Futures pricing

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This document contains lecture slides on futures, forwards, swaps, and related concepts. It includes examples of calculating forward and futures prices using the cost of carry model, and examples of hedging with futures contracts. It also provides practice problems for valuing interest rate swaps and calculating swap rates and cash flows given term structure data. The document is intended to teach students about derivative pricing and the use of different derivative contracts.

© 2018 Dr. N. Richie, UNCW 1
Futures, Forwards, and Swaps

© 2018 Dr. N. Richie, UNCW 2
Futures and Forwards
Cost of Carry Model

© 2018 Dr. N. Richie, UNCW 3
You are considering the purchase of an
asset four months from now. The asset is
currently trading in the spot market for
$250. The risk-free rate is 4%.
(A) Calculate the arbitrage-free forward price on this asset.
(B) If a dealer offers you a forward contract at a price lower than you
calculated in (A), what transactions would earn you an arbitrage
profit?
(B) If a dealer offers you a forward price higher than you calculated
in (A), what transactions would earn you an arbitrage profit?
(C) After one month, the asset is trading for $240 in the spot market.
What is the value of the forward contract in (A)? Is this a gain or
a loss?

© 2018 Dr. N. Richie, UNCW 4
Consider an asset currently worth $75.
An investor is concerned that the asset
may decline in value over the next 6
months and enters a futures contract to
hedge the risk. The risk-free rate is 6%.
(A) Should the investor go long or short to hedge the risk?
(B) What is the arbitrage-free futures price of the contract?
(C) If the asset is trading for $80 in the spot market 2
months later, what is the value of the futures contract
at that time? Is this a gain or loss to the investor?

© 2018 Dr. N. Richie, UNCW 5
Futures and Forwards
Currency Forwards

Source: Chance, D., 2003, Analysis of Derivatives for the CFA Program, AIMR, p. 70-78.
© 2018 Dr. N. Richie, UNCW 6

Source: Chance, D., 2003, Analysis of Derivatives for the CFA Program, AIMR, p. 70-78.
© 2018 Dr. N. Richie, UNCW 7

© 2018 Dr. N. Richie, UNCW 8
Interest Rate Swaps

© 2018 Dr. N. Richie, UNCW 9
Problem 1: Consider a 1-year interest rate swap
to pay fixed and receive floating with quarterly
payments and a $15 million notional principal.
Calculate the swap fixed rate and the first net
payment, given the current term structure of
LIBOR
ti L0(ti)
90 4.50%
180 5.00%
270 5.25%
360 5.80%

© 2018 Dr. N. Richie, UNCW 10
Problem 1: Calculate the value of the swap
in 30 days later (A) from the point of view
of the fixed rate payer and (B) from the
point of view of the floating rate payer. The
new term structure is:
ti L30(ti)
60 4.75%
150 4.65%
240 4.25%
330 3.90%

© 2018 Dr. N. Richie, UNCW 11
Problem 2: Consider a 2-year interest rate swap
to pay fixed and receive floating with semi-
annual payments and a $40 million notional
principal. Calculate the swap fixed rate and the
first net payment, given the current term
structure of LIBOR
ti L0(ti)
180 6.25%
360 5.80%
540 5.40%
720 5.15%

© 2018 Dr. N. Richie, UNCW 12
Problem 2: Calculate the value of the swap
120 days later. The new term structure is:
ti L120(ti)
60 4.50%
240 4.80%
420 5.75%
600 6.15%

Question 1 (17 marks) HiSpeed Ltd. plans to manufacture cross-country skiing equipment. Its cash flows are highly dependent on the weather in early winter. HiSpeed operates under ideal conditions of uncertainty. On August 1, 2014, the beginning of its first year in business, HiSpeed acquires equipment to be used in its operations. The equipment will last two years, at which time its salvage value will be zero. The company finances the equipment purchase by issuing common shares. HiSpeed’s annual net cash flows will be $800 if the weather is snowy and $300 if it is not snowy. Assume that cash flows are received at year end. In each year, the objective probability that the weather is snowy is 0.7 and 0.3 that it is not snowy. The interest rate in the economy is 3% in both years. HiSpeed will pay a dividend of $50 at the end of each year of operation. Required a. (9 marks) In 2014, the weather is snowy. Prepare a statement of financial position as at July 31, 2015, the end of HiSpeed’s first year of operations, and an income statement for the year. b. (2 marks) What timing of revenue recognition is implicit in the income statement you have prepared in part (a)? When ideal conditions do not hold, is this timing of revenue recognition relevant? Is it reliable? Explain. c. (6 marks) Assume that HiSpeed paid the present value you calculated in part (a) for its equipment. Calculate HiSpeed’s net income for the year ended July 31, 2015 on a historical cost basis, assuming that equipment is depreciated on a straight-line basis. Under the more realistic assumption that ideal conditions do not hold, which measure of net income is most relevant? Which is most reliable? Why? Question 2 (18 marks) Prem has $2,000 that he wishes to invest for one year. He has narrowed his choices down to one of the following two actions: i: Buy bonds of X Ltd., a company that has a very high debt-to-equity ratio. These bonds pay 8% interest, unless X defaults, in which case Prem will receive no interest but will recover his principal. (a1) ii: Buy Canada Savings Bonds, paying 3% interest. (a2) Prem assesses the prior probability of X Ltd. defaulting as 0.40. His utility for money is given by the square root of the amount of his net payoff. That is, if he buys the Canada Savings Bonds, his net payoff is $60, yielding utility of √60 = 7.75, and so on. Prem is a rational decision maker. Required a. (4 marks) Based on his prior probability calculations, which action should Prem take? Show your calculations. b. (9 marks) Before making a final decision, Prem decides he needs more information. He obtains X Ltd.’s current financial statements and examines its times-interest-earned ratio. This ratio can be either high or low. Upon calculating the ratio, Prem observes that it is low. On the basis of his prior experience in bond investments, Prem knows the following conditional probabilities: Debt-to-Equity Ratio Future State Low High ND (no default) 0.50 0.50 D ( ...

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