Question

Alright Insurance has total assets of $140 million consisting of $50 million in 2-year, 6 percent Treasury notes, and $90 million in 10-year, 7.2 percent fixed-rate Baa bonds. These assets are funded by $100 million 5-year, 5 percent fixed-rate GICs, and equity. Market interest rates are expected to increase by 1 percent to 11 percent in the next year. If this occurs, what will be the effect on the market value of equity of Alright?

Answer 1

Firstly we need to calculate duration of each security to calculate expected changes in market value as result of increase in market ineterest rate.

Price of debt security decreased with increase in market interest rate.

So let calculate duration

Average duration of assets	1.94 (50/140) + 7.18 (90/140)-4.49(100/140)
	2.10 years

Change in market value	duration * total value * change in ineterst rate/ 1.1 = 2.10 * 140 M *0.01/1.1
Change in market value	= - 2.674546 M

Hence market value will be decreased by  - 2.674546 M due to increase in market interest rate by 1%

Working Note Calculation of Duration

50,000,000	6%
Year	Interest	PV @ 10%	PV	PV * Year
1	3,000,000	0.9091	2,727,273	2,727,273
2	3,000,000	0.8264	2,479,339	4,958,678
2	50,000,000	0.8264	41,322,314	82,644,628
		Current value	46,528,926	90,330,579
		Duration= (cumulative PV * year)/ (current value)	90330579/ 46528926	1.94
90,000,000	7.2%
Year	Interest	PV @ 10%	PV	PV * Year
1	6,480,000	0.9091	5,890,909	5,890,909
2	6,480,000	0.8264	5,355,372	10,710,744
3	6,480,000	0.7513	4,868,520	14,605,560
4	6,480,000	0.6830	4,425,927	17,703,709
5	6,480,000	0.6209	4,023,570	20,117,851
6	6,480,000	0.5645	3,657,791	21,946,746
7	6,480,000	0.5132	3,325,265	23,276,852
8	6,480,000	0.4665	3,022,968	24,183,743
9	6,480,000	0.4241	2,748,153	24,733,373
10	6,480,000	0.3855	2,498,321	24,983,205
10	90,000,000	0.3855	34,698,896	346,988,960
		Current value	74,515,691	535,141,652
		Duration= (cumulative PV * year)/ (current value)	535141652/ 74515691	7.18
100,000,000	5%
Year	Interest	PV @ 10%	PV	PV * Year
1	5,000,000	0.909090909	4,545,455	4,545,455
2	5,000,000	0.826446281	4,132,231	8,264,463
3	5,000,000	0.751314801	3,756,574	11,269,722
4	5,000,000	0.683013455	3,415,067	13,660,269
5	5,000,000	0.620921323	3,104,607	15,523,033
5	100,000,000	0.620921323	62,092,132	310,460,662
		Current value	81,046,066	363,723,603
		Duration= (cumulative PV * year)/ (current value)	363723603 / 81046066	4.49