I
n this chapter we examine a single trade in detail. We begin with the pretrade process of finding a prospective trade, measure and forecast volatility, then execute and hedge the options. Most of the actual trading consists of rehedging according to our predetermined plan and constantly reevaluating the position so that our exposure is a reflection of our current thoughts. Finally, we exit the trade and go through the post-trade analysis.PRETRADE ANALYSIS
June 25, 2007
Apple computer (AAPL) was a darling of the market. Positioned at the con- fluence of the fashion and technology industries, it could seemingly do no wrong as its share price increased to over $125 per share. Over the previ- ous five years it had rallied on a split-adjusted basis from $8.57, an increase of 1,358 percent, as compared to a gain of 54 percent for the S&P 500. The iPod was a cultural phenomenon and the Mac versus PC commercials were generally adored. The iPhone launch scheduled for June 29 was expected to be the catalyst for another explosive burst.1Apple was a perfect example of the stock that people many expected to rally and rally big. Conversely,
1An excellent appraisal of the attitudes of the first group of iPhone buyers was pro- vided by Charles Golvin of Forrester Research on CNBC’sMorning Callof July 2, 2007. He noted that Apple had to sell to others beyond this hardcore group who 165
the hype was attracting the standard number of contrarian types who were predicting a huge impending flop. This is the sort of situation that can eas- ily result in overpriced options as directional traders bet on large moves, bidding up the value of both puts and calls.
July implied volatility had been going progressively more bid for sev- eral weeks, rallying from the mid-twenties to the high thirties. Figures 9.1 to 9.5 show the various volatility measurements.
0 0.1 0.2 0.3 0.4 0.5 0.6
Date
Close-to-Close Volatility
3/24/06 7/2/06 10/10/06 1/18/07 4/28/07 8/6/07
FIGURE 9.1 The 30-Day Close-to-Close Volatility
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Date
Parkinson Volatility
3/24/06 7/2/06 10/10/06 1/18/07 4/28/07 8/6/07
FIGURE 9.2 The 30-Day Parkinson Volatility
bought the iPhone for “fantasy fulfillment” and “the realization of all their dreams.”
This comment reflects both the bullish hype from one group and the bearish re- sponse from another.
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Date
Garman-Klass Volatility
3/24/06 7/2/06 10/10/06 1/18/07 4/28/07 8/6/07
FIGURE 9.3 The 30-Day Garman-Klass Volatility
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
Date
Rogers-Satchell Volatility
3/24/06 7/2/06 10/10/06 1/18/07 4/28/07 8/6/07
FIGURE 9.4 The 30-Day Rogers-Satchell Volatility
0 0.1 0.2 0.3 0.4 0.5 0.6
Date
Yang-Zhang Volatility
3/24/06 7/2/06 10/10/06 1/18/07 4/28/07 8/6/07
FIGURE 9.5 The 30-Day Yang-Zhang Volatility
TABLE 9.1 Volatility Estimates
Yang-Zhang 31.1
Close-to-close 28.3
Parkinson 27.2
Garman-Klass 29.9
Rogers-Satchell 27.4
GARCH 36.1
High-frequency 21.0
Table 9.1 shows the numerical values of all the volatility estimates, and Figure 9.6 uses the volatility cone to put the current situation into a historical context.
After some discussion and eyeballing the data, we arrived at a con- sensus forecast of 29 for realized volatility over the next three weeks (the duration of the July option contracts). July implied volatility was 41 bid.
This gave an edge of 41 percent. The normal spread for AAPL was around 20 to 25 percent. To put this in context of the overall market, the VIX was trading 16.5 and our forecast volatility was 12.6 percent for an edge of 31 percent. This spread was a little higher than usual but not dramatically so.
At this point we were reasonably confident that we had an edge in the spread between implied volatility and realized volatility, both on absolute and relative levels. We also had a clear catalyst that had caused this spread and which we thought was being overplayed by the popular media. We decided to go short AAPL implied volatility.
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
30 60 90 120
Time (Days)
Annualized Volatility
FIGURE 9.6 The Two-Year Volatility Cone for AAPL
The Trade During the afternoon of June 25 we started to sell. We sold a 12 lot of July 125 calls at 5.1 and bought 500 shares at 124.08 (giving an implied volatility of 41.2). Later, as the market broke, we sold 50 of the July 125 straddles at 10.7 and sold 300 shares at 122.27 (implied volatility of 40.85). At the end of the day we were short $1,450 vega, giving us an ex- pected profit of roughly $16,000. Our hedging band, using the Zakamouline scheme, was initially 800 shares around the BSM delta (so we considered any position within 800 shares of flat to be not worth hedging).
Daily Position
Underlying Delta Gamma Theta Vega
122.34 106 −346 1,135 −1.451
Haircut $51,015
Daily P/L $(121)
Total P/L $(121)
June 26, 2007
AAPL opened slightly higher at 123.97, in line with a slight rally in the over- all market. The stock dropped later in the morning. We sold 50 more 125 calls (at an implied volatility of 42) and underhedged them slightly to stay within the delta band. Our total expected P/L was now $20,000 and our hedging band had widened to 1000 shares. The stock came off further later in the day.
Daily Position
Underlying Delta Gamma Theta Vega
119.65 180 −470 1,666 −1,919
Haircut $68,893
Daily P/L $(4,832)
Total P/L $(4,953)
June 27, 2007
This was a very quiet day. No hedging was required.
Daily Position
Underlying Delta Gamma Theta Vega
121.99 −562 −519 1,716 −1995
Haircut $89,645
Daily P/L $5,338
Total $385
June 28, 2007
This was another very quiet day. No hedging required.
Daily Position
Underlying Delta Gamma Theta Vega
120.56 −56 −552 1,569 −1,869
Haircut $80,582
Daily P/L $7,044
Total P/L $7,429
June 29, 2007
There was a slight rally in the stock and some general choppiness, as iPhone-related chatter seemed to be having some effect. We had to buy in 400 shares on the rally.
Daily Position
Underlying Delta Gamma Theta Vega
122.04 −298 −566 1,707 −1,911
Haircut $84,623
Daily P/L $(823)
Total P/L $6,606
July 2, 2007
There was practically no movement at all in the stock today. Volatility soft- ened considerably to 34 and we tried to buy some back on the bid. We were not filled.
Daily Position
Underlying Delta Gamma Theta Vega
121.26 714 −654 1446 −1683
Haircut $86,127
Daily P/L $7,044
Total P/L $7,429
July 3, 2007
This morning we decided to liquidate the position if at all possible. Implied volatility had softened, we had realized a good proportion of our expected P/L and we had few other positions in our book. This gave us an issue
with lack of diversification and we had to be more risk averse, particularly with the July 4 holiday coming up. Further, we expected volatility to soften before the holiday, which would make our liquidation easy even if we had to lift offers.
We bought back our shorts at an average implied volatility of 29.
Daily P/L $11,783.75 Total P/L $18,389.75
POST-TRADE ANALYSIS
In seven days we made $18,390 on an average haircut of $76,805, thus giv- ing a return on haircut of 23.9 percent (we can neglect the effect of inter- est here as it was only about $100). We lost money on three days, but on the first of these we were incurring costs by actively crossing the bid/ask spread in the options, and on the second day we were happy enough to sell more on the offer as the implied volatility went slightly more bid. We don’t really have enough data points to break this particular trade down further.
This trade was unreasonably successful. We made almost exactly what we hoped for and did it in seven days, instead of having to hold the posi- tion until expiration as we had planned. This is vastly preferable and is a compelling reason to look for trades with specifically timed catalysts that could cause implied volatility to move your way. Having to hold a trade until expiration obviously exposes us to more risk.
Our decision to exit was perfectly timed, as at 9:00A.M. EST the stock began a strong rally to close at 127. This would not have worked out well for us. Implied volatility rose to 43 and we would have lost money hedging our short gamma. This would be inevitable regardless of our specific hedg- ing policy, as a daily range of this size would imply a volatility of about 110 percent. Being short from 30 would have been a loser.
However, if we held our trade until expiration we would still have made money. Running the trade as a paper trade until expiration, and hedging according to the strategy we would have used, gave a P/L profile as shown in Table 9.2 and Figure 9.7.
This is not the perfect trade that we achieved by exiting early, but it is a solid winner. As our pretrade analysis indicated, we had enough of a margin for error that the large move on July 5 wasn’t enough to turn the trade into a loser.
We do these trades on the premise that implied volatility is incorrect over the lifetime of the option. It is average volatility that is important.
TABLE 9.2 The P/L of the Paper Trade Held until Expiry
Date P/L Total P/L
6/25/2007 $(121) $(121)
6/26/2007 $(4,832) $(4,953)
6/27/2007 $5,338 $385
6/28/2007 $7,044 $7,429
6/29/2007 $(823) $6,606
7/2/2007 $7,044 $13,650
7/3/2007 $321 $13,971
7/5/2007 $(21,766) $(7,795)
7/6/2007 $5,112 $(2,683)
7/9/2007 $(584) $(3,267)
7/10/2007 $2,618 $(649)
7/11/2007 $3,414 $2,765
7/12/2007 $2,989 $5,753
7/13/2007 $(476) $5,277
7/16/2007 $(9) $5,268
7/17/2007 $3,045 $8,313
7/18/2007 $(1,305) $7,008
7/19/2007 $1,160 $8,168
7/20/2007 $(1,450) $6,718
We can afford to have a few bad days. The actual close-to-close realized volatility was 30.1 percent. We sold an average level of about 41.6 percent and our initial vega was about 1,900. We would have thereby expected to make $1,900×(41.6−30.1)=$21,850. So we were actually unlucky, but not because we predicted volatility incorrectly—we were almost exactly
$(10,000)
$(5,000)
$0
$5,000
$10,000
$15,000
$20,000
Date
Total P/L
6/22/07 6/27/07 7/2/07 7/7/07 7/12/07 7/17/07 7/22/07
FIGURE 9.7 The Theoretical P/L for the AAPL Trade
correct in our prediction. We were unlucky because we had a large move that took us away from our short strike. The move occurred where we were short gamma, and then it was quiet when we didn’t have much volatility exposure.
What should we have done if we had not exited the trade on July 3?
We would have taken a nasty hit on the 5th. We should then reevaluate whether we have edge left at the new forecast volatility, the new implied volatility, and the amount of vega we still have remaining. We should do this continually for all trades. If we still like the trade we should stick with it. We may even want to add more.
We should never get stopped out of a trade just because we have lost money. We exit trades if we no longer like them—losing money, while deeply unpleasant, should never be the sole criterion for exiting. A ba- sic trader clich ´e is to always have a stop, but this is overly simplistic as it doesn’t take into account the dynamics of the trade. We expect high volatility to be transient, so stopping ourselves out after every high volatil- ity burst is not a good idea. Instead of a stop based purely on our P/L, we have a plan based on our edge evaluation and our initial trade size. Trades going bad shouldn’t be too painful if they are kept small enough.
SUMMARY
An old trading adage is to “plan the trade then trade the plan.”
r Look for situations where implied volatility differs significantly from your forecasts, both for the specific stock and in context of the market.
r Evaluate the fundamental cause for this divergence.
r Execute the trade in appropriate size and hedge to within your pre- determined hedging bands.
r Hold until either your edge is realized, your volatility forecast changes significantly or the position expires.
r Continually evaluate risk in context of your overall portfolio.
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C H A P T E R 10