Log in / Register
Home arrow Economics arrow Bond Math
< Prev   CONTENTS   Next >


Bond prices change from day to day because of the passage of time. We see this in Figure 2.2, where the zero-coupon corporate bond price rises smoothly over time from 60 to 100. The other reason why bond prices change is that, in reality, the yield never is constant. Think of the yield as the investor's required rate of return for holding the bond to its maturity and bearing the default risk. If for some reason investors require a higher (or lower) return for the bond, the price must fall (or rise).

It is useful for analysis to break a corporate bond yield into a benchmark and a spread over (or, perhaps, under) that benchmark. Then changes in the corporate yield are due to changes in the benchmark, changes in the spread, or some combination thereof. In financial markets where there is a deep and liquid government bond market – for example, the U.S. and the U.K. – the obvious benchmark is the Treasury yield for a comparable maturity. In the euro-zone currencies, fixed rates on euro-denominated interest rate swaps are used for the benchmark because the various government bonds trade at varying yields.

Changes in benchmark yields typically reflect macroeconomic events, such as changes in expected inflation, foreign exchange rates, international capital flows, the business cycle, and monetary and fiscal policy. The idea is that these factors impact to varying degrees all market interest rates and all points along the yield curve. Changes in the spread, however, reflect micro- economic factors specific to the particular bond, for instance, its liquidity and tax status and potential losses if the issuer defaults.

Let's now revisit the example in which the investor buys the 10-year corporate zero at 60 and sells the bond two years later at 68. As we saw above, the 2-year horizon yield of 6.357% is higher than the original yield of 5.174% because at sale the 8-year bond is priced to yield only 4.879%. So, why does the yield fall? Perhaps the investor correctly anticipates lower inflation, which later reduces benchmark Treasury yields. Perhaps the investor is fortunate in buying a corporate bond that later is upgraded by the credit rating agencies, thereby reducing the spread over the benchmark. Another possibility is that Treasury yields and corporate spreads do not change at all. Maybe all that happens is that the corporate bond yield curve remains remarkably stable and upward sloping. When the bond is purchased, the 8-year and 10-year yields are 4.879% and 5.174%, and two years later the yield curve has the same shape and level.

The strategy of buying a longer-maturity bond with the intent to sell prior to maturity is known as riding, or rolling down, the yield curve. This can be very attractive when short-term rates are lower than long-term rates. The risk is that yields are higher when the bond needs be sold. To test out this strategy, let's assume that at first 2-year corporate zeros are priced at 95 to yield only 2.581% (s.a.).

The lure of buying the 10-year zero yielding 5.174% is apparent.

A breakeven rate is very useful in assessing the risk in the “maturity extension” strategy. We can use 2.581% to get the sale price at which trying to ride or roll down the yield curve underperforms the more direct horizonmatching alternative. That price turns out to be 63.158.

Note that the 10-year zero would generate 6.454 in interest income over the two years because the price on the constant-yield price trajectory is 66.454. So, the strategy does well as long as the capital loss is no more than 3.296 (= 66.454 – 63.158). That price corresponds to a breakeven yield of 5.827% on 8-year corporate zeros.

The investor's choice so far is: Buy the 2-year zero and lock in a horizon yield of 2.581%, assuming no default, or buy the 10-year zero and achieve a higher rate of return if 8-year yields turn out to be less than the breakeven rate of 5.827%, again assuming no default. If the current 8-year yield is 4.879%, there is a cushion of 94.8 basis points: 5.827% – 4.879% = 0.948%. Obviously, the investor could consider other alternatives as well, for instance, buying the 3-year or 5-year corporate zero. The breakeven rates on those give the investor a full range of maturity choices, each having its own risk profile.

Found a mistake? Please highlight the word and press Shift + Enter  
< Prev   CONTENTS   Next >
Business & Finance
Computer Science
Language & Literature
Political science