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 =
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$30 - $25 + $0.10
$25
= 20.4%
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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
Choice 4
Choice 2
Choice 3
___
Resulting
Resulting
Resulting
Number
Number
Payoff
Payoff
Number
1-50
$1,000
$110
1-50
Resulting
Payoff
$200
51-100
$ 90
51-100
Table 2.4-$89,000
Four Risky
100
Alternatives
Avg.
$100
Avg.
$100
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Number
1-90
$
Avg.
Payoff
$ 50
0 91-100
$100
1-99
$550
Avg.
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