Question

Stephen just bought 1 contract of put options and, at the same time, 2 contracts of call options on the Swiss francs (SF) at the strike price of 60 cents per franc. Each option contract is for SF 12,000. The option will expire in three months. The put premium is 2.50 cents per SF and the call premium is 2.00 cents per SF.

(1) Diagram the ‘combined’ dollar profit schedule against the future spot exchange rate.

(2) Compute and show the breakeven future spot exchange rates on the diagram.

(3) What are the maximum possible loss and maximum possible profit in dollar terms?

Answer 1

1]

Payoff of a long call option = Max[S-X, 0] - P

Payoff of a long put option = Max[X-S, 0] - P

S = underlying price at expiry,

X = strike price

P = premium

Each contract is for 12,000 SF, hence the premiums and the payoffs are multiplied by 12,000 for each contract

1 Exchange rate at Payoff Payoff Net expiry of Long of Long Payoff (cents per Call (in Put (in (in franc cents cents) cents) 45.00 (48,000) 150,000 102,000 46.00 (48,000) 138,000 90,000 47.00 (48,000) 126,000 78,000 48.00 148.000 114.000 66.000 49.00 148,000) 102.000 54.000 50.00 148,000) 90,000 42.000 51.00 (48,000) 78,000 30.000 52.00 (48,000) 66,000 18,000 53.00 (48,000) 54,000 6,000 53.50 (48,000) 48,000 54.00 (48,000) 42,000 (6,000) 5500 (48,000) 30,000 (18,000) 56.00 (48,000) 18,000 (30,000) 57.00 (48,000) 6,000 (42,000) 58.00 (48,000) (6.000) (54,000) 5900 (48,000) (18,000) (66,000) 60.00 (48,000) (30,000) (78,000) 61.00 (24,000) (30,000) (54,000) 62.00 (30,000) (30,000) 63.00 24,000 (30,000) (6.000) 63.25 30,000 130,000) 48,000 (30,000) 18,000 65.00 72,000 130,000) 42,000 66.00 96,000 130,000) 66,000 67.00 120,000 (30,000) 90,000 68.00 144,000 130,000) 114,000 69.00 168,000 130,000) 138,000 70.00 192,000 (30,000) 162,000 71.00 216,000 (30,000) 186,000 72.00 240,000 130,000) 210,000 73.00 264,000 130,000) 234,000 74.00 288,000 (30,000) 258,000 75.00 312,000 (30,000) 282,000 64.00

Exchange rate at expiry (cents per Payoff of Long Call (in 1 franc) cents) 245 - (MAX(A2-60,0)-21*2*12000 3 46 =(MAX(A3-60,0)-2)*2*12000 447 =(MAX(A4-60,0)-2)*2*12000 548 =(MAX(A5-60,0)-2)*2*12000 6 49 =(MAX(A6-60,0)-2)*2*12000 T 50 =(MAX(A7-60,0)-2)*2*12000 8 51 =(MAX(A8-60,0)-2)*2*12000 9 52 =(MAX(A9-60,0)-2)*2*12000 1053 =(MAX(A10-60,0)-2)*2*12000 1153.5 =(MAX(A11-60,0)-2)'2*12000 12 54 =(MAX(A12-60,0)-2)*2*12000 13 55 =(MAX(A13-60,0)-2)*2*12000 14 56 = {MAX(A14-60,0)-2)*2*12000 15 57 =(MAX(A15-60,0)-2)*2*12000 16 58 =(MAX(A16-60,0)-2)*2*12000 17 59 =(MAX(A17-60,0)-2)*2*12000 18 60 =(MAX(A18-60,0)-2)*2*12000 19 61 =(MAX(A19-60,0)-2)*2*12000 20 62 =(MAX(A20-60,0)-2)*2*12000 21 63 = {MAX(A21-60,0)-2)*2*12000 22 63.25 =(MAX(A22-60,0)-2)*2*12000 23 64 =(MAX(A23-60,0)-2)'2*12000 24 65 =(MAX(A24-60,0)-2)*2*12000 25 66 =(MAX[A25-60,0)-2)*2*12000 26 67 =(MAX(A26-60,0)-2)*2*12000 27 68 =(MAX(A27-60,0)-2)*2*12000 28 69 =(MAX(A28-60,0)-2)*2*12000 29 70 =(MAX(A29-60.03-2)*2*12000 30 71 =(MAX(A30-60.0)-21*2*12000 31 72 =(MAX(A31-60,0)-21*2*12000 32 73 = [MAX(A32-60,0)-21*2*12000 33 74 - (MAX(A33-60.03-2)*2*12000 34 75 =(MAX[A34-60.0)-21*2*12000 Payoff of Long Put (in cents =(MAX(60-A2,0)-2.5)*12000 =(MAX(60-A3,0)-2.5)*12000 =(MAX(60-A4,0)-2.5)*12000 =(MAX(60-A5,0)-2.5)*12000 =(MAX(60-A6,0)-2.5)*12000 =(MAX(60-A7,0)-2.5)*12000 =(MAX(60-A8,0)-2.5)*12000 =(MAX(60-A9,0)-2.5)*12000 =(MAX(60-A10,0)-2.5)*12000 =(MAX(60-A110)-2.5) 12000 =(MAX(60-A12,0)-2.5) 12000 =(MAX(60-A13,0)-2.5) 12000 =(MAX(60-A14,0)-2.5) 12000 =(MAX(60-A15,0)-2.5) 12000 =(MAX(60-A16,0)-2.5) 12000 =(MAX(60-A17,0)-2.5)*12000 =(MAX(60-A18,0)-2.5) 12000 =(MAX(60-A19,0)-2.5) 12000 =(MAX(60-A20,0)-2.5)*12000 =(MAX(60-A21,0)-2.5) 12000 =(MAX(60-A22,0)-2.5) 12000 =(MAX(60-A23,0)-2.5) 12000 =(MAX(60-A24.0)-2.5) 12000 =(MAX(60-A250)-2.5)*12000 =(MAX(60-A26,0)-2.5)*12000 -{MAX(60-A27.0)-2.5) 12000 =(MAX(60-A28.0)-2.5) 12000 =(MAX(60-A29.0)-2.5) 12000 =(MAX(60-A30.0)-2.512000 =(MAX(60-A310)-2.5) 12000 MAX160-A3201-25112000 =(MAX60-A33,0)-2.5*12000 =(MAX(60-A34.0)-2.5)*12000 Net Payoff (in cents) -B2.02 -B3.03 -B4.04 .B5.05 -B6 C6 -B7-C7 -B8.08 - B9.C9 -B10 C10 B11-C11 B12 C12 -B13C13 B14.C14 B15.C15 -B16C16 -B17-C17 -B18C18 - B19-C19 =B20.C20 -B21-C21 -B22.C22 =B23.C23 -B24.C24 =B25.C25 -B26.C26 -B27.27 -B28.C28 -B29.C29 =B30.C30 -B31-C31 -B32.C32 =B33.C33 =B34-C34

Net Payoff (in cents) 300.000 250000 200.000 150,000 300,000 50,000 4.00 46.00 47.00 48.00 19.00 50.00 51.00 52.00 53.00 53.50 54.00 55.00 56.00 57.00 58.00 99.00 60.00 61.00 62.00 8.00 63.25 64.00 65.00 66.00 67.00 60.00 60.00 20.00 21.00 72.00 73.00 74.00 75.00 150,000) 4300,000 Nu Payall not

2]

In the diagram, the breakeven future spot exchange rates are where the payoff line (yellow) intersects the horizontal axis.

Lower breakeven = strike price - total premium paid = 60 + (2.00 + 2.00 + 2.50) = 53.50

3]

Maximum loss = total premium paid * SF per contract

Maximum loss = (2.00 + 2.00 + 2.50) * 12,000 = 78,000 cents, or $7,800

Maximum profit = potentially unlimited (as Stephen holds only long positions in both the call and put contracts)