Question

Consider the following step up security ($1,000 par) with semi-annual coupons (all CFs are at the end of the semi-annual):

Year	1	2	3
Coupon rate	3%	4%	5%

16. Manager B plans to buy the security at middle of year 1 (after the 1st coupon payment) and hold it to maturity with YTM of 4.2%. What is the security’s Mod Duration (in years) at the middle of year 1? Round the final answer to nearest 3 decimals i.e. 1.234.

Answer 1

Mod Duration or Modified Duration refers to the Price Volatality and is given by :

Macaulays duration/Periodic Ytm factor

Now Macaulays duration is the average waiting time for the cash flows of the bond and is given by :

Sigma of PV of cash flows discounted by Ytm×time periods of receiving CF

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Sigma of PV of cash flows discounted at Ytm

Year(x)	cash flows	P.V.at Ytm(w)	Wx
1	15(3/2=1.5%of1000)	15/1.021=14.691	14.691
2	20	19.186	38.371
3	20	18.791	56.373
4	25	23.006	92.023
5	1025	923.837	4919.183
	Total	1000	5120.641
	Macaulays Duration		5120.641/1000
			5.121 half years
			5.121/2=2.561years

Mod duration=2.561/1.021=2.508%