FIN $629-$ Asset Liability Management Home Work $4$

Problem $1$

Consider the following two banks:

$$ Bank A has assets composed solely of a $14-$year, zero$-$coupon bond with a current

value of $$1,000,000$ and a maturity value of $$1,800,000.$ It is financed by a $12-$year, $9\%$

coupon, $$1,000,000$ face value bond to yield $9\mathrm{.}5\%$ return.

$$ Bank B has assets composed solely of a $14-$year, $10\%$ coupon, $$1\mathrm{.}7$ million bond with a

$11\%$ yield to maturity. It is financed with a $16-$year, zero$-$coupon bond with a current

value of $$1,500,000$ and a maturity value of $$3,100,000.$

All securities$,$ accept the zero$-$coupon bond, pay interest semi$-$annually and the zero$-$

coupon bond has semi$-$annual compounding period. Suppose that interest rates are

expected to rise by $0\mathrm{.}75\%(75$ basis points$).$

a$)$ How do the values of the assets and liabilities of each bank change with changes in

the interest rate?

Problem $2$

Consider the following two banks:

$$ Bank $1$ has assets composed solely of a $12-$year, $12\%$ coupon, $$1$ million bond with a

$12\%$ yield to maturity. It is financed with a $12-$year, $10\%$ coupon, $$1$million bond with a

$10\%$ YTM$.$

$$ Bank $2$ has assets composed solely of a $9-$year, $12\%,$ zero$-$coupon bond with a current

value of $$894,006\mathrm{.}20$ and a maturity value of $$1,976,362\mathrm{.}88.$ It is financed by a $12-$year,

$8\mathrm{.}275\%$coupon, $$1,000,000$ face value bond with a yield to maturity of $10\%.$

All securities$,$ accept the zero$-$coupon bond, pay interest semi$-$annually and the zero$-$

coupon bond has semi$-$annual compounding period.

a$)$ If interest rates rise by $1\%($or $100$ bps$).$ How do the values of the assets and liabilities

of each bank change?

Problem $3$

Suppose that you are long in $4-$year bonds and you want to use $3-$year bonds to hedge

the interest rate risk. The data on these bonds are

Bond Yield Duration Volatility $(\%)$

$3-$year $0\mathrm{.}102\mathrm{.}752\mathrm{.}50$

$4-$year $0\mathrm{.}103\mathrm{.}523\mathrm{.}20$

To hedge the long position in $4-$year bond, we need to sell $3-$year bond. How much to

sell?

Problem $4$

Following are the given data for Bank A$.$ It is assumed that the profit margin of bank is derived

from the rate$-$sensitive assets and liabilities only. The current interest rate in market is $13\%,$ but

it is estimated to fall by $1\%.$ With a view of integrated bank management, show how changes in

interest rates affect the ROE of banks. Interpret the change in ROE due to the change in interest

rate.

A ROE of Bank decreased due to changes in interest rate.

B ROE of Bank had no effect due to changes in interest rate.

C ROE of Bank is zero to changes in interest rate.

D ROE of Bank increased due to changes in interest rate.

Problem $5$

ASSETS $($$$)$ LIABILITIES $($$$)$

Required reserve $1,504$ Demand deposits $1,309$

Commercial loan: NOW accounts $1,150$

Floating$-$rate $1,200$ MMDAs $1,800$

Fixed$-$rate $507$ CDs:

Consumer loan $3,002$ Short$-$term $150$

Mortgages: $1-5$ years

Floating$-$rate $1,200$ Long$-$term bonds $704$

Fixed$-$rate $703$ capital $2,900$

Treasury securities:

Short$-$term $1,900$

Long$-$term $1,005$

Bank deploys a deposit of $$1,005,000\mathrm{.}00$ for $1$ year at $4\mathrm{.}5\%($floating rate$)$ in a car loan for

$$1,000,000\mathrm{.}00,$ with repayment of $4$ years and interest $9\mathrm{.}17\%$ fixed rate. Calculate the net

interest income.

A The net interest increased income is $$47,159.$

B The net interest increased income is $$47,168.$

C The net interest increased income is $$47,145.$

D The net interest increased income is $$47,149.$