Security Market Line
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Foundations of Finance
Pearson Prentice Hall