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examples long butterflies

The above covered write example describes this extremely popular strategy (most common in the equity market). The covered write consists of long an underlying instrument and short a call. The package emulates or is synthetically a short put. Out-of-the-money calls are usually written during a given expiration month against5 each loo shares of stock to enhance the investors rate of return. The premium collected is an enhancement if the call expires worthless and the stock is the same price or higher. It is also an enhancement if the call is assigned when in-

Exception for Covered Write vs. Short Put

A short put differs from a covered write when a stock is involved in a merger, buyout, or special dividend. In such a case, a person short the put would not participate in some benefits that a shareholder would. In a partial tender offer, where part of the purchase is with stock and part is with cash or other instruments, there can be a wide disparity between the synthetic relationships (see Stocks Involved in Tender Offers in Chapter 3). Briefly, it would be more profitable to have the covered write in the case of a partial tender offer than a short put.

5 Against

Against is synonymous with versus, meaning offset or hedged . If I have long deltas with one set of contracts and short deltas to offset them using other contracts, it is said that the first set of contracts are against the second set.

©2001 Charles M. Cottle

charlescottle@sbcglobal.net



the-money because the writers total proceeds on the sale of his or her shares is the strike price plus the premium collected and that had to have been greater than the available stock price at the time of the call sale. It would not turn out to be an enhancement if the call expired worthless while the stock declined an even greater amount than the premium collected.

This is why covered writes are not suitable for everyone. There are risks to the downside. It can suit long-term retirement account investments as well as widows, orphans and other trust-funders very well, that is, people who never intend to sell their stock.

It was a very popular strategy during the bull market of the 1980s, but unfortunately brokers were putting the wrong kind of clients into the covered writes. It is not prudent for some investors to initiate long stock/short call positions as a spread. If a broker had asked these same people whether they would have liked to sell puts naked, they may well have hung up on him. These positions added to the 1987 crash because they created more positions that had to be liquidated or required new hedges, which helped to create selling pressure and panic.

My friend Joe put it best when he said of the October 1987 crash, What do you expect when 350 million shares in New York have to be hedged with 350 kids from Highland Park? (Suburb on Chicagos North Shore where many of the traders in the S&P 500 futures and OEX pits live or grew up.) A covered write offers a limited amount of protection and is inadequate in a severe market decline. The sad truth is that many of the brokers themselves were shocked when they realized just how inadequate these so-called hedges were. I would not call a covered write a hedge , although it can be a reasonable strategy for some people.

It is important to understand the nature of risk and the synthetic properties that are inherent in options. People too often look at how much they can win and not often enough at what they can lose. This approach has made many people rich, but it is unfortunately only a matter of time before the market eventually ruins those who carry positions that they were not prepared to deal with under different scenarios. Traders often suffer from tunnel vision and lose sight of the fact that they hold a position on a security that they never wanted. It is usually too late to act by the time that they realize this.

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LOCKS

Synthetics are most useful to arbitrageurs who look for opportunities to purchase one instrument cheaper than they sell another or to purchase a combination of instruments that emulate and/or offset their initial purchase, with the intent of profiting from a mispriced relationship. Some arbitrages or arbs involve straightforward strategies while others, such as those that involve interest and dividend streams, may be somewhat complicated and non-transparent6.

To make the best possible use of synthetics and dissection as tools for trading derivatives, one has to have an understanding of the properties pertaining to locked positions or locks. Lock is a term used to describe a position that has locked in a profit or a loss and theoretically cannot lose any money from that point forward. Spreads that are commonly referred to as locks are conversions/reversals, boxes, and jelly rolls. Boxes and jelly rolls are a combination of the conversion/reversal. This explanation of locked positions will therefore concentrate on the conversion/reversal.

SYNTHESIS: USING A CONVERSION/REVERSAL (C/R)

A conversion is a spread consisting of long underlying, long put, and short call with the same strike at the same expiration (+ u + p - c). A reversal is the opposite spread, consisting of short underlying, short put, and long call (- u - p + c). Notice that a reversal is the reverse of a conversion. This means that if two parties trade this spread with each other, one would end up with the conversion and the other with the reversal. If the trade is executed at fair value, there will be no profit or loss. The object for each party is to trade into the conversion or the reversal at better than fair value.

Non-transparent

A nontransparent value is one that has other income or expenses associated with it and is not clearly visible (e.g., if you buy stock today and hold it for one year, the cost is greater than the purchase price today because you are either forgoing the interest (implicit interest) on the money you paid or you have to borrow money to buy it with and pay interest on that. Of course, if you receive dividends, your cost is reduced to some extent.

©2001 Charles M. Cottle

charlescottle@sbcglobal.net



FAIR VALUE EQUATIONS

The conversion/reversal is a forward value (because it represents interest or interest minus dividend flows until expiration). It can be positive or negative (+/-) and is expressed as a debit (dr.) or a credit (cr.). In other words, the C/R is a spread where the strike and call are traded (a strike is not traded but upon exercise the underlying is traded at the strikes price) against or versus (vs.) the underlying and put. The price is equal to either a small debit (paid) or a small credit (received).

C/R = (k + c) vs. (u + p) where:

k is the strike price c is the call price

u is the underlying price (stock, futures, cash instrument or cash index) p is the put price.

The conversion/reversal price is equal to the difference between (k + c) and (u + p). Again, the k value, though not actually traded, is the price at which the underlying will eventually be transacted upon exercise. It is therefore accounted for in the computation of the spread price.

Buy Sell The conversion price is: (u + p) - (k + c)

Buy Sell

The reversal price is: (k + c) - (u + p)

Suppose that in this example the C/R is theoretically worth zero (and it would be if the amount of quarterly dividend was equal to the cost of carry until expiration). The conversion + u + p - c = 0, and the reversal - u - p + c = 0. Each is considered to be flat7 by many traders. The profit for a market maker (who competes to buy on the bid and sell

7 Flat

Conversions and reversals are not always flat (see Chapter 3). C/Rs are really flat only if the option contract is designed with futures-style margining, and the underlying is a future. With futures-style margining, a fraction of the full amount of the purchase or sale price of the options can be margined with U.S. Treasury bills instead of using cash. Interest would not be a factor because there is no cash flow. In this example, the dividend, although not specified, happens to be equal to the present cost of carry so that for today: k + c = u + p.

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at the ask price) for example, comes from transacting the trades. If (k + c) and (u + p) are not equal, then a profit or loss is made. If either side of the equation is sold for a higher price than the other is bought, then the trader has locked in a profit. The following two examples illustrate profitable trades. Each generates a .25 credit (received) on the three-legged transaction, that is, a profit. The option prices in the examples are different for the reversal than they are for the conversion. If they were the same then one of the trades would have had to have been done for a .25 debit (paid), that is a loss.

For the following examples, assume that the theoretical values (TV)8 for the 100 strike options at the stock price of 101.00 are 2.00 for the call and 1.00 for the put.

Reversal example:

The c is bought at 1.85 when the market is 1.85 (bid) - 2.15 (ask) The u is sold (shorted) at 101.00

The p is sold (shorted) at 1.10 when the market is .90 - 1.10

Consider that the k is bought at 100.00. It represents the stocks purchase price at expiration because the trader will either exercise the 100 call if it is in the money or be assigned on the 100 put if it is in the money. So:

k + c versus u + p

100 + 1.85 paid and 101.00 + 1.10 received

101.85 debit add 102.10 credit

Net Result: .25 credit

Therefore, the net result is a reversal that has been executed for a .25 credit (received). Since k and c were bought cheaper than u and p were sold, the reversal was traded for a profit.

Conversion example:

The c is sold (shorted) at 2.15 when the market is 1.85 (bid) - 2.15 (ask) The u is bought at 101.00

The p is bought at .90 when the market is .90 - 1.10

Theoretical Value

An estimated price of a call or put derived from a mathematical model, such as the Black-Scholes or binomial models.

©2001 Charles M. Cottle

charlescottle@sbcglobal.net



Consider that the k is sold at 100.00. Again, it represents the stocks sale price at expiration because the trader will either be assigned on the call if it is in-the-money (ITM), or exercise the put if it is in-the-money. So:

k + c versus u + p

100 + 2.15 received and 101.00 + .90 paid

102.15 credit add 101.90 debit

Net Result: .25 credit

Therefore, the net result is a conversion that has been executed for a .25 credit (received). Since u and p were bought cheaper than k and c were sold, the conversion was traded into for a profit.

At this point, there is very little to worry about for a while but by the time expiration approaches, pin risk9 may become a problem and perhaps there will be an opportunity for an early exercise depending on where the stock is trading at the time. Details on these factors and more in Chapter 3.

PUT-CALL PARITY

Put-call parity is an equation used in option pricing models to describe the relationship between puts and calls. If you have the call or put price you could derive the other by using this equation. Position dissection uses it to prove that a dissected position has the same risk profile as the original raw position. To show you a simple way to demonstrate the put-call parity, I will use the fair values from the last example for a conversion (+ u + p - c). The call price is 2.00, the put price is 1.00, and the underlying is 101.00. More scientific approaches can be found in other options books that emphasize the mathematical equations10. Here is a simple way to understand that this conversion basically does not

9 Pin Risk

The risk to a trader who is short an option that, at expiration, the underlying stock price is equal to (or pinned to ) the short options strike price. If this happens, he will not know whether he will be assigned on his short option. The risk is that the trader doesnt know if he will have no stock position, a short stock position (if he was short a call), or a long stock position (if he was short a put) on the Monday following expiration and thus be subject to an adverse price move in the stock.

10 Mathematical Equations

Option Pricing and Investment Strategies by Richard M. Bookstaber, 3rd ed. pp. 28-29.

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make or lose anything by expiration irrespective of where the underlying settles owing to the put-call parity.

By performing what-if analyses, it can be determined that the position breaks even at all levels. Begin by checking, for example, at 101.00 (the current stock price), 100.00 (the strike price), and then twice the strike price at 200.00 and half the strike price at 50.00. What is the theoretical value and P&L at each of these price levels for the three instruments traded? What is their sum? If the sum is zero then there is no profit or loss.

In Exhibit 1-1, the theoretical value at each of the test levels is shown. If the option is in the money, it is worth the intrinsic value, which is the difference between the strike and the underlying price. If the option is out of the money, it is worthless. Remember that the underlying was bought at 101.00, the 100 put was bought at a fair value of 1.00, and the 100 call was sold at a fair value of 2.00.

The trade in Exhibit 1-1 will be worth zero at expiration. It follows that if either spread in the previous reversal and conversion examples was executed for a .25 credit, there would be a .25 profit. Notice also that the mnemonic, CUP can be used to remember this type of what-if example. How full will your CUP be after the trade?

EXHIBIT 1-1

+u at 101 / + 100p at 1 / - 100c at 2 (The slashes / represent position separators).

@ 50

TV P&L

0 + 2

50 - 51

50 + 49

@ 100 TV P&L

0 -J 0

@ 101 TV P&L

1 + 1

101 0

@ 102 TV P&L

102 + 1

@ 200 TV P&L

100 - 98

200 + 99 0

In reality, locks do not usually trade at expiration unless they are at the money (to avoid pin risk). Consider the calculations in Exhibit 1-2. Unlike the last example, this assumes an exercise of the in-the-money option. At expiration there is an exercise (X). The trader delivers the stock, that is, the к is sold at 100.00. The premium of the exercised option is retained in a short option and lost in a long option.

©2001 Charles M. Cottle

charlescottle@sbcglobal.net



Notice that the end result is again zero, which proves that this particular conversion is flat.

EXHIBIT 1-2

Exercise to Deliver the Underlying Stock at a Sales Price of 100 +u at 101 / +100p at 1 / - 100c at 2 / -k at 100

@ 50 TV P&L

@ 100 TV P&L

@ 101 TV P&L

@ 102 TV P&L

@ 200 TV P&L

0 + 2

0 + 2

X + 2

X + 2

X + 2

50 - 51

100 - 1

101 0

102 + 1

200 + 99

X - 1

0 - 1

0 - 1

0 - 1

0- 1

100 + 50

no X* 0

100 - 1

100 -2

100 - 100

*Pin Risk. Assume no exercise and cover short stock at 100

POSITION DISSECTION - LESSON I

Position dissection works under the premise that locked positions such as conversions, reversals, and boxes can be removed from the position because they are basically neutral and can be used as filters to uncover and detect different aspects about a position that may not at first be apparent. Dissection allows the user to alter his or her perception of a position in order to have more information about how to proceed with a trade and measure risk.

Begin by carding up the position, which simply means to write it down. The origin of the word carding comes from the trading floors where many traders still use position cards to keep track of their positions.

There are numerous ways to card up trades and account for position changes, but the format used in this book will be easy to follow and consistent. Whichever way works best for the individual is fine as long as it is methodical and consistent. It is strongly recommended, however, that in the beginning trades be written down and the synthesis performed by hand even though most traders have access to computers. This promotes understanding and makes it easier to memorize the position. All positions will be displayed in the format shown in Exhibit 1-3. Raw refers to the actual position. Net refers to the position after dissection or synthesis.

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EXHIBIT 1-3

Format for Displaying Positions

Underlying (u)

Net Calls

Raw Calls

(+/-)

Raw Puts

Net Puts

(nc)

(rc)

(rp)

(np)

long

short

long

short

long

short

long

short

Strike 1 Strike 2 Strike 3 etc.

(n cc)

net call contracts

net put contracts

(npc)

(+/-)

(+/-)

(+/-)

(+/-)

NET CALL CONTRACTS AND NET PUT CONTRACTS

When the market makes a large move in either direction it is very important to know the amount of net call contracts (ncc) and net put contracts (npc) in your position. Net calls are the sum of all the calls, plus any underlying contracts (add underlying amount if long the underlying or subtract if short the underlying). Net puts are the sum of all the puts, minus any underlying contracts (subtract underlying amount if long the underlying or add if short the underlying). In other words, if the market crashes a trader wants to know the net amount of puts that he or she will have which will trade at parity or turn into underlying either through exercise or assignment. Put parity options move one to one against the underlying, while call parity options move one to one with the underlying. Put parity options move one to one against the underlying, while call parity options move one to one with the underlying. Therefore, being short (-)10oo underlying wins and loses as much as long (+)10 parity puts does so that is +10p for the net put contracts count and short -10c for the net call contracts. Since the trader has +20c and -10м, in this position, he has net +10c for his net call count.

Net contracts should be tallied at the bottom of each T account at all stages of each dissection. This is the first of the checks and balances for possible errors in dissecting positions. If the net contracts from one stage to the next differ, an error has occurred and it must be found before

©2001 Charles M. Cottle

charlescottle@sbcglobal.net



continuing. Without this special check, an error in judgment could lead to false conclusions about the risk in a given position. It is therefore strongly recommended that net contracts be checked following each stage of the dissection.

COMMON LOCKS CARDED UP

In Exhibit 1-4, section A, one can see that a conversion (top) is the exact opposite of a reversal (bottom). Sometimes the spread is referred to by one name: conversion/reversal. Section B shows a long box (top) and short box (bottom). Section C shows a long jelly roll (top) and short jelly roll (bottom). The top jelly roll is regarded as long because it is long time (long the further dated combo11 and short the near term). The opposite is true for the short jelly roll.

EXHIBIT 1-4

Position Configurations

May 99 Conversion

Long May 98/99 Box

Long May/June 99 Jelly Roll

May +1u

1 99 1

May 98

1 99 1

1 99 1

June

May 99Reversal

Short May 98/99 Box

Short May/June 99 Jelly Roll

May -1u

May 198 1 99

June 1 99 1

Section A

Section B

Section C

11 Combo

Trading jargon for a combination. Usually refers to a same strike call and put combo where one is long and the other is short, creating synthetic underlying and is often another term for synthetic stock. When synthetic stock, a combo must be composed of calls and puts on the same stock, strike price and expiration. The amount of long options and short options nets out to zero. Buying a combo is buying synthetic stock; selling a combo is selling synthetic stock. For example, a long 60 combo is long 1*60 call and short 1*60 put. Another type of combo can consist of options at two different strikes in which case it would not be synthetic stock.

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