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**Exam FM/2 Review Forwards, futures, & swaps**

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**Four ways to purchase a stock**

Outright purchase Receive now Pay now: Borrow to pay for the stock Pay later: Prepaid forward contract Receive in future Forward contract Pay in future:

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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

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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

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**Swaps Simply a series of forward contracts Payment Types**

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

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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

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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

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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

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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

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Problem 5 Take these forward prices for forward contracts of Stock ABC: Years to Exp. Forward Price 1 $ Take these spot rates of interest: Term to maturity Spot Rate % 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

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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%

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