EXAM FM/2 REVIEWFORWARDS, FUTURES, & SWAPS

Four ways to purchase a stock Outright purchase

Receive now Pay now:

Borrow to pay for the stock Receive now Pay later:

Prepaid forward contract Receive in future Pay now:

Forward contract Receive in future Pay in future:

𝑆0 𝑆0𝑒𝛿𝑡 𝑆0 − 𝑃𝑉(𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠)

Notes Cost of carry

Difference between interest and dividend rates Cost for you to borrow and buy stock, then hold it

Implied repo rate- interest rate used to find forward price

Cash and Carry Short a forward contract and buy the asset Pays off if forward price is too high

Futures contracts Simply a standardized forward contract, sold in

exchanges Marked-to-market

Changes in value are settled daily through parties Parties maintain margin accounts to cover these changes

Swaps Simply a series of forward contracts Payment

Prepaid- pay now Postpaid- pay at end Level annual payments- most common

Types Commodity, eg. price of corn Interest rate Foreign currency Any of these could be deferred, or start in the future

Problem 1 The current price of a stock is $84. A one-year forward

contract is entered into. It is expected that 4 quarterly dividends of $5 each will be paid on the stock starting 3 months from now. The 4th dividend will be paid one day before expiration of the forward contract. The risk-free interest rate is 6% compounded quarterly. What is the price of a prepaid forward contract?ASM p.612

Answer: $64.73

Problem 2 A stock index pays dividends continuously at a

constant rate of 5% per annum. The current price of one unit of the index is $50. What is the price of a prepaid forward contract for delivery of one of the index in 3 months?ASM p.612

Answer: $49.38

Problem 3 A stock has a current price of $65. A dividend of

$3.25 is expected to be paid in 6 months. The risk-free interest rate is 10% effective per annum. X is the forward price of a one-year forward contact that has the stock as the underlying asset. Determine X.ASM p.612

Answer: $68.09

Problem 4 Suppose a stock index is currently priced at $1,500,

and the 12-month forward price on that index is $1,550. Let the annualized dividend yield on the index be 2%, and let the continuously compounded annual rate of (risk-free) interest be 8%. What would the profit or loss at forward maturity (12 months from now) under a cash-and-carry strategy?ASM p.613

Answer: $42.75 loss

Problem 5 Take these forward prices for forward contracts of

Stock ABC:Years to Exp. Forward Price

1 $1002 1103 120

Take these spot rates of interest:Term to maturity Spot Rate

1 3.0%2 3.53 3.8

X is the level swap price under a 3-year swap contract with the same underlying asset. Determine X.ASM p.630

Answer: $109.56

Problem 6 Two interest rate forward contracts are available for

interest payments due 1 and 2 years from now. The forward interest rates in these contracts are based on a one-year spot rate of 5% and a 2-year spot rate of 5.5%. X is the level swap interest rate in a 2-year interest rate swap contract that is equivalent to the two forward contracts. Determine X.ASM p.630

Answer: 5.49%