In: Finance
Consider the following two banks: Bank 1 has assets composed solely of a 10-year, 14.00 percent coupon, $3.0 million loan with a 14.00 percent yield to maturity. It is financed with a 10-year, 10 percent coupon, $3.0 million CD with a 10 percent yield to maturity. Bank 2 has assets composed solely of a 7-year, 14.00 percent, zero-coupon bond with a current value of $2,677,410.23 and a maturity value of $6,699,600.06. It is financed by a 10-year, 8.25 percent coupon, $3,000,000 face value CD with a yield to maturity of 10 percent. All securities except the zero-coupon bond pay interest annually. a. If interest rates rise by 1 percent (100 basis points), what is the difference in the value of the assets and liabilities of each bank? (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places. (e.g., 32.16))
As a first step let's calculate the modified duration of each of the two sides of the balance sheet. I have used the excel function namely DURATION and MDURATION to get the output. Please see the table below:
Type | Settlement | Maturity | Coupon | Yield | Frequency | Basis | Duration | Modified Duration |
A | B | C | D | E | F | '=DURATION(A,B,C,D,E,F) | '=MDURATION(A,B,C,D,E,F) | |
Bank 1 | ||||||||
Asset | 1/1/2019 | 1/1/2029 | 14.000% | 14.00% | 1 | 1 | 5.95 | 5.22 |
Liabilities | 1/1/2019 | 1/1/2029 | 10.000% | 10.00% | 1 | 1 | 6.76 | 6.14 |
Bank 2 | ||||||||
Asset | 1/1/2019 | 1/1/2026 | 0.000% | 14.00% | 1 | 1 | 7.00 | 6.14 |
Liabilities | 1/1/2019 | 1/1/2029 | 8.250% | 10.00% | 1 | 1 | 7.00 | 6.37 |
%age change in the value of a security = - modified duration x %age change in interest rate
%age change in interest rate = + 100 bps = + 1.00%
Since all the instruments of Bank 1 have yield to maturity same as the coupon rate, their market value will be same as their respective face value.
For Bank2, market value of the liability = -PV (Rate, period, pmt, FV) = - PV (10%, 10, 8.25% x 3000000, 3000000) = 2,677,410.23
Type | Market value | % change | New Value |
Bank 1 | A | B | C = A x (1 + B) |
Asset | 3,000,000.00 | -5.22% | 2,843,516.53 |
Liabilities | 3,000,000.00 | -6.14% | 2,815,662.99 |
Difference | 27,853.54 | ||
Bank 2 | |||
Asset | 2,677,410.23 | -6.14% | 2,513,007.85 |
Liabilities | 2,677,410.23 | -6.37% | 2,506,931.26 |
Difference | 6,076.59 |
The difference in the value of the assets and liabilities of each bank:
Bank 1 = $ 27,853.54
Bank 2 = $ 6,076.59