| Expected Production | E(P yr) = S 0 Y yr * 500 acres / 10 |
| Number of futures contracts (real value) | E(P yr) /5000 |
| Number of options contracts (real value) | E(P yr) /5000 |
| Number of futures contracts (integer value) | n f = Int( E(Y yr) /5000 )floor |
| Number of options contracts (integer value) | n o = Int( E(Y yr) /5000 )floor |
| Transaction Costs | Futures: TCF = n f * $40 Options: TCO = n o * $60 |
Margin |
Mg = F1 * n f * 7% |
Marked to market gains or losses |
MM t = - (F t - Ft-1) * n f |
| Interest on maintenance margin short hedge | |
| Interest assessed when account is negative | Ic t = (MM t )_ * (rpt - rft) |
| Interest gained when account is positive | Ig t = (MM t )+ * rf t |
| Interest assessed on the life of the option: | Io = (n o * OP 1 * 5000) * (rp 1 * (T - t)/48 ) |
| Account Balance | |
| Account in Week 1 | Acct 1 = MM 1 |
| Account in Week 2 to week T-1 | Acct t = (MM t + Ic t + Ig t ) + Acct t-1 |
| Account in Week T | Acct T = (MM T + I c T + Ig T ) + Acct T-1 |
| Interest on initial margin | I Mg = ( (rp t - rf t) * (T - t)/48 ) * Mg |
| Interest on transactions costs | |
| Interest cost on TCF | I TCf = (rp 1 * (T - t)/48 ) * TCF |
| on TCO | ITCo = (rp 1 * (T - t)/48 ) * TCO |
| Revenue from futures | RF = Acct T - TCF - ITCf - Img |
| Revenue from options | RO = (OP T - OP 1) * n o - TCO - Io - ITCo |
| Revenue from cash sale | RC = yT * PT |
| Total variable costs | TVCT = vcT * acres |
| Net returns | |
| futures strategies | TR = (RC + RF) - TVCT |
| synthetic put and mixed hedge/put | TR = (RC + RF + RO ) - TVCT |
| Where: |
|
Y yr, is yield in year yr E(Y yr) is the expected yield in year yr based on the 10 year rolling average yield n f, is the number of futures contracts n o, is the number of options contracts Int( . )floor, is the integer operator that rounds down to the nearest integer TCF, transaction cost for futures TCO, transaction cost for options Mg, is the 7% margin of the value of the initiated futures contracts t, is the weekly period counter in the hedging season T, is the final period in the hedging season F1, F t, and Ft-1 are the futures prices in period 1, period t and period t-1 MM t is the marked to market gains or losses in period t rp t, is the prime rate in period t rf t, is the risk free rate in period t Ic t, is the interest cost assessed on the futures account when it is negative Ig t, is the interest revenue gained on the futures account when it is positive ( . )_ is a function operator that returns a value when argument is negative ( . )+ is a function operator that returns a value when argument is positive Io, is interest cost assessed on the life of the option OP 1, is the option premium in period 1 OP T, is the option premium in final period of the option life Acct 1, Acct t, Acct T, Acct T-1 this is the running futures account in periods 1, t, T, and T-1, respectively I Mg, is the interest cost on money borrowed to cover the initial margin I TCf, is the interest cost on money borrowed to pay futures transaction cost ITCo, is the interest cost on money borrowed to pay options transaction cost T- t, the number of periods in the hedging season RF, revenue from futures RO, revenue from options RC, revenue from cash sale PT, spot cash price at harvest TVCT, total variable cost at harvest vcT, variable costs per acre at harvest TR, Total Revenue |
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