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Consider a two-year bond with a yield to maturity of 7% and an annual coupon rate of 5%. The bond is currently traded at $96.38, and the duration of the bond is 1.95 years. If the bond's yield to maturity changes to 11%, estimate its price change by using its duration.

Question

Consider a two-year bond with a yield to maturity of 7% and an annual coupon rate of 5%. The bond is currently traded at $96.38, and the duration of the bond is 1.95 years. If the bond's yield to maturity changes to 11%, estimate its price change by using its duration.

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Solution

To estimate the price change of the bond using its duration, we can use the formula for the duration approximation of the price change:

ΔP/P = -D * ΔY

Where: ΔP/P is the percentage change in price, D is the duration of the bond, ΔY is the change in yield to maturity.

First, we need to calculate the change in yield to maturity (ΔY). The yield to maturity changes from 7% to 11%, so ΔY = 11% - 7% = 4% = 0.04.

Then, we can substitute the values into the formula:

ΔP/P = -1.95 * 0.04 = -0.078

So, the percentage change in price is -7.8%.

Finally, to find the price change (ΔP), we multiply the percentage change by the initial price of the bond:

ΔP = -7.8% * 96.38=96.38 = -7.52

So, if the bond's yield to maturity changes to 11%, its price is estimated to decrease by $7.52.

This problem has been solved

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