Chapter 11 Trading Strategies with Options Paul Koch

Chapter 11. Trading Strategies with Options © Paul Koch 1 -1 I. Basic Combinations. A. Calls & Puts can be combined with other building blocks (Stocks & Bonds) to give any payoff pattern desired. 1. Assume European options with same exp. (T), K, & underlying. 2. Already know payoff patterns for buying & selling calls & puts: a. Calls. +c _______│_______S -c _______│____S _____K b. Puts. K +p _______│_______S -p _______│____S K______ K 3. Consider payoffs for long & short positions on: a. Stocks. +S _______│_______S K b. Bonds. _______│____S K +B _______│_______S K -S -B _______│____ S _ _ _K _ _ _ _

I. B. Protective Put (S+P) © Paul Koch 1 -2 B. Buy Stock (+S) and Buy Put (+P) Value +S +P S

I. C. Principal - Protected Note* (B+C) © Paul Koch 1 -3 C. Buy Bond (+B) and Buy Call (+C) Value +B +C B+C S * If you buy a zero-coupon, deep discount bond, the initial outlay (B) is small (esp. if r is high); If volatility of S is low, call (C) is cheap; Then the initial cost (B+C) may be set ≈ K (PPN). Then your principal is protected (worst outcome; S < K, call OTM, get to keep Bond payoff (K).

I. D. Put-Call Parity (S+P = B+C) © Paul Koch 1 -4 D. B & C give same payoff pattern (S+P = B+C) Value +S +P S+P +B +C B+C S

I. E. Writing a Covered Call (+S - C) © Paul Koch 1 -5 E. Buy Stock (+S) and Sell Call (-C) Value +S -C S+P = B+C ↓ +S-C -B = -P S

I. F. Buying a Straddle (+C+P) © Paul Koch 1 -6 F. Buy Call (+C) and Buy Put (+P), with same K Value +C +P C+P S

I. G. Selling a Straddle (-C-P) © Paul Koch 1 -7 G. Sell a Call (-C) and Sell a Put (-P), with same K Value -C -P -C - P S

I. H. Buying a Strangle (+C+P) – with Different K’s © Paul Koch 1 -8 H. Buy Call with K 2; Buy Put with K 1, with different K (K 1 < K 2) Value +C 2 +P 1 C 2+P 1 S K 1 K 2

II. How to Plot Payoff Pattern for Any Combination © Paul Koch 1 -9 Problem: Given any Combination of shares, bonds, & options, graph the Payoff Pattern for the Intrinsic Value; show slopes of line segments; & show break-even points. Three Steps: 1. Compute the initial cost / revenue of the Combination, and get values of S where all options are worth zero (ATM or OTM). For these values of S, Combination is worth the initial cost / revenue. 2. Get values of S where one option is ITM. For these values of S, Combination Value = initial cost / revenue + intrinsic value of this option. 3. Get values of S where next option is ITM. For these values of S, Combination Value = old value + intrinsic value of this option. Continue until you examine all values of S, for all options in combination.

II. How to Plot Payoff Pattern for Any Combination © Paul Koch 1 -10 Example 1: Strip; Buy 1 Call & 2 Puts with same K = $50; C = $5; P = $6. 1. Initial Cost = (-1) x ($5) + (-2) x ($6) = -$17. At S = K = $50, both options ATM, Combination Value = -$17. 2. If S > $50, Call ITM, Combination Value = -$17 + 1(S - K). (coeff. of S = +1) 3. If S < $50, Puts ITM, Combination Value = -$17 + 2(K - S). (coeff. of S = -2) K = $50 ______________________________ S $41. 50 │ $67 │ │ │ slope = -2 │ slope = +1 │ │ -17 │ │

II. How to Plot Payoff Pattern for Any Combination © Paul Koch 1 -11 Example 2: Buy 1 Call with K 1 = $40 (C 1 = $8); Sell 2 Calls with K 2 = $45 (C 2 = $5). 1. Initial Cost = (-1) x ($8) + (+2) x ($5) = +$2. If S < K 1 = $40, both options OTM, Combination Value = +$2. (coeff of S = 0) 2. If 40 < S < $45, C 1 is ITM, Value = +$2 + 1(S - K 1). (coeff = +1) 3. If S > $45, C 1 & C 2 are ITM, Value = +$2 + 1(S - K 1) - 2(S - K 2). (coeff = -1) K = $40 K = $45 │ 7│ │ │ slope = +1 │ │ slope = -1 2│ slope = 0 │ ___________________________ S │ $45 $52 │

II. A. Bull Spread with Calls (C 1 - C 2) © Paul Koch 1 -12 A. Buy Call with K 1 (pay C 1); Sell Call with K 2 (receive C 2) Value (K 1 < K 2); Thus (C 1 > C 2); So (-C 1 +C 2) < 0; initial outflow (left) +C 2 K 1 (-C 1 +C 2) -C 1 K 2 S

II. B. Bull Spread with Puts (P 1 - P 2) © Paul Koch 1 -13 B. Buy Put with K 1 (pay P 1); Value Sell Put with K 2 (receive P 2) (K 1 < K 2); Thus (P 1 < P 2); So (-P 1 +P 2) > 0; initial inflow (right) +P 2 (-P 1 +P 2 ) K 1 -P 1 K 2 S

II. C. Bear Spread with Calls (C 2 - C 1) © Paul Koch 1 -14 C. Sell Call with K 1 (receive C 1); Buy Call with K 2 (pay C 2) Value (+C 1 -C 2) (K 1 < K 2); Thus (C 1 > C 2); So (+C 1 -C 2) > 0; initial inflow (left) C 1 K 1 C 2 K 2 S

II. D. Bear Spread with Puts (P 2 - P 1) © Paul Koch 1 -15 D. Sell Put with K 1 (receive P 1); Buy Put with K 2 (pay P 2) Value (K 1 < K 2); Thus (P 1 < P 2); So (+P 1 -P 2) < 0; initial outflow (right) P 1 K 1 S K 2 P 2 (+P 1 -P 2)

II. E. Butterfly Spread with Calls (C 1 - 2 C 2 + C 3) © Paul Koch 1 -16 E. Buy 1 Call with K 1; Sell 2 Calls with K 2; Buy 1 Call with K 3 (K 1 < K 2 < K 3); Thus, (C 1 > C 2 > C 3); initial outflow (left).

II. F. Butterfly Spread with Puts (P 1 - 2 P 2 + P 3) © Paul Koch 1 -17 F. Buy 1 Put with K 1; Sell 2 Puts with K 2; Buy 1 Put with K 3 (K 1 < K 2 < K 3); Thus, (P 1 < P 2 < P 3); initial outflow (right).

III. A. Graphing Total, Intrinsic, and Extrinsic Value © Paul Koch 1 -18 Total Value K S Intrinsic Value S K Extrinsic Value K S

III. B. Buy Calendar Spread using Calls (+C 2 - C 1) © Paul Koch 1 -19 B. Buy Call with maturity, T 2 ; Sell Call with maturity, T 1 ; (T 2 > T 1); Thus, (C 2 > C 1); initial outflow (left).

III. C. Buy Calendar Spread using Puts (+P 2 - P 1) © Paul Koch 1 -20 C. Buy Put with maturity, T 2 ; Sell Put with maturity, T 1 ; (T 2 > T 1); Thus, (P 2 > P 1); initial outflow (right).

IV. Interest Rate Option Combinations (Hull Chap 21) © Paul Koch 1 -21 A. Using Options on Eurodollar Futures. 1. ED Futures Contract Characteristics : (Review) a. Underlying Asset - ED deposit with 3 -month maturity. b. ED rates are quoted on an interest-bearing basis, assuming a 360 -day year. c. Each ED futures contract represents $1 MM of face value ED deposits maturing 3 months after contract expiration. d. 40 different contracts trade at any point in time; contracts mature in Mar, Je, Sept, and Dec, 10 years out. e. Settlement is in cash; price is established by a survey of current ED rates. f. ED futures trade according to an index; Q = 100 - R = 100 - (futures rate); e. g. , If futures rate = 8. 50%, Q = 91. 50, and interest outlay promised would be (. 0850) x ($1, 000) x (90 / 360) = $21, 250. g. Each basis point in the futures rate means a $25 change in value of contract: [ (. 0001) x ($1, 000) x (90 / 360) ] = $25 ] h. The ED futures is truly a futures on an interest rate. (The T. Bill futures is a futures on a 90 -day T. Bill. )

IV. A. Using Options on ED Futures © Paul Koch 1 -22 2. Example: Long Hedge with ED futures for a Bank. (more Review) Jan. 6: Bank expects $1 MM payment on May 11 (4 months). Anticipates investing funds in 3 -month ED deposits. Cash Market risk exposure: Bank would like to invest @ today’s ED rate, but won’t have funds for 4 mo. If ED rate , bank will realize opportunity loss (will have to invest the $1 MM at lower ED rates). Long Hedge: Buy ED futures today (promise to deposit later @ R). Then if cash rates , futures rates (R) will & futures prices (Q) will . So long futures position will to offset opportunity loss in cash mkt. The best ED futures to buy is June contract; expires soonest after May 11. Jan. 6 May 11 June 14 |_____________________|_______| $1 MM receivable due May 11. Cash: Plan to invest $1 MM on May 11 Futures: Buy 1 ED futures. Invest the $1 MM in ED deposits. Sell futures contract.

IV. A. Using Options on ED Futures © Paul Koch 1 -23 3. Data for example – (more Review) Jan. 6: Cash market ED rate (LIBOR) = RS = 3. 38% (S 1 = 96. 62) June ED futures rate (LIBOR) = RF = 3. 85% (F 1 = 96. 15) ; Basis = (S 1 - F 1) =. 47% May 11: Cash market ED rate = 3. 03% (S 2 = 96. 97) June ED futures rate = 3. 60% (F 2 = 96. 40) ; Basis = (S 2 - F 2) =. 57% ________________________________________ Date Cash Market Futures Market Basis 1/6 bank plans to invest $1 MM at cash rate = S 0 = 3. 38% 5 / 11 bank invests $1 MM in 3 -mo ED at cash rate = S 1 = 3. 03% Net Effect opport. loss = 3. 38 - 3. 03 =. 35% (35) x ($25) = $875 bank buys 1 Je ED futures at futures rate = R 0 = 3. 85% . 47% bank sells 1 June ED futures at futures rate = R 1 = 3. 60% . 57% futures gain = 3. 85 - 3. 60 =. 25% (25) x ($25) = $625 Cumulative Investment Income: Interest @ 3. 03% = $1, 000 (. 0303) (90/360) = $7, 575 Profit from futures trades: = $625 Total: $8, 200 Effective Return = [ $8, 200 / $1, 000 ] x (360 / 90) = 3. 28% (10 bp worse than spot market = change in basis). This is basis risk. change. 10% .

IV. A. Using Options on ED Futures © Paul Koch 1 -24 4. Using Options on ED futures to build Floors, Caps, & Collars. a. ED futures contract: Buy ; Promise to buy ED ( lend @ forward ED rate); Sell ; Promise to sell ED (borrow @ forward ED rate). [ Lock in R. ] b. Call option on ED futures: Right to buy ED futures (lend @ forward ED rate). c. Put option on ED futures: Right to sell ED futures (borrow @ fwd ED rate). d. Lender? Want to buy ED in future. To hedge risk of loss with falling rates: i. Buy ED futures. If rates , lock in min. lending rate. --(hedged) But if rates , opportunity loss (could have loaned at higher rates). ii. Buy Call option on ED futures. If rates , lock in min. lending rate. NOW if rates , lend at higher rates! Call is OTM - interest rate Floor. e. Borrower? Want to sell ED in future. To hedge risk of loss with rising rates: i. Sell ED futures. If rates , lock in max. borrowing rate. --(hedged) But if rates , opportunity loss (could have borrowed at lower rates). ii. Buy Put option on ED futures. If rates , lock in max. borrowing rate. NOW if rates , borrow at lower rates! Put is OTM - interest rate Cap. f. Combining Call & Put on ED futures gives Collar.

IV. A. Using Options on ED Futures © Paul Koch 1 -25 5. Example: Building Interest Rate Collar for a bank. Cap: Buy a Put. Strike Option Price Premium 96. 00. 13 96. 50. 40 96. 25. 23 Cap at 4%; 0. 02 0. 11 0. 13 Floor: Sell a Call. Strike Option Price Premium 96. 75. 02 96. 50. 05 Floor at 3¼ %; Both: Collar. Range of Net Borrowing Cost Premium. 3¼% - 4%. 11 = $275 3¼% - 3½%. 38 = $950 3½% - 3¾%. 18 = $450. Collar: Net Cost = 11 basis points. | | | 96. 00 96. 75 Sell call | > Futures Price (Q) | | Buy put | Loss a. CAP borrowing rates @ 4% Must pay 13 bp for this Put i. If ED rates above 4%, ii. If ED rates below 4%, by buying a Put with K = 96. 00 (= 100 - 4). (13 x $25 = $325). Q below 96. 00, & Put is ITM – Cap at 4%. Q above 96. 00, & Put is OTM – Borrow at < 4%. b. If you don’t think ED rates will below, say, 3. 25%, can recover some of cost by selling a Call with K = 96. 75 (= 100 - 3. 25). Receive 2 bp ($50). i. If ED rates below 3. 25%, Q above 96. 75%, & Call is ITM – Floor at 3. 25%.