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CHAPTER TWO
UNDERSTANDING
RISK AND RETURN
Practical Investment Management
Robert A. Strong
Outline
 Return





Holding Period Return
Yield and Appreciation
The Time Value of Money
Compounding
Compound Annual Return
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Outline
 Risk
 Risk vs. Uncertainty
 Dispersion and the Chance of Loss
 The Problem with Losses
• Big Losses
• Small Losses
• Risk and the Time Horizon
 Risk Aversion
• Risk Aversion and Rational People
• Risk and Time
 Partitioning Risk
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Outline
 More on the Relationship between Risk and
Return
 The Direct Relationship
 Risk, Return, and Dominance
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Introduction
 A dollar today is worth more than a dollar
tomorrow.
 A safe dollar is worth more than a risky
dollar.
 People have different degrees of risk
aversion. Some are more willing to take a
chance than others.
 A tradeoff exists between risk and return.
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Holding Period Return
 The simplest measure of return is the
holding period return.
Holding
period =
return
Ending _ Beginning
+
value
value
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Income
Beginning value
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Holding Period Return
Example :
Buy 100 shares
at $25 per share
Dividend of
$0.10 per share
Sell the shares
at $30 per share
Time
Holding period return =
$30 - $25 + $0.10
= 20.4%
$25
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Holding Period Return
 Holding period return is independent of the
passage of time.
 When comparing investments, the periods
should all be of the same length.
 When there are stock splits or other
corporate actions, care should be taken to
ensure that the correct value is used for
calculating the holding period return.
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Yield and Appreciation
Current yield is annual income
divided by current price.
Dividend yield is used for stocks
whose income comes exclusively
from dividends.
Example :
For a stock selling for $40 and expected to
pay $1 in dividends over the next year ,
current yield = $1 / $40 = 2.5% .
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Yield and Appreciation
Appreciation is the increase in
value of an investment
independent of its yield.
It excludes accrued interest, as
well as increases in value which
are due to additional deposits.
Example :
When a stock bought at $95 rises to $97.50,
it has appreciated by $2.50, or
$2.50 / $95 = 2.6% .
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The Time Value of Money
 The time value of money is the notion that
a dollar today is worth more than a dollar
tomorrow.
n
P×(1+r) = F
where P
F
r
and n
=
=
=
=
present value (i.e. price today)
future value
interest rate per period
number of periods
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The Time Value of Money
 The current price of any financial asset
should be the present value of its expected
future cash flows.
Example :
What is the most that an investor would pay for
a zero coupon bond which matures in 4 years'
time, and has a redemption value of $1,000?
The interest rate is 9.19% .
P × ( 1 + 0.0919 )4 = $1,000
 P = $703.50
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The Time Value of Money
 Many securities pay more than one cash flow
over their lives. In particular, an annuity is a
series of equal and evenly spaced payments.
 A convenient expression for the present value
of an annuity is:
1
1 
PC 
n
 r r 1  r  
where C = coupon or periodic payment
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The Time Value of Money
Insert Figure 2.1 here.
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Compounding
 Compounding refers to the earning of
interest on interest that is earned previously.
r

F  P 1  
 n
nt
where r = annual interest rate
n = number of compounding periods per year
and t = investment horizon in years
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Compounding
 The more frequent the compounding, the
greater the interest earned.
 In the limit, compounding occurs
continuously, and F approaches Pert.
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Compound Annual Return
Compound annual return is the
annual interest rate that makes the
time value of money relationship
hold.
It is also known as the effective
annual rate.
Example :
A nondividend-paying stock bought 4.5 years ago
at $40 and sold today at $78 has a compound
annual return of R, where $40(1+R)4.5=$78.
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Risk vs. Uncertainty
 A truly risky situation must
involve a chance of loss.
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Dispersion and the Chance of Loss
 There are 2 aspects to risk - the average
outcome and the scattering of the possible
outcomes about this average.
 A common measure of statistical
dispersion is variance. The standard
deviation is the square root of the variance.
n
Variance   xi  x  prob(i )
2
i 1
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Dispersion and the Chance of Loss
Insert Figure 2-3 here.
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The Problem with Losses
 Big losses - a large one-period loss can
overwhelm a series of gains
 Small losses - can be a problem too if they
occur too often
 Risk and the time horizon - as the time
horizon increases, the probability of losing
money decreases but the amount of money
that may be lost increases.
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Small Losses
Insert Figure 2-4 here.
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Risk and the Time Horizon
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Risk Aversion and Rational People
 A safe (certain) dollar is worth more than a
risky dollar.
 A rational person will choose a certain
dollar over a risky dollar.
 Risk averse persons will take risks, when
they expect to be rewarded for taking the
risks.
 People have different degrees of risk
aversion. Some are more willing to take a
chance than others.
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Risk Aversion and Rational People
Choice 1
Resulting
Choice 2
Choice 3
Resulting
Resulting
Payoff
Resulting
Number
Payoff
Number
1-50
$110
1-50
$200
1-90
$ 50
1-99
51-100
$ 90
51-100
$
91-100
$550
100
Avg.
$100
Avg.
$100
Avg.
$100
Avg.
0
Number
Choice 4 ___
Payoff
Number Payoff
$1,000
-$89,000
$ 100
Table 2.4 Four Risky Alternatives
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Risk and Time
 Probability theory deals with how much
and how likely, but says nothing about
when.
 Forecast variance increases indefinitely as
the length of the forecast period
approaches infinity.
 To be comparable, returns must be
measured over consistent time intervals.
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Risk and Time
 While the returns over a long horizon may
be more uncertain, history suggests that
over long periods of time, the likelihood
that the investment will lose money is less.
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Partitioning Risk
 Undiversifiable risk is risk that must be
borne by virtue of being in the market.
It is also known as systematic risk or
market risk, and is measured by beta.
 Diversifiable risk is also known as
unsystematic risk.
 Total risk = undiversifiable risk
+ diversifiable risk
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Partitioning Risk
 Business risk - the variability in a firm's
sales, or its ability to sell its product
 Financial risk - associated with the
financial structure of the firm
 Purchasing power risk - the possibility that
the rate of return on an investment will be
insufficient to offset the rise in the cost of
living
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Partitioning Risk
 Interest rate risk - the chance of a loss in
portfolio value due to an adverse change in
interest rate
 Foreign exchange risk - the possibility of
loss due to adverse changes in the relative
values of world currencies
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Partitioning Risk
 Political risk - the possibility that a
government will interfere with a firm's
preferred manner of conducting business
 Social risk - the potentially adverse impact
changing public attitudes can have on a
firm's ability to sell its product
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Partitioning Risk
Insert Figure 2-5 here.
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Partitioning Risk
Insert Figure 2-6 here.
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The Direct Relationship between Risk and Return
Insert Figure 2-7 here.
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The Direct Relationship between Risk and Return
 Empirical financial research reveals clear
evidence of the direct relationship between
systematic risk and expected return, i.e.
riskier securities earn higher returns on
average.
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The Direct Relationship between Risk and Return
Insert Figure 2-8 here.
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Risk, Return, and Dominance
 An investment alternative shows
dominance over another if it offers the
same expected return for less risk, or if the
security has a higher expected return than
another security of comparable risk.
 Equivalent assets should sell for the same
price. This is known as the law of one
price.
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Risk, Return, and Dominance
Insert Figure 2-9 here.
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Review
 Return





Holding Period Return
Yield and Appreciation
The Time Value of Money
Compounding
Compound Annual Return
South-Western / Thomson Learning © 2004
2 - 39
Review
 Risk
 Risk vs. Uncertainty
 Dispersion and the Chance of Loss
 The Problem with Losses
• Big Losses
• Small Losses
• Risk and the Time Horizon
 Risk Aversion
• Risk Aversion and Rational People
• Risk and Time
 Partitioning Risk
South-Western / Thomson Learning © 2004
2 - 40
Review
 More on the Relationship between Risk and
Return
 The Direct Relationship
 Risk, Return, and Dominance
South-Western / Thomson Learning © 2004
2 - 41