Consider the following two banks: Bank 1 has assets composed solely of a 8-year, 12 percent...

Consider the following two banks:

Bank 1 has assets composed solely of a 8-year, 12 percent coupon, $1 million loan with a 12 percent yield to maturity. It is financed with a 8-year, 10 percent coupon, $900,000 face value CD with a 8 percent yield to maturity.
Bank 2 has assets composed solely of a 10-year, 12 percent, zero-coupon bond with a maturity value of $2,800,000. It is financed with a 9-year, 8.3 percent coupon, $1,000,000 face value CD with a yield to maturity of 10 percent.

All securities except the zero-coupon bond pay interest annually.

What are the durations of the assets and liabilities of each bank?

What are the expected changes in net value of each bank based on durations for a 5% decrease in interest rate in assets and 4% decrease in interest rate in liabilities?

Expert Solution

i). Bank 1: Asset duration = 5.56 years; Liability duration = 5.99 years

Bank 2: Asset duration = 10 years (duration of a zero coupon bond is its time to maturity); Liability duration = 6.55 years

ii). Change in net value of Bank 1 = 25,801

Change in net value of Bank 2 = 187,672

(Calculations shown in the table below)

jeff jeffy answered 6 days ago

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