A 6% coupon bond paying interest annually has a modified duration of 10 years, sells for $800, and is priced at a yield to maturity of 8%. If the YTM increases to 9%, what is the predicted dollar change in price based on the bond’s duration?

(Round to 2 decimal places.)

Question

A 6% coupon bond paying interest annually has a modified duration of 10 years, sells for $800, and is priced at a yield to maturity of 8%. If the YTM increases to 9%, what is the predicted dollar change in price based on the bond’s duration?

(Round to 2 decimal places.)

BlackTom AI · Accepted Answer

To estimate how much the bond’s price will change when yields rise, we can use the duration approximation.

First, note the key inputs: the bond has a modified duration (Macaulay duration adjusted for yield) of 10 years, its current price is $800, and the yield to maturity increases from 8% to 9%, which is a change in yield Δy = 0.01 (or 1 percentage point).

The basic duration rule of thumb is: ΔP ≈ -Duration × Δy × P. Here, Duration is 10 years, Δy is 0.01, and P is 800.

Compute the product: Duration × Δy = 10 × 0.01 = 0.10. Then multiply by the price: 0.10 × 800 = 80. The negative sign reflects the inverse relationship between yield and price.

Therefore, ΔP ≈ -80.00. This means the bond’s price is predicted to drop by about $80 when the yield increases by 1 percentage point, given the duration assumption.

If you compare this to the provided numerical answer, the magnitude is 80.00 and the sign is negative, indicating a price decrease in response to higher yields.

Keep in mind that this is an approximation that assumes small changes in yield and linear behavior around the initial yield; actual price change may differ slightly due to convexity and other factors.

A 6% coupon bond paying interest annually has a modified duration of 10 years, sells for $800, and is priced at a yield to maturity of 8%. If the YTM increases to 9%, what is the predicted dollar change in price based on the bond’s duration? (Round to 2 decimal places.)Numerical

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