Bank of Charub ($ million)

Assets:

270 day US Treasury bills $500m

2 year consumer loans

Fixed rate, 12% p.a. annually $275m

7 year commercial loans $350m

Fixed rate, 9% p.a. annually

10 year fixed rate mortgages $675m

Fixed rate, 6.5% p.a. monthly

10 year floating rate mortgages $125m

LIBOR+50bp, monthly roll date

Liabilities and Net Worth:

1 year Certificates of Deposit $550m

Demand Deposits $750m

2 year Bonds $175m

Fixed rate, 7.5% p.a. annually

Overnight Fed Funds $350m

Equity $100m

Notes: The 1 year Certificates of Deposit pay 1.95% p.a. annually. The demand deposits are non-interest bearing and have a duration of zero. The 7 year commercial loans have a duration of 4.75 years. The fixed rate mortgages have a duration of 8.3 years. All values are market values.

1. What is the duration of the floating rate mortgages? a. 0.25 years b. 10 years c. 2 years d. 0.08 years e. There is not enough information to answer the question. 2. What is the duration of the 2 year bonds they are selling at par at 7.5% p.a. interest, compounded annually? a. 1.93 years b. 1 year c. 2 years d. 1.5 years e. 3.86 years 3. What is the face value of the 2 year consumer loans if they yield 6% p.a. with a coupon rate of 12% p.a. paid annually? a. $175 million b. $165 million c. $247.7 million d. $155 million e. $172 million 4. What is the duration of the 2 year consumer loans if they yield 6% p.a. with a coupon rate of 12% p.a. paid annually? a. 1.87 years b. 3.84 years c. 2 years d. 0.5 years e. 1.9 years 5. What is the convexity of the 2 year consumer loans if they yield 6% p.a. with a coupon rate of 12% p.a. paid annually? a. 4.98 b. 2.83 c. 3.85 d. 1.95 e. 2.01 6. What is the duration of the bank's assets? a. 1.05 years b. 4.24 years c. 0.94 years d. 0.49 years e. 3.85 years

7. What is the duration of the bank's liabilities?

a. 1.05 years

b. 4.24 years

c. 0.94 years

d. 0.49 years

e. 3.85 years

8. What is the bank's duration gap?

a. -0.49 years

b. +4.24 years

c. -0.94 years

d. -2.81 years

e. +3.78 years

9. What is the impact on the bank's equity values if interest rates increase 25 basis points? (That is, R/(1+R) is equal to an increase of 25 basis points.) a. -$12.69 million

b. +$12.69 million

c. -$18.19 million

d. +$18.19 million

e. -$25,000

10. What is the Bank of Charub's interest rate risk exposure?

a. Exposed to interest rate declines because a negative duration gap implies that equity values decline when interest rates fall.

b. Exposed to interest rate increases because a negative duration gap implies that equity values decline when interest rates rise.

c. Exposed to interest rate declines because a positive duration gap implies that equity values decline when interest rates fall.

d. Exposed to interest rate increases because a positive duration gap implies that equity values decline when interest rates rise.

e. The Bank of Charub has no interest rate risk exposure.

11. Which of the following can be used to hedge Bank of Charub's interest rate risk exposure?

a. Sell futures and/or sell puts to construct a short hedge.

b. Buy futures and/or sell puts to construct a short hedge.

c. Buy futures and/or buy puts to construct a long hedge.

d. Sell futures and/or sell puts to construct a long hedge.

e. Sell futures and/or buy puts to construct a short hedge.

12. Use the following US Treasury bill futures contract to construct a perfect (nave) hedge. The June contract is currently price at 97.5. (Assume that all interest rates increase by 25 basis points.)

a. Sell one US Treasury bill futures contract at 97.5

b. Buy one US Treasury bill futures contract at 97.5.

c. Sell 28,780 US Treasury bill futures contracts at 97.5

d. Buy 28,780 US Treasury bill futures contracts at 97.5

e. Sell 100 US Treasury bill futures contracts at 97.5.

13. What is the dollar price of the US Treasury bill futures contract in question 12?

a. $975,000

b. $97,500

c. $993,681

d. $996,208

e. $97.50

14. Use an at the money US Treasury bill futures option to construct a perfect (nave) hedge of Bank of Charub's interest rate risk. (Assume that all interest rates increase by 25 basis points.)

a. Sell one put option at 97.5.

b. Buy one call option at 97.5.

c. Buy 58,577 put options at 97.5.

d. Buy 58,577 call options at 97.5

e. Buy one put option at 97.5.

15. What might prevent the hedges in questions 12 and 14 from completely eliminating Bank of Charub's interest rate risk exposure?

a. Incorrect calculation of the number of contracts.

b. Basis risk.

c. Pricing errors.

d. Failure to execute the order.

e. Unanticipated shifts in interest rates.

Can you answer part 7,8,9,10,11,12,13,14 and 15. I need explanation and calculations for only 7-15. Thanks.