Question

National Tiny Bank (NTB) has $12,000 in total assets. Its asset portfolio currently has a duration of 4 years. NTB is considering buying a three year Treasury security that has a 7% annual coupon. (1) If the market value of the security is currently $875, what is the duration of the Treasury security? (2) If NTB buys the security, what will be the new duration of its asset portfolio?

Answer 1

1)
Duration is the average waiting time for receiving the cash flow from a bong, also known as Macaulay Duration
YTM = (Interest + ((Face Value - Current Price)/time)) / ((Face Value + Current Price)/2)
Face Value = 1000
Current Price = 875
Interest 7% i.e. 70
N = 3years
YTM = (70 + ((1000 - 875)/3)) / (1000 + 875)/2
YTM = 11.91%
Year(A)	Cash Flow(B)	PV of Cash flow @ 11.91% (C=(B/1.1191^A))	Weighted Time(D=A*C)
1	70	62.55	62.55
2	70	55.89	111.79
3	1070	763.44	2290.33
	Total	881.89	2464.67
Duration = 2464.67/881.89
Duration of Treasury Security= 2.79 years
2)
Duration of New portfolio will be calculated as a weighted average of Current assets and Treasury Security
	Assets	Value	Weight(of Total)(A)	Duration(B)	Average(C=A*B)
	Current Assets	12000	0.93	4.00	3.73
	Treasury Security	875	0.07	2.79	0.19
		12875			3.92
	Duration of new portfolio = 3.92 years