《商业银行管理》课后习题答案Problem7

Problems

7-1. What kind of futures or options hedges would be called for in the following situations?

a. Interest rates are expected to decline and First National Bank of Canton expects a sharp seasonal rise in loan demand in the upcoming spring quarter.

First National can expect lower loan revenue unless it uses long futures hedges in which contracts for government securities are first purchased and then sold at a profit as security prices rise provided interest rate really do fall. A similar gain could be made using call options on government securities or on financial futures contracts.

b. Silsbee State Bank has interest-sensitive assets of $79 million and interest-sensitive liabilities of $68 million over the next 30 days and market interest rates are expected to fall.

Sislbee State Bank’s interest-sensitive assets exceed its interest-sensitive liabilities by $11 million which means the bank will be open to loss if interest rates fall. The bank could purchase financial futures contracts for subsequent sale or use a call option on government securities or financial futures contracts approximately equal in dollar volume to the $11 million interest-sensitive gap.

c. A survey of Tuskee Bank’s corporate loan customers this month (October) indicates that, on balance, this group of firms will need to draw $155 million from their credit lines in November and D ecember, which is $80 million more than the bank’s management has forecasted and prepared for. The bank’s economist has predicted a significant increase in money market rates over the next 60 days.

The forecast of higher interest rates means the bank must borrow at a higher interest cost which, other things held equal, will lower its net interest margin. To offset the expected higher borrowing costs the bank's management should consider a short sale of financial futures contracts or a put option approximately equal in volume to the additional loan demand. Either government securities or EuroCDs would be good instruments to consider using in the futures market or in the option market.

d. Settlement Hills National Bank reports that its interest-sensitive liabilities for the next week will be approximately $42 million, while interest-sensitive assets will approach $31 million. Data provided by the Federal Reserve Board suggests a near-term rise in money market interest rates.

Settlement Hills National Bank has interest-sensitive liabilities greater than interest-sensitive assets by $11 million. If interest rates rise, the bank's net interest margin will likely be squeezed due to the faster rise in liability costs. Sales of financial futures contracts followed by a subsequent purchase or put options would probably help here.

e. Caufield Bank and Trust Company finds that its portfolio of earning assets as an average duration of 1.35 years and its liabilities have an average duration of .95 years. Interest rates are expected to rise by 50 basis points between now and year-end

Caufield Bank and Trust Company has an asset duration of 1.35 years and a liabilities duration of 0.95. A 50-basis point rise in money-market rates would reduce asset values relative to liabilities which means its net worth would decline. The bank should consider short sales of government futures contracts or put options on these securities or on their related futures contracts.

7-3. A bank plans to borrow $55 million in the money market for one month at a current interest rate of 8.5 percent with an interest-rate cap on this borrowing of 10 percent. Suppose money market interest rates climb to 11.5 percent as soon as the borrowing occurs. How much total interest will the bank owe?

Total Amount Interest Number of Months

Interest Owed = Borrowed * Rate Charged * 12

= $55 million x 0.115 x 112

= $0.527 million or $527,000.

7-9. Silver Beach National Bank wants to purchase a portfolio of million-dollar-denomination commercial loans with an expected average rate of return of 11 percent. However, when funds become available to purchase the loans in 6 months, market interest rates are expected to be in the 10 percent range. If the total size of the portfolio is $100 million and Treasury Bill options are available today at a market price of $890,000 (per million-dollar contract) upon payment of a $12,000 premium and we forecast a rise in market value of $900,000, what before-tax profit could the bank earn from this transaction?

The relevant before-tax profit formula is:

Before-Tax Profit = $900,000 - $890,000 - $12,000 = -$2,000.

In this case there is no option profit, only a loss due to the failure of T-bill prices to rise enough to fully cover the option premium. Because interest rates are expected to fall, a call option would be appropriate.

7-10. Treasury bill futures contracts carry denominations of $1 million but have a current market value of $960,000. Suppose the duration of these bills is 0.33 years and market interest rates fall from 4 percent to 3 percent. What change in the index value of these futures contracts will occur?

Change in Value of T-Bill Futures 0.04) (1.01- x $960,000 x years .33- +=

= +$3046.15

7-11. Suppose a bank wants to hedge its overall asset-liability position using T-bond futures contracts. Given the information below:

Total assets $853 million Duration of bank assets 3.5 years Total liabilities $790 million Duration of bank liabilities 1.7 years Price of futures $95,000 Duration of T-bonds 9.5 years

Please calculate the approximate number of futures contracts the bank will need to fully cover the interest-rate risk it faces? Number of Futures Contracts Needed = mill. $.095 x years 5.9mill. $835 x years) 1.7 x mill.

$835mill.

$790 - years (3.5

= 1750.14 contracts

7-12. By what amount will the market value of Treasury bond futures contracts change if they have a duration of 8.80 years, a current market price of $98,500, and if interest rates rise from 8.50 to 9.50 percent?

Changes in Value of T-Bond Futures Contract 0.0850) (10.01 x

$98,500 x years 8.80- ++=

= -$7988.94

7-13. Cleberg National Bank reports that its assets have a duration of 1.90 years while liabilities average 1.12 years in duration. To hedge its duration gap management wants to employ T-bond futures contracts that have a current price of $99,250 and a duration of 9 years. The ba nk's assets total $144 million and liabilities total $132 million. Approximately how many futures contracts for T-bonds will the bank need to cover its interest-rate risk exposure?

Number of T-Bond Futures Contracts Needed

million 09925 . * years 9million 144$*)12.1*million

144$million

$132 - years (1.90

=

140.79 contracts