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I have the following question from Hull, problem 6.14:


A five-year bond with a yield of 11% (continuously compounded) pays an 8% coupon at the end of each year.

(c) Use the duration to calculate the effect on the bond’s price of a 0.2% decrease in its yield.


The solution is as follows:

Since, with the notation in the chapter $$\begin{align}\Delta B & = -BD\Delta y \qquad (1)\end{align}$$ the effect on the bond’s price of a 0.2% decrease in its yield is: $$\$86.80\times4.256\times 0.002 = 0.74$$


However the bonds price B is \$86.80, and the $\Delta y$ indicates a change, where by notation a decrease is negative, and an increase is positive. So based from this, and using formula (1) shouldn't the equation be:

$$-\$86.80 \times 4.256 \times(-0.002) = 0.74$$


Question:

Is this a mistake in the text book, or is my approach incorrect?

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Highly off-topic, but you are correct. The book however is not wrong, the authors just canceled out the negatives to provide short solutions. The solutions tend to be rather brief if i remember correctly.

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