THE ECONOMICS OF MONEY,BANKING, AND FINANCIAL MARKETS 104

72

PA R T I I

APP LI CAT IO N

Financial Markets

Calculating the Rate of Return
What would the rate of return be on a bond bought for $1000 and sold one year
later for $800? The bond has a face value of $1000 and a coupon rate of 8%.

Solution

The rate of return on the bond for holding it one year is ,12%.
RET +

C + Pt +1 , Pt
Pt

where
C
+ coupon payment + $1000 * 0.08 + $80
Pt * 1 + price of the bond one year later + $800
Pt
+ price of the bond today
+ $1000
Thus
RET +

$80 + ($800 , $1000)

, $120
+
+ , 0.12 + ,12%
$1000
$1000

A convenient way to rewrite the return formula in Equation 8 is to recognize
that it can be split into two separate terms:
RET+

Pt + 1 , Pt
C
+
Pt
Pt

The first term is the current yield ic (the coupon payment over the purchase price):
C
+ ic
Pt
The second term is the rate of capital gain, or the change in the bond s price relative to the initial purchase price:
Pt +1 , Pt
+g
Pt
where g + rate of capital gain. Equation 8 can then be rewritten as
RET + ic + g

(9)

which shows that the return on a bond is the current yield ic plus the rate of capital gain g. This rewritten formula illustrates the point we just discovered. Even for

a bond for which the current yield ic is an accurate measure of the yield to maturity, the return can differ substantially from the interest rate. Returns will differ
from the interest rate especially if there are sizable fluctuations in the price of the
bond that produce substantial capital gains or losses.