Question

Consider a Maxi bank with the following balance sheet (M means million):

Assets	Value	Duration of the Asset	Convexity of the Asset
5yr bond bought at a yield of 3.4% (lending money)	$550M	4.562	12.026
12yr bond bought at a yield of 4% (lending money)	$800M	9.453	53.565

Liabilities	Value	Duration of the Liability	Convexity of the Liability
2yr bond sold at a yield of 2.4% (borrowing money)	$300M	1.941	2.384
4yr bond sold at a yield of 2.8% (borrowing money)	$500M	3.759	8.206

1. Calculate the duration and convexity of the both asset and liability sides;

2. If the interest rates go up by 1%, using the duration and convexity rule to determine the net worth of the bank and the equity to asset ratio;

3. In c)’s scenario, to maintain the equity to asset ratio at 40% which is required by the regulation, the bank decides to raise cash (zero duration and zero convexity) from the equity holders. How much cash does the bank need to raise?

Answer 1

Answer :

(b).

Year	Value	Weight	Duration	Effective duration	Convexity	Effective convexity
Asset	-	-	-	-	-	-
	A	X	B	X*B	C	X*C
5	500	38%	4.562	1.75	12.03	4.63
12	800	62%	9.453	5.82	53.57	32.97
-	1300	-	-	7.57	Total	37.59
Liabilities	-	-	-	-	-	-
2	300	38%	1.941	0.73	2.38	0.89
4	500	63%	3.759	2.35	8.21	5.13
-	800	-	-	3.08	Total	6.02

(c).

Year	Yield %	Change	Value	Duration	Convexity	Bond price	(t^2)/2	New bond price
Assets	-	-	-	-	-	-	-	-
		t	A	B	C	M = A*B	-	-
5	3.40	1	500	4.562	12.03	2281	0.5	5590.731
12	4.00	1	800	9.453	53.57	7562.4	0.5	138615.0108
-	-	-	1300	-	Total	9843.4	-	144205.7418
Liabilities	-	-	-	-	-	-	-	-
2	2.4	1	300	1.941	2.38	582.3	0.5	146.1573
4	2.8	1	500	3.759	8.21	1879.5	0.5	2526.048
-	-	-	800	-	Total	2461.8	-	2672.2053

Total Assets	9843.4	144205.7418
Total Liabilities	2461.8	2672.2053
Balannce	7381.6	141533.537

(d).

Year	Yield %	Change	Value	Duration	Convexity	Bond price	(t^2)/2	New bond price
Assets	-	-	-	-	-	-	-	-
-	-	t	A	B	C	M=A*B	-	-
5	3.40	1	500	43562	12.03	2281	0.5	5590.731
12	4.00	1	800	9.453	53.57	7562.4	0.5	138615.0108
-	-	-	1300	-	Total	9843.4	-	144205.7418
Liabilities	-	-	-	-	-	-	-	-
2	2.4	1	300	1.941	2.38	582.3	0.5	146.1573
4	2.8	1	500	3.759	8.21	18779.5	0.5	2526.048
-	-	-	800	-	Total	2461.8	-	2672.2053

Total Assets	9843.4	144205.7418
Total Liabilities	2461.8	2672.2053
Balannce	7381.6	141533.537

Old equity to asset ratio = $141,533.537 / $144,205.7418 = 0.98

Cash to be raised = value of equity - [(New equity to assetf ratio / New equity to asset ratio)*value of equity]

= $141,533.537 - [(0.4 / 0.98)*$141,533.537)

= $83,852 million (rounded off)

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