I know it is a silly question but I need some help on it!
In the below question in schweser, in calculating the contract price, why do we multiply by the interest rate to the power of the contract expiration date. As far as I understand, this will help me calculate the price at expiry but not the current contract price.
A stock is currently priced at $30 and is expected to pay a dividend of $0.30 20 days and 65 days from now. The contract price for a 60-day forward contract when the interest rate is 5% is closest to: A. $29.46. B. $29.70. C. $29.94. The dividend in 65 days occurs after the contract has matured, so it’s not relevant to computing the forward price.
The contract expires in 60 days. So your risk free rate compounded by 60/365 (using 365 day convention) is how much the forward contract should be valued… Is that your question?
You do power contract to its expiration date to value a contract at a given date. For better understanding, exactly you power (T-t)/T since your (likely) 1 Y contract is expiring in 60 days and suppose now is 305 th day in position, you power at (365-305)/365 which is 60/365.
You should deduct PV from the Spot value of only relevant interim cash flows and relevant CFs are dividends paid out only during a contract term.
You compound it because that’s what the book says to do. If you didnt compound it, what would you do? Simple growth or just default to 1 year growth?
By compounding, its obviously more accurate than simple growth. For the economics section, the book has you use the simple math. So that would by just 60/360 multiplied by the risk free rate. For the Der section, the book says to compound it with 365 day convention. And then then some calculations with indexes indexes or options, you sometimes have continues compound. e(risk_free * days/365)
Contract price is something which both parties agree upon at the initiation. For no arbitrage, Forward price must be equal to FV (S-carry benefits+carry costs).