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71
Lecture Notes 9
Introduction to Capital Markets
Returns on stock
• There are two components to the return on stocks. First, most, but not all stocks, pay a cash
div
idend
usually once a quarter. Second, the price of a stock can change from one year to the next.
The change in the stock price is also part of the return whether or not the
capital gain or loss
is
actually
realized
. Someone who does not realize their gain can be considered to have reinvested
their income in the stock.
• For a dividend
D
t
+1
paid at the end of the current period, and using
P
t
for the price of the stock,
the total percentage return on a stock can be written
(1)
• When one examines the longer term return on a range of different stocks or portfolios of stocks
one finds that, in general, those assets or portfolios with the highest
variation
in returns from one
year to the next also tend to have the highest
average
return. Here the average return is calculated
as follows. Suppose the percentage returns over
T
years were
R
1
,
R
2
,
R
3
, …,
R
T
. The
average
per
centage return
R
would then be
1
(2)
Returns on bonds
• Government bonds are usually regarded as the
least risky
type of bond. Since the government has
1.
Note that this
arithmetic average
differs from the
geometric average
which can be defined as the constant rate of
return that would have produced the same
total
return over the
T
years as the actual
holding return
obtained over that
period. Specifically, the geometric average return
R
is given by
R
t
1
+
D
t
1
+
P
t

P
t
1
+
P
t
–
()
P
t

+
=
1
R
+
T
1
R
1
+
1
R
2
+
&
1
R
T
+
1
R
t
+
t
1
=
T
∏
==
R
R
1
R
2
&
R
T
+++
T

1
T

R
t
t
1
=
T
∑
≡
=
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the legal right to take resources (through taxes) to pay off its obligations, it is commonly believed
that there is no
default risk
for government debt.
2
• The lack of default risk does not, however, make government debt riskless. Longer term govern
ment bonds are issued with a
coupon payment
that will guarantee, at the time the bond is sold,
that an investor can earn a fixed nominal return by holding the bond to maturity. Shorter term
Treasury Bills (or TBills) are auctioned once a week and are typically pure discount bonds. Giv
en the auction price, an investor can also guarantee the return on TBills by holding them to ma
turity, at which point they are redeemed by the Treasury for their face value. The return on both
TBills and longer term government bonds is not fixed in advance, however, if neither type of
bond is held to maturity. If interest rates change before the bond matures the market price of the
bond will change so that the effective return matches the new market interest rate. An increase in
interest rates will lead to a fall in the price of the bond and vice versa.
• Furthermore, even if a bond is held to maturity, its expost
real
return will vary if the
inflation
rate
varies. Variability in the inflation rate therefore raises the risk associated with investing in
government bonds and makes them less attractive to risk averse investors.
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This note was uploaded on 12/20/2011 for the course ECON 448 taught by Professor Bejan during the Spring '06 term at Rice.
 Spring '06
 Bejan

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