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Four ways to purchase a stock ο Outright purchase ο Receive now ο Pay now: ο π0 Borrow to pay for the stock ο Receive now ο Pay later: ο π0 π πΏπ‘ Prepaid forward contract ο Receive in future ο Pay now: ο π0 β ππ(πππ£ππππππ ) Forward contract ο Receive in future ο Pay in future: Notes ο Cost of carry ο Difference between interest and dividend rates ο Cost for you to borrow and buy stock, then hold it ο ο Implied repo rate- interest rate used to find forward price Cash and Carry ο Short a forward contract and buy the asset ο Pays off if forward price is too high Futures contracts ο ο Simply a standardized forward contract, sold in exchanges Marked-to-market ο Changes in value are settled daily through parties ο Parties maintain margin accounts to cover these changes Swaps ο ο Simply a series of forward contracts Payment ο Prepaid- pay now ο Postpaid- pay at end ο Level annual payments- most common ο Types ο Commodity, eg. price of corn ο Interest rate ο Foreign currency ο Any of these could be deferred, or start in the future Problem 1 ο 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 ο 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 ο 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 ο Suppose a stock index is currently priced at $1,500, and the 12month 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 ο ο ο 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 ο 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%