

Investment
Analysis & Portfolio Management
(FIN630)
VU
Lesson
# 31
UNDERSTANDING
RISK AND RETURN
INTRODUCTION:
Two
key concepts provide the
foundation for the field of
finance. The first is A
dollar today
is
worth more than a dollar
tomorrow, and is often called
the time value of money.
The
second
is a safe dollar is worth
more than a risky dollar.
Anyone who studies finance
learns
the
universal application of these statements
and rational decision making.
The tradeoff
between
risk and return is the
principles theme in the
investment decision.
Most
people are risk averse, which
does not mean, however,
they will not take a risk.
It
means
the only take a risk when
they expect to be rewarded
for taking it. People
have
different
degrees of risk aversion;
some are more willing to
take a chance than are
others.
People
invest because they hope to get a
return from their
investment. Return is the
good
stuff
that makes people feel
better or improves their standard of
living. Risk is the bad
stuff
of
risk averse person seeks to
avoid. It is a fact of investment
life and is unavoidable
for
anyone
who seeks more than a
trivial rate of return. This
chapter explores the
fundamental
principles
underlying the relationship
between risk and
return.
RETURN:
Some
return measures are more
useful than others. It is
important to understand
the
calculation
and limitations of various
measures.
Holding
Period Return:
The
simplest measure of return is
the holding period return.
This calculation is
independent
of
the passage of time and
incorporates only a beginning
point and an ending
point.
Holding
period return = Ending value
Beginning value + Income
Beginning
value
Someone
might buy 100 shares of
stock at $25, receives a 10 cent per
share dividend, and
later
sell the shares for
$30. The holding period
return is
$30 $25
+ $0.10 = 20.4%
$25
It
makes no difference if the
holding period return is
calculated on the basis of a
single share
or 100
shares. The holding period
return is exactly the same
because every term is
multiplied
by 100.
Has
this investment done well?
The answer depends on how
much time transpired
between
the
purchase and the sale. If the
stock was acquired in 1989 and sold in
2000, the total
gain
of
20.4% is less than what
could have been earned in a
bank account. If, however,
the stock
was purchased 60
days ago, the return is
handsome.
Because
we are accustomed to thinking of the
rates of return on an annual
basis, it is
common
to annualize returns. To annualize
returns, multiply the
holding period return
by
175
Investment
Analysis & Portfolio Management
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the
fraction 365/days in the
holding period. In the
previous example, the 20.4%
return came
from
and holding period of 60 days:
20.4% (365/60) =
124.1%.
Holding
period returns must be used
with caution. When comparing
investment, the periods
should
all be the same length.
With a collection of stocks, comparing
returns over calendar
year
1999 or returns over the
past five years is acceptable. One
cannot, however,
meaningfully
compare Stock A's 1999 return
with Stock B's 19941999
return.
When
calculating holding period
returns, look out for
stock splits or other
corporate actions
that
would muddy the water.
For example, in September
1999, your mother points
out that
she
purchased 100 shares of WalMart at $25 in September,
1990. Today's Wall
Street
Journal
reports a WMT price of $44½, and
this modest increase surprises hard
given all the
recent
news about the companies
nationwide growth. Capital
appreciation over this
nine
year
period seems to be ($44.50
$25)/ $25 = 78.0%.
Mom
is overlooking the fact that
the firm split its
stock two for one in
February 1993 and
again in
April 1999. A two for one
stock split effectively cuts
the share price in
half.
Someone
who owned 100 shares of WMT in
early 1990 would have owned
400 shares in
September
1999. Anyone unaware of the
stock split would calculate
an incorrect holding
period
return. The split per se
would not affect the
true return if it is correctly
accounted for
in
the calculation. The
calculation appreciation on Mom's
stock is actually
4($44.50)
25 = 612.0%
$25
Yield
and Appreciation:
A
certain amount of ambiguity
surrounds the term yield in
the investment business. To
many
(probable most) people involved
with investments, when yield
is used by itself, it
usually
refers to the dollar amount
an investment "throws off" as
dividends or interest.
This
definition
will be followed in this book.
The financial pages indicate
the yield of stocks and
bonds.
Technically, the newspaper shows
the current yield, which is
the annual income an
investment,
is expected to generate divided by its
current market price. For a
common stock
whose
income comes exclusively
from dividends, the current
yield is typically referred to
as
the
dividend yield.
A
stock might currently sell
for $40 and be expected to pay $1 in
dividends over the next
12
months.
The newspaper will show its
current yield as 2.5%  the
$1 dividend divided by
the
$40 current share
price.
Another
stock might excellent
prospects for the coming
year and be recommended by many
investment
advisors. It might, however,
pay no dividends. The fact
that a stock pays no
dividends
does not mean it is a poor
investment. Consider Microsoft.
Ask a stockbroker
"What
is Microsoft's yield?" and the
answer will be "zero". The
uninitiated person might
wonder
why anyone would ever buy a
stock that was not expected to
yield anything. The
explanation
lies within another
component of return:
appreciation.
Appreciation
is the increase in the value
of an investment independent of its
yield. When
people
speak of a stock going up,
they are talking about
its appreciation. Suppose
an
investor
buys MSFT at $95, and it
rises to $97½. It appreciated by
$2½, or $2.50/$95 =
2.6
%. If it is paid
no dividend, its yield was
zero. Contrast the MSFT
investment with an
interest
earning savings account in
which a saver deposits $95 to accumulate
interest. One
year
later the account contains
$97.50. Even though these
situations might seem
identical,
176
Investment
Analysis & Portfolio Management
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technically
the savings account showed a
yield of 2.6% and appreciation of
zero. The
increase
in value comes from the
interest earned that is left
in the account.
Accrued
interest does not count as
depreciation, nor does an
increase in account and
value
due to
additional deposits. Suppose an investor
opens a brokerage account and buys
stocks
for
$25,000. Five years later
the account is worth
$45,000. It is meaningless to say
the
account
appreciated by $20,000 if the investor
has been depositing $150 per
month into the
account.
A good part of increases is because of
the additional investment,
not because of
investment
performance.
This
point is especially important
when reviewing portfolios
managed by an outside
agency.
Don't
assume that because the YWCA
endowment fund is worth $200,000
more now than it
was
last year that the
fund management was good. The
fund managers should not get
credit
for
bequests or other deposits
into the fund over
the past year.
The
Time Value of
Money:
The
notion that one dollar
received today is more
valuable than one dollar
received
tomorrow
is usually called the time
value of money. It is one of the
two key concepts in
finance
that form the basis
for most valuation equations
and pricing and relationships.
Financial
theory states that the
current price of any
financial asset should be
the present
value
of its expected future cash
flows. You have to understand
the time value of money
to
properly
calculate present values.
Time
value of money problems
involves the relationship
among present values,
future
values,
interest rates and time periods.
Most problems involve
solving for one of
these
values
when the other three
are known. The simplest
time value of money problem
is the
single
sum problem and can easily be
illustrated in the corporate
bond market.
PepsiCo
Capital Resources has a bond
issue coming due in the year
2004. Assume the
redemption
date is four years from
today. At that time, the
company must pay $1,000
for
each
of its bonds when presented
for redemption. Unlike most
bond issues, these bonds
pay
no
periodic interest. Because of
the time value of money,
investors are unwilling to
pay
$1,000
today for a security that
will be worth $1,000 in four years by
providing no interest
income.
This bond must sell at a
discount in the
marketplace.
How
much should the discount
be? The answer depends on
the rate of return available
on
other
investments of comparable risk in
the marketplace. Suppose the
Wall Street Journal
shows
the price of this bond as
$730. Barring default, this
bond will gradually rise in
value
to be
worth $1,000 on its redemption
date. The $270 increase in
value is the bond
holder's
return.
From these values we can
calculate the investors
anticipated holding period
return:
$1,000
$730 = 36.99%
$730
The
holding period of return is
not particularly useful in
this context because it
ignores the
time
value of money. What we
really want to know is the
annual interest rate that
would
cause
a $730 investment to appreciate to $1,000
in four years. That is, we
want to know the
value
of R in equation:
P (1 + R)
n = F
Where
P = present value (i.e., price
today)
F =
future value
177
Investment
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R =
interest rate per period
n =
number of periods
Substituting
our numbers, $730 (1 + R) 4 = $1,000. We find R =
8.19%.
Support
economic conditions change. Investors
become pessimistic about the
future and
government's
ability to keep inflation
under control. As a consequence, market
interest rates
rise by one
point. Investors are no
longer willing to accept an
8.19% rate of return on a
bond
of
this risk; they won't
settle for less than
9.19%. What is the most an
investor could pay
for
the
bond to achieve this rate of
return? In other words, what
is P, the present value (price
of
the
bond) in the following
equation?
P (1 +
.0919) 4
=
$1,000
Rearranging
and doing the math,
($1,000)
P=
1
(1.0919)
4
=
0.7035 ($1,000)
=
$703.50
If
the investor pays $703.50 and receives$1,000 in
four years, the compound
annual return
would
be 9.19%.the factor 0.7035 is called
the discount factor for
four years at 9.19%.
Financial
calculators are preprogrammed to
compute these factors for
time value of money
problems.
Factors are also routinely presented in
tabular form in the back of
accounting and
finance
textbooks.
Many
securities pay more than one
cash flow over their
life. Adelphia Communications,
a
cable TV
company, also has a bond
maturing in the year 2004,
but this bond pays $95
per
year
in interest. Its value
logically should be influenced by
these additional cash flows.
An
investor
in this bond receives a single
sum of $1,000 in four years,
but also receives an
annuity
of $95 per year for the four
years. An Annuity is a series of evenly
spaced, equal
dollar
payments.
An
investor in this bond receives
income from two sources: the
return of the $1,000
principal
in 4 years, and the $95 per year annuity.
One way to determine the
present value
of
the annuity is to decompose it
into four single sums of $95
each and find the
present
value
of each, but this method is
inefficient. A more convenient
expression for the
present
value
of an annuity is shown
below:
P = C
[1/R 1/R (1 + R) n]
Where
C = periodic payment
Suppose
the risk of this bond is
comparable to that of the
PepsiCo capital resources
board,
and is
trading at a price that also
implies a 9.19% rate of return.
The present value of
the
annuity
is then
P = $95
[1/.0919 1/.0919 (1 +
.0919)4] = $306.49
The
present value of the $1,000
return of principle is
$1,000 =
$703.51
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(1.0919)4
The
bondholder is entitled to both
the return of principle and
the annuity, so the
bond
market
price must be the sum of
these two values: $306.49 + $703.51 =
$1,010.
The
holding period return over
the remaining 4 years of this
bond's life would be
$1,000
$ 1,010 + 4($95) =
36.63%
$1,010
Compounding:
Compounding
refers to the earning of
interest on previously earned
interest. Its effects
are
more
pronounced as the frequency
with which interest is
computed and credited to
the
principal
balance increases. At a financial
institution, interest on a savings
account might be
calculated
once per year, semiannually, quarterly,
monthly, or daily. Each of these
methods
constitutes
discreet compounding because the
number of times per year the
bank calculates
the
interest can be counted.
Suppose
an account earns 8% per year,
compounded quarterly. In this scenario,
the account
holder
does not earn 8% every three
months. Rather, the account
is credited with ¼ of 8%
four
times per year. After three
months, an initial deposit of $100 would
earn $2, resulting
in an
account balance of $102. Three
months later, the $102 has
earned 2%, so its value
is
$102(1.02)
= $104.04. Interest is added again
three months later, and once
more at the end
of
the year. At the end of one
year account is worth
$100(1.02)4
=
$108.24.
If
the 8% interest were
compounded annually, at the end of one
year the account
balance
would
be $100(1.08), or $108.00. Note
that with quarterly
compounding the account
earns
24 cents
more than with annual
compounding. The rule is
this: if money is invested at
an
annual
rate of R for t years an interest is
compounded n times per year and
multiply the
number
of years in the problem by n.
mathematically,
F = P (1 +
R/n) nt
Where
F = future value
n =
number of compounding periods per
year
t =
investment horizon in years
Compounding
can also occur hourly, by the
minute, by the second, or by any
arbitrarily
small
time interval. In the limit,
compounding occurs continuously,
with an in finite a
number
of time intervals. This
changes the equation
to
F = P (1 +
R/∞)
∞t
This
mathematical result forms
the basis for natural
logarithms. The quantity (1 +
R/n) nt
approaches
eRt as n approaches
infinity. The value e is
2.71828. Most financial
calculators
have
e programmed as an internal function.
The equation can be restated
as
F =
PeRt
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Compound
Annual Return:
The
compound annual rate is a more
useful return measure than
the holding period return.
It
takes
account of the time value of
money and the fact that
investment horizons are
not
always
the same. This is also
called the effective annual
rate.
Supports
an investor paid $40 for a nonand
dividend paying stock for
4.5 years ago. Today
the
stock sells for $78.
Assuming no stock splits
along the way, the
holding period return
is
($78
$40)/ $40 = 95%.After 4.5 years
have passed, the 95%
figure probably lacks a
frame
of
reference for performance
comparison purposes. Because we are
accustomed to thinking
of
interest rates per year, we
usually look at annual
returns to provide that
frame of
reference.
The compound annual return
is the annual interest rate
that makes the time
value
of
money relationship hold:
$40(1 + R) 4.5
= $78. In
this equation, R is 16%, a
meaningful
number.
It tells us that if the $40 had
been invested at 16%, after
4.5 years the
investment
would
be worth $78. The compound
annual returns on competing
investments can be
directly
compared.
A danger
with compound annual
returns, however, stems from
computing them over
short
periods of
time. Suppose WalMart
closes today at $51, a $1.00
from yesterday's close.
What
is the compound annual
return? Solve for R in the
equation $50(1 + R) 1/365 = $51.
The
answer is 137,641%! Associating
this annual rate with your
$50 WalMart stock
means
that
in 12 months, a share would be
worth $68,870  not a likely
scenario.
A
recent new story provides a
useful example of the
importance of associating time
with
returns.
In January 1928, Julia Ford
Bundy Blue, a widow of one of
the founders of
international
business machines, bequeathed 100
shares of IBM trust on behalf of
a
retirement
home Altadena, California. At
that time and the stock
sold for $123 per share,
making
the bequest worth $12,300.
66 years later the trust
dissolved and paid $4.5
million
to
the retirement home. The
Associated Press reported this
story with the headline,
"66 year
old
IBM stock yields 36,600 percent."
The headline creates two
problems here. First is
the
incorrect
use of the terms yield.
Increase in principle value is
not part of yield. Second,
the
appreciation
occurred over 66 years, so the
36,600% figure needs to be
translated to frame
of
reference terms. A fund that
began with a value of $12,300 and 66
years later was worth
$4.5
million showed a compound
annual return of 9.35% per
year over the same
period. The
latter
figure, however, does not
make headlines.
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