Question

1. Construct a synthetic position providing full information on combined payoff and profit for all levels of open market / spot prices to expire in 3 months. The nominal annual interest rate is 8% and the current spot price for the stock is $40.
2. What is this position called? (Graph the position for visualization)
3. Identify its purpose – arbitrage, hedge, or speculation.

Your position includes the following items – buy a stock and buy a put; sell two calls and buy one call.

Stock: The price of the stock varies with the open market cash prices, in increments of $5 with a range between $20,$25,$30…..and $60.

Buy Put: strike $35; Premium $0.44

Write two calls: strike for both $40; Premium for each is $2.78

Buy call: strike $45; Premium $0.97

Answer 1

Part (a)

Profit / (Loss) from a buy position in the stock = S - S₀

Profit / (Loss) from the buy position in call option = max (S - K, 0) - C

Profit / (Loss) from the buy position in put option = max (K - S, 0) - P

Profit / (Loss) from the sell (write) position in call option = C- max (S - K, 0)

Profit / (Loss) from the sell (write) position in put option = P - max (K - S, 0)

where S₀ = stock price initially, S = stock price at the time of expiration, K = strike price, C or P is the Call or Put premium

Our Profit / (Loss) from each of the position and then from the combines position is shown below in the table:

Stock Price	Profit / (Loss) from buy position in stock	Profit / (Loss) from buy position in P1	Profit / (Loss) from sell position in C1	Profit / (Loss) from buy position in C2	Total Profit / (Loss)
S	A = S - S0	B =max(35 - S, 0) - 0.44	C =2 x (2.78 - max(S - 40, 0)	D =max(S - 45, 0) - 0.97	A + B + C + D
20	-20	14.56	5.56	-0.97	-0.85
25	-15	9.56	5.56	-0.97	-0.85
30	-10	4.56	5.56	-0.97	-0.85
35	-5	-0.44	5.56	-0.97	-0.85
40	0	-0.44	5.56	-0.97	4.15
45	5	-0.44	-4.44	-0.97	-0.85
50	10	-0.44	-14.44	4.03	-0.85
55	15	-0.44	-24.44	9.03	-0.85
60	20	-0.44	-34.44	14.03	-0.85

Part (b)

This trading strategy is called "Iron Butterfly"

Part (c)

Purpose: Speculation specially when the trader believes that stock price is going to traded within range bounds and will have limited volatility.