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Bonds and Treasuries

What is the relationship between interest rates and bond prices?

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2009-04-05 22:35:30
2009-04-05 22:35:30

There is an inverse relationship between price and yield: when interest rates are rising, bond prices are falling, and vice versa. The easiest way to understand this is to think logically about an investment. You buy a bond for $100 that pays a certain interest rate (coupon). Interest rates (coupons) go up. That same bond, to pay then-current rates, would have to cost less: maybe you would pay $90 the same bonds if rates go up. Ignoring discount factors, here is a simplified example, a 1-year bond. Let's say you bought a 1-year bond when the 1-year interest rate was 4.00%. The bond's principal (amount you pay, and will receive back at maturity) is $100. The coupon (interest) you will receive is 4.00% * $100 = $4.00. Today: You Pay $100.00 Year 1: You receive $4.00 Year 1 (Maturity): You Receive $100 Interest Rate = $4.00 / $100.00 = 4.00% Now, today, assume the 1-year interest rate is 4.25%. Would you still pay $100 for a bond that pays 4.00%? No. You could buy a new 1-year bond for $100 and get 4.25%. So, to pay 4.25% on a bond that was originally issued with a 4.00% coupon, you would need to pay less. How much less? Today: You Pay X Year 1: You Receive $4.00 Year 1 (Maturity): You Receive $100 The interest you receive + the difference between the redemption price ($100) and the initial price paid (X) should give you 4.25%: [ ($100 - X) + $4.00 ] / X = 4.25% $104 - X = 4.25% * X $104 = 4.25% * X + X $104 = X (4.25% + 1) $104 / (1.0425) = X X = $99.76 So, to get a 4.25% yield, you would pay $99.75 for a bond with a 4.00% coupon. In addition to the fact that bond prices and yields are inversely related, there are also several other bond pricing relationships: * An increase in bond's yield to maturity results in a smaller price decline than the price gain associated with a decrease of equal magnitude in yield. This phenomenon is called convexity. * Prices of long term bonds tend to be more sensitive to interest rate changes than prices of short term bonds. * For coupon bonds, as maturity increases, the sensitivity of bond prices to changes in yields increases at a decreasing rate. * Interest rate risk is inversely related to the bond's coupon rate. (Prices of high coupon bonds are less sensitive to changes in interest rates than prices of low coupon bonds. Zero coupon bonds are the most sensitive.) * The sensitivity of a bond's price to a change in yield is inversely related to the yield at maturity at which the bond is now selling.

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