A bond currently sells for $950 based on a par value of $1,000 and promises $100 in interest for three years before being retired. Yields to maturity on comparable-quality securities are currently at 12 percent. What is the bond’s duration? Suppose interest rates in the market fall to 10 percent.

Question

A bond currently sells for $950 based on a par value of $1,000 and promises $100 in interest for three years before being retired. Yields to maturity on comparable-quality securities are currently at 12 percent. What is the bond’s duration? Suppose interest rates in the market fall to 10 percent. What will be the approximate percent change in the bond’s price?

Accepted Answer

		Present	Present
		Value	Value of	Weight
Year	Cash	Factor	Cash	Of Each	Duration
	Flow	at 12%	Flow	Cash Flow	Components
1	$100	0.893	$89.30	(89.30/950) = 0.0940	0.094
2	100	0.797	79.7	(79.70/950) = 0.0839	0.1678
3	1100	0.712	783.2	(783.20/950) = 0.8244	2.4733
					2.7351 years

Clearly the bond's duration is 2.7351 years. If interest in the market fall to 10 percent, the approximate percentage change in the bond's price will be:

Percentage Change in Price = [latex]- D imes \frac{\Delta i }{(1+ i )} imes 100 \%[/latex]

[latex]=-2.7351 imes \frac{-.02}{(1+.12)} imes 100 \%=4.884 ext { percent }[/latex]

Question 10.22: A bond currently sells for $950 based on a par value of $1,0...

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