Rate of Return versus Yield to Maturity
Our 6 percent coupon bond with maturity 2002 currently
has 3 years left until maturity and sells today for $1,010.77. Its yield to
maturity is 5.6 percent. Suppose that
by the end of the year, interest rates have fallen and the bond s yield to
maturity is now only 4 percent. What will be the bond s rate of return? At the end of the year, the bond will have
only 2 years to maturity. If investors then demand an interest rate of 4
percent, the value of the bond will be
You invested $1,010.77. At the end of the year you
receive a coupon payment of $60 and have a bond worth $1,037.72. Your rate of
return is therefore The yield to
maturity at the start of the year was 5.6 percent. However, because interest
rates fell during the year, the bond price rose and this increased the rate of return.
Is there any connection
between yield to maturity and the rate of return during a particular period?
Yes: If the bond s yield to maturity remains
unchanged during an investment period, its rate of return will equal
that yield. We can check this by assuming that the yield on 6 percent Treasury bonds stays at 5.6 percent. If
investors still demand an interest rate of 5.6 percent at the end of the year,
the value of the bond will be
At the end of the year you receive a coupon payment of
$60 and have a bond worth $1,007.37, slightly less than you paid for it. Your
total profit is $60 + ($1,007.37
$1,010.77) = $56.60. The return on your investment is therefore
$56.60/$1,010.77 = .056, or 5.6 percent, just equal to the yield to maturity.
When interest rates do not change, the bond price changes
with time so that the total return on the bond is equal to the yield to
maturity. If the bond s yield to
maturity increases, the rate of return during the period will be less than that
yield. If the yield decreases, the rate of
return will be greater than the yield.
The solid curve in Figure 3.5 plots the price of a
30-year maturity, 6 percent Treasury bond over time assuming that its yield to
maturity remains at 5.6 percent. The
price declines gradually until the maturity date, when it finally reaches face
value. In each period, the price decline offsets the coupon income by just enough to reduce total return to 5.6
percent. The dashed curve in Figure 3.5 shows the corresponding price path for
a low- coupon bond currently selling at a discount to face value. In this case,
the coupon income would provide less than a competitive rate of return, so the bond sells below par. Its price
gradually approaches face value, however, and the price gain each year brings
its total return up to the market interest rate.
Category: Cash flows
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