1. Exam FM/2 Review Forwards, futures, & swaps

2. 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:

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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%