Question

A soybean farmer is hedging production using a fence composed of the two following options positions on Nov 18 soybean futures: Holding a put with a $10.00 strike price and a premium of $0.39 Writing a call with a $11.20 strike price and a premium of $0.29 (Note: Assume an expected basis of -$0.55, and a current futures price of $10.30)

a) Calculate both the minimum expected selling price and maximum net selling price of the fence.

b) Draw the pay-off diagram for the fence described above.

Answer 1

Holding a put with a K_P = $ 10.00 strike price and a premium of P = $ 0.39

Writing a call with a K_C = $ 11.20 strike price and a premium of C = $ 0.29

(Note: Assume an expected basis of -$0.55, and a current futures price of $10.30)

Part (a)

Minimum selling price = K_P - P + C - basis = 10 - 0.39 + 0.29 - (- 0.55) = $ 10.45

Maximum net selling price of the fence =  K_C - P + C - basis = 11.20 - 0.39 + 0.29 - (- 0.55) = $ 11.65

Part (b)

Payoff equation = Payoff from holding the put + payoff from writing the call = max (K_P - S, 0) - P + C - max (S - K_C, 0) where S is the spot price = max (10 - S, 0) - 0.39 + 0.29 - max (S - 11.20, 0) = max (10 - S, 0) - max (S - 11.20, 0) - 0.10

Payoff matrix is:

S	Gain / (Loss)
	max (10 - S, 0) - max (S - 11.20, 0) - 0.10
7.00	2.90
8.00	1.90
9.00	0.90
9.90	(0.00)
10.00	(0.10)
11.00	(0.10)
12.00	(0.90)
13.00	(1.90)
14.00	(2.90)
15.00	(3.90)