- 1998: Volume 7, No. 5 How's That Spelled?

I'm beginning to think market pundits can't spell. They seem to think "volatility" is a four-letter word. No doubt both bulls and bears have been driven crazy by recently roiling markets —down 512 Dow points one day, up 288 the next. But volatility traders often revel in such tumult.

Strictly speaking, volatility is direction-neutral. Markets can be described as either volatile or non-volatile, regardless of whether prices are rising, falling, or holding steady. Using options, volatility traders can profit no matter what direction a market may move. But the success of volatility trading depends upon a trader's ability to recognize variations from market "normalcy." But normalcy is a moving target. "Wide" trading ranges seem relatively narrow when a market moves 20 percent or 50 percent higher. A 550-point drop means less with regard to volatility when the market's at 9,000 as opposed to 2,000. In fact, the bull market of the 90s has been the cause for market volatility's overall shrinkage from previous levels.

The statistic that measures the speed of past market movement is historic volatility. A market described as exhibiting 20 percent volatility, simplistically, stands about a 67 percent chance of being within 20 percent of current levels a year from now. Now, the statistical reality of volatility may mean little to the average investor, except perhaps as a gauge for comparison. For example, 20-day historic volatility of the Dow Jones Industrial Average recently was 35 percent. That of the Pacific Stock Exchange Technology Index was about 52 percent. Without having to resort to complex math, we can confirm the intuitive notion that technology stocks are half again as volatile as blue chip stocks.

A measure of volatility is also embedded in option prices. Implied volatility is the option market's prediction of future price movements. It's a risk factor that directly influences the price of options. As volatility estimates rise, all other factors being held constant, option premiums rise. Bring down the volatility estimate, and option prices collapse as a consequence.

A volatility trade is any position which is primarily sensitive to either actual (historic) or implied volatility. Volatility traders speculate on changes in either or both. To see how such changes can be exploited, we have to first understand a few of the risk factors associated with options. Then, with that knowledge, we can look at recent market activity to see what opportunities presented themselves to volatility traders.

The Greeks

Traders analyze options for several risk factors (colloquially known as "Greeks") including:

Delta—the measure of change in an option premium for each single point change in the underlying asset's price; a measure of bullishness/bearishness.

Gamma—the expected change in delta for each one point change in the underlying asset.

Theta—the speed of option premium erosion as expiration approaches.

Vega—the expected change in option premium for each percentage point change in implied volatility.

All these factors can be expressed as positive or negative values. Because a volatility position focuses on volatility, rather than on direction, it's initially "delta-neutral." But a volatility position will have either positive or negative gamma, theta, and vega, reflecting a desire for greater or lesser volatility in the underlying market or in the options' implied volatility. We can summarize the outlooks reflected by the Greeks in the above table.

Traders take positions when they believe prices do not reflect true value. Since the value of options is determined by the future volatility of the underlying asset over the life of the option, and since prices are determined by implied volatility, volatility positions are undertaken when traders believe that future market volatility will vary from current implied volatility.

In general, if future volatility is expected to be greater than current implied volatility, positions with positive gamma need to be selected, such as long straddles, long strangles, backspreads, short calendar spreads, or short butterfly spreads. Conversely, when market volatility is expected to be lower than current implied volatility, short, or negative gamma positions such as short straddles, short strangles, front spreads, long calendar spreads, or long butterfly spreads should be undertaken. Even if implied volatility moves against the trader, as long as market volatility moves as forecast versus the implied volatility of the initial position, a profit should result. That is, with the exception of calendar spreads which are sensitive to shifts in implied volatility as well as to changes in market volatility. A trader's experience of the characteristics of the option market will be the most significant determinant of the perceived "cheapness" or "richness" of option premiums.

Examples can be found in the recent activity of the technology sector. Throughout the summer months of 1998, the PSE Tech 100 Index traded in a range between 320 and 360 with an average 20-day historic volatility of around 27 percent. Based on technical analysis, a trader might have had a notion that the market was due for a breakout. While leaning to a downside bias, the trader harbors a fair degree of uncertainty as to the ultimate direction the market may follow. PSE Tech 100 options looked like this as of August 26, 1998 when the PSE Tech 100 Index was at 335.41:

Expiration
Call		Put
	Sep
	320	4 5/8 -5
14 5/8	330	7 7/8
8 1/4 - 8 3/4	340	12
	Oct
	330	13
14 5/8	340

Trading Opportunities

Several possibilities are presented by this market including those illustrated in Tables 1 - 6.

Table 1

If delta is... positive negative	the underlying asset should... rise in price (long calls/short puts) decline in price (long puts/short calls)
If gamma is... positive negative	the underlying asset should... make a big or sudden move stay stable or move slowly
If theta is... positive negative	the underlying asset should... increase position value decrease position value
If vega is... positive negative	the underlying asset should... rise fall

Note the large theta exposure displayed in Table 2, showing the risk of time decay and the benefit derived if implied volatility ratcheted upward (vega). Expiration breakeven points would be 360 1/4 and 319 3/4. This position offers open-ended profit potential with risk limited to the 20 1/4 debit.

Table 2

Long Sep 340C/340P Straddle
	Premium	Implied Volatility	Delta	Gamma	Theta	Vega
L 340C	-8 1/4	28.71	457	16	-221	342
S 340P	-12	29.21	-541	16	-34	347
	-20 1/4		-84	32	-255	689

Like the straddle, the strangle shown in Table 3 is heavily skewed toward increased implied volatility, and exposed to time decay. Open-ended profits are available outside the breakeven points of 356 1/8 and 313 7/8, while the loss exposure is limited to only 16 1/8 because an out-of-the-money put was employed.

Table 3

	Premium	Implied Volatility	Delta	Gamma	Theta	Vega
L 340C	-8 1/4	28.71	457	16	-221	342
S 330P	-7 7/8	31.59	-391	14	-199	332
	-16 1/8		66	30	-420	674

In Table 4 we see that, while modest exposure to time decay is secured by trading a butterfly, little benefit would be derived from any increase in implied volatility here. More importantly, the premium structure makes this an unprofitable possibility. The maximum potential gain is only 3/8 (the difference between the strike price interval from the middle strike price to that of an adjacent "wing," less the debit). That gain would almost certainly be eaten up in transaction costs.

Table 4

	Premium	Implied Volatility	Delta	Gamma	Theta	Vega
S 320P	4 5/8	32.49	261	-12	177	-282
L 330P	-7 7/8	31.59	-391	14	-199	332
L 330C	-14 5/8	32.68	607	14	-247	332
S 340C	8 1/4	28.71	-457	-16	221	-342
	-9 5/8		20	0	-48	40

In Table 5, more puts are bought than sold, in ratio, to bring the net delta toward neutrality. Should the market move to the upside, the net credit represents the maximum profit potential available. A move to the downside, however, offers open-ended profit. Risk is limited to the difference between the strike prices less the net credit, or 8 1/8, should the market trade to 330 at expiration.

Table 5

	Premium	Implied Volatility	Delta	Gamma	Theta	Vega
S 5 330P	-8 3/4	30.08	1934	-74	943	-1653
L 7 320P	-35	33.82	-1877	79	-1311	2000
	1 7/8		57	5	-368	347

The calendar spread shown in Table 6 is the only position illustrated that has negative vega, indicating its sensitivity to implied volatility in addition to actual market volatility. The outlook here is that implied volatility will end up below market volatility so that much of the net credit can be retained.

Table 6

	Premium	Implied Volatility	Delta	Gamma	Theta	Vega
L 340 Sep C	-8 3/4	30.18	461	15	-232	343
S 340 Oct C	14 5/8	31.16	-499	-10	170	-506
	5 7/8		-38	5	-62	-163

Results

Just three trade days later, the market plunged, dragging the PSE Tech 100 Index down 16 percent to 280.25. As a result, 20-day historic volatility ballooned to nearly 46 percent. Implied volatilities also mushroomed that day, averaging 48 percent for puts and 47 percent for calls. Our positions would have looked like this by the end of the trading day:

Long Sep 340C/340P Straddle
Premium	Implied Volatility
L 340C 3/16	39.89
S 340P 59 3/8	45.21
59 9/16	Net gain 39 5/16
Long Sep 340C/330P Strangle
Premium	Implied Volatility
L 340C 3/16	38.39
S 330P 50	47.45
50 3/16	Net gain 34 1/8
Sep 320/330 Put Backspread
Premium	Implied Volatility
S 5 330P -255	44.98
L 7 320P 286 1/8	47.68
31 1/8	Net gain 29 1/4
Short Call Calendar Spread
Premium	Implied Volatility
L 340 Sep C 3/16	39.89
S 340 Oct C 3 1/8	45.56
-2 15/16	Net gain 2 15/16

While all the volatility positions produced profits, some were more highly leveraged than others. The strangle, for example, yielded better than 211 percent before transaction costs. The reason, of course, was the combination of large positive vega and market action pushing the put deep into the money. Similar results were obtained from the straddle, but at a higher initial premium cost. Both the straddle and the strangle could be done in a cash account with a relatively low level of account approval.

The other positions require margin and account approval for spread trading and naked writing, making these positions suitable only for more sophisticated and risk-savvy traders.

Gains could still have been engendered in these positions (with the exception of the calendar spread) perhaps only to a lesser degree, had implied volatility, but not market volatility increased. Had a breakout occurred to the upside, these positions could have also produced profits. In the case of the put backspread, of course, such profits would have been rather small, but that was the result of trader bias at the outset.

Keeping these trades in mind, volatility doesn't seem such a bad word after all. In fact, it may in current markets be another way for some traders to spell R-E-L-I-E-F.

Brad Zigler is the Director of Options Marketing, Research & Education at the Pacific Exchange in San Francisco. Mr. Zigler represents the Pacific Exchange at the Options Industry Council, an exchange consortium dedicated to educating brokers and the public on the uses of options as risk management tools. Mr. Zigler can be reached at droption@aol.com. Options on the PSE Tech 100 Index are traded on the Pacific Exchange. Futures on the PSE Tech 100 Index trade on the New York Futures Exchange division of the New York Cotton Exchange.