Midpoint
Expectationin Range
39.0040.0041.0042.00
0.01330.02160.03350.0499
0.01330.00830.01190.0164
–6817.50–4567.50–4192.50–3817.50
–90.67–37.81–49.92–62.54
43.0044.0045.0046.00
0.07150.09890.13260.1723
0.02160.02750.03360.0398
–3442.50–3067.50–2692.50–2317.50
–74.44–84.22–90.51–92.19
47.0048.0049.0050.00
0.21790.26860.32350.3812
0.04560.05070.05480.0577
–1942.50–1567.50–1192.50–817.50
–88.56–79.49–65.39–47.20
51.0052.0053.0054.00
0.44050.50000.55840.6144
0.05930.05950.05840.0561
–442.50–67.50+307.50+682.50
–26.24–4.02+17.95+38.27
55.0056.0057.0058.00
0.66720.71610.76040.8000
0.05280.04880.04430.0396
+1057.50+1432.50+1807.50+2182.50
+55.85+69.94+80.15+86.44
59.0060.0061.0062.00
0.83480.86500.89070.9124
0.03480.03020.02570.0217
+2557.50+2932.50+3307.50+3682.50
+89.04+88.42+85.14+79.84
63.0064.00
0.93040.9452
0.01800.0148
+4057.50+4432.50
+73.16+65.66
Overall expectation:
$–63.34
market differs from that of another. Also, the volatility of any single marketvaries over time, due to changes in market factors and traders’ sentiments.
Volatility—One Measure of a MarketThere are lots of ways to view and compute the volatility of a market. Onefrequently used is called either historical or statistical volatility, typicallyabbreviated as HV or SV. I prefer the term statistical volatility and that’s whatwe’ll use throughout the text. This is a simple if mildly tedious calculation.
56TABLE 3.2
TRADING OPTIONS TO WIN
Expectation for a Purchase and Call Write
ObjectPrice
ProbabilityBelow Object Price
Probabilityof Range
Profit/Loss atRange Midpoint
Expectationin Range
39.0040.0041.0042.00
0.01330.02160.03350.0499
0.01330.00830.01190.0164
–5880.00–3630.00–3255.00–2880.00
–78.20–30.05–38.76–47.18
43.0044.0045.0046.00
0.07150.09890.13260.1723
0.02160.02750.03360.0398
–2505.00–2130.00–1755.00–1380.00
–54.17–58.48–58.99–54.89
47.0048.0049.0050.00
0.21790.26860.32350.3812
0.04560.05070.05480.0577
–1005.00–630.00–255.00+120.00
–45.82–31.95–13.98+6.93
51.0052.0053.0054.00
0.44050.50000.55840.6144
0.05930.05950.05840.0561
+495.00+870.00+1245.00+1620.00
+29.35+51.75+72.66+90.83
55.0056.0057.0058.00
0.66720.71610.76040.8000
0.05280.04880.04430.0396
+1995.00+2062.50+2062.50+2062.50
+105.36+100.70+91.46+81.68
59.0060.0061.0062.00
0.83480.86500.89070.9124
0.03480.03020.02570.0217
+2062.50+2062.50+2062.50+2062.50
+71.81+62.19+53.09+44.72
63.0064.00
0.93040.9452
0.01800.0148
+2062.50+2062.50
+37.19+30.55
Overall expectation:
$417.80
When we want to find the 30-day statistical volatility of an asset, we start bytaking the daily change in the price of the asset, expressed as the closingprice divided by the previous day’s closing price, for each of the past 30 days.To satisfy the lognormal nature of the model, we then take the natural logarithm, loge, of each of these 30 price changes, and next compute the standarddeviation of the set of these logarithms.The result of this calculation is the immediate 30-day statistical volatility. Volatilities are almost always stated as annual figures, though, so we’ve
Profitability 101
57
one final step yet to go. To annualize our calculation, we must multiply ourresult by the square root of the number of trading days in the year. Some authors, Larry McMillan among them, use 260 for this figure in every year. Someuse 256, whose square root is 16 (very conveniently), some count up the actual number of trading days in the current year. All these work well for ourpurposes, so just choose your favorite.I know some very masochistic people, but I’ve yet to meet any traderwho actually sits down and manually performs these calculations each day(or each week, or ever for that matter) for all the markets that might be ofinterest at any given time. SVs are available from commercial quotationservices, from many brokerages (be sure to specify the term of the volatility to your broker, 20-day, 60-day, 6-month, or whichever you prefer), andfrom a considerable and growing body of Internet sites. Some of these sitesprovide volatility figures at no charge, some have nominal fees, but a fewwill try to take a hefty bite out of your wallet and are to be avoided. Traderswhom you know personally and who use volatility calculations in theirtrading will surely have them available.If you’re comfortable with spreadsheet programs, you can easily andcheaply acquire your own database of historical prices, a means of acquiringeach day’s closing prices (even at no cost, on sundry Internet sites), and whipup the appropriate spreadsheet. You’ll have all the SVs you want every day,with just a few clicks of the mouse. There are also several worthwhile commercial software packages, ranging in price from modest to ridiculous, thatinclude historical price databases and volatility calculators, among a largenumber of other features.
Some Fruits of the Volatility TreeOne of the many profitable implications of volatility is the concept that wecan calculate the theoretical fair value of an asset’s various options. Granted,the values we’ll obtain from this calculation are, again, only approximations,and almost assuredly will not match the actual prices of the options that wesee in the marketplace. We can easily trade and prosper with these approximations, though, because “the market” is the sum of the actions of peopleover time, and, in broad, it bears no resemblance whatever to a precisioninstrument. In addition, we must remember in the first place that the lognormal curve is only a model of the future distribution of prices, an approximation to be respected and applied as we find useful . . . but notworshipped.Let’s be candid with each other, shall we? The real world is not lognormal. It would be terrifically convenient if it were, but it isn’t. Just becausethe theoretical prices of a market’s options don’t match the actual prices weobserve in the market, does this imply a failure of the model? It does not,
58
TRADING OPTIONS TO WIN
for the actual price of any option at any time represents the various marketparticipants’ collective view of what the price of that option “should” be atthat specific point in time. For clarification of this point, we can look to theheating oil market.Everyone who trades heating oil is well aware that heating oil distributors begin building their inventories in the late summer and that consumers,particularly homeowners, tend to buy the bulk of their heating oil in the autumn. Most years, due to this concentration of demand, heating oil pricestend to rise during one or another portion of the time from July through earlyOctober. In anticipation of this, option traders in heating oil will on occasionbe bidding rather eagerly for these months’ call options even earlier in theyear, and the actual market price of these calls will acquire a premium, sometimes a very large one, over their computed theoretical fair values.In order to use the disparity between an option’s theoretical fair valueand its actual market value to our advantage, we first need to measure thisdisparity. Fortunately, there is a measure ready-made for us. When we compute the theoretical fair value of an option, we use the SV of the underlyingmarket, among other inputs. When we observe that the actual market priceof the option differs from its computed fair value, we very rationally concludethat the volatility of the option must be different from that of the underlyingmarket.Before, when we were computing the option’s fair value, we wanted toknow a price; now, we know the price of the option by observation, but notits volatility. To obtain this number, we just apply the fair value calculationbackwards, so to speak. The result of our calculation is the famous impliedvolatility, the IV of the option, so called because it is the volatility the underlying asset should have in order for a fair value calculation to yield the actual option price we observe in the market at this time.If you’re familiar with options trading, you may be saying to yourself,“Stu, everybody knows this stuff, let’s get on with making a profit.” I mustrespectfully disagree with you here. The large majority of non-professionaltraders, in my experience, do not have nearly enough exposure to or appreciation of the concept of volatility, for there are few other fields of humanactivity in which it is so immediately significant and so prominent.The experienced options trader knows full well that volatility and itsimplications are essential considerations, whether using options to reducerisk in an existing position or designing high-expectation trades using options in their own right. It is every bit as important to the trader to be familiar and comfortable with the details of removing risk and putting expectationin his favor as it is to the banker or to the bookmaker. Options are one of
Profitability 101
59
our tools for accomplishing this, and understanding the basics of volatilityand its related topics is necessary to the effective use of this tool.
Everything Changes over Time,Including VolatilityVolatilities change over time, just as prices do. The SV of a market and theIVs of its associated options react to the same news and market developments as does the price of the asset, but they do not necessarily react in thesame way or to the same extent. When SV and IVs diverge considerably, asfor instance they sometimes do before an important supply/demand reportis issued, we can listen for the sound of opportunity knocking. In such acase, the IVs of the options may rise well above the underlying market’s SVand we can look around for cautious ways to sell this excess volatility,which will be represented in the market by relatively high option prices.Conversely, when SV is depressed and the IVs of the options are even moredepressed, it’s generally profitable to look at buying some selection oflonger-term options, which, given the low volatilities, will tend very stronglyto be underpriced to some degree.If we trade only in assets, we are completely dependent on the movement of the asset’s price for our profit. This is not the case when trading options, whether by themselves or in combination with their underlying assets.Trades are commonplace that reap a tasty profit solely from changes in IV,even when the price of the asset does nothing or moves in slightly the wrongdirection over a period of time. Further, when we use options in our trading, we can on many occasions enlist the most inexorable force in the universe on our side. That force is time, and it is a very powerful ally indeed.One enormously pleasant thing about volatilities, SV especially, and especially in futures markets, is that they tend to persist within a measurablerange for long periods of time, and during these periods they tend even morestrongly to revert to the mean semiregularly. When a market’s SV has variedfrom 8% to 14% consistently for years, under a variety of market conditions,through euphoria and calamity, the trader who observes SV approaching either end of the range can, much more often than not, construct a trade having a high positive expectation.Figures 3.6 through 3.10 illustrate the persistence of SV ranges in fivewidely different futures markets from 1998 into 2002. For these examples,I chose the 60-day SV of the nearest contract, but it doesn’t make a wholelot of difference what term of volatility we examine. Figure 3.11 is the 120-daySV for Swiss franc futures, and you’ll notice a clear degree of symmetry between that figure and its 60-day cousin, Figure 3.10.
60
TRADING OPTIONS TO WIN
35
Percent
30252015
FIGURE 3.6
3/1/02
12/1/01
9/1/01
6/1/01
3/1/01
12/1/00
9/1/00
6/1/00
3/1/00
12/1/99
9/1/99
6/1/99
3/1/99
10
COMEX high-grade copper 60-day statistical volatility, 1999–2002.
Percent
1009080706050
FIGURE 3.7
6/1/02
2/1/02
10/1/01
6/1/01
2/1/01
10/1/00
6/1/00
2/1/00
10/1/99
6/1/99
2/1/99
10/1/98
6/1/98
403020
NYBOT coffee “C” 60-day statistical volatility, 1998–2002.
Implied Volatility and DeltaThe study of volatility doesn’t only suggest possible trading strategies andpotentially advantageous situations. We’re interested in figuring the expectation of trades we might enter, are we not? Absolutely we are, and the notion of volatility provides us with a couple of ways to do this. The morecomplex way is to perform a series of calculations using the various formulae of whichever model we may be using. The simpler way is just to use
61
Profitability 101
7060
Percent
50403020
FIGURE 3.8
2/1/02
10/1/01
6/1/01
2/1/01
10/1/00
6/1/00
2/1/00
10/1/99
6/1/99
2/1/99
10/1/98
6/1/98
10
CME lean hogs 60-day statistical volatility, 1998–2002.
151413Percent
1211109876
FIGURE 3.91998–2002.
2/1/02
10/1/01
6/1/01
2/1/01
10/1/00
6/1/00
2/1/00
10/1/99
6/1/99
2/1/99
10/1/98
6/1/98
5
CBOT 30-year Treasury bonds 60-day statistical volatility,
62
TRADING OPTIONS TO WIN
1514
Percent
1312111098
FIGURE 3.10
2/1/02
10/1/01
6/1/01
2/1/01
10/1/00
6/1/00
2/1/00
10/1/99
6/1/99
2/1/99
10/1/98
6/1/98
7
CMME/IMM Swiss franc 60-day statistical volatility, 1998–2002.
14
Percent
13121110
FIGURE 3.11
2/1/02
10/1/01
6/1/01
2/1/01
10/1/00
6/1/00
2/1/00
10/1/99
6/1/99
2/1/99
10/1/98
8
6/1/98
9
CMME/IMM Swiss franc 120-day statistical volatility, 1998–2002.
a couple of the results of these calculations, which are almost universallyavailable from the same folks from whom we obtain SVs (if we don’t calculate them ourselves, of course).To find an approximate probability of an asset’s price moving from A toB over a known period of time, we can first apply the measure called delta.
Profitability 101
63
In the simple lognormal pricing model, the delta of the X-strike call optionturns out to be a decently close approximation of the probability of thefuture price of an asset being at or above X when the option expires. Suppose that the price of an asset is 50, and that the actual price of a 90-day, 60strike call option is 1.00. If we calculate this option’s 90-day IV, along theway we obtain the delta of the option as a free bonus. If the delta of the option turns out to be 0.20, then we can say that the rough probability of theasset’s price being above 60 in 90 days’ time is equal to 0.20. Stated anotherway, the asset price 90 days from now can be expected to be below 60 inabout 80 cases out of 100.Delta has another practical use. By its definition in the model, it is themeasure of how much an option’s price can be expected to change if theprice of the underlying asset changes by one unit. In the preceding example, if the price of the asset would move from 50 to 51 tomorrow, the modelwould predict the price of the 60-strike call to move to 1.20. If the assetprice moved down to 49, this option’s delta indicates we would expect theprice of the call to fall to 0.80.If you’re wondering about the delta of the underlying asset itself, it’s always 1.00, and this is perfectly sensible. Every time the price of an assetmoves one unit, it moves exactly one unit, whereas the price of any of itsoptions will only move a fraction of one unit (with rare exceptions). Whenwe buy an asset and write a call option against it, we obtain the delta of thewhole position by adding up the deltas of both parts of the position. In ourexample here, the total position delta is 0.80, which is just another way ofsaying that if the asset were to move to 51, we’d gain 1.00 point on the assetand expect to lose 0.20 point on the option, gaining 0.80 point net.Computing any position’s total delta is a snap, no matter how complex the position may be. If we buy an asset, buy a call option, or write aput option, the delta of any of these is a positive number. If we sell shortan asset, write a call, or buy a put, these items’ deltas are negative numbers. Add up the deltas of each position in the trade and we’re done. If thisresult is a positive number, we will almost always profit if the price of theasset rises; if the total delta is negative, we’ll nearly invariably profit if theprice of the asset falls. Delta, however, changes from day to day (andeven from minute to minute), and must be recomputed for any position atleast daily, lest we find ourselves in what amounts to a very unprofitabletime warp.As you undoubtedly and rightly suspect, there’s a whole lot more to thesubject of IV and delta, and for that matter a whole bunch of related topics.Perfectly true, but all things in good time. The good news is that, after allthis preliminary, we finally have enough information in hand to take a good,hard look at the expectation of a real-world trade.
64
TRADING OPTIONS TO WIN
The Toxic Waste of Markets—Using Expectationto Avoid Hype and NonsenseRegardless of whether you’ve ever traded an option in your life, if you’vetraded in any market for any length of time, you almost certainly have runacross the claims of some number of promoters, usually titled somethinglike “Fantastic Profits in Options,” or something equally flatulent. Thesetypes of claims and promotions too frequently employ, as their “secretstrategy” or “lesson of a lifetime” or some such bilge, the tactic of buyingcall options whose striking price is way the heck away from the underlyingasset’s current price.If some month’s crude oil futures are at $25.00/bbl, a way-out-of-themoney option, or WOOM as I always call it, might be the 31.00- or 32.00strike call. The types of promoters I’m talking about don’t deal in WOOMs,though. No, no, they rave about WTBOOMs, options that are way-theBLEEP-out-of-the-money, the 39.00- or 40.00-strike calls, or even higherstrike ones. Typically, they’ll “recommend” that the suck-, uh, trader buysuch options with a term of six months or nine months or a year.All right, let’s play these sleazeballs’ little game—on paper only, ofcourse, since we really don’t want to contribute to their upkeep. Let’scrunch the numbers on a trade this type of lowlife might advocate and keepa sharp eye on the expectation of the trade throughout. “Hey, why botherwith these clowns?” someone is asking. Fair question. For a very good reason: it’s not enough to look at a prospective trade and say, “That’s a loser”or “That should be profitable.”We want to understand how traders lose by ignoring expectation andusing disadvantageous strategies, and also learn to construct strategies thateliminate or reverse these disadvantages. More than this, we want to knowhow to recognize the difference between a profit opportunity and an accidental purchase of the Brooklyn Bridge, and the way to do so is to watchexpectation in action. As a side benefit of this little analysis, we will alsopermanently vaccinate ourselves against these types of hyped promotionalviruses. Here we go.“Upcoming Iraqi War Threatens World Oil Supply!” “Experts SaySupply Deficit Can Exceed 3 Million Barrels A Day!” “During DesertStorm, Oil Prices Rose 200 %!” “$70.00 Oil? It Will Happen When TheBombs Fall!”So rave the headlines in the promotional mailer or on the Internet site,both of which doubtless prattle on for quite a while, with lots and lots ofexclamation points (I’m actually skimping here on the number you’re apt tosee in such a promotion). The hype hints strongly at astonishing profits to
65
Profitability 101
be made in anticipating political developments by buying six-month call options in crude oil with a striking price of 40.00. Well, well, WTBOOM,boomity, boom. As I write this on May 17, 2002, the market in NYMEX December 2002 crude oil, ticker symbol CLZ, settled at 26.15 and Decembercrude oil’s 6-month SV is 32.4%. Table 3.3 shows the pertinent data for theexpectation of this trade, evaluated according to the lognormal model.One fact, not included in the table, about the CLZ call options tonightis that they’re right near their theoretical fair value until we get into WTBOOM-land. The other way to say this is that the calls’ IVs are about equalto the SV of CLZ itself. Evidently, option traders in crude oil don’t seem toshare our hypester’s optimism right now. The WOOM and WTBOOM callsare a tad pricier than they should theoretically be, so if we purchase these,we’ll be paying up a notch—not necessarily a sin, but hardly advantageouseither. We’ll assume that we can buy the CLZ 40 calls with just 1 point ofslippage, so we’ll be paying 0.11, or 11 points, $110.00 plus a $15.00 commission, thus $125.00 including our unavoidable contest risk.The main portion of our expectation in this trade is easy to compute. IfCLZ is not above $40.00 when the December options expire, we’ll lose ourentire purchase price and contest risk, so this portion of the expectation in
TABLE 3.3
Expectation of Buying CLZ 40.00 Calls on May 17, 2002
StrikePrice
OptionPrice
Delta× 100
ProbabilityBelow*
Probability ofRange
Profit at RangeMidpoint
Expectation inRange
40.0041.0042.0043.00
0.1000.0600.0400.035
4.402.932.171.93
0.96640.97780.98370.9857
0.96640.01140.00590.0020
–125.00350.001350.002350.00
–120.803.997.994.70
44.0045.0046.0047.00
0.0320.0300.0230.018
1.801.671.331.14
0.98680.98790.99050.9919
0.00110.00110.00260.0014
3350.004350.005350.006350.00
3.744.6413.949.06
48.0049.0050.0051.00
0.0140.0120.0100.009
0.950.850.730.71
0.99330.99410.99500.9952
0.00140.00080.00090.0002
7350.008350.009350.0010350.00
10.116.468.551.86
52.00
0.008
0.64
0.9957
0.0005
11350.00
5.62
Overall expectation:Notes: CLZ = 26.15; Z options expire 11/17/2002.
*Probability of being below the striking price on the same line.
$–40.15
66
TRADING OPTIONS TO WIN
this trade is perfectly clear. As Table 3.3 shows, the delta of the CLZ 40 callis 0.042 tonight. Hmmm. Only about 42 times out of 1,000 will the markettheoretically be above 40.00 when our options expire? We’ll lose all our capital and costs in this trade roughly 95.8% of the time? Geez, that’s terrible. Idon’t know about you, but I want a second opinion on this deal! We can easily get one, too, but to do so we must digress for a moment.
The Bad News Only Gets WorseIn fact, the situation is actually worse than this for the option buyer in thisor any purchase of WTBOOM call options. The delta figures of WTBOOMcall options are over-optimistic, proportionally too high. Why so? The unmodified normal distribution curve is perfectly symmetric, but we aren’tusing that curve, are we? We aren’t, and the lognormal curve we are