A bank has DA = 2.5 years, DL= 0.80 years, and k = 92%. Assets are...

A bank has DA = 2.5 years, DL= 0.80 years, and k = 92%. Assets are equal to $1,200 million. According to the duration gap model, find the change in the direction and magnitude of interest rate that would make the institution insolvent if rates are currently 5 percent?

please answer in excel format

Expert Solution

Ans	Assets	$1200
	K	92%
	D_A	2.5
	D_L	0.8
	R	5%
	In order to find the change in direction and magnitude of interest rate, we solve the following equation:

	*= - (1-K) Assets = - [DA - (KDL) Assets * Change in interest/(1+interest rate)**
	= - (1-0.92) * 1200 = -[2.5 - (0.920.80)1200*Change in interest/ (1.05)
	Solving for change in interest we get,
	LHS	-96
	RHS	= -[2.5 - (0.920.80)1200*Change in interest/ (1.05)
	Equating LHS = RHS
	-96	= - [ 2.5 - (883.20 * change in interest / 1.05)]
	96	=2.50 - [883.20 *change in interest/1.05]
	Change in interest = 0.0476 or 476 basis points

Assets	$1200
K	0.92
D_A	2.5
D_L	0.8
R	0.05
In order to find the change in direction and magnitude of interest rate, we solve the following equation:
*= - (1-K) Assets = - [DA - (KDL) Assets * Change in interest/(1+interest rate)**
= - (1-0.92) * 1200 = -[2.5 - (0.920.80)1200*Change in interest/ (1.05)
Solving for change in interest we get,
LHS	=- (1-0.92) * 1200
RHS	= -[2.5 - (0.920.80)1200*Change in interest/ (1.05)
Equating LHS = RHS
-96	= - [ 2.5 - (883.20 * change in interest / 1.05)]
96	=2.50 - [883.20 *change in interest/1.05]
Change in interest = 0.0476 or 476 basis points

jeff jeffy answered 2 years ago

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