Problem 5.29

A stock is expected to pay a dividend of $1 per share in two months and in five months. The stock price is $50, and the risk-free rate of interest is 8% per annum with continuous compounding for all maturities. An investor has just taken a short position in a six-month forward contract on the stock.

a)What are the forward price and the initial value of the forward contract?

b)Three months later, the price of the stock is $48 and the risk-free rate of interest is still 8% per annum. What are the forward price and the value of the short position in the forward contract?

1.Suppose you have a loan of $10,000,000 outstanding, on which you will have to make a floating-rate interest rate payment on Monday, March 1^st. The interest payment is determined based on a 3-month LIBOR rate on that day. You fear that in the next several days the rate might rise. So, you hedge yourself by trading Eurodollar futures.Assume that you enter the position at close of day on Tuesday, February 23d.

a.In order to hedge yourself, which position in Eurodollar futures will you take (i.e. buy or sell, contract maturity, and the number of contracts)?

b.What is the value of your futures position onTuesday, February 23d?

c.What is your daily gain or loss on your futures position (on Wednesday, Thursday, Friday, and Monday)?

d.What is the interest rate payment that you have to make on Monday, March 1^st, on your $10,000,000 loan?

e.What is the net cost to you, taking into account the gains/losses on your hedge, plus the interest payment on the loan (ignore the time value of money)?

2.Companies A and B have been offered the following rates per annum on a $20 million five-year loan:

Fixed rate

Floating rate

Company A

12.0%

LIBOR + 0.1%

Company B

13.4%

LIBOR + 0.6%

Company A requires a floating-rate loan; company B requires a fixed-rate loan.Design a swap that will appearequallyattractive to both companies (that is they split possible savings equally).

Hint: figure out a range for the swap rate.

3.Consider the following borrowing costs faced by the following 3 companies:

Fixed rate

Floating rate

Company A

7.0%

LIBOR + 0.1%

Company B

6.5%

LIBOR - 0.1%

Company C

7.3%

LIBOR + 0.2%

If company A wants to borrow floating-rate funds, what is the lowest possible cost of funds that this company could achieve?Assume that if any two companies enter into the swap transaction, they split the possible savingsequally.

Hint: consider all possible ways that company A could borrow floating-rate funds.

Daily Settlements for Eurodollar Futures (FINAL)Trade Date:02/24/2021 (Wednesday)

Month

Open

High

Low

Last

Change

Settle

Estimated Volume

Prior Day Open Interest

MAR 21

99.8375

99.8425

99.8325

99.8350

-.0050

99.8350

212,701

1,075,658

APR 21

109.9850

109.9850

109.9840

109.9850

-.0050

99.8500

5,674

57,652

MAY 21

99.8550

99.8550

99.8450

99.8500

-.0050

99.8500

3,027

16,817

JUN 21

99.8550

99.8550

99.8400

99.8450

-.0050

99.8450

139,383

1,111,270

JLY 21

99.8500

99.8500

99.8450

99.8450

-.0050

99.8450

621

7,412

Daily Settlements for Eurodollar Futures (FINAL)Trade Date:02/26/2021 (Friday)

Month

Open

High

Low

Last

Change

Settle

Estimated Volume

Prior Day Open Interest

MAR 21

99.8175

99.8250

99.8150

99.8200

-.0025

99.8200

254,930

1,059,745

APR 21

109.9830

109.9840

109.9825

109.9840

-.0100

99.8300

32,206

66,121

MAY 21

99.8350

99.8400

99.8250

99.8400

-.0100

99.8300

10,262

20,860

JUN 21

99.8300

99.8400

99.8150

99.8350

-.0050

99.8300

353,085

1,132,124

JLY 21

99.8250

99.8300

99.8200

99.8300

-.0100

99.8250

1,752

7,334

Daily Settlements for Eurodollar Futures (FINAL)Trade Date:03/01/2021 (Monday)

Month

Open

High

Low

Last

Change

Settle

Estimated Volume

Prior Day Open Interest

MAR 21

99.8200

99.8300

99.8175

99.8300

+.0075

99.8275

121,969

1,066,052

APR 21

109.9830

109.9840

109.9830

109.9840

+.0100

99.8400

5,051

76,673

MAY 21

99.8350

99.8450

99.8350

99.8400

+.0100

99.8400

1,156

22,512

JUN 21

99.8400

99.8450

99.8300

99.8450

+.0100

99.8400

133,756

1,081,375

JLY 21

99.8350

99.8400B

99.8350

99.8400B

+.0100

99.8350

61

8,377

3-month LIBOR rate:

February 23, 20210.18750

February 24, 20210.18975

February 25, 20210.19050

February 26, 20210.18838

March 1, 20210.18425