Question

Consider a 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

If the yield rate go up by 1%, using the duration and convexity rule to determine the net worth of the bank and the equity to asset ratio;

PLEASE EXPLAIN HOW TO FIND THE NEW BOND PRICE & MENTION THE FORMULA USED CLEARLY

NEW YIELD RATE CALCULATION

Answer 1

duration and convexity approach = --Duration * % change in Y + 1/2 * convexity * (% change in Y) ^ 2   

Liability  

2yr bond

--1.941 * 1% + 1/2 * 2.384 * 1%^2 = 1.92% (Bond price will fall by 1.92%) value = ( $294.24 M )

4 yr bond

--3.759 * 1% + 1/ 2 * 8.206 * 1%^2 = 3.717% ( Bond price will fall by 3.717%) value = ( $481.41M )

ASSET

5 yr

--4.562 * 1% + 1/2 * 12.026* 1%^2 = 4.50% ( Bond price will fall by 4.50% ) value = ( $ 525.25 M)

12 yrs

--9.453 * 1% + 1/2 * 53.565 * 1%^2 = 9.185% ( Bond price will fall by 9.185% ) Value = ( $ 726.52M )

networth = ASSET -- LIABILITIES

1251.77M -- 775.62M = 476.15M

Equity asset ratio

equity / asset

476.15M / 1251.77M

= 38%