4: Valuing Bonds4-2d BOND PrICeS AND INTereST rATeS
A bond’s market price changes frequently as time passes. Whether a bond sells at a discount or a
premium, its price will converge to face value (plus the final interest payment) as the maturity date
draws near. Imagine a bond that matures one day from now. The bond’s final cash flow consists of its face
value plus the last coupon payment. If this payment arrives just one day in the future, you determine
the bond’s price by discounting this payment for one day. Therefore, the price and the final payment are
virtually identical.Interest rate risk
Between the time that a bond is issued and when it matures, a variety of economic forces can change its
price, but the most important factor is the prevailing market interest rate. In turn, the market interest
rate may change as a result of numerous macroeconomic factors such as alterations to the money supply,
inflation expectations and real growth of the economy.
When the market’s required return on a bond changes, the bond’s price changes in the opposite
direction. The higher the bond’s required return, the lower its price, and vice-versa. Interest rate risk is the
risk resulting from changes in market interest rates causing changes in bond prices. How much a bond’s
price responds to changes in required returns (and, therefore, how much interest-rate risk is associated
with a particular bond) depends on several factors, especially the bond’s maturity.
Figure 4.2 shows how the prices of two bonds change as their required returns change. Both
bonds pay a 6% coupon, but one matures in two years, whereas the other matures in 10 years. As the
figure shows, when the required return equals the coupon rate, 6%, both bonds trade at their face
values. However, as the required return increases, the bonds’ prices fall. The decline in the 10-year
bond’s price exceeds that of the two-year bond. Likewise, as the required return decreases, the prices
of both bonds increase. But the 10-year bond’s price increases faster than does that of the two-year
bond. The general lessons are: (1) bond prices and interest rates move in opposite directions; and (2)
the prices of long-term bonds display greater sensitivity to changes in interest rates than do the prices of
short-term bonds.^6Forces Driving Interest-rate risk
Figure 4.2 illustrates the importance of interest-rate risk – the risk that results from changes in market
interest rates moving bond prices. Figure 4.3 shows just how volatile interest rates have been in
Australia. The graph shows the historical YTM on 10-year Australian government bonds for the period
1971–2015.^7 The yields offered by these bonds peaked in 1981 at almost 14%, but recently Treasury
bond yields have been much lower. The point of the graph is simple: because interest rates fluctuate
widely, investors must be cognisant of the interest-rate risk inherent in these instruments.6 Another, more technical factor affecting the bond price changes in response to changes in interest rates is the magnitude of the coupon rate.
All else being equal, the value of a bond with a lower coupon rate will be more responsive to changes in interest rates than will a bond with
a higher coupon rate. This occurs because a given change in interest rates – say, 1% – would represent a greater percentage rate change for
a low coupon bond (for example, 16.7% [1%/6%] change for a 6% coupon bond) than for a higher coupon bond (for example, 12.5% [1%/8%]
change for an 8% coupon bond).
7 We discuss the specific features of Treasury securities later in this chapter. The line in Figure 4.3 shows what the YTM was on a newly
issued 10-year Treasury bond in each year from 1981 to 2015. In other words, at each point on the graph, you are looking at the yield on a
bond with a constant maturity of 10 years.LO4.3
interest rate risk
The risk resulting from
changes in market interest
rates causing fluctuations in
a bond’s price. Also, the risk
of suffering losses as a result
of unanticipated changes in
market interest rates