Question

A trader conducts a trading strategy by selling a call option with a strike price of $50 for $3 and selling a put option with a strike price of $40 for $4. Please draw a profit diagram of this strategy and identify the maximum gain, maximum loss, and break-even point. Hint: Write down a profit analysis matrix to help you draw the payoff lines.

Answer 1

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

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

S = underlying price at expiry,

X = strike price

P = premium received

A B C D ($2) ($1) Stock price at 1 expiry 2 $30 3 $31 4 $32 5 $33 6 $34 7 $35 8 $36 9 $37 10 $38 11 $39 12 $40 13 $41 14 $42 15 $43 16 $44 17 $45 $46 19 $47 20 $48 21 $49 22 23 $51 24 $52 25 $53 26 $54 27 $55 28 $56 29 $57 30 $58 31 $59 32 . Short Call Short Put Net ($50) ($40) Payoff $3 (56) ($3) $3 ($5) $3 (54) ($1) $3 ($3) $0 $3 ($2) $1 $3 $2 $3 $0 $3 $3 $1 $4 $3 $2 $5 $3 $3 $6 $3 $4 $7 $3 $4 $7 $3 $4 $7 $3 $4 $7 $3 $4 $7 $3 $4 $7 $3 $4 $7 $3 $4 $7 $3 $4 $7 $3 $4 $7 $3 $4 $7 $2 $4 $6 $1 $4 $5 $0 $4 $4 ($1) $4 $3 ($2) $4 $2 ($3) $4 $1 ($4) $4 $0 ($5) $4 ($1) ($6) $4 ($2) ($7) $4 ($3) 00 $50 $60

A B D Stock price 1 at expiry 2 30 3 31 4 32 5 33 6 34 7 35 8 36 9 37 10 38 11 39 12 40 13 41 1442 1543 16 44 17 45 18 46 19 47 20 48 21 49 22 50 23 51 24 52 25 53 26 54 Short Call ($50) Short Put ($40) =3-MAX(0, A2-50) =4-MAX(0,40-A2) =3-MAX(0, A3-50) =4-MAX(0,40-A3) =3-MAX(0,A4-50) =4-MAX(0,40-44) =3-MAX(0,A5-50) =4-MAX(0,40-A5) =3-MAX(0,A6-50) =4-MAX(0,40-26) =3-MAX(0,A7-50) =4-MAX(0,40-A7) =3-MAX(0, A8-50) =4-MAX(0,40-48) =3-MAX(0,A9-50) =4-MAX(0,40-49) =3-MAX(0,A10-50) -4-MAX(0,40-A10) =3-MAX(0,A11-50) =4-MAX(0,40-A11) =3-MAX(0,A12-50) =4-MAX(0,40-A12) =3-MAX(0,A13-50) =4-MAX(0,40-A13) =3-MAX(0, A14-50) =4-MAX(0,40-A14) =3-MAX(0, A15-50) =4-MAX(0,40-A15) =3-MAX(0, A16-50) =4-MAX(0,40-A16) =3-MAX(0,A17-50) =4-MAX(0,40-A17) -3-MAX(0,A18-50)=4-MAX(0,40-A18) =3-MAX(0, A19-50) =4-MAX(0,40-A19) =3-MAX(0, A20-50) =4-MAX(0,40-A20) =3-MAX(0, A21-50) =4-MAX(0,40-A21) =3-MAX(0, A22-50) =4-MAX(0,40-A22) =3-MAX(0, A23-50) =4-MAX(0,40-A23) =3-MAX(0,A24-50) =4-MAX(0,40-A24) =3-MAX(0, A25-50) =4-MAX(0,40-A25) =3-MAX(0, A26-50) =4-MAX(0,40-A26) =3-MAX(0,A27-50) =4-MAX(0,40-A27) =3-MAX(0, A28-50) =4-MAX(0,40-A28) =3-MAX(0, A29-50) =4-MAX(0,40-A29) =3-MAX(0,A30-50) =4-MAX(0,40-A30) =3-MAX(0,A31-50) =4-MAX(0,40-A31) -3-MAX(0,A32-50)=4-MAX(0,40-A32) Net Payoff =SUM(B2:C2) =SUM(B3:03) =SUM(B4:04) =SUM(B5:C5) =SUM(B6:06) =SUM(B7:07) =SUM(B8:08) =SUM(B9:09) =SUM(B10:010) =SUM(B11:011) =SUM(B12:012) =SUM(B13:013) =SUM(B14:C14) =SUM(B15:015) =SUM(B16:016) =SUM(B17:C17) =SUM(B18:C18) =SUM(B19:C19) =SUM(B20:C20) =SUM(B21:C21) =SUM(B22:C22) =SUM(B23:C23) =SUM(B24:C24) =SUM(B25:C25) =SUM(B26:C26) =SUM(B27:C27) =SUM(B28:C28) =SUM(B29:C29) =SUM(B30:C30) =SUM(B31:C31) =SUM(B32:C32) 27 55 28 56 29 57 30 58 31 59 32 60

Net Payoff $8 a $6 $4 $2 O SO $30 $31 $32 $33 $34 $35 $36 $37 $38 $39 $40 $41 $42 $43 $44 $45 $46 $47 $48 $49 $50 $51 $52 $53 $54 $55 $56 $57 $58 $59 $60 ($2) (54) -Net Payoff

Maximum gain = $7

Maximum loss = potentially unlimited (both the options are sold naked)

Upper breakeven = $57

Lower breakeven = $33