Futures price rises by $1 per bushel to $8.80 by late August: If the futures price is $8.80 a month from now, the premium on each put option contract would decrease to 21¢, a loss of 41¢/bu. Since two put options were purchased for the hedge, the total loss on the option position is 2 x 41¢ = 82¢/bu. This is 18¢/bu. less than the $1 increase in the futures price used to determine the RP payout, so the farmer is 18¢/bu. better off than he would have been from using a futures hedge.

If the hedger lifts the hedge at the end of August and sells the two put options to salvage the remaining premium, and if the futures price is still $6.80 in October, the hedging loss would be $114.80/acre (140 bushels x -82¢/bu.) and total revenue, borrowing from the July 24 farmdoc daily post, would be $1,107.20/acre ($870 crop revenue + $352 RP payment - $114.80 hedging loss), or $25.20/acre more than with the futures hedge. Alternatively, the farmer could hold the options until October and maintain the hedge against the possibility of a sudden collapse in prices. However, if there is no change in the futures price, maintaining the hedge will result in further time value erosion that will adversely affect the net income, as shown in the next example.

 

Futures price rises by $1 per bushel to $8.80 by late October: If the futures price is $8.80 at the end of the October, the premium on each put option contract would be just 4¢, for a loss of 62 – 4 = 58¢ on each put. Since two put options were purchased for the hedge, the total loss on the option position is 2 x 58¢ = $1.16/bu. Notice that this amount is 16/bu. more than the $1 increase in the futures price used to determine the RP payout, so the farmer is 16¢/bu. worse off than he would have been from using a futures hedge. Furthermore, maintaining the option hedge between late August and late October without any further change in the futures price would result in a loss of time value of 34¢/bu. (82¢ – $1.16).

On a per-acre basis, the hedging loss would be $162.40/acre (140 bu. x -$1.16/bu.) and the total revenue would be $1,059.60/acre ($870 crop revenue + $352 RP payment - $162.40 hedging loss), or $22.40/acre less than with the futures hedge. The difference of 34¢/bu. ($1.16 – 0.82) or $47.60 per acre ($1,059.60 – 1,107.20) between late August and late October is due entirely to the erosion in the time value component of the option premium.