Financial Markets and Institutions (2-downloads)

622

Part 7 The Management of Financial Institutions

Exchange Rates (Dollars/Pound)

Period

Rate

Spot

1.5342

March

1.6212

June

1.6901

September

1.7549

December

1.8416

22. From the previous question, rates do indeed fall as

expected, and the T-bond contract is priced at 103

5/32. If Springer closes its futures position, what is the

gain or loss? How well does this offset the approxi-

mate change in equity value?

23. A bank issues a $100,000 fixed-rate 30-year mortgage

with a nominal annual rate of 4.5%. If the required

rate drops to 4.0% immediately after the mortgage

is issued, what is the impact on the value of the mort-

gage? Assume the bank hedged the position with a

short position in two 10-year T-bond futures. The

original price was 64 12/32 and expired at 67 16/32 on

a $100,000 face value contract. What was the gain on

the futures? What is the total impact on the bank?

24. A bank customer will be going to London in June to

purchase £100,000 in new inventory. The current spot

and futures exchange rates are as follows:

27. A banker commits to a two-year $5,000,000 commer-

cial loan and expects to fulfill the agreement in

30 days. The interest rate will be determined at that

time. Currently, rates are 7.5% for such loans. To

hedge against rates falling, the banker buys a 30-day

interest-rate floor with a floor rate of 7.5% on a

notional amount of $10,000,000. After 30 days, actual

rates fall to 7.2%. What is the expected interest

income from the loan each year? How much did the

option pay?

28. A trust manager for a $100,000,000 stock portfolio

wants to minimize short-term downside risk using

Dow put options. The options expire in 60 days, have

a strike price of 9,700, and a premium of $50. The

Dow is currently at 10,100. How many options should

she use? Long or short? How much will this cost? If

the portfolio is perfectly correlated with the Dow,

what is the portfolio value when the option expires,

including the premium paid?

29. A swap agreement calls for Durbin Industries to pay

interest annually based on a rate of 1.5% over the one-

year T-bill rate, currently 6%. In return, Durbin

receives interest at a rate of 6% on a fixed-rate basis.

The notional principal for the swap is $50,000. What is

Durbin’s net interest for the year after the agreement?

30. North-Northwest Bank (NNWB) has a differential

advantage in issuing variable-rate mortgages, but does

not want the interest income risk associated with

such loans. The bank currently has a portfolio of

$25,000,000 in mortgages with an APR of prime +150

basis points, reset monthly. Prime is currently 4%. An

investment bank has arranged for NNWB to swap into

a fixed interest payment of 6.5% on a notional amount

of $25,000,000 in return for its variable interest

income. If NNWB agrees to this, what interest is

received and given in the first month? What if prime

suddenly increased 200 basis points?

The customer enters into a position in June futures to

fully hedge her position. When June arrives, the

actual exchange rate is $1.725 per pound. How much

did she save?

25. Consider a put contract on a T-bond with an exer-

cise price of 101 12/32. The contract represents

$100,000 of bond principal and had a premium of

$750. The actual T-bond price falls to 98 16/32 at the

expiration. What is the gain or loss on the position?

26. Consider a put contract on a T-bond with an exer-

cise price of 101 12/32. The contract represents

$100,000 of bond principal and has a premium of

$750. The actual T-bond price is currently 100 1/32.

How can you arbitrage this situation?

---

Chapter 24 Hedging with Financial Derivatives