Question

An investor buys 100 shares of a stock, shorts 60 call options on the stock with strike price of $20 and buys 60 put options on the stock with strike price of $10. All options are one-year European options. Draw a diagram illustrating the value of the investor’s portfolio as a function of the stock price after one year.

Answer 1

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

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

S = underlying price at expiry,

X = strike price

Value of portfolio = value of stock + payoff of short call options + payoff of long put options

$7 $9 $0 $0 Stock price Short Call Long Put Value of after 1 year ($20)*60 ($10)*60 stock $600 $0 $0 $540 $100 $0 $480 $200 $420 $300 $360 $400 $300 $500 $240 $600 $180 $700 $120 $800 $60 $900 $10 $1,000 $11 $1,100 $12 $1,200 $13 $1,300 $14 $1,400 $15 $1,500 $16 $1,600 $17 $1,700 $18 $1,800 $19 $0 $1,900 $20 $0 $2,000 $21 ($60) $2,100 $22 ($120) $0 $2,200 $23 ($180) $2,300 $24 ($240) $2,400 $25 ($300) $2,500 $26 ($360) $2,600 $27 ($420) $2,700 ($480) $2,800 $29 ($540) $2,900 $30 ($600) $3,000 Value of portfolio $600 $640 $680 $720 $760 $800 $840 $880 $920 $960 $1,000 $1,100 $1,200 $1,300 $1,400 $1,500 $1,600 $1,700 $1,800 $1,900 $2,000 $2,040 $2,080 $2,120 $2,160 $2,200 $2,240 $2,280 $2,320 $2,360 $2,400 $0 $0 $0 $0 $0 $0 $28 $0

1 2 Stock price after 1 year 0 42 5 3 6 4 9 7 108 119 12 13 14 15 16 17 18 19 20 10 11 12 13 14 15 16 17 18 Short Call ($20)'60 Long Put ($10)'60 =(-MAX(O,A2-20))*60 =(MAX(10-A2,0))*60 =(-MAXO, A3-20))*60 =(MAX(10-A3,0))*60 =(-MAXO,A4-20))*60 =(MAX(10-A4,0))*60 =(-MAXO, A5-20))*60 =(MAX(10-A5,0))*60 = (-MAX(O, A6-20))*60 =(MAX(10-A6,0))*60 =(-MAXO,A7-20))*60 =(MAX(10-A7,0))*60 =(-MAX(O,A8-20))*60 =(MAX(10-A8,0))*60 = (-MAX(O,A9-20))*60 =(MAX(10-A9,0))*60 =(-MAXO, A 10-20))*60 =(MAX(10-A10,0))*60 =(-MAXO,A11-20))*60 =(MAX(10-A11,0))*60 =(-MAX(O, A12-20))*60 =(MAX(10-A12,0))*60 =(-MAXO A13-20))*60 =(MAX(10-A13,0))*60 =(-MAX(O, A14-20))*60 =(MAX(10-A14,0))*60 =(-MAXO A15-20))*60 =(MAX(10-A15,0))*60 =(-MAXO,A16-20))*60 =(MAX(10-A16,0))*60 =(-MAXO,A17-20))60 =(MAX(10-A17,0))*60 =(-MAXO, A 18-20))*60 =(MAX(10-A18,0))*60 =(-MAXO A 19-20))*60 =(MAX(10-A19,0))*60 =(-MAX(O, A20-20))*60 =(MAX(10-A20,0))*60 =(-MAX(0, A21-20))*60 =(MAX(10-A21,0))*60 =(-MAXO,A22-20))*60 =(MAX(10-A22,0))*60 =C-MAXO,A23-20))*60 =(MAX(10-A23,0))*60 =(-MAXO,A24-20))*60 =(MAX(10-A24,0))*60 =(-MAX(O, A25-20))*60 =(MAX(10-A25,0))*60 =(-MAX(O, A26-20))*60 =(MAX(10-A26,0))*60 =(-MAXO, A27-20))*60 =(MAX(10-A27,0))*60 =(-MAXO,A28-20))*60 =(MAX(10-A28,0))*60 =(-MAX(O, A29-20))*60 =(MAX(10-A29,0))*60 =(-MAX(O,A30-20))*60 =(MAX(10-A30,0))*60 =(-MAX(O, A31-20))*60 =(MAX(10-A31,0))*60 =(-MAX(O,A32-20))*60 =(MAX(10-A32,0))*60 Value of stock Value of portfolio = A2 100 = SUM(B2:D2) =A3100 =SUM(B3:03) = SUM(B4:04) = A5'100 = SUM(B5:05) =A6'100 = SUM(B6:06) =A7*100 =SUM(B7:07) =A8'100 = SUM(B8:08) =A9 100 =SUM(B9:09) =A10'100 = SUM(B10:010) =A11100 =SUM(B11:011) =A12 100 =SUM(B12:012) =A13100 = SUM(B13:013) =A14100 = SUM(B14:014) = A15'100 = SUM(B15:D15) =A16'100 =SUM(B16:016) =A17100 = SUM(B17:017) =A18'100 =SUM(B18:018) = A19 100 = SUM(B19:019) =A20'100 = SUM(B20:D20) = A21100 =SUM(B21:D21) =A22100 =SUM(B22:022) = A23100 = SUM(B23:D23) =A24'100 = SUM(B24:D24) =A25-100 =SUM(B25:025) = A26'100 =SUM(B26:D26) = A27100 = SUM(B27:D27) = A28'100 = SUM(B28:028) = A29 100 =SUM(B29:029) =A30100 = SUM(B30:D30) =A31' 100 =SUM(B31:031) =A32' 100 ESUM(B32:032) 22 20 23 21 24 22

Value of portfolio = value of stock + payoff of short call options + payoff of long put options