How Do I Calculate Interest Rate Sensitivity on Bonds?

A bond is a loan. When you buy one, you pay the current price of the bond in return for periodic interest payments, or "coupon payments," and return of the bond's face value at a specified maturity. For example, a 10-year, 6 percent bond with a face value of $1,000 will pay you interest of $60 a year until maturity in 10 years, and then pay you the face value of $1,000. Rate sensitivity measures how much the price of the bond would change due to interest rate changes, which is important if you plan to sell the bond before maturity. On the day of maturity, the price will always equal the face value.

How Do I Calculate Interest Rate Sensitivity on Bonds?
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Bond Prices

To understand rate sensitivity, you first must understand how interest rates affect bond prices. A typical bond pays a fixed amount of interest each year, called the annual coupon, until maturity. If prevailing interest rates rise after the bond is issued, newer bonds will pay higher coupons than the older one. Since the older bond is now less desirable than the new ones, its price falls. This is the general rule: When interest rates go in one direction, bond prices go in the other. Interest rate sensitivity tells you how much the bond price will change.

Current Yield

One other important term to understand is yield. The current yield on a bond is its annual coupon divided by its current price. If the current price is equal to the face value, which is often the case for newly issued bonds, then the yield is equal to the fixed interest rate of the bond. A 6 percent bond with a face value of $1,000 and a price of $1,000 will have a current yield of 6 percent. A higher price would lower the yield; a lower price would raise the yield. For example, if the price fell to $960, the yield would rise to $60/$960, or 6.25 percent.

Sensitivity Calculation

There are several ways to measure interest rate sensitivity. A set of related calculations, known as duration, require extensive computations. But you can get a good estimate of sensitivity by remembering that if interest rates change by 1 percentage point, a bond's price will change in the opposite direction by about 1 percent for each year until maturity.

Example Calculations

Consider what would happen, if prevailing interest rates were to rise 1 percentage point, to a bond with 10 years until maturity and a current yield of 6 percent. The bond price would drop by 4 percent, which is the sum of a 1 percent drop per year for 10 years plus the current yield of 6 percent, or [(-0.01/year * 10 years) + 0.06]. If the bond price had been $1,000, its new price after the interest rate rise would drop by (-0.4 * $1,000) or $40, to $960.

By comparing the sensitivity of different bonds to interest rate changes, you know how exposed you would be to sudden changes in prevailing interest rates. For example, if you are worried that interest rates might rise, you might select shorter-term bonds, because they are less sensitive. If the example bond had a 3-year maturity and a yield of 2 percent, the bond would lose only [(-0.01/year * 3 years) + 0.02] or -1 percent, for a new price of [$1,000 + ($1,000 * -0.01)], or $990.

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