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Exam FM/2 Review Forwards, 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: . Notes.
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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:
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 $100 2 110 3 120 • Take these spot rates of interest:Term to maturity Spot Rate 1 3.0% 2 3.5 3 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%
