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Risk management
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1
Trading Strategies using Options on Derivatives
2
TopicsIntroduction
Strategies for a single option and a stock Covered call
Spreads and spread trading Bull call spread
Combinations Long Straddle Strangle Short Straddle
Other strategies Box spread Calendar spread Diagonal spread Butterfly spread
Conclusion
3
IntroductionFactors affecting the option price
Current stock price S0
Strike price K Time to expiration T Volatility of the stock σ Risk-free interest rate r Dividend expected before the option expiration
Options can be combined to create a range of payoffs - looking at holding a ‘portfolio’ vs. a single stock or option
For simplicity, we will ignore the time value of money – thus the profit for any strategy will be the final payoff – initial cost
Including transaction costs will not change the strategy being discussed. It is not included in the examples shown.
4
Single Option and a Stock
Covered Call: Long in the stock S and short in the Call•The covered call strategy works for the stocks for
which one does not expect a lot of upside or downside
•This strategy decreases risk but also the profit potential
•It is considered a conservative strategyConsider the following example of ABC Company
Stock price S0 = 63 Strike price K = 67 Time to expiration T = 3 mo (Sep 09) Call premium c = 1 (currently out-of-the money)
5
Single Option and a StockStock Price @ Expirati
on Long Stock Short Call Portfolio
55 -800 100 -700
56 -700 100 -600
57 -600 100 -500
58 -500 100 -400
59 -400 100 -300
60 -300 100 -200
61 -200 100 -100
62 -100 100 0
63 0 100 100
64 100 100 200
65 200 100 300
66 300 100 400
67 400 100 500
68 500 0 500
69 600 -100 500
70 700 -200 500
71 800 -300 500
72 900 -400 500
73 1000 -500 500
74 1100 -600 500
75 1200 -700 500
-1000
-500
0
500
1000
1500
55 57 59 61 63 65 67 69 71 73 75
Long S Short C Port
6
Single Option and a StockStock Price @ Expirati
on Long Stock Short Call Portfolio
55 -800 100 -700
56 -700 100 -600
57 -600 100 -500
58 -500 100 -400
59 -400 100 -300
60 -300 100 -200
61 -200 100 -100
62 -100 100 0
63 0 100 100
64 100 100 200
65 200 100 300
66 300 100 400
67 400 100 500
68 500 0 500
69 600 -100 500
70 700 -200 500
71 800 -300 500
72 900 -400 500
73 1000 -500 500
74 1100 -600 500
75 1200 -700 500
Long Stock• Investor owns 100 share at Rs.63. So for any
change in price above Rs.63 there is a profit and for any change in price below Rs.63 there is a loss incurred
Short Call (investor has sold a call option)• Investor has received the premium of Rs.1 per
share for 100 shares • The option will be exercised by the holder only
if the ST is above K or else it will expire unused• When exercised the investor will lose the
difference in the ST and K but will always have the initial premium collected
• If ST = 70 then investor has to sell the shares at 67 and incur a loss: (67-70)*100 + 100 = -200
Portfolio• Sum of the two positions
7
Spreads & Spread Trading
Spread trading involves taking a position in two or more options at the same time
Bull spread: When the investor expects the stock price to increase – buy a call option with a strike price and sell a call option on the same stock with a higher strike price. Both options have the same expiration date
Bear spread: When the investor expects the stock price to decrease – buy a put option with a strike price and sell a put option on the same stock with a lower strike price. Both options have the same expiration date.
8
Spreads & Spread Trading
Consider the following example of ABC Company Stock price S0 = 63
Strike price K = 67 Call premium (K=67) c = 1 (currently out-of–the
money) Strike price K = 70 Call premium (K=70) c’ = 0.75(out-of-the money and lower
premium)
Time to expiration T = 3 mo (Sep 09)
For a bull call spread go long in the K=67 call option and short in the K=70 call option
9
Spreads & Spread TradingStock
Price @ Expirati
onLong C
(lower K)Short C
(Higher K) Portfolio
55 -100 75 -2556 -100 75 -25
57 -100 75 -2558 -100 75 -25
59 -100 75 -25
60 -100 75 -2561 -100 75 -25
62 -100 75 -2563 -100 75 -25
64 -100 75 -2565 -100 75 -25
66 -100 75 -25
67 -100 75 -2568 0 75 75
69 100 75 17570 200 75 275
71 300 -25 275
72 400 -125 27573 500 -225 275
74 600 -325 27575 700 -425 275
-2000
-1500
-1000
-500
0
500
1000
1500
2000
Long C Short C Port
10
Spreads & Spread TradingStock
Price @ Expirati
onLong C
(lower K)Short C
(Higher K) Portfolio
55 -100 75 -2556 -100 75 -25
57 -100 75 -2558 -100 75 -25
59 -100 75 -25
60 -100 75 -2561 -100 75 -25
62 -100 75 -2563 -100 75 -25
64 -100 75 -2565 -100 75 -25
66 -100 75 -25
67 -100 75 -2568 0 75 75
69 100 75 17570 200 75 275
71 300 -25 275
72 400 -125 27573 500 -225 275
74 600 -325 27575 700 -425 275
Long Call (Lower K)
• The call option will be exercised only if the ST is > K (67). However, a premium of Rs.100 has been paid for the option
• At ST = 68 the investor makes no profit or loss
Short Call (Higher K)• Investor has received the premium of Rs.0.75
per share for 100 shares = Rs.75 • The option will be exercised by the holder only
if the ST is above K (70) or else expire unused
• When exercised the investor will lose the difference in the ST and K but will always have the initial premium collected
Portfolio• Sum of the two positions This is a limited-risk limited-profit strategyThe portfolio profit is capped at the difference in
the strike price less the difference in the premium
11
Combinations
Combination involves taking a position in both a call and put on the underlying stock at the same time. Traders and investors are ‘betting’ on the volatility of the stock price
Long Straddle: Buy a call and put option with the same strike price and expiration date. Close to at-the-money options work best. The premium on these options could be high.
Strangle: Buy an out-of the-money call and put option with different strike prices to reduce the cost. This is a low cost trade needing a high volatility to be profitable
12
CombinationsShort Straddle: Short a call and a put on the same stock with the same strike price and expiration date. Investors and traders are expecting volatility and the stock to trade in a range. Unexpectedly if the stock declines rapidly, the risk is high. Barings Bank fiasco.
Consider the following example of ABC Company Stock price S0 = 63
Strike price K = 67 Call premium (K=67) c = 1 (currently out-of–the
money) Put premium (K=67)p = 4 (currently in-the money) Time to expiration T = 3 mo (Sep 09)
13
Combinations – Long StraddleStock Price @ Expirati
on Long Call Long Put Portfoio
55 -100 800 700
56 -100 700 600
57 -100 600 500
58 -100 500 400
59 -100 400 300
60 -100 300 200
61 -100 200 100
62 -100 100 0
63 -100 0 -100
64 -100 -100 -200
65 -100 -200 -300
66 -100 -300 -400
67 -100 -400 -500
68 0 -400 -400
69 100 -400 -300
70 200 -400 -200
71 300 -400 -100
72 400 -400 0
73 500 -400 100
74 600 -400 200
75 700 -400 300
-1000
-500
0
500
1000
1500
2000
Long C Long P Port
14
Combinations – Long StraddleStock Price @ Expirati
on Long Call Long Put Portfoio
55 -100 800 700
56 -100 700 600
57 -100 600 500
58 -100 500 400
59 -100 400 300
60 -100 300 200
61 -100 200 100
62 -100 100 0
63 -100 0 -100
64 -100 -100 -200
65 -100 -200 -300
66 -100 -300 -400
67 -100 -400 -500
68 0 -400 -400
69 100 -400 -300
70 200 -400 -200
71 300 -400 -100
72 400 -400 0
73 500 -400 100
74 600 -400 200
75 700 -400 300
Long Call
• The call option will be exercised only if the ST is > K (67). However a premium of Rs.100 has been paid for the option
• At ST = 68 investor make no profit or loss
Long Put• The put option will be exercised if the stock
price ST is < K (67). A premium of Rs.400 has been paid for the in-the money put
• When exercised the investor will gain the difference in the ST and K but reduced by the premium paid
• For ST between 63 and 67 the investor loses some portion of the premium paid and for ST > 67 the investor loses the entire premium
Portfolio• Sum of the two positions
15
Combinations – Strangle
The idea in a Strangle is to profit on the volatility of the stock movement but also reduce the cost. As such the volatility has to be significant to realize a profit.
Consider the following example of ABC Company Stock price S0 = 63Strike price (call) Kc = 67Call premium (K=67) c = 1 (currently out-of-money)Strike price (put) Kp = 61Put premium (K=61)p = 0.25 (currently out-of-money)Time to expiration T = 3 mo (Sep 09)
16
Combinations – StrangleStock Price @ Expirati
on Long C Long Put Portfolio
55 -100 575 47556 -100 475 375
57 -100 375 27558 -100 275 175
59 -100 175 75
60 -100 75 -2561 -100 -25 -125
62 -100 -25 -12563 -100 -25 -125
64 -100 -25 -12565 -100 -25 -125
66 -100 -25 -125
67 -100 -25 -12568 0 -25 -25
69 100 -25 7570 200 -25 175
71 300 -25 275
72 400 -25 37573 500 -25 475
74 600 -25 57575 700 -25 675
-500
0
500
1000
1500
2000
Long C Long P Port
17
Combinations – StrangleStock
Price @ Expirati
on Long C Long Put Portfolio
55 -100 575 47556 -100 475 375
57 -100 375 27558 -100 275 175
59 -100 175 75
60 -100 75 -2561 -100 -25 -125
62 -100 -25 -12563 -100 -25 -125
64 -100 -25 -12565 -100 -25 -125
66 -100 -25 -125
67 -100 -25 -12568 0 -25 -25
69 100 -25 7570 200 -25 175
71 300 -25 275
72 400 -25 37573 500 -25 475
74 600 -25 57575 700 -25 675
Long Call
• The call option will be exercised only if the ST is > K (67). However a premium of Rs.100 has been paid for the option
• At ST = 68 investor make no profit or loss
Long Put• The put option will be exercised if the stock
price ST is < K (61). A premium of Rs.25 has been paid for the out-of-the money put
• When exercised the investor will gain the difference in the ST and K but reduced by the premium paid
• For ST > 61 the entire premium is lost
Portfolio• Sum of the two positions Note that the cost of this strategy was lesser than
the Straddle since the premiums were lower
18
Combinations – Short StraddleThe investor writes an uncovered call and an uncovered put on the same stock, same expiration and same strike price. Together the strategy is expected to be ‘neutral’ if the stock trades within a range. However, large potential loss exists should the stock movement be unexpected. The profit potential is limited to the premiums of the put and call. It is a highly risky strategy.
Consider the following example of ABC Company Stock price S0 = 63Strike price (call) K = 67Call premium (K=67) c = 1 (currently out-of-money)Put premium (K=61)p = 4 (currently in-the money)Time to expiration T = 3 mo (Sep 09)
19
Combinations – Short StraddleStock Price @ Expirati
on Short C Short P Portfolio
55 100 -800 -70056 100 -700 -600
57 100 -600 -50058 100 -500 -400
59 100 -400 -300
60 100 -300 -20061 100 -200 -100
62 100 -100 063 100 0 100
64 100 100 20065 100 200 300
66 100 300 400
67 100 400 50068 0 400 400
69 -100 400 30070 -200 400 200
71 -300 400 100
72 -400 400 073 -500 400 -100
74 -600 400 -20075 -700 400 -300
-2000
-1500
-1000
-500
0
500
1000
Short C Short P Port
20
Combinations – Short StraddleStock Price @ Expirati
on Short C Short P Portfolio
55 100 -800 -70056 100 -700 -600
57 100 -600 -50058 100 -500 -400
59 100 -400 -300
60 100 -300 -20061 100 -200 -100
62 100 -100 063 100 0 100
64 100 100 20065 100 200 300
66 100 300 400
67 100 400 50068 0 400 400
69 -100 400 30070 -200 400 200
71 -300 400 100
72 -400 400 073 -500 400 -100
74 -600 400 -20075 -700 400 -300
Short Call • The call option will be exercised by the holder only
if the ST is > K (67). However a premium of Rs.100 has been received
• At ST = 68 investor makes no profit or loss
• Being uncovered the loss potential is highShort Put• The put option will be exercised by the holder if the
stock price ST is < K (67). A premium of Rs.400 has been received by the investor
• When exercised the investor will lose the difference in the ST and K but compensated for by the premium received
• For ST > 67 the investor only receives the premium
Portfolio• Sum of the two positions As the stock price increases the loss on the short call
is much greater than the premium received for the short put. Thus the loss potential is high
21
Combinations – Short StraddleNick Leeson Story
• Invested in Nikkei 225 stock index futures – made losses when the Nikkei dropped due to the Kobe earthquake (unexpected event)
• To recoup the losses created a short straddle (uncovered and highly risky) on the Nikkei expecting it to stabilize and trade within a range(19000)
• His straddle positions ranged from 18,500 – 20,000• Nikkei dropped way below and Nick Leeson incurred 1.4b
losses and Barings filed for bankruptcy.
22
Other Strategies
Theoretically if European options with expiration at time T exist for every single strike price then it is possible to construct any payoff with a combination of these
Box Spread: This is a combination of a bull call spread with strike price K1 and K2 and a bear put spread at the same two strike prices. When K2 > K1, buy a call option at K1 and sell a call option at K2 & buy a put option at K2 and sell a put option at K1
This combination does not work with American options
23
Other StrategiesCalendar spread or Horizontal spread: The combination is developed using options with different expiration dates but with the same strike price
Diagonal spread: The strike price and the expiration dates of the options are different
Butterfly spread: involves options with three different strike prices and same expiration date. Either all puts or all calls can be used for this strategy. The idea is to buy a call (long) with at strike price K1 and another at strike price K2 and short two calls with a strike price K3 midway between K1 and K2. Usually potential gain and loss is limited
24
Other Strategies - Butterfly
Consider the following example of XYZ Co.
Stock price S0 = 75.28Strike price (Low call) K1 = 72Call premium c1 = 6.10 (in-the-money)Strike price (High call) K2 = 78Call premium c2 = 2.60 (currently out-of-money)Strike price (Mid call) K3 = 75Call premium c3 = 4.10 (almost at-the money)Time to expiration T = 3 mo (Sep 09)
Investor: one long c1, one long c2, two short c3
25
Other Strategies - ButterflyStock
Price @ Expirati
on L C(Hi K) LC (Lo K) Sh C (2 ) Portfolio65 -260 -610 820 -5066 -260 -610 820 -5067 -260 -610 820 -5068 -260 -610 820 -5069 -260 -610 820 -5070 -260 -610 820 -5071 -260 -610 820 -5072 -260 -610 820 -5073 -260 -510 820 5074 -260 -410 820 15075 -260 -310 820 25076 -260 -210 620 15077 -260 -110 420 5078 -260 -10 220 -5079 -160 90 20 -5080 -60 190 -180 -5081 40 290 -380 -5082 140 390 -580 -5083 240 490 -780 -5084 340 590 -980 -5085 440 690 -1180 -50
-1500
-1000
-500
0
500
1000
65 67 69 71 73 75 77 79 81 83 85
L C(Hi K) LC (Lo K) Sh C (2 ) Portfolio
26
Other Strategies - ButterflyStock
Price @ Expirati
on L C(Hi K) LC (Lo K) Sh C (2 ) Portfolio65 -260 -610 820 -5066 -260 -610 820 -5067 -260 -610 820 -5068 -260 -610 820 -5069 -260 -610 820 -5070 -260 -610 820 -5071 -260 -610 820 -5072 -260 -610 820 -5073 -260 -510 820 5074 -260 -410 820 15075 -260 -310 820 25076 -260 -210 620 15077 -260 -110 420 5078 -260 -10 220 -5079 -160 90 20 -5080 -60 190 -180 -5081 40 290 -380 -5082 140 390 -580 -5083 240 490 -780 -5084 340 590 -980 -5085 440 690 -1180 -50
Long Call (high)
• The call option will be exercised only if the ST is > K1 (78). However a premium of Rs.260 has been paid upfront
• For ST > 78 the upward profit potential is high
Long Call (low)
• The call option will be exercised only if the ST is > K2 (72). However a premium of Rs.610 has been paid upfront
• For ST > 72 the ‘loss’ initially decreases and then the profit potential set in
• Short Call (midway)• The call option will be exercised by the holder only if
the ST is > K3 (75). However a premium of Rs. 820 (for 2 trades) has been received by the investor
Portfolio
• For ST below 73 or above 77 the loss of the portfolio is the maximum initial outlay = (-260 –610 + 820 = 50)
• Maximum profit is at the midway strike price of Rs.75 This is used when the trading range is expected to be
narrow and investor does not want to use an uncovered straddle.
27
Other Strategies - Butterfly
Forbes.com OptionsFlash by Andrew Wilkinson 06.23.09 1:35 PM ET
Betting On A Big Downside For Apple
Apple Inc.: In the July contract and with shares in Apple easing 2.6% to $133.74, one option investor is betting on a 17.5% price decline in shares of the iPhone-maker to $110 within the next three weeks. A put butterfly combination was bought at the 100/110 and 120 strikes for a net premium of 64 cents. In this combination the investor sells twice as many put options at the central strike price against the purchase of puts at the two outer strikes. With this combination involving strike prices exactly $10 wide, the maximum profit of that strike distance less the premium amounts to$9.34 per contract in the event that the share price arrives at expiration at $110. Options implied volatilities are higher by almost 9% on the share price decline. The bearish activity comes shortly after the company released news that founder Steve Jobs underwent a liver transplant during personal leave two months ago.
28
Conclusions
• Any payoff strategy can be developed using a combination of options – very exciting and challenging!
• Many strategies are risky and have a significant downside potential
• Prudent financial risk management is critical to success in trading
29
Thank You!