Question

3. (13 points) Consider a 10 year zero coupon bond trading at a price to produce 5% annual compounding yield of 5%.

Answer 1

Bond Duration would be used to measure the % change in market price due to change in market interest rate
Lets suppose face value of zero coupon bond is 1000
Maculay's duration of zero coupon bonds is always equals to maturity period so in this case maculay's duration is 10 years
Modified duration of zero coupon bond	Maculay's duration/(1+YTM)	YTM =5% Maculay's duration duration = 10 Years	10/(1.05)	9.52
% change in price	-Modified duration*change in interest rate	-9.52%
Price of zero coupon bond =face value/(1+r)^n face value =1000 r =5% n =10	1000/(1.05)^10	613.9133
Change in price	current price*(1-% change in price)	613.91*(1-.0952)	555.47