Question

Make sure that the calculations are done in Excel, and that the formulas you use are in the cells. If you simply have values in all the cells you will not get credit for this part of the assignment. a.) Fair Forward Price (spreadsheet tab "Forwards") Input information Asset Price $88.22 Assume the interest rate is 2.35% compounded continuously for all maturities. Assume the asset pays a fixed dividend of $13 in 1 month, and $14 in 7 months. Output Calculate the fair market forward price for: a 2-month forward, a 6-month forward, and a 1-year forward b.) Arbitrage (spreadsheet tab "Forwards") Input information Assume that the information in part (a) is still applicable, but that the forward contracts are trading at the following prices: 2-month forward $75.25 6-month forward $71.77 1-year forward $64.34 Output Describe the strategy you would use to achieve arbitrage profits (if possible), and calculate the arbitrage profit for each of the three forward contracts. For each strategy assume that it will cost you $2.5 to execute all the trades (round trip), as your total transaction cost (subtract $2.50 at the end).

Answer 1

The fair price of forward contracts for a dividend paying asset is given by

F = (S-I) e^ (rt)

where S is the spot price , I is the present value of expected dividends occuring within the maturity period, r is the continuously compounded interest rate and t is the time till maturity of forward contract

Present value of Dividend after 1 month = $13* e^(-0.0235*1/12) = $12.9745

Present value of Dividend after 7 months = $14* e^(-0.0235*7/12) = $13.8094

So,

Fair price of 2 month forward = (88.22-12.9745)*e^(0.0235*2/12) = $75.54

Fair price of 6 month forward = (88.22-12.9745)*e^(0.0235*6/12) = $76.13

Fair price of 1 year forward = (88.22-12.9745-13.8094)*e^(0.0235*1) = $62.90

b) As the difference between Fair price and Actual price of 2 month forward is only $0.29 and there is a $2.5 transaction cost , arbitrage is not possible  

As the difference between Fair price and Actual price of 1 year forward is only $1.44 and there is a $2.5 transaction cost , arbitrage is not possible

Arbitrage is possible in 6 month forward as follows

1. Today, Short Sell 1unit of Asset at $88.22 and out of it, invest an amount of $12.98 for one month and remaining amount of $75.24 for six month at 2.35%

2. Today, Buy 1 unit of Asset in futures and fix the price at $71.77

3. After one month, get $12.98*e^(0.0235*1/12) =$13 from your investment , pay the borrower of the asset the required $13 dividend

4. After 6 months, get $75.24*e^(0.0235*6/12) =$76.13 from your investment, buy the asset back at $71.77, pay the transaction cost of $2.5 and get remaining $1.86 as arbitrage profit