

Investment
Analysis & Portfolio Management
(FIN630)
VU
Lesson
# 32
UNDERSTANDING
RISK AND RETURN
Contd...
RISK:
It is
not sensible to talk about
investment returns without
talking about risk,
because
investment
decisions involve a tradeoff between
the tworeturn and risk are
opposite
sides
of the same coin. Investors
must constantly be aware of the
risk they are
assuming,
know
what it can do to their investment
decisions, and be prepared for the
consequences.
Investors
should be "willing to purchase a
particular asset if the expected
return is, adequate
to
compensate for the risk,
but they must understand
that their expectation about
the asset's
return
may not materialize. If not,
the realized return will
differ from the expected
return. In
fact,
realized returns on securities
show considerable variability sometimes
they are larger
than
expected, and other times they
are smaller than expected, or
even negative.
Although
investors
may receive their expected
returns on risky securities on a
longrun average
basis,
they
often fail to do so on a shortrun
basis.
SOURCES
OF RISK:
What
makes a financial asset
risky? Traditionally, investors
have talked about
several
sources
of total risk, such as
interest rate risk and market
risk, which are
explained
below,
because these terms are
used so widely, Following
this discussion, we will define
the
modern
portfolio sources of risk,
which will be used later
when we discuss portfolio
and
capital
market theory.
1.
Interest Rate
Risk:
The
variability in a security's return
resulting from changes in
the level of interest rates
is
referred
to as interest rate risk. Such
changes generally affect
securities inversely; that
is,
other
things being equal, security
prices move inversely to interest
rates. Interest rate
risk
affects
bonds more directly than
common stocks, but it affects
both and is a very
important
consideration
for most investors.
2.
Market Risk:
The
variability in returns resulting
from fluctuations in the
overall market that is,
the
aggregate
stock market is referred to as
market risk. All securities
are exposed to market
risk,
although it affects primarily
common stocks.
Market
risk includes a wide range of
factors exogenous to securities
themselves, including
recessions,
wars, structural changes in
the economy, and changes in
consumer preferences.
3.
Inflation Risk:
A
factor affecting all securities is
purchasing power risk, or
the chance that the
purchasing
power
of invested dollars will decline/With
uncertain inflation, the
real (inflationadjusted)
return
involves risk even if the
nominal return is safe
(e.g., a Treasury bond).
This risk is
related
to interest rate risk, since interest
rates generally rise as inflation
increases, because
lenders
demand additional inflation premiums to
compensate for the loss of
purchasing
power.
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4.
Business Risk:
The
risk of doing business in a
particular industry or environment is
called business risk.
For
example, AT&T, the traditional
telephone powerhouse, faces
major changes today
in
the
rapidly changing telecommunications
industry.
5.
Financial Risk:
Financial
risk is associated with the
use of debt financing by companies. The
larger the
proportion
of assets financed by debt (as
opposed to equity), the
larger the variability in
the
returns,
other things being equal.
Financial risk involves the
concept of financial
leverage,
which
is explained in managerial finance
courses.
6.
Liquidity Risk:
Liquidity
risk is the risk associated
with the particular
secondary market in which a
security
trades. An
investment that can be bought or
sold quickly and without
significant price
concession is
considered to be liquid. The more
uncertainty about the time
element arid the
price
concession, the greater the liquidity
risk. A Treasury bill has
little or no liquidity
risk,
whereas a
small overthecounter (OTC)
stock may have substantial
liquidity risk.
7.
Exchange Rate
Risk:
All
investors who invest
internationally in today's increasingly
global investment arena
face
the
prospect of uncertainty in the returns
after theyconvert the
foreign gains back to their
own
currency Unlike the past
when most U.S. investors
ignored international
investing
alternatives,
investors today must
recognize and understand exchange rate
risk, which can
be
defined as the variability in
returns on securities caused by
currency fluctuations.
Exchange
rate risk is sometimes called currency
risk.
For
example, a U.S. investor who
buys a German stock
denominated in marks
must
ultimately
convert the returns from
this stock back to dollars. If
the exchange rate has
moved
against the investor, losses
from these" exchange rate' movements can
partially or
totally
negate the original return
earned.
8.
Country Risk:
Country
risk, also referred to as political
risk, is an important risk
for investors today
probably
more important now than in
the past. With mote
investors investing
internationally,
both directly and indirectly,
the political, and therefore
economic, stability
and
viability of a country's economy
need to be considered. The United
States arguably has
the
lowest country, risk, and
other countries can be judged on
arelative basis using
the
United
States as a benchmark. Examplesof
countries that needed
careful monitoring in
the
1990s
because of country risk
included the, former Soviet
Union ^and Yugoslavia,
China,
Hong
Kong, and Smith Africa. In
theearly part of the
twentyfirst century, several
countries
in
South America, Turkey, Russia, and
Hong Kong, among others,
require careful
attention.
TYPES
OF RISK:
Thus
far, our discussion has
concerned the total risk of
an asset, which is one
important
consideration
in investment analysis. However,
modern investment analysis categorizes
the
traditional
sources of risk identified
previously as .causing variability in
returns into two
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general
types: those that are
pervasive in nature, such as
market risk or interest rate
risk, and
those
that are specific to a
particular security issue, such as
business or financial
risk.
Therefore,
we must consider these two
categories of total
risk.
Dividing
total risk into its
two components, a general
(market) component and a
specific
(issuer) component, we have
systematic risk and nonsystematic
risk, which are
additive:
Total
risk = General risk +
Specific risk
=
Market risk + Issuer
risk
=
Systematic risk + Nonsystematic
risk
Systematic
(Market) Risk:
Risk
attributable to broad macro factors
affecting all
securities
Systematic
Risk is an investor can construct a
diversified portfolio and eliminate pan
of the
total
risk, the diversifiable or
nonmarket part. What is
left is the nondiversifiable
portion
or
the market risk. Variability
in a security's total returns
that is directly associated
with
overall
movements in the general
market or economy is called
systematic (market)
risk.
Virtually
all securities have some
systematic risk, whether bonds or stocks,
because
systematic
risk directly encompasses
the interest rate, market,
and inflation risks.
The
investor
cannot escape this part of
the risk, because no matter
how well he or she
diversifies,
the risk of the overall
market cannot be avoided. If
the stock market
declines
sharply,
most stocks will be adversely affected;
if it rises strongly, as in the
last few months
of
1982, most stocks will appreciate in
value. These movements occur
regardless of what
any
single investor does.
Clearly, market risk is
critical to all
investors.
Nonsystematic
(Nonmarket) Risk:
Risk
attributable to factors unique to the
security
Nonsystematic
Risk is the variability in a
security's total returns not
related to overall
market
variability is called the
nonsystematic (nonmarket) risk.
This risk 1s unique to
a
particular
security and is associated with
such factors as business and
financial risk as
well
as
liquidity risk. Although all
securities tend to have some
nonsystematic risk, it is
generally
connected
with common stocks.
MEASURING
RETURNS:
1.
Total Return:
Percentage
measure relating all cash
flows on a security for a given
time period 10 its
purchase
price
A
correct returns measure must
incorporate the two
components of return, yield and
price
change, as
discussed earlier. Returns
across time or from
different securities can be
measured
and compared using the total
return concept. Formally,
the total return (TR)
for a
given
holding period is a decimal
(or percentage) number relating
all the cash
flows
received
by an investor during any
designated time period to
the purchase price of
the
asset.
Total return is defined
as:
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TR =
Any cash payments received +
Price changes over the
period
Price
at which the asset is
purchased
The
dollar price change over the
period, defined as the
difference between the
beginning (or
purchase)
price and, the ending
(or sale) price, can be either
positive (sales price
exceeds
purchase
price), negative (purchase
price exceeds sales price),
or zero. The cash
payments
can be
either positive or zero.
Netting the two items in
the numerator together and
dividing
by
the purchase price results in a
decimal return figure that
can easily be converted
into
percentage
form. Note that in using
the TR, the two
components of return, yield and
price
change,
have been measured.
The
general equation for
calculating TR is;
TR =
CFt + (PE  PB)
PB
=
CFt + PC
PB
Where;
CFt = cash flows during
the measurement period t
PE = price at the end of period
t or sale price
PB = purchase price of the asset
or price at the beginning of
the period
PC = change in
price during the period, or
PE minus PB
The
cash flow for bond
pomes from the interest
payments received, and that
for a stock
comes
from the dividends received.
For some assets, such as a
warrant or a stock that
pays
no
dividends, there is only a
price change.
2.
Return Relative:
It is
often necessary to measure
returns on a slightly different
basis than TRs. This
is
particularly
true when calculating either
a cumulative wealth index or a
geometric mean,
both
of which are explained
below, because negative
returns cannot be used in
the
calculation.
The return relative (RR)
solves this problem by
adding 1.0 to the total
return.
RR = TR in
decimal form +
1.0
TR in
decimal form = RR 
1.0
Although
return relatives may be less
than 1.0, they will be greater
than zero, thereby
eliminating
negative numbers.
3.
Cumulative Wealth
Index:
Cumulative
wealth over time given an
initial wealth and a series of
returns on some asset
Return
measures such as TRs measure
changes in the level of
wealth. At times, however,
it
is
more desirable to measure levels of
wealth {or prices) rather
than changes. In other
words,
we measure the cumulative
effect of returns over time
given some stated
beginning
dollar
amount invested, which
typically is shown as $1 for
convenience. Having
calculated
ending
wealth (cumulative wealth)
over some period on the
base of a beginning $1, it
is
simple
enough to multiply by the
actual beginning amount,
such as $10,000 or $100,000 or
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whatever
the number is. The
value of the cumulative
wealth index, CWIn is
computed, as:
CWIn = WI0 (1 + TR1) (1 +
TR2) ... (1 + TRn)
Where;
CWIB = the cumulative wealth
index as of the end of period
n
WI0 = the beginning index
value, typically $1
TR1, n = the periodic TRs in
decimal form
Taking
a Global Perspective:
International
investing offers potential
return opportunities and potential
reduction in risk
through
diversification. Based on the
historical record, investments in
certain foreign
markets
would have increased
investor returns during
certain periodsof time.
However,
investors
need to understand how
thesereturns are calculated and
the risk they are
taking.
International
Returns and Currency
Risk:
When
investors buy and sell
assets in other countries,
they must consider exchange
rate
risk
or currency risk. This risk
can convert a gain from an
investment into .a loss or a loss
from
an investment into a gain. We
need to remember that
international stocks are
priced
in
local currencies, for
example, a Swiss stock is priced in Swiss
francs and a Japanese
stock
is priced in yen. For a U.S.
investor, the ultimate
return to him or her in
spendable
dollars
depends upon the rate of
exchange between the foreign
currency and the dollar,
and
this
rate typically changes daily.
Currency risk is the risk
that the changes in the
value of the
dollar
and the foreign currency
involved will be unfavorable; however,
like risk in general,
currency
risk can work to the
investor's favor, enhancing
the return that would
otherwise be
received.
An
investment denominated in an appreciating
currency relative to the
investor's domestic
currency
will experience a gain from
the currency movement whereas an
investment
denominated
in a depreciating currency relative to
the investor's domestic
currency will
experience
a decrease in the return
because of the currency
movement. Said
differently,
when
you buy a foreign asset,
you are selling the
dollar, and when you cash in
by selling the
asset,
you are buying back the
dollar.
Total
return in = RR x Ending value of
foreign currency
Domestic
terms
Beginning
value of foreign
currency
SUMMARY
STATISTICS FOR
RETURNS:
The
total return, return
relative, and wealth index
are useful measures of
return for a
specified
period of time. Also needed
in investment analysis are
statistics to describe a
series
of returns. "For example,
investing in a particular stock
for 10 years or a different
stock
in each of 10 years could result in 10
TRs, which must be described
by one or more
statistics.
Two such measures used
with returns data are
described below.
Arithmetic
Mean the
best known statistic to most
people is the arithmetic mean.
Therefore,
when
someone refers to the mean
return they usually are
referring to the arithmetic
mean
unless
otherwise specified. The
arithmetic mean, customarily designated
by the symbol;
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X(Xbar),
of a set of values is calculated
as:
X=∑X
n
or
the sum of each of the
values being considered divided by
the total, number of values
n.
Geometric
Mean the
arithmetic mean return is an appropriate
measure of the
central
tendency
of a distribution consisting of returns
calculated for a particular
time" period, such
as 10
years. However, when
percentage changes in value
over time are involved, as a
result
of
compounding, the arithmetic mean of
these changes can be misleading. A
different mean,
the
geometric mean, is needed to describe
accurately the "true"
average rate of return,
over
multiple
periods.
The
geometric mean return measures
the compound rate of growth
over time. It is
often
used
in investments and finance to reflect
the steady growth rate of invested
funds over
some
past period; that is,
the uniform rate at which
money actually few over
time per
period.
Therefore, it allows us to measure
the realized change in wealth
over multiple
periods.
.
The
geometric mean is defined as the
nth root of the product
resulting from multiplying
a
series
of return relatives
together,
G =
[(1 + TR1) (1 +
TR2)... (1 + TRn)]1/n  1
where
TR is a series of total returns in
decimal form. Note that
adding 1.0 to each
total
return
produces a return relative. Return
relatives are used in
calculating geometric mean
returns,
because TRs, which can be
negative, cannot be
used.
Arithmetic
Mean versus Geometric
Mean:
When
should we use the arithmetic
mean and when should we use
the geometric mean to
describe
the returns from financial
assets? The answer depends
on the investor's
objective:
The
arithmetic mean is a better measure of
average (typical) performance
over single
periods. It is
the best estimate of the expected
return for next
period.
The
geometric mean is a better measure of
the change in wealth over
the past (multiple
periods).
It is a backwardlooking concept,
measuring the realized
compound rate of return
at
which money grew over a
specified period.
Inflation
Adjusted Returns:
All of
the returns discussed above
art nominal returns, or
money returns. They
measure
dollar
amounts or changes but say
nothing about the purchasing
power of these dollars.
To
capture
this dimension, we need to
consider real returns, or
inflationadjusted returns. To
calculate
inflationadjusted returns, we divide 1 +
nominal total return by 1 +
the inflation
rate,
this calculation is sometimes simplified
by subtracting rather than
dividing, producing
a close
approximation.
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TRIA = (1 + TR)  1
(1 +
IF)
Where;
TRIA = the inflationadjusted
total return
IF
= the
rate of inflation
This
equation applies to both individual years
and average total
returns.
Risk
Premiums:
A
risk premium is the
additional return investors
expect to receive, or did
receive, by taking
on
increasing amounts of risk. It
measures the payoff for
taking various types of
risk. Such
premiums
can be calculated between any
two classes of
securities.
An
oftendiscussed risk premium is
the equity risk premium,
defined as the
difference
between
the return on stocks and a riskfree rate
(proxied by the return on
Treasury bills).
The
equity risk premium measures
the additional compensation
for assuming risk,
since
Treasury
bills have no practical risk
(on a nominal basis). Obviously,
common stock
investors
care whether the expected
risk premium is 5 percent, or 8
percent, because that
affects
what they earn on their
investment in stocks. Holding interest
rates constant, a
narrowing
of the equity risk premium
implies a decline in the rate of
return on steaks,
because
the amount carried beyond
the riskfree rate is reduced.
MORE ON THE
RELATIONSHIP BETWEEN RISK
AND RETURN:
Risk
and potential return need to be
analyzed together throughout
the investment
decision
making
process. Considering their
relationship is a big part of
what investment advisers get
paid to
do.
The
Direct Relationship:
The
fundamental relationship between
risk and return is well known to
those who
have
studied the market.
The
more risk someone bears,
the higher are their
expected return. It also points out
that
some
rate of return can be earned without
bearing any risk, and is
called the riskless rate
of
interest,
or the risk free rate in
finance theory. Two
important points should be
noted. First,
the
riskreturn relationship is based on
expected return. Expected return is a
before the fact,
not
after the fact concept. It
is not correct to say that
riskier securities have
higher returns,
although
people often make this statement. If
riskier securities always had a
higher return
they
would not be risky. Sometimes an
investor is hurt by a risk
taken that resulted in
a
negative
return. Such is the essence
of risk.
The
second important point is
that the risk we are
talking about is unavoidable,
or
undiversifiable,
risk. An investor is not
generally rewarded for
bearing risk that could
have
been
diversified away.
Empirical
financial research reveals
clear evidence of the direct
relationship between
systematic
risk and expected return. Riskier
portfolios, on average, earn
higher.
Additionally,
returns on well diversified
portfolios tend to plot in a
generally linear
fashion.
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The
point of this discussion is
that whether looking ahead
to possible future returns or
looking
back at realized results, a person can
usually observe this direct
relationship
between
risk and return. Once again,
though, it is not accurate to conclude
that "higher risk
means
higher return." Risky
investments often lose money
for their owners over
the short
run.
They may also earn less than
"safer" investments.
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