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Futures Basics
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Futures
Trading Code
Measurement
Contract Unit (Multiplier)
Spot Price
Notional Value
Convenience Yield
Forward Price
Cash upon expiry
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Gold (comex gold)(GC)troy ounces100x 1,200.00 = 120,000.00 50 1,250.00 125,000.00
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Spot price in 1 year
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 Scenario 1 1,400.00
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Notional Value 140,000.00
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Difference 15,000.00
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Scenario 2 1,100.00
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Notional Value 110,000.00
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Difference (15,000.00)
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Fair Value of a Futures Contract
December 2024 crude oil
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S0 Spot price of underlying at time zero
 $ 40.00 Decision
Number of Contract
Price (USD)Point Value
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r risk free rate annualized0.05Buy1501000
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Time to delivery, denoted in years
3Sell1511000
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Contract Unit1P&L1000
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F0 forward/futures price today
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f value of the futures contract today
 $ 43.00 long the future
Unrealized profit or loss is absolutely real
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e Eulers number 2.71828DecisionNumber of ContractsPrice (USD)Point Value
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Buy51251.50100
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Receives $ 43.00 Sell51249.00100
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F0 forward/futures price today $ 40.50 P&L-1250
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Earnings $ 2.50
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S&P 500 June 2025 e-mini future
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Fair Value of a Futures Contract - Dividend, Storage Costs, Currency, Convenience YieldDecisionDate
Number of Contracts
Price (USD)Point Value
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S0 Spot price of underlying at time zero
40.00
Price for a futures contract modified to take into account dividend yield
SellDay 11270050
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r risk free rate annualized0.05HoldDay 11269050
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Time to delivery, denoted in years
3P&L500
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Contract Unit1
Price for a futures contract modified to take into account storage costs
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F0 forward/futures price today
S&P 500 June 2025 e-mini future
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f value of the futures contract today
43.00DecisionDate
Number of Contracts
Price (USD)Point Value
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e Eulers number 2.71828
Price for a futures contract modified for currency futures
SellDay 11270050
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q dividend yield0.005HoldDay 11269050
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u storage costs0.01P&L for day 1500
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y convenience yield0.04
Price for a futures contract with a convenience yield.
Day2 1275050
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rf exchange rate of a currency0.73P&L for day 2
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Dividend
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Receives43
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F0 forward/futures price today40.45254046
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Earnings2.547459537
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Storage Costs
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Receives43
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F0 forward/futures price today40.60452217
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Earnings2.395477825
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Currency
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Receives43
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F0 forward/futures price today34.28965452
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Earnings8.710345484
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Convenience yield
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Receives43.00
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Owes40.2005007
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Earnings2.80
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Contract Unit and Contract Notional Value
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Futures
Trading Code
Contract Unit (Multiplier)MeasurementPriceNotional Value
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Gold (comex gold)(GC)100troy ouncesx2025.5=202,550
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WTI Crude Oil(CL)1,000 barrels of oilx69.98=69,980
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E-mini S&P 500(ES)$50 multiplier x S&P500 pointsx4140.75=207,038
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Hedge strategyNotional Contracts
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10,000,000รท207,038=48.30042867
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Minimum Price Fluctuation
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Futures
Trading Code
ExpirationTick SizePrice Change by a tickContract unitMinimum Price Fluctuation (Change)
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WTI Crude Oil(CL)June0.01x69.98=100010
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69.9910
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70.0010
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70.0110
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70.0210
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70.0310
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E-mini S&P 500(ES)June0.25x2174.00=5012.5
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2174.2512.5
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2174.5012.5
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2174.7512.5
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2175.0012.5
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2175.2512.5
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2175.5012.5
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2175.7512.5
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US Treasury 5-Year T-Note
(ZF)June0.0078125x=$100,000
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