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| Table
2. Simulation Model for Iowa and Ohio Model Farms |
| Expected
Production |
E(P
yr) = 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 for Futures: |
TCF
= n f * $40 |
| Transaction
Costs for 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 |
| Interest
cost 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:
P yr, is
production in year yr
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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