Question

What is the modified duration of a three-year $1,000 par value bond with a 5% coupon paid semi- annually that is priced to yield 4%? 2.61 5.37 2.77 5.65 Question 6 4 pts You own two bonds. You have $2,000,000 in Bond A which has a modified duration of 8.14. You have $2,250,000 in Bond B which has a modified duration of 4.23. If rates rise by 50 basis points, what would be the approximate impact of the value of your portfolio? Gain $64,493.75 Lose $96,487.50 Gain $96,487.50 Lose $64,493.75

Answer 1

Modified duration is calculated below:

Period	Payment time	CF	Discount factor	PV	Weight	Weight x payment time
1	0.50	25	1/(1+0.04/2)^1=0.9804	25x0.9804=24.51	24.51/1028.007=0.024	0.012
2	1.00	25	1/(1+0.04/2)^2=0.9612	25x0.9612=24.029	24.029/1028.007=0.023	0.023
3	1.50	25	1/(1+0.04/2)^3=0.9423	25x0.9423=23.558	23.558/1028.007=0.023	0.034
4	2.00	25	1/(1+0.04/2)^4=0.9238	25x0.9238=23.096	23.096/1028.007=0.022	0.045
5	2.50	25	1/(1+0.04/2)^5=0.9057	25x0.9057=22.643	22.643/1028.007=0.022	0.055
6	3.00	1025	1/(1+0.04/2)^6=0.888	1025x0.888=910.171	910.171/1028.007=0.885	2.656
				Sum of all PV = 1028.007	Macaulay duration = sum of weighted payments	2.826
					Modified duration = Macaulay's duration/(1+YTM/n)	2.826/(1+0.04/2) = 2.770

So the modified duration is 2.77 and the correct option is option 4

q6) First of all when interest rate rises, the price of the bond falls so the two options which say we will get a gain can be eliminated

Next the duration indicates the change in the portfolio value to a 100 bps or 1% change in the interest rate, here we are given the change in interest rate as 50bps so we need to divide the duration percents by 2

So the duration bond value calculation is as follows:

Bond	Value	Duration	1% Change
A	2000000	0.0814	-0.0814 x 2000000 = -162800
B	2250000	0.0423	-0.0423 x 2250000 = -95175
		Total change	-162800-95175 = -257975
		Change for 50BPS	-257975/4 = - 64493.75

So the correct option is 4th one

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