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Chapter 2
RISK AND RETURN BASICS
Chapter 2 Questions
What are the sources of investment
returns?
How can returns be measured?
How can we compute returns on
investments outside of their home
country?
Chapter 2 Questions
What is risk and how is it measured?
How is expected return and risk
estimated via scenario analysis?
What are the components of an
investment’s required return to investors
and why might they change over time?
Sources of Investment
Returns
Investments provide two basic types of return:
Income returns

The owner of an investment has the right to any
cash flows paid by the investment.
Changes in price or value

The owner of an investment receives the benefit of
increases in value and bears the risk for any
decreases in value.
Income Returns
Cash payments,
usually received
regularly over the
life of the
investment.
Examples: Coupon
interest payments
from bonds,
Common and
preferred stock
dividend payments.
Returns From Changes
in Value
Investors also
experience capital gains
or losses as the value
of their investment
changes over time.
For example, a stock
may pay a $1 dividend
while its value falls from
$30 to $25 over the
same time period.
Investment Strategy
Generally, the income returns from an investment are
“in your pocket” cash flows.
Over time, your portfolio will grow much faster if you
reinvest these cash flows and put the full power of
compound interest in your favor.
Dividend reinvestment plans (DRIPs) provide a tool
for this to happen automatically; similarly, Mutual
Funds allow for automatic reinvestment of income.
See Exhibit 2.5 for an illustration of the benefit of
reinvesting income.
Measuring Returns
Dollar Returns


How much money was made on an investment
over some period of time?
Total Dollar Return = Income + Price Change
Holding Period Return

By dividing the Total Dollar Return by the
Purchase Price (or Beginning Price), we can
better gauge a return by incorporating the size of
the investment made in order to get the dollar
return.
Annualized Returns
If we have return or income/price change
information over a time period in excess of
one year, we usually want to annualize the
rate of return in order to facilitate
comparisons with other investment returns.
Another useful measure:
Return Relative = Income + Ending Value
Purchase Price
Annualized Returns
Annualized HPR = (1 + HPR)1/n – 1
Annualized HPR = (Return Relative)1/n – 1
With returns computed on an
annualized basis, they are now
comparable with all other annualized
returns.
Returns on Overseas
Investments
A holding period return on a foreign
investment generally needs to be
translated back into the home country
return.
If the exchange rate has changed over
the life of the investment, the home
country return (HCR) can be very
different than the foreign return (FR).
Returns on Foreign
Investments
HCR Relative = FR Relative (Current
Exchange Rate/Initial Exchange Rate)
HCR=(1 + FR)Current Exchange Rate – 1
Initial Exchange Rate
Measuring Historic
Returns
Starting with annualized Holding Period
Returns, we often want to calculate
some measure of the “average” return
over time on an investment.
Two commonly used measures of
average:
Arithmetic Mean
 Geometric Mean

Arithmetic Mean Return
The arithmetic mean is the “simple average”
of a series of returns.
Calculated by summing all of the returns in
the series and dividing by the number of
values.
RA = (SHPR)/n
Oddly enough, earning the arithmetic mean
return for n years is not generally equivalent
to the actual amount of money earned by the
investment over all n time periods.
Arithmetic Mean
Example
Year Holding Period Return
1
10%
2
30%
3
-20%
4
0%
5
20%
RA = (SHPR)/n = 40/5 = 8%
Geometric Mean Return
The geometric mean is the one return that, if
earned in each of the n years of an
investment’s life, gives the same total dollar
result as the actual investment.
It is calculated as the nth root of the product
of all of the n return relatives of the
investment.
RG = [P(Return Relatives)]1/n – 1
Geometric Mean
Example
Year Holding Period Return Return Relative
1
10%
1.10
2
30%
1.30
3
-20%
0.80
4
0%
1.00
5
20%
1.20
RG = [(1.10)(1.30)(.80)(1.00)(1.20)]1/5 – 1
RG = .0654 or 6.54%
Arithmetic vs.
Geometric
To ponder which is the superior measure,
consider the same example with a $1000
initial investment. How much would be
accumulated?
Year Holding Period Return Investment Value
1
10%
$1,100
2
30%
$1,430
3
-20%
$1,144
4
0%
$1,144
5
20%
$1,373
Arithmetic vs.
Geometric
How much would be accumulated if you
earned the arithmetic mean over the same
time period?
Value = $1,000 (1.08)5 = $1,469
How much would be accumulated if you
earned the geometric mean over the same
time period?
Value = $1,000 (1.0654)5 = $1,373
Notice that only the geometric mean gives the
same return as the underlying series of
returns.
Scenario Analysis
While historic returns, or past realized
returns, are important, investment decisions
are inherently forward-looking.
We often employ scenario or “what if?”
analysis in order to make better decisions,
given the uncertain future.
Scenario analysis involves looking at different
outcomes for returns along with their
associated probabilities of occurrence.
Expected Rates of
Return
Expected rates of return are calculated
by determining the possible returns (Ri)
for some investment in the future, and
weighting each possible return by its
own probability (Pi).
E(R) = S Pi Ri
Expected Return
Example
Economic Conditions Probability Return
Strong
.20
40%
Average
.50
12%
Weak
.30
-20%
E(R) = .20(40%) + .50 (12%) + .30 (-20%)
E(R) = 8%
What is risk?
Risk is the uncertainty associated with the
return on an investment.
Risk can impact all components of return
through:



Fluctuations in income returns;
Fluctuations in price changes of the investment;
Fluctuations in reinvestment rates of return.
Sources of Risk
Systematic Risk Factors


Affect many investment returns simultaneously;
their impact is pervasive.
Examples: changes in interest rates and the state
of the macro-economy.
Asset-specific Risk Factors


Affect only one or a small number of investment
returns; come from the characteristics of the
specific investment.
Examples: poor management, competitive
pressures.
How can we measure
risk?
Since risk is related to variability and
uncertainty, we can use measures of
variability to assess risk.
The variance and its positive square root, the
standard deviation, are such measures.

Measure “total risk” of an investment, the
combined effects of systematic and asset-specific
risk factors.
Variance of Historic Returns
s2 = [S(Rt-RA)2]/n-1
Standard Deviation of
Historic Returns
Year Holding Period Return
1
10%
RA = 8%
2
30%
s2 = 370
3
-20%
s = 19.2%
4
0%
5
20%
s2 = [(10-8)2+(30-8)2+(-20-8)2+(0-8)2+(20-8)2]/4
= [4+484+784+64+144]/4
= [1480]/4
Coefficient of Variation
The coefficient of variation is the ratio of the
standard deviation divided by the return on
the investment; it is a measure of risk per unit
of return.
CV = s/RA
The higher the coefficient of variation, the
riskier the investment.
From the previous example, the coefficient of
variation would be:
CV =19.2%/8% = 2.40
Measuring Risk Through
Scenario Analysis
If we are considering various scenarios
of return in the future, we can still
calculate the variance and standard
deviation of returns, now just from a
probability distribution.
s2 = SPi(Ri-E(R))2
Standard Deviation of
Expected Returns
Economic Conditions Probability Return
Strong
.20
40%
Average
.50
12%
Weak
.30
-20%
E(R) = 8%
s2 = .20 (40-8)2 +.50 (12-8)2 + .30 (-20-8)2
s2 = 448
s = 21.2%
Note: CV = 21.2%/8% = 2.65
Components of Return
Recall from Chapter 1 that the required rate
of return on an investment is the sum of the
risk-free rate (RFR) of return available in the
market and a risk premium (RP) to
compensate the investor for risk.
Required Return = RFR + RP
The Capital Market Line (CML) is a visual
representation of how risk is rewarded in the
market for investments.
Components of Return
Over Time
What changes the required return on an
investment over time?
Anything that changes the risk-free rate or the
investment’s risk premium.


Changes in the real risk-free rate of return and the
expected rate of inflation (both impacting the
nominal risk-free rate, factors that shift the CML).
Changes in the investment’s specific risk (a
movement along the CML) and the premium
required in the marketplace for bearing risk
(changing the slope of the CML).