Chapter 5:
Risk and Rates of Return
Risk and Rates of Return:
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Chapter Outline:
Types of Return.
Types of Risk.
 Expected Rate of Return.
The Measurement of Risk.
The Return of A Portfolio.
The Concept of Beta.
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Types of Return:
Expected Return.
Required Return.
Realized Return.
Expected Return Expressed as a
Probability.
Investment returns.
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Expected Return:
The return that an investor expects to earn
on an asset, given its risk, price, growth
potential, etc.
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Required Return (K) :
The return that an investor requires on an
asset given its risk and market interest rates.
The required return for bearing a certain
level of risk.
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Realized Return:
The sum of income and capital gains earned
on an investment.
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Expected Return Expressed as
a Probability:
The expected value is the sum of each
outcome multiplied by the probability of
occurrence.
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Investment returns:
The rate of return on an investment can be calculated as
follows:
(Amount received – Amount invested)
Return =
________________________
Amount invested
For example, if $1,000 is invested and $1,100 is returned
after one year, the rate of return for this investment is:
($1,100 - $1,000) / $1,000 = 10%.
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Types of Risk:
What is Risk?
Nondiversifiable Risk.
Diversifiable Risk.
 Investment Risk.
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What is Risk?
 The chance that some unfavorable event
will occur.
The possibility that an actual return will
differ from our expected return.
Uncertainty in the distribution of possible
outcomes.
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Nondiversifiable Risk:
Known as Market risk or Systematic risk.
This type of risk can not be diversified
away.
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Nondiversifiable Risk:
Unexpected changes in interest rates.
Unexpected changes in cash flows due to
tax rate changes, foreign competition, and
the overall business cycle.
Political Events
International Events
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Diversifiable Risk:
Known as Company-unique risk or
Unsystematic risk.
This type of risk can be reduced through
diversification.
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Diversifiable Risk:
A company’s labor force goes on strike.
A company’s top management dies.
A huge oil tank bursts and floods a
company’s production area.
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What is investment risk?
Two types of investment risk
Stand-alone risk
Portfolio risk
Investment risk is related to the probability of
earning a low or negative actual return.
The greater the chance of lower than expected or
negative returns, the riskier the investment.
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What is investment risk?
Stand-alone risk: The risk an investor
would face if he or she held only one
asset.
Portfolio risk: The risk an investor
would face if he or she held more than
one assets, an investment portfolio.
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Expected Rate of Return:
The rate of return expected to be realized
from an investment; the weighted average
of the probability distribution of possible
results.
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Calculating the Expected Rate
of Return:
 See the example in the book pages 172173.
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The Measurement of Risk:
 Measuring the stand alone risk using the
standard deviation.
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Standard Deviation as a
Measure of Risk:
It can serve as an absolute measure of
return variability.
the higher the standard deviation, the
greater the uncertainty concerning the actual
outcome
We can use it to determine the likelihood
that an actual outcome will be greater or
less than a particular amount
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Standard Deviation:
Standard deviation is a measure of the
dispersion of possible outcomes.
The greater the standard deviation, the
greater the uncertainty, and therefore , the
greater the risk.
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Standard Deviation
Calculation:
  Standard deviation


Variance 
n
2
 (k  k̂ ) P
i1
2
i
i
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Standard Deviation
Calculation:
 See the example in the book page 175.
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Coefficient of Variation (CV)
A standardized measure of dispersion about the
expected value, that shows the risk per unit of
return.
Std dev 
CV 
 ^
Mean
k
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The Return of A Portfolio:
Portfolio: is a combination of two or more
securities or assets
Investors rarely place their entire wealth into
a single asset or investment (risky). Rather,
they construct portfolio or group of
investment
Combining several securities in a portfolio
can actually reduce overall risk.
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Diversification:
Investing in more than one security to
reduce risk.
If two stocks are perfectly positively
correlated, diversification has no effect on
risk.
If two stocks are perfectly negatively
correlated, the portfolio is perfectly
diversified.
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Returns distribution for two perfectly
negatively correlated stocks (ρ = -1.0):
Stock W
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Stock M
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Portfolio WM
25
15
15
0
0
15
0
-10
-10
-10
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Returns distribution for two perfectly
positively correlated stocks (ρ = 1.0):
Stock M’
Stock M
Portfolio MM’
25
25
25
15
15
15
0
0
0
-10
-10
-10
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Portfolio Return:
The expected return of a portfolio is simply a
weighted average of the expected return of the
securities comprising that portfolio
Rp 
m
w
j 1
j
Rj
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Calculating Portfolio Standard
Deviation: page 182.
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Failure to diversify:
If an investor chooses to hold a one-stock portfolio
(exposed to more risk than a diversified investor),
would the investor be compensated for the risk they
bear?
NO!
Stand-alone risk is not important to a welldiversified investor.
Rational, risk-averse investors are concerned
with σp, which is based upon market risk.
No compensation should be earned for holding
unnecessary, diversifiable risk.
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The Concept of Beta :
Measures a stock’s market risk, and shows
a stock’s volatility relative to the market.
Indicates how risky a stock is if the stock is
held in a well-diversified portfolio.
Average relationship between a stock’s
returns and the market’s returns
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Beta Coefficients:
The market’s beta is 1.
A firm that has a beta = 1, this firm’ stock
no more no less riskier than the market.
A firm with a beta > 1, this firm’s stock is
more risky than the market.
A firm with a beta < 1, this firm’s stock is
less risky than the market.
Most stocks have betas in the range of 0.5
to 1.5.
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The Calculation of Beta
Coefficient:
Run a Regression Analysis of past returns
on a stock versus past returns on the market.
The slope of the regression line, i.e. the
characteristic line, is defined as the beta
coefficient.
The greater the slope of the characteristic
line for a stock, the greater its systematic
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High and Low Betas:
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Can the Beta of a Stock be
Negative?
Yes, if the correlation between Stock and
the market is negative.
If the correlation is negative, the regression
line would slope downward, and the beta
would be negative.
However, a negative beta is highly unlikely.
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Beta and the Security Market
Line (SML):
The greater the beta of a stock, the greater the
relevant risk of that stock, and the greater the
return required.
Assume that unsystematic risk is diversified
away, the required rate of return for a stock is
calculated using CAPM equation:
R j  R f  ( Rm  R f ) j
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Volatility Versus Risk:
 Earning Volatility does not necessarily
imply investment risk.
 Earning Volatility could imply risk
depending on the causes.
 Stock price volatility does signify risk.
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