tructure of the company
has changed; perhaps it is being taken over, or perhaps the company· has acquired
another company nearly its size. In either case, it is possible that the combined enti
ty's stock will be less volatile than the original company's stock was. As the takeover
is in the process of being consummated, the implied volatility of the company's
options will drop, giving the false impression that they are cheap.
In a similar vein, a company may mature, perhaps issuing more shares of stock,
or perhaps building such a.., good earnings stream that the stock is considered less
volatile than it formerly was. Some of the Internet companies will be classic cases: In
the beginning they were high-flying stocks with plenty of price movement, so the
options traded with a relatively high degree of implied volatility. However, as the com
pany matures, it buys other Internet companies and then perhaps even merges with a
large, established company (America Online and Time-Warner Communications, for
example). In these cases, actual (statistical) volatility will diminish as the company
matures, and implied volatility will do the same. On the surface, a buyer of volatility
may see the reduced volatility as an attractive buying situation, but upon further
inspection he may find that it is justified. If the decrease in implied volatility seems
justified, a buyer of volatility should ignore it and look for other opportunities.
All volatility traders should be suspicious when volatility seems to be extreme -
either too expensive or too cheap. The trader should investigate the possibilities as to
why volatility is trading at such extreme levels. In some cases, the supply and demand
of the public just pushes the options to extreme levels; there is nothing more involved
than that. Those are the best volatility trading situations. However, if there is a hint
that the volatility has gotten to an extreme reading because of some logical (but per
haps nonpublic) reason, then the volatility trader should be suspicious and should
probably avoid the trade. Typically this happens with expensive options.
Buyers of volatility really have little to fear if they miscalculate and thus buy an
option that appears inexpensive but turns out not to be, in reality. The volatility buyer
might lose money if he does this, and overpaying for options constantly will lead to
ruin, but an occasional mistake will probably not be fatal.
748 Part VI: Measuring and Trading Volatility
Sellers of volatility, however, have to be a lot more careful. One mistake could
be the last one. Selling naked calls that seem terrifically expensive by historic stan
dards could be ruinous if a takeover bid subsequently emerges at a large premium to
the stock's current price. Even put sellers must be careful, although a lot of traders
think that selling naked puts is safe because it's the same as buying stock. But who
ever said buying stock wasn't risky? If the stock literally collapses - falling from 80,
say, to 15 or 20, as Oxford Health did, or from 30 to 2 as Sunrise Technology did -
then a put seller will be buried. Since the risk of loss from naked option selling is
large, one could be wiped out by a huge gap opening. That's why it's imperative to
study why the options are expensive before one sells them. If it's known, for exam
ple, that a small biotech company is awaiting FDA trial results in two weeks,~and all
the options suddenly become expensive, the volatility seller should not attempt to be
a hero. It's obvious that at least some traders believe that there is a chance for the
stock to gap in price dramatically. It would be better to find some other situation in
which to sell options.
The seller of futures options or index options should be cautious too, although
there can't be takeovers in those markets, nor can there be a huge earnings surprise
or other corporate event that causes a big gap. The futures markets, though do have
things like crop reports and government economic data to deal with, and those can
create volatile situations, too. The bottom line is that volatility selling - even hedged
volatility selling - can be taxing and aggravating if one has sold volatility in front of
what turns out to be a news item that justifies the expensive volatility.
SUMMARY
Volatility trading is a predictable way to approach the market, because volatility
almost invariably trades in a range and therefore its value can be estimated with a
great deal more precision than can the actual prices of the underlyings. Even so, one
must be careful in his approach to volatility trading, because diligent research is
needed to determine if, in fact, volatility is "cheap" or "expensive." As with any sys
tematic approach to the market, if one is sloppy about his research, he cannot expect
to achieve superior results. In the next few chapters, a good deal of time will be spent
to give the reader a good understanding of how volatility affects positions and how it
can be used to construct trades with positive expected rates of return.
· GHAR:f ER :8'7 . . -
How Volatility Affects
Popular Strategies
The previous chapter addressed the calculation or interpretation of implied volatili
ty, and how to relate it to historic volatility. Another, related topic that is important is
how implied volatility affects a specific option strategy. Simplistically, one might think
that the effect of a change in implied volatility on an option position would be a sim
ple matter to discern; but in reality, most traders don't have a complete grasp of the
ways that volatility affects option positions. In some cases, especially option spreads
or more complex positions, one may not have an intuitive "picture" of how his posi
tion is going to be affected by a change in implied volatility. In this chapter, we'll
attempt a relatively thorough review of how implied volatility changes affect most of
the popular option strategies.


complete grasp of the
ways that volatility affects option positions. In some cases, especially option spreads
or more complex positions, one may not have an intuitive "picture" of how his posi
tion is going to be affected by a change in implied volatility. In this chapter, we'll
attempt a relatively thorough review of how implied volatility changes affect most of
the popular option strategies.
There are ways to use computer analysis to "draw" a picture of this volatiiity
effect, of course, and that will be discussed momentarily. But an option strategist
should have some idea of the general changes that a position will undergo if implied
volatility changes. Before getting into the individual strategies, it is important that
one understands some of the basics of the effect of volatility on an option's price.
VEGA
Technically speaking, the term that one uses to quantify the impact of volatility
changes on the price of an option is called the vega of the option. In this chapter, the
references will be to vega, but the emphasis here is on practicality, so the descriptions
749
750 Part VI: Measuring and Trading Volatility
of how volatility affects option positions will be in plain English as well as in the more
mathematical realm of vega. Having said that, let's define vega so that it is understood
for later use in the chapter.
Simply stated, vega is the amount by which an option's price changes when
volatility changes by one percentage point.
Example: XYZ is selling at 50, and the July 50 call is trading at 7.25. Assume that
there is no dividend, that short-term interest rates are 5%, and that July expiration is
exactly three months away. With this information, one can determine that the implied
volatility of the July 50 call is 70%. That's a fairly high number, so one can surmise
that XYZ is a volatile stock. What would the option price be if implied volatility were
rise to 71 %? Using a model, one can determine that the July 50 call would theoreti
cally be worth 7.35 if that happened. Hence, the vega of this option is 0.10 (to two
decimal places). That is, the option price increased by 10 cents, from 7.25 to 7.35,
when volatility rose by one percentage point. (Note that "percentage point" here
means a full point increase in volatility, from 70% to 71 %.)
What if implied volatility had decreased instead? Once again, one can use the
model to determine the change in the option price. In this case, using an implied
volatility of 69% and keeping everything else the same, the option would then theo
retically be worth 7.15- again, a 0.10 change in price (this time, a decrease in price).
This example points out an interesting and important aspect of how volatility
affects a call option: If implied volatility increases, the price of the option will
increase, and if implied volatility decreases, the price of the option will decrease.
Thus, there is a direct relationship between an option's price and its implied volatili-
ty.
Mathematically speaking, vega is the partial derivative of the Black-Scholes
model (or whatever model you're using to price options) with respect to volatility. In
the above example, the vega of the July 50 call, with XYZ at 50, can be computed to
be 0.098 - very near the value of 0.10 that one arrived at by inspection.
Vega also has a direct relationship with the price of a put. That is, as implied
volatility rises, the price of a put will rise as well.
Example: Using the same criteria as in the last example, suppose that XYZ is trading
at 50, that July is three months away, that short-term interest rates are 5%, and that
there is no dividend. In that case, the following theoretical put and call prices would
apply at the stated implied volatilities:
Chapter 37: How Volatility Affects Popular Strategies 751
Stock Price July 50 call July 50 put Implied Volatility Put's Vega
50 7.15 6.54 69% 0.10
7.25 6.64 70% 0.10
7.35 6.74 71% 0.10
Thus, the put's vega is 0.10, too - the same as the call's vega was.
In fact, it can be stated that a call and a put with the same terms have the same
vega. To prove this, one need only refer to the arbitrage equation for a conversion. If
the call increases in price and everything else remains equal - interest rates, stock
price, and striking price - then the put price must increase by the same amount. A
change in implied volatility will cause such a change in the call price, and a similar
change in the put price. Hence, the vega of the put and the call must be the same.
It is also important to know how the vega changes as other factors change, par
ticularly as the stock price changes, or as time changes. The following examples con
tain several tables that illustrate the behavior of vega in a typically fluctuating envi
ronment.
Example: In this case, let the stock price fluctuate while holding interest rate (5% ),
implied volatility (70%), time (3 months), dividends (0), and the strike price (50) con
stant. See Table 37-1.
In these cases, vega drops when the stock price does, too, but it remains fairly
constant if the stock rises. It is interesting to note, though, that in the real world,
when the underlying drops in price especially if it does so quickly, in a panic mode
- implied volatility can increase dramatically. Such an increase may be of great ben
efit to a call holder, serving to mitigate his losses, perhaps. This concept will be dis
cussed further later in this chapter.
TABLE 37-1
Implied Volatility Theoretical
Stock Price July 50 Call Price Coll Price Vega
30 70% 0.47 0.028
40 2.62 0.073
50 7.25 0.098
60 14.07 0.092
70 22.35 0.091
752 Part VI: Measuring and Trading Volatility
The above example assumed that the stock was making instantaneous changes
in price. In reality, of course, time would be passing as well, and that affects the vega
too. Table 37-2 shows how the vega changes when time changes, all other factors
being equal.
Example: In this example, the follow

eBooks\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012)\Lawrence G. McMillan - Options as a Strategic Investment_ Fifth Edition-Prentice Hall Press (2012).pdf


2 0.073
50 7.25 0.098
60 14.07 0.092
70 22.35 0.091
752 Part VI: Measuring and Trading Volatility
The above example assumed that the stock was making instantaneous changes
in price. In reality, of course, time would be passing as well, and that affects the vega
too. Table 37-2 shows how the vega changes when time changes, all other factors
being equal.
Example: In this example, the following items are held fixed: stock price (50), strike
price (50), implied volatility (70%), risk-free interest rate (5%), and dividend\(0). But
now, we let time fluctuate.
Table 37-2 clearly shows that the passage of time results not only in a decreas
ing call price, but in a decreasing vega as well. This makes sense, of course, since one
cannot expect an increase in implied volatility to have much of an effect on a very
short-term option - certainly not to the extent that it would affect a LEAPS option.
Some readers might be wondering how changes in implied volatility itself would
affect the vega. This might be called the "vega of the vega," although I've never actu
ally heard it referred to in that manner. The next table explores that concept.
Example: Again, some factors will be kept constant - the stock price (50), the time
to July expiration (3 months), the risk-free interest rate (5%), and the dividend (0).
Table 37-3 allows implied volatility to fluctuate and shows what the theoretical price
of a July 50 call would be, as well as its vega, at those volatilities.
Thus, Table 37-3 shows that vega is surprisingly constant over a wide range of
implied volatilities. That's the real reason why no one bothers with "vega of the vega."
Vega begins to decline only if implied volatility gets exceedingly high, and implied
volatilities of that magnitude are relatively rare.
One can also compute the distance a stock would need to rise in order to over
come a decrease in volatility. Consider Figure 37-1, which shows the theoretical price
TABLE 37-2
Implied Time Theoretical
Stock Price Volatility Remaining Call Price Vega
50 70% One year 14.60 0.182
Six months 10.32 0.135
Three months 7.25 0.098
Two months 5.87 0.080
One month 4.16 0.058
Two weeks 2.87 0.039
One week 1.96 0.028
One day 0.73 0.010
Chapter 37: How Volatility Affeds Popular Strategies
TABLE 37-3
Implied
Stock Price Volatility
50 10%
30%
50%
70%
100%
150%
200%
Theoretical
Coll Price
1.34
3.31
5.28
7.25
10.16
14.90
19.41
753
Vega
0.097
0.099
0.099
0.098
0.096
0.093
0.088
of a 6-month call option with differing implied volatilities. Suppose one buys an
option that currently has implied volatility of 170% (the top curve on the graph).
Later, investor perceptions of volatility diminish, and the option is trading with an
implied volatility of 140%. That means that the option is now "residing" on the sec
ond curve from the top of the list. Judging from the general distance between those
two curves, the option has probably lost between 5 and 8 points of value due to the
drop in implied volatility.
Here's another way to think about it. Again, suppose one buys an at-the-money
option (stock price = 100) when its implied volatility is 170%. That option value is
marked as point A on the graph in Figure 37-1. Later, the option's implied volatility
drops to 140%. How much does the stock have to rise in order to overcome the loss
of implied volatility? The horizontal line from point A to point B shows that the
option value is the same on each line. Then, dropping a vertical line from B down to
point C, we see that point C is at a stock price of about 109. Thus, the stock would
have to rise 9 points just to keep the option value constant, if implied volatility drops
from 170% to 140%.
IMPLIED VOLATILITY AND DELTA
Figure 37-1 shows another rather unusual effect: When implied volatility gets very
high, the delta of the option doesn't change much. Simplistically, the delta of an
option measures how much the option changes in price when the stock moves one
point. Mathematically, the delta is the first partial derivative of the option model with
respect to stock price. Geometrically, that means that the delta of an option is the
slope of a line drawn tangent to the curve in the preceding chart.
754 Part VI: Measuring and Trading Volatility
FIGURE 37-1.
Theoretical option prices at differing implied
volatilities (6-month calls).
80
70
Q) 60
(.)
·;:::
Cl.. 50
C:
0
·a 40
0
30
20
10
Stock Price
60 80 100 C 120 140
_JY.._
170%
140%
110%
80%
50%
20%
The bottom line in Figure 37-1 (where implied volatility= 20%) has a distinct
curvature to it when the stock price is between about 80 and 120. Thus the delta
ranges from a fairly low number (when the stock is near 80) to a rather high number
(when the stock is near 120). Now look at the top line on the chart, where implied
volatility= 170%. It's almost a straight line from the lower left to the upper right! The
slope of a straight line is constant. This tells us that the delta (which is the slope)
barely changes for such an expensive option - whether the stock is trading at 60 or
it's trading at 150! That fact alone is usually surprising to many.
In addition, the value of this delta can be measured: It's 0. 70 or higher from a
stock price of 80 all the way up to 150. Among other things, this means that an out~
of-the-money option that has extremely high implied volatility has a fairly high delta
- and can be expected to mirror stock price movements more closely than one might
think, were he not privy to the delta.
Figure 37-2 follows through on this concept, showing how the delta of an option
varies with implied volatility. From this chart, it is clear how much the delta of an
option varies when the implied volatility is 20%, as compared to how little it varies
when implied volatility is extremely high.
That data is interesting enough by itself, but it becomes even more thought-pro
voking when one conside


gure 37-2 follows through on this concept, showing how the delta of an option
varies with implied volatility. From this chart, it is clear how much the delta of an
option varies when the implied volatility is 20%, as compared to how little it varies
when implied volatility is extremely high.
That data is interesting enough by itself, but it becomes even more thought-pro
voking when one considers that a change in the implied volatility of his option (vega)
also can mean a significant change in the delta of the option. In one sense, it explains
why, in the first chart (Figure 37-1), the stock could rise 9 points and yet the option
holder made nothing, because implied volatility declined from 170% to 140%.
Chapter 37: How Volatility Affects Popular Strategies
EFFECTS ON NEUTRALITY
755
A popular concept that uses delta is the "delta-neutral" spread a spread whose prof
itability is supposedly ambivalent to market movement, at least for short time frames
and limited stock price changes. Anything that significantly affects the delta of an
option can affect this neutrality, thus causing a delta-neutral position to become
unbalanced ( or, more likely, causing one's intuition to be wrong regarding what con
stitutes a delta-neutral spread in the first place).
Let's use a familiar strategy, the straddle purchase, as an example. Simplistically,
when one buys a straddle, he merely buys a put and a call with the same terms and
doesn't get any fancier than that. However, it may be the case that, due to the deltas
of the options involved, that approach is biased to the upside, and a neutral straddle
position should be established instead.
Example: Suppose that XYZ is trading at 100, that the options have an implied
volatility of 40%, and that one is considering buying a six-month straddle with a strik
ing price of 100. The following data summarize the situation, including the option
prices and the deltas:
XYZ Common: l 00; Implied Volatility: 40%
Option
XYZ October l 00 call
XYZ October l 00 put
FIGURE 37-2.
Price
12.00
10.00
Delta
0.60
-0.40
Value of delta of a 6-month option at differing implied volatilities.
90
80
70
.!!l
ai 60
Cl
C: 50 ,g
8° 40
30
20
10
60 80 100
Stock Price
120 140
756 Part VI: Measuring and Trading Volatility
Notice that the stock price is equal to the strike price (100). However, the deltas
are not at all equal. In fact, the delta of the call is 1.5 times that of the put (in absolute
value). One must buy three puts and two calls in order to have a delta-neutral posi
tion.
Most experienced option traders know that the delta of an at-the-money call is
somewhat higher than that of an at-the-money put. Consequently, they often esti
mate, without checking, that buying three puts and two calls produces a delta-neu
tral "straddle buy." However, consider a similar situation, but with a much higher
implied volatility- 110%, say.
AAA Common: 100; Implied Volatility: 110%
Option
AAA October 100 call
AAA October 1 00 put
Price
31.00
28.00
Delta
0.67
-0.33
The delta-neutral ratio here is two-to-one (67 divided by 33), not three-to-two
as in the earlier case - even though both stock prices are 100 and both sets of options
have six months remaining. This is a big difference in the delta-neutral ratio, espe
cially if one is trading a large quantity of options. This shows how different levels of
implied volatility can alter one's perception of what is a neutral position. It also points
out that one can't necessarily rely on his intuition; it is always best to check with a
model.
Carrying this thought a step further, one must be mindful of a change in implied
volatility if he wants to keep his position delta-neutral. If the implied volatility of AAA
options should drop significantly, the 2-to-l ratio will no longer be neutral, even if the
stock is still trading at 100. Hence, a trader wishing to remain delta-neutral must
monitor not only changes in stock price, but changes in implied volatility as well. For
more complex strategies, one will also find the delta-neutral ratio changing due to a
change in implied volatility.
The preceding examples summarize the major variables that might affect the
vega and also show how vega affects things other than itself, such as delta and, there
fore, delta neutrality. By the way, the vega of the underlying is zero; an increase in
implied volatility does not affect the price of the underlying instrument at all, in the
ory. In reality, if options get very expensive (i.e., implied volatility spikes up), that
usually brings traders into a stock and so the stock price will change. But that's not a
mathematical relationship, just a market cause-and-effect relationship.
Chapter 37: How Volatility Affects Popular Strategies
POSITION VEGA
757
As can be done with delta or with any other of the partial derivatives of the model,
one can compute a position vega - the vega of an entire position. The position vega
is determined by multiplying the individual option vegas by the quantity of options
bought or sold. The "position vega" is merely the quantity of options held, times the
vega, times the shares per options ( which is normally 100).
Example: Using a simple call spread as an example, assume the following prices
exist:
Security Position Vega Position Vego
XYZ Stock No position
XYZ July 50 call Long 3 calls 0.098 +0.294
XYZ July 70 call Short 5 calls 0.076 -0.380
Net Position Vega: -0.086
This concept is very important to a volatility trader, for it tells him if he has con
structed a position that is going to behave in the manner he expects. For example,
suppose that one identifies expensive options, and he figures that implied volatility
will decrease, eventually becoming more in line with its historical norms. Then he
would want to construct a position with a negative position vega. A negative position
vega indicates that the position will profit if implied volatility de


position that is going to behave in the manner he expects. For example,
suppose that one identifies expensive options, and he figures that implied volatility
will decrease, eventually becoming more in line with its historical norms. Then he
would want to construct a position with a negative position vega. A negative position
vega indicates that the position will profit if implied volatility decreases. Conversely,
a buyer of volatility - one who identifies some underpriced situation - would want to
construct a position with a positive position vega, for such a position will profit if
implied volatility rises. In either case, other factors such as delta, time to expiration,
and so forth will have an effect on the position's actual dollar profit, but the concept
of position vega is still important to a volatility trader. It does no good to identify
cheap options, for example, and then establish some strange spread with a negative
position vega. Such a construct would be at odds with one's intended purpose - in
this case, buying cheap options.
OUTRIGHT OPTION PURCHASES AND SALES
Let us now begin to investigate the affects of implied volatility on various strategies,
beginning with the simplest strategy of all - the outright option purchase. It was
already shown that implied volatility affects the price of an individual call or put in a
758 Part VI: Measuring and Trading Volatility
direct manner. That is, an increase in implied volatility will cause the option price to
rise, while a decrease in volatility will cause a decline in the option price. That piece
of information is the most important one of all, for it imparts what an option trader
needs to know: An explosion in implied volatility is a boon to an option owner, but
can be a devastating detriment to an option seller, especially a naked option seller.
A couple of examples might demonstrate more clearly just how powerful the
effect of implied volatility is, even when there isn't much time remaining in the life
of an option. One should understand the notion that an increase in implied volatility
can overcome days, even weeks, of time decay. This first example attempts to quan
tify that statement somewhat.
Example: Suppose that XYZ is trading at 100 and one is interested in analyzing a 3-
month call with striking price of 100. Furthermore, suppose that implied volatility is
currently at 20%. Given these assumptions, the Black-Scholes model tells us that the
call would be trading at a price of 4.64.
Stock Price:
Strike Price:
Time Remaining:
Implied Volatility:
Theoretical Call Value:
100
100
3 months
20%
4.64
Now, suppose that a month passes. If implied volatility remained the same
(20% ), the call would lose nearly a point of value due to time decay. However, how
much would implied volatility have had to increase to completely counteract the
effect of that time decay? That is, after a month has passed, what implied volatility
will yield a call price of 4.64? lt turns out to be just under 26%.
Stock Price:
Strike Price:
Time Remaining:
Implied Volatility:
Theoretical Call Value:
100
100
2 months
25.9%
4.64
What would happen after another month passes? There is, of course, some
implied volatility at which the call would still be worth 4.64, but is it so high as to be
unreasonable? Actually, it turns out that if implied volatility increases to about 38%,
the call will still be worth 4.64, even with only one month of life remaining:
Chapter 37: How Volatility Affects Popular Strategies
Stock Price:
Strike Price:
Time Remaining:
Implied Volatility:
Theoretical Call Value:
100
100
1 month
38.1%
4.64
759
So, if implied volatility increases from 20% to 26% over the first month, then
this call option would still be trading at the same price - 4.64. That's not an unusual
increase in implied volatility; increases of that magnitude, 20% to 26%, happen all
the time. For it to then increase from 26% to 38% over the next month is probably
less likely, but it is certainly not out of the question. There have been many times in
the past when just such an increase has been possible - during any of the August,
September, or October bear markets or mini-crashes, for example. Also, such an
increase in implied volatility might occur if there were takeover rumors in this stock,
or if the entire market became more volatile, as was the case in the latter half of the
1990s.
Perhaps this example was distorted by the fact that an implied volatility of 20%
is a fairly low number to begin with. What would a similar example look like if one
started out with a much higher implied volatility - say, 80%?
Example: Making the same assumptions as in the previous example, but now setting
the implied volatility to a much higher level of 80%, the Black-Scholes model now
says that the call would be worth a price of 16.45:
Stock Price:
Strike Price:
Time Remaining:
Implied Volatility:
Theoretical Call Value:
100
100
3 months
80%
16.45
Again, one must ask the question: "If a month passes, what implied volatility
would be necessary for the Black-Scholes model to yield a price of 16.45?" In this
case, it turns out to be an implied volatility of just over 99%.
Stock Price:
Strike Price:
Time Remaining:
Implied Volatility:
Theoretical Call Value:
100
100
2 months
99.4%
16.45
758 Part VI: Measuring and Trading Volatility
direct manner. That is, an increase in implied volatility will cause the option price to
rise, while a decrease in volatility will cause a decline in the option price. That piece
of information is the most important one of all, for it imparts what an option trader
needs to know: An explosion in implied volatility is a boon to an option owner, but
can be a devastating detriment to an option seller, especially a naked option seller.
A couple of examples might demonstrate more clearly just how powerful the
effect of implied volatility is, even when there is


e. That piece
of information is the most important one of all, for it imparts what an option trader
needs to know: An explosion in implied volatility is a boon to an option owner, but
can be a devastating detriment to an option seller, especially a naked option seller.
A couple of examples might demonstrate more clearly just how powerful the
effect of implied volatility is, even when there isn't much time remaining in the life
of an option. One should understand the notion that an increase in implied volatility
can overcome days, even weeks, of time decay. This first example attempts to quan
tify that statement somewhat.
Example: Suppose that XYZ is trading at 100 and one is interested in analyzing a 3-
month call with striking price of 100. Furthermore, suppose that implied volatility is
currently at 20%. Given these assumptions, the Black-Scholes model tells us that the
call would be trading at a price of 4.64.
Stock Price:
Strike Price:
Time Remaining:
Implied Volatility:
Theoretical Call Value:
100
100
3 months
20%
4.64
Now, suppose that a month passes. If implied volatility remained the same
(20% ), the call would lose nearly a point of value due to time decay. However, how
much would implied volatility have had to increase to completely counteract the
effect of that time decay? That is, after a month has passed, what implied volatility
will yield a call price of 4.64? It turns out to be just under 26%.
Stock Price:
Strike Price:
Time Remaining:
Implied Volatility:
Theoretical Call Value:
100
100
2 months
25.9%
4.64
What would happen after another month passes? There is, of course, some
implied volatility at which the call would still be worth 4.64, but is it so high as to be
unreasonable? Actually, it turns out that if implied volatility increases to about 38%,
the call will still be worth 4.64, even with only one month of life remaining:
Chapter 37: How Volatility Affects Popular Strategies
Stock Price:
Strike Price:
Time Remaining:
Implied Volatility:
Theoretical Call Value:
100
100
1 month
38.1%
4.64
759
So, if implied volatility increases from 20% to 26% over the first month, then
this call option would still be trading at the same price 4.64. That's not an unusual
increase in implied volatility; increases of that magnitude, 20% to 26%, happen all
the time. For it to then increase from 26% to 38% over the next month is probably
less likely, but it is certainly not out of the question. There have been many times in
the past when just such an increase has been possible - during any of the August,
September, or October bear markets or mini-crashes, for example. Also, such an
increase in implied volatility might occur if there were takeover rumors in this stock,
or if the entire market became more volatile, as was the case in the latter half of the
1990s.
Perhaps this example was distorted by the fact that an implied volatility of 20%
is a fairly low number to begin with. What would a similar example look like if one
started out with a much higher implied volatility say, 80%?
Example: Making the same assumptions as in the previous example, but now setting
the implied volatility to a much higher level of 80%, the Black-Scholes model now
says that the call would be worth a price of 16.45:
Stock Price:
Strike Price:
Time Remaining:
Implied Volatility:
Theoretical Call Value:
100
100
3 months
80%
16.45
Again, one must ask the question: "If a month passes, what implied volatility
would be necessary for the Black-Scholes model to yield a price of 16.45?" In this
case, it turns out to be an implied volatility of just over 99%.
Stock Price:
Strike Price:
Time Remaining:
Implied Volatility:
Theoretical Call Value:
100
100
2 months
99.4%
16.45
760 Part VI: Measuring and Trading Volatility
Finally, to be able to completely compare this example with the previous one, it
is necessary to see what implied volatility would have to rise to in order to offset the
effect of yet another month's time decay. It turns out to be over 140%:
Stock Price:
Strike Price:
Time Remaining:
Implied Volatility:
Theoretical Call Value:
100
100
1 month
140.9%
16.45
Table 37-4 summarizes the results of these examples, showing the levels to
which implied volatility would have to rise to maintain the call's value as time passes.
Are the volatility increases in the latter example less likely to occur than the
ones in the former example? Probably yes - certainly the last one, in which implied
volatility would have to increase from 80% to nearly 141 % in order to maintain the
call's value. However, in another sense, it may seem more reasonable: Note that the
increase in volatility from 20% to 26% is a 30% increase. That is, 20% times 1.30
equals 26%. That's what's required to maintain the call's value for the lower volatility
over the first month - an increase in the magnitude of implied volatility of 30%. At
the higher volatility, though, an increase in magnitude of only about 25% is required
(from 80% to 99%). Thus, in those terms, the two appear on more equal footing.
What makes the top line of Table 37-4 appear more likely than the bottom line
is merely the fact that an experienced option trader knows that many stocks have
implied volatilities that can fluctuate in the 20% to 40% range quite easily. However,
there are far fewer stocks that have implied volatilities in the higher range. In fact,
until the Internet stocks got hot in the latter portion of the 1990s, the only ones with
volatilities like those were very low-priced, extremely volatile stocks. Hence one's
experience factor is lower with such high implied volatility stocks, but it doesn't mean
that the volatility fluctuations appearing in Table 37-4 are impossible.
If the reader has access to a software program containing the Black-Scholes
model, he can experiment with other situations to see how powerful the effect of
implied volatilit


re very low-priced, extremely volatile stocks. Hence one's
experience factor is lower with such high implied volatility stocks, but it doesn't mean
that the volatility fluctuations appearing in Table 37-4 are impossible.
If the reader has access to a software program containing the Black-Scholes
model, he can experiment with other situations to see how powerful the effect of
implied volatility is. For example, without going into as much detail, if one takes the
case of a 12-month option whose initial implied volatility is 20%, all it takes to main-
TABLE 37-4
Initial Implied
Volatility
20%
80%
Volatility Leveled Required to Maintain Call Value ...
... After One Month ... After Two Months
26%
99%
38%
141%
Chapter 37: How Volatility Affects Popular Strategies 761
tain the call's value over a 6-month time period is an increase in implied volatility to
27%. Taken from the viewpoint of the option seller, this is perhaps most enlighten
ing: If you sell a one-year (LEAPS) option and six months pass, during which time
implied volatility increases from 20% to 27% - certainly quite possible -you will have
made nothing! The call will still be selling for the same price, assuming the stock is
still selling for the same price.
Finally, it was mentioned earlier that implied volatility often explodes during a
market crash. In fact, one could determine just how much of an increase in implied
volatility would be necessary in a market crash in order to maintain the call's value.
This is similar to the first example in this section, but now the stock price will be
allowed to decrease as well. Table 37-5, then, shows what implied volatility would be
required to maintain the call's initial value (a price of 4.64), when the stock price falls.
The other factors remain the same: time remaining (3 months), striking price (100),
and interest rate (5% ). Again, this table shows instantaneous price changes. In real
life, a slightly higher implied volatility would be necessary, because each market crash
could take a day or two.
Thus, from Table 37-5, one could say that even if the underlying stock dropped
20 points (which is 20% in this case) in one day, yet implied volatility exploded from
20% to 67% at the same time, the call's value would be unchanged! Could such an
outrageous thing happen? It has: In the Crash of '87, the market plummeted 22% in
one day, while the Volatility Index ($VIX) theoretically rose from 36% to 150% in one
day. In fact, call buyers of some $OEX options actually broke even or made a little
money due to the explosion in implied volatility, despite the fact that the worst mar
ket crash in history had occurred.
If nothing else, these examples should impart to the reader how important it is
to be aware of implied volatility at the time an option position is established. If you
are buying options, and you buy them when implied volatility is "low," you stand to
TABLE 37-5
Stock Price
100
95
90
85
80
75
70
Implied Volatility Necessary for Call to Maintain Value
20% (the initial parameters)
33%
44%
55%
67%
78%
89%
762 Part VI: Measuring and Trading Volatility
benefit if implied volatility merely returns to "normal" levels while you hold the posi
tion. Of course, having the underlying increase in price is also important.
Conversely, an option seller should be keenly aware of implied volatility when
the option is initially sold - perhaps even more so than the buyer of an option. This
pertains equally well to naked option writers and to covered option writers. If implied
volatility is "too low" when the option writing position is established, then an increase
(or worse, an explosion) in implied volatility will be very detrimental to the position,
completely overcoming the effects of time decay. Hence, an option writer should not
just sell options because he thinks he is collecting time decay each day that passes.
That may be true, but an increase in implied volatility can completely domin.ate what
little time decay might exist, especially for a longer-term option.
In a similar manner, a decrease in implied volatility can be just as important.
Thus, if the call buyer purchases options that are "too costly," ones in which implied
volatility is "too high," then he could lose money even if the underlying makes a mod
est move in his favor.
In the next chapters, the topic of just how an option buyer or seller should
measure implied volatility to determine what is "too low" or "too high" will be dis
cussed. For now, suffice it to grasp the general concept that a change in implied
volatility can have substantial effects on an option's price far greater effects than the
passage of time can have.
In fact, all of this calls into question just exactly what time value premium is.
That part of an option's value that is not intrinsic value is really affected much more
by volatility than it is by time decay, yet it carries the term "time value premium."
TIME VALUE PREMIUM IS A MISNOMER
Many (perhaps novice) option traders seem to think of time as the main antagonist to
an option buyer. However, when one really thinks about it, he should realize that the
portion of an option that is not intrinsic value is really much more related to stock
price movement and/or volatility than anything else, at least in the short term. For
this reason, it might be beneficial to more closely analyze just what the "excess value"
portion of an option represents and why a buyer should not primarily think of it as
time value premium.
An option's price is composed of two parts: (1) intrinsic value, which is the "real"
part of the option's value - the distance by which the option is in-the-money, and (2)
"excess value" - often called time value premium. There are actually five factors that
affect the "excess value" portion of an option. Eventually, time will dominate them
Chapter 37: How Volah'lity Affects Popular Strategies 763
all, but the longer


sed of two parts: (1) intrinsic value, which is the "real"
part of the option's value - the distance by which the option is in-the-money, and (2)
"excess value" - often called time value premium. There are actually five factors that
affect the "excess value" portion of an option. Eventually, time will dominate them
Chapter 37: How Volah'lity Affects Popular Strategies 763
all, but the longer the life of the option, the more the other factors influence the
"excess value."
The five factors influencing excess value are:
1. stock price movements,
2. changes in implied volatility,
3. the passage of time,
4. changes in the dividend (if any exist), and
5. changes in interest rates.
Each is stated in terms of a movement or change; that is, these are not static
things. In fact, to measure them one uses the "greeks": delta, vega, theta, (there is no
"greek" for dividend change), and rho. Typically, the effect of a change in dividend or
a change in interest rate is small (although a large dividend change or an interest rate
change on a very long-term option can produce visible changes in the prices of
options).
If everything remains static, then time decay will eventually wipe out all of the
excess value of an option. That's why it's called time value premium. But things don't
ever remain static, and on a daily basis, time decay is small, so it is the remaining two
factors that are most important.
Example: XYZ is trading at 82 in late November. The January 80 call is trading at 8.
Thus, the intrinsic value is 2 (82 minus 80) and the excess value is 6 (8 minus 2). If
the stock is still at 82 at January expiration, the option will of course only be worth 2,
and one will say that the 6 points of excess value that was lost was due to time decay.
But on that day in late November, the other factors are much more dominant.
On this particular day, the implied volatility of this option is just over 50%. One
can determine that the call's greeks are:
Delta: 0.60
Vega: 0.13
Theta: -0.06
This means, for example, that time decay is only 6 cents per day. It would
increase as time went by, but even with a day or so to go, theta would not increase
above about 20 cents unless volatility increased or the stock moved closer to the
strike price.
From the above figures, one can see - and this should be intuitively appealing that
the biggest factor influencing the price of the option is stock price movement (delta).
764 Part VI: Measuring and Trading VolatiRty
It's a little unfair to say that, because it's conceivable (although unlikely) that volatil
ity could jump by a large enough margin to become a greater factor than delta for
one day's move in the option. Furthermore, since this option is composed mostly of
excess value, these more dominant forces influence the excess value more than time
decay does.
There is a direct relationship between vega and excess value. That is, if implied
volatility increases, the excess value portion of the option will increase and, if implied
volatility decreases, so will excess value.
The relationship between delta and excess value is not so straightforward. The
farther the stock moves away from the strike, the more this will have the effect of
shrinking the excess value. If the call is in-the-money (as in the above example), then
an increase in stock price will result in a decrease of excess value. That is, a deeply in
the-money option is composed primarily of intrinsic value, while excess value is quite
small. However, when the call is out-of-the-money, the effect is just the opposite:
Then, an increase in call price will result in an increase in excess value, because the
stock price increase is bringing the stock closer to the option's striking price.
For some readers, the following may help to conceptualize this concept. The
part of the delta that addresses excess value is this:
Out-of-the-money call: 100% of the delta affects the excess value.
In-the-money call: "1.00 minus delta" affects the excess value. (So, if a call is very
deeply in-the-money and has a delta of 0.95, then the delta only has 1.00 - 0.95,
or 0.05, room to increase. Hence it has little effect on what small amount of
excess value remains in this deeply in-the-money call.)
These relationships are not static, of course. Suppose, for example, that in the
same situation of the stock trading at 82 and the January 80 call trading at 8, there is
only week remaining until expiration! Then the implied volatility would be 155%
(high, but not unheard of in volatile times). The greeks would bear a significantly dif
ferent relationship to each other in this case, though:
Delta: 0.59
Vega: 0.044
Theta: -0 .5 1
This very short-term option has about the same delta as its counterpart in the previ
ous example (the delta of an at-the-money option is generally slightly above 0.50).
Meanwhile, vega has shrunk. The effect of a change in volatility on such a short-term
option is actually about a third of what it was in the previous example. However, time
decay in this example is huge, amounting to half a point per day in this option.
Chapter 37: How Volatility Affects Popular Strategies 765
So now one has the idea of how the excess value is affected by the "big three"
of stock price movement, change in implied volatility, and passage of time. How can
one use this to his advantage? First of all, one can see that an option's excess value
may be due much more to the potential volatility of the underlying stock, and there
fore to the option's implied volatility, than to time.
As a result of the above information regarding excess value, one shouldn't think
that he can easily go around selling what appear to be options with a lot of excess
value and then expect time to bring in the profits for him. In fact, there may be a lot
of volatility both actual and implied - keeping that excess value nearly intact for a
fairly long period of time. In fact, in the coming ch


e.
As a result of the above information regarding excess value, one shouldn't think
that he can easily go around selling what appear to be options with a lot of excess
value and then expect time to bring in the profits for him. In fact, there may be a lot
of volatility both actual and implied - keeping that excess value nearly intact for a
fairly long period of time. In fact, in the coming chapters on volatility estimation, it
will be shown that option buyers have a much better chance of success than conven
tional wisdom has maintained.
VOLATILITY AND THE PUT OPTION
While it is obvious that an increase in implied volatility ½ill increase the price of a put
option, much as was shown for a call option in. the preceding discussion, there are
certain differences between a put and a call, so a little review of the put option itself
may be useful. A put option tends to lose its premium fairly quickly as it becomes an
in-the-money option. This is due to the realities of conversion arbitrage. In a con
version arbitrage, an arbitrageur or market-maker buys stock and buys the put, while
selling the call. If he carries the position to expiration, he will have to pay carrying
costs on the debit incurred to establish the position. Furthermore, he would earn any
dividends that might be paid while he holds the position. This information was pre
sented in a slightly different form in the chapter on arbitrage, but it is recounted
here:
In a perfect world, all option prices would be so accurate that there would be
no profit available from a conversion. That is, the following equation (1) would apply:
(1) Call price+ Strike price - Stock price - Put price+ Dividend- Carrying cost= 0
where carrying cost = strike price/ (1 + r)t
t = time to expiration
r = interest rate
Now, it is also known that the time value premium of a put is the amount by which
its value exceeds intrinsic value. The intrinsic value of an in-the-money put option is
merely the difference between the strike price and the stock price. Hence, one can
write the following equation (2) for the time value premium (TVP) of an in-the
money put option:
766 Part VI: Measuring and Trading Volatility
(2) Put TVP = Put price - Strike price + Stock price
The arbitrage equation, (1), can be rewritten as:
(3) Put price - Strike price+ Stock price= Call price+ Dividends - Carrying cost
and substituting equation (2) for the terms in equation (3), one arrives at:
( 4) Put TVP = Call price + Dividends - Carrying cost
In other words, the time value premium of an in-the-money put is the same as the
(out-of-the-money) call price, plus any dividends to be ea med until expiration, less
any carrying costs over that same time period.
Assuming that the dividend is small or zero (as it is for most stocks), one can see
that an in-the-money put would lose its time value premium whenever carrying costs
exceed the value of the out-of-the-money call. Since these carrying costs can be rel
atively large ( the carrying cost is the interest being paid on the entire debit of the
position - and that debit is approximately equal to the strike price), they can quickly
dominate the price of an out-of-the-money call. Hence, the time value premium of
an in-the-money put disappears rather quickly.
This is important information for put option buyers, because they must under
stand that a put won't appreciate in value as much as one might expect, even when
the stock drops, since the put loses its time value premium quickly. It's even more
important information for put sellers: A short put is at risk of assignment as soon as
there is no time value premium left in the put. Thus, a put can be assigned well in
advance of expiration even a LEAPS put!
Now, returning to the main topic of how implied volatility affects a position, one
can ask himself how an increase or decrease in implied volatility would affect equa
tion ( 4) above. If implied volatility increases, the call price would increase, and if the
increase were great enough, might impart some time value premium to the put.
Hence, an increase in implied volatility also may increase the price of a put, but if the
put is too far in-the-nwney, a modest increase in implied volatility still won't budge
the put. That is, an increase in implied volatility would increase the value of the call,
but until it increases enough to be greater than the carrying costs, an in-the-money
put will remain at parity, and thus a short put would still remain at risk of assignment.
STRADDLE OR STRANGLE BUYING AND SELLING
Since owning a straddle involves owning both a put and a call with the same terms,
it is fairly evident that an increase in implied volatility will be very beneficial for a
straddle buyer. A sort of double benefit occurs if implied volatility rises, for it will
Chapter 37: How Volatility Affects Popular Strategies 767
positively affect both the put and the call in a long straddle. Thus, if a straddle buyer
is careful to buy straddles in situations in which implied volatility is "low," he can
make money in one of two ways. Either (1) the underlying price makes a move great
enough in magnitude to exceed the initial cost of the straddle, or (2) implied volatil
ity increases quickly enough to overcome the deleterious effects of time decay.
Conversely, a straddle seller risks just the opposite - potentially devastating loss
es if implied volatility should increase dramatically. However, the straddle seller can
register gains faster than just the rate of time decay would indicate if implied volatil
ity decreases. Thus, it is very important when selling options - and this applies to cov
ered options as well as to naked ones - to sell only when implied volatility is "high."
A strangle is the same as a straddle, except that the call and put have different
striking prices. Typically, the call strike price is higher than the put strike price.
Naked option sellers often prefer selling stra


atil
ity decreases. Thus, it is very important when selling options - and this applies to cov
ered options as well as to naked ones - to sell only when implied volatility is "high."
A strangle is the same as a straddle, except that the call and put have different
striking prices. Typically, the call strike price is higher than the put strike price.
Naked option sellers often prefer selling strangles in which the options are well out
of-the-money, so that there is less chance of them having any intrinsic value when
they expire. Strangles behave much like straddles do with respect to changes in
implied volatility.
The concepts of straddle ownership will be discussed in much more detail in the
following chapters. Moreover, the general concept of option buying versus option
selling will receive a great deal of attention.
CALL BULL SPREADS
In this section, the bull spread strategy will be examined to see how it is affected by
changes in implied volatility. Let's look at a call bull spread and see how implied
volatility changes might affect the price of the spread if all else remains equal. Make
the following assumptions:
Assumption Set 1 :
Stock Price: 1 00
Time to Expiration: 4 months
Position: long Call Struck at 90
Short Call Struck at 110
Ask yourself this simple question: If the stock remains unchanged at 100, and implied
volatility increases dramatically, will the price of the 90-110 call bull spread grow or
shrink? Answer before reading on.
The truth is that, if implied volatility increases, the price of the spread will
shrink. I would suspect that this comes as something of a surprise to a good number
of readers. Table 37-6 contains some examples, generated from a Black-Scholes
768
TABLE 37-6
Implied
Volatility
20%
30%
40%
50%
60%
70%
80%
Stock Price = I 00
Part VI: Measuring and Trading VolatHity
90-110 Call
Bull Spread
(Theoretical Value)
10.54
9.97
9.54
9.18
8.87
8.58
8.30
model, using the assumptions stated above, the most important of which is that the
stock is at 100 in all cases in this table.
One should be aware that it would probably be difficult to actually trade the
spread at the theoretical value, due to the bid-asked spread in the options.
Nevertheless, the impact of implied volatility is clear.
One can quantify the amount by which an option position will change for each
percentage point of increase in implied volatility. Recall that this measure is called
the vega of the option or option position. In a call bull spread, one would subtract the
vega of the call that is sold from that of the call that is bought in order to arrive at the
position vega of the call bull spread. Table 37-7 is a reprint of Table 37-6, but now
including the vega.
Since these vegas are all negative, they indicate that the spread will shrink in
value if implied volatility rises and that the spread will expand in value if implied
TABLE 37-7
90-110 Call
Implied Bull Spread Position
Volatility (Theoretical Value) Vega
20% 10.54 -0.67
30% 9.97 -0.48
40% 9.54 -0.38
50% 9.18 -0.33
60% 8.87 -0.30
70% 8.58 -0.28
80% 8.30 -0.26
Chapter 37: How VolatHity Afleds Popular Strategies 769
volatility decreases. Again, these statements may seem contrary to what one would
expect from a bullish call position.
Of course, it's highly unlikely that implied volatility would change much in the
course of just one day while the stock price remained unchanged. So, to get a bet
ter handle on what to expect, one really to needs to look at what might happen at
some future time (say a couple of weeks hence) at various stock prices. The graph
in Figure 37-3 begins the investigation of these more complex scenarios.
The profit curve shown in Figure 37-3 makes certain assumptions: (1) The bull
spread assumes the details in Assumption Set 1, above; (2) the spread was bought
with an implied volatility of 20% and remained at that level when the profit picture
above was drawn; and (3) 30 days have passed since the spread was bought. Under
these assumptions, the profit graph shows that the bull spread conforms quite well to
what one would expect; that is, the shape of this curve is pretty much like that of a
bull spread at expiration, although if you look closely you'll see that it doesn't widen
out to nearly its maximum gain or loss potential until the stock is well above llO or
below 90 the strike prices used in the spread.
Now observe what happens if one keeps all the other assumptions the same,
except one. In this case, assume implied volatility was 80% at purchase and remains
at 80% one month later. The comparison is shown in Figure 37-4. The 80% curve is
overlaid on top of the 20% curve shown earlier. The contrast is quite startling.
Instead of looking like a bull spread, the profit curve that uses 80% implied volatili-
FIGURE 37-3.
Bull spread profit picture in 30 days, at 20% IV.
1000
500
<J)
<J)
0 0 ...J
?i:: 70 80 90 100 110 120 130 140
e a.
"' -500
Stock Price
770 Part VI: Measuring and Trading Volatility
FIGURE 37-4.
Bull spread profit picture in 30 days.
1000
500
iv=80%
(/)
(/)
0
0 -' :;:,
70 801 90 e
~
a.
fl'>
-500
130 140
iv= 20%
-1000 Stock
ty is a rather flat thing, sloping only slightly upward - and exhibiting far less risk and
reward potential than its lower implied volatility counterpart. This points out anoth
er important fact: For volatile stocks, one cannot expect a 4-rrwnth bull spread to
expand or contract much during the first rrwnth of life, even if the stock makes a sub
stantial rrwve. Longer-term spreads have even less movement.
As a corollary, note that if implied volatility shrinks while the stock rises, the
profit outlook will improve. Graphically, using Figure 37-4, if one's profit picture
moves from the 80% curve to the 20% curve on the right-hand side of the chart, that
is a positive development. Of course, if the stock drops and the implied volatility
drops too, then one's los


spreads have even less movement.
As a corollary, note that if implied volatility shrinks while the stock rises, the
profit outlook will improve. Graphically, using Figure 37-4, if one's profit picture
moves from the 80% curve to the 20% curve on the right-hand side of the chart, that
is a positive development. Of course, if the stock drops and the implied volatility
drops too, then one's losses would be worse - witness the left-hand side of the graph
in Figure 37-4.
A graph could be drawn that would incorporate other implied volatilities, but
that would be overkill. The profit graphs of the other spreads from Tables 37-6 or
37-7 would lie between the two curves shown in Figure 37-4.
If this discussion had looked at bull spreads as put credit spreads instead of call
debit spreads, perhaps these conclusions would not have seemed so unusual.
Experienced option traders already understand much of what has been shown here,
but less experienced traders may find this information to be different from what they
expected.
Some general facts can be drawn about the bull spread strategy. Perhaps the
most important one is that, if used on a volatile stock, you won't get much expansion
in the spread even if the stock makes a nice move upward in your favor. In fact, for
Cbapter 37: How Volatility Affects Popular Strategies 771
high implied volatility situations, the bull spread won't expand out to its maximum
price until expiration draws nigh. That can be frustrating and disappointing.
Often, the bull spread is established because the option trader feels the options
are "too expensive" and thus the spread strategy is a way to cut down on the total
debit invested. However, the ultimate penalty paid is great. Consider the fact that,
if the stock rose from 100 to 130 in 30 days, any reasonable four-month call pur
chase (i.e., with a strike initially near the current stock price) would make a nice
profit, while the bull spread barely ekes out a 5-point gain. To wit, the graph in
Figure 37-5 compares the purchase of the at-the-money call with a striking price of
100 and the 90-110 call bull spread, both having implied volatility of 80%. Quite
clearly, the call purchase dominates to a great extent on an upward move. Of course,
the call purchase does worse on the downside, but since these are bullish strategies,
one would have to assume that the trader had a positive outlook for the stock when
the position was established. Hence, what happens on the downside is not primary
in his thinking.
The bull spread and the call purchase have opposite position vegas, too. That is,
a rise in implied volatility will help the call purchase but will harm the bull spread
( and vice versa). Thus, the call purchase and the bull spread are not very similar posi
tions at all.
If one wants to use the bull spread to effectively reduce the cost of buying an
expensive at-the-money option, then at least make sure the striking prices are quite
FIGURE 37-5.
Call buy versus bull spread in 30 days; IV = 80%.
Cl)
~
2500
2000
1500
1000
e 500
Cl.
-500
-1000
Outright Call Buy
Bull Spread
---
140
Stock
772 Part VI: Measuring and Trading Volatility
wide apart. That will allow for a reasonable amount of price appreciation in the bull
spread if the underlying rises in price. Also, one might want to consider establishing
the bull spread with striking prices that are both out-of-the-money. Then, if the stock
rallies strongly, a greater percentage gain can be had by the spreader. Still, though,
the facts described above cannot be overcome; they can only possibly be mitigated
by such actions.
A FAMILIAR SCENARIO?
Often, one may be deluded into thinking that the two positions are more similar than
they are. For example, one does some sort of analysis - it does not matter if it's fun
damental or technical - and comes to a conclusion that the stock ( or futures contract
or index) is ready for a bullish move. Furthermore, he wants to use options to imple
ment his strategy. But, upon inspecting the actual market prices, he finds that the
options seem rather expensive. So, he thinks, "Why not use a bull spread instead? It
costs less and it's bullish, too."
Fairly quickly, the underlying moves higher - a good prediction by the trader,
and a timely one as well. If the move is a violent one, especially in the futures mar
ket, implied volatility might increase as well. If you had bought calls, you'd be a happy
camper. But if you bought the bull spread, you are not only highly disappointed, but
you are now facing the prospect of having to hold the spread for several more weeks
(perhaps months) before your spread widens out to anything even approaching the
maximum profit potential.
Sound familiar? Every option trader has probably done himself in with this line
of thinking at one time or another. At least, now you know the reason why: High or
increasing implied volatility is not a friend of the bull spread, while it is a friendly ally
of the outright call purchase. Somewhat surprisingly, many option traders don't real
ize the difference between these two strategies, which they probably consider to be
somewhat similar in nature.
So, be careful when using bull spreads. If you really think a call option is too
expensive and want to reduce its cost, ti:y this strategy: Buy the call and simultane
ously sell a credit put spread (bull spread) using slightly out-of-the-money puts. This
strategy reduces the call's net cost and maintains upside potential (although it
increases downside risk, but at least it is still a fixed risk).
Example: With XYZ at 100, a trader is bullish and wants to buy the July 100 calls,
which expire in two months. However, upon inspection, he finds that they are trad
ing at 10 - an implied volatility of 59%. He knows that, historically, the implied
volatility of this stock's options range from approximately 40% to 60%, so these are
Chapter 37: How Volatility Affec


ast it is still a fixed risk).
Example: With XYZ at 100, a trader is bullish and wants to buy the July 100 calls,
which expire in two months. However, upon inspection, he finds that they are trad
ing at 10 - an implied volatility of 59%. He knows that, historically, the implied
volatility of this stock's options range from approximately 40% to 60%, so these are
Chapter 37: How Volatility Affects Popular Strategies 773
very expensive options. If he buys them now and implied volatility returns to its
median range near 50%, he will suffer from the decrease in implied volatility.
As a possible remedy, he considers selling an out-of-the-money put credit
spread at the same time that he buys the calls. The credit from this spread will act as
a means of reducing the net cost of the calls. If he's right and the stock goes up, all
will be well. However, the introduction of the put spread into the mix has introduced
some additional downside risk.
Suppose the following prices exist:
XYZ: 100
July 100 call: 10 (as stated above)
July 90 put: 5
July 80 put: 2
The entire bullish position would now consist of the following:
Buy 1 July 100 call at 1 0
Buy 1 July 80 put at 2
Sell 1 July 90 put at 5
Net expenditure: 7 point debit (plus commission)
Figure 37-6 shows the profitability, at expiration, of both the outright call pur
chase and the bullish position constructed above.
FIGURE 37-6.
Profitability at expiration.
2000
Bullish Spread //
/
1000
"' "' 0 ...J
87 :!::
Outright Call Purchase
e 0
C. 70 80 90
<Ft 100 /100 ,,....... ___
120
-1000
Stock
-2000
774 Part VI: Measuring and Trading Volatility
First, one can see that the bullish spread position has a total risk of 17 points, if
X'YZ is below 80 (the lower striking price of the put spread) at expiration. That, of
course, is more than the 10-point cost of the July 100 call by itself, but if one is using
a trading stop of any sort, he probably would not be at risk for the entire 17 points,
since he wouldn't hold on while the stock fell all the way to 80 and below. Note also
that the bullish spread position would have a loss of 10 points (the same as the call)
at a price of 87 for the common at expiration. Hence, the combined position actual
ly has less risk than the outright call purchase as long as XYZ is 87 or higher at expi
ration. Since one is supposedly bullish initially when establishing this strategy, it
seems likely that he would figure the stock would be 87 or higher at expiration. ·
Figure 37-7 offers another comparison, that of the two positions after 30 days
have passed. Note that the spread position once again does better on the upside and
worse on the downside. The crossover point between the two curves is at about a
price of95. That is, ifXYZ is above 95 in 30 days, the bullish spread position will out
perform the call buy.
One final point should be made regarding the investment required. The out
right call purchase requires an investment of $1,000 - the cost of the long call. The
bullish spread position requires that $1,000, plus $700 for the spread (IO-point dif
ference in the strikes, less the 3-point credit received for selling the spread). That's a
total of $1,700, the risk of the bullish spread position. Hence, the rate of return might
favor the outright call purchase, depending on how far the stock rallies.
FIGURE 37-7.
Results of the two positions in 30 days.
Cl)
_g
:;::,
e
Cl..
~
1000
-1000
-2000-
Spread
95
110
Stock
/
Outright Call Purchase
120
Chapter 37: How Volatility Affects Popular Strategies 775
Overall, the bullish spread position is an attractive alternative to an outright call
purchase, especially when the call is overpriced. The spread does risk a greater
amount of money if the underlying stock should collapse heavily. Still, if one is truly
bullish, and if one employs a reasonably tight downside stop on his entire position,
this spread can perform better than the outright purchase of an overpriced call.
VERTICAL PUT SPREADS
Also of interest is the effect that implied volatility has on put spreads. One of the
more popular strategies involving puts is the sale of a credit spread - a bull spread
with puts. Assume that a stock is selling at 100, and one is going to sell a put with a
110 strike and buy a put with a 90 strike. That is a put credit (bull) spread. Also
assume that the options have four months of life remaining. (See Table 37-8.)
One would not rationally sell this credit spread if implied volatility were as low
as 20%, because at that low level of volatility, the in-the-money December llO put is
trading for 10 dollars - parity - and thus would immediately be at risk of early
assignment. But one can see that an increase in implied volatility increases the value
of the spread. Now, if one had sold this spread to begin with, he would thus be los
ing money when implied volatility increased. This was proven with call bull spreads,
too: They lose money when implied volatility increases. Conversely, of course, the
put credit spread makes money when implied volatility decreases.
What happens after thirty days have passed? Figure 37-8 shows just two cases
- implied volatility at 30% and implied volatility at 80%. One can surmise that other
levels of implied volatility between 30% and 80% would have profit graphs that lie
between the two shown in Figure 37-8.
TABLE 37·8
Implied
Volatility
20%
30%
40%
50%
60%
70%
80%
*Short option trading at parity
90-110
Put Bull Spread
(Theoretical Value)
9.15 er*
9.70 er
10.12 er
10.46 er
10.78 er
11.05 er
11.33 er
174 Part VI: Measuring and Trading Volatility
First, one can see that the bullish spread position has a total risk of 17 points, if
XYZ is below 80 (the lower striking price of the put spread) at expiration. That, of
course, is more than the 10-point cost of the July 100 call by itself, but if one is using
a trading stop of any sort, he probably would not


.46 er
10.78 er
11.05 er
11.33 er
174 Part VI: Measuring and Trading Volatility
First, one can see that the bullish spread position has a total risk of 17 points, if
XYZ is below 80 (the lower striking price of the put spread) at expiration. That, of
course, is more than the 10-point cost of the July 100 call by itself, but if one is using
a trading stop of any sort, he probably would not be at risk for the entire 17 points,
since he wouldn't hold on while the stock fell all the way to 80 and below. Note also
that the bullish spread position would have a loss of 10 points (the same as the call)
at a price of 87 for the common at expiration. Hence, the combined position actual
ly has less risk than the outright call purchase as long as XYZ is 87 or higher at expi
ration. Since one is supposedly bullish initially when establishing this strategy, it
seems likely that he would figure the stock would be 87 or higher at expiration.
Figure 37-7 offers another comparison, that of the two positions after 30 days
have passed. Note that the spread position once again does better on the upside and
worse on the downside. The crossover point between the two curves is at about a
price of 95. That is, ifXYZ is above 95 in 30 days, the bullish spread position will out
perform the call buy.
One final point should be made regarding the investment required. The out
right call purchase requires an investment of $1,000 - the cost of the long call. The
bullish spread position requires that $1,000, plus $700 for the spread (IO-point dif
ference in the strikes, less the 3-point credit received for selling the spread). That's a
total of $1,700, the risk of the bullish spread position. Hence, the rate of return might
favor the outright call purchase, depending on how far the stock rallies.
FIGURE 37-7.
Results of the two positions in 30 days.
1000
en
Ill
0
...J
O 70 :;::,
~ ... a.
w
-1000
-2000-
80
95
Bullish Spread
Stock
Spread
110
/
1/
Outright Call Purchase
120
Chapter 37: How Volatility Affects Popular Strategies 775
Overall, the bullish spread position is an attractive alternative to an outright call
purchase, especially when the call is overpriced. The spread does risk a greater
amount of money if the underlying stock should collapse heavily. Still, if one is truly
bullish, and if one employs a reasonably tight downside stop on his entire position,
this spread can perform better than the outright purchase of an overpriced call.
VERTICAL PUT SPREADS
Also of interest is the effect that implied volatility has on put spreads. One of the
more popular strategies involving puts is the sale of a credit spread - a bull spread
with puts. Assume that a stock is selling at 100, and one is going to sell a put with a
110 strike and buy a put with a 90 strike. That is a put credit (bull) spread. Also
assume that the options have four months of life remaining. (See Table 37-8.)
One would not rationally sell this credit spread if implied volatility were as low
as 20%, because at that low level of volatility, the in-the-money December llO put is
trading for 10 dollars - parity - and thus would immediately be at risk of early
assignment. But one can see that an increase in implied volatility increases the value
of the spread. Now, if one had sold this spread to begin with, he would thus be los
ing money when implied volatility increased. This was proven with call bull spreads,
too: They lose money when implied volatility increases. Conversely, of course, the
put credit spread makes money when implied volatility decreases.
What happens after thirty days have passed? Figure 37-8 shows just two cases
- implied volatility at 30% and implied volatility at 80%. One can surmise that other
levels of implied volatility between 30% and 80% would have profit graphs that lie
between the two shown in Figure 37-8.
TABLE 37-8
Implied
Volatility
20%
30%
40%
50%
60%
70%
80%
*Short option trading at parity
90-110
Put Bull Spread
(Theoretical Value)
9.15 er*
9.70 er
10. 12 er
10.46 er
10.78 er
11.05 er
11.33 er
776
FIGURE 37-8.
Put credit (bull) spread profit in 30 days.
1000
500
- 1000 _ _,±8±
Assignment Risk Area
IV=30%
Stock
Part VI: Measuring and Trading Volatility
-~
IV= 30%
130 140
First, one can observe that a bull put spread does not widen out to anywhere
near its maximum potential if implied volatility increases. The same thing was seen
with the call bull spread in the previous section. But a put bull spreader is caught in
another trap: If implied volatility falls and the stock falls too, the risk of early assign
ment materializes quicky. Note the shaded area at the lower left of the graph, extend
ing from a price of about 94 on down. After thirty days (so there would be three
months life remaining at that point in time), if implied volatility is 30%, the 110 put
(the short put) would be trading at parity for stock prices of 94 and below. Thus, it
would be at risk of early assignment. If implied volatility were even lower, the puts
would be at parity for much higher stock prices.
Now, in and of itself, early assignment on an equity or futures put spread is not
necessarily a terrible thing. There will be a request for additional margin (because
the stock has to be paid for or the futures contract margined), but the risk is still the
same in dollar terms. Of course, the request for extra margin could be backbreaking
for a stock trader if he can't afford to fully pay for the stock, and the early assignment
would probably incur additional commission costs, too. However, with cash-based
index options there is a more serious increase in risk after an early assignment,
because one is left with only the long side of the spread. If that option happens to
have substantial value, then there is considerable risk if the underlying should quick
ly move higher. In fact, by the time one unwinds the spread, he might actually end
up losing


commission costs, too. However, with cash-based
index options there is a more serious increase in risk after an early assignment,
because one is left with only the long side of the spread. If that option happens to
have substantial value, then there is considerable risk if the underlying should quick
ly move higher. In fact, by the time one unwinds the spread, he might actually end
up losing more than his original limited risk amount - all due to the early assignment.
(This could happen if the underlying first plunges in price, placing both options
Chapter 37: How Volatility Affects Popular Strategies 777
deeply in-the-money, after which one gets assigned on the short put option, followed
by the underlying then dramatically rising in price.)
The lesson to be learned is this: If one is considering using bull spreads in which
at least one of the options is at- or in-the-rrwney, then a call bull spread is a superior
choice over a put bull spread. Early assignment is not really a consideration for most
call spreads.
In both cases, however, a more serious problem exists, and that is that the
spread does not widen out much even when the stock makes a nice bullish move.
Thus, once again it is actually better to buy a call option in most cases than to use the
bull spread, because profits are larger and an increase in implied volatility is a favor
able thing for an outright call buyer.
Note that these effects are similar, but much less pronounced, for out-of-the
money put credit spreads. Still, it should be noted that an increase in implied volatil
ity will harm an out-of-the-money put credit spread, too. Hence, if the underlying
goes into a rapid fall (crash, plunge), then implied volatility usually increases quickly
and dramatically. So an out-of-the-money credit spreader is hit with the double
whammy of expanding implied volatility and the fact that the underlying is fast
approaching the strike price of his options, . thereby expanding the price of the
spread.
PUT BEAR SPREADS
What about the put spread in a bearish situation? In a vertical put spread one buys
the put with the higher strike and sells the put with the lower strike to construct a
simple put bear spread. Actually, a sudden increase in implied volatility is of help to
the bear put spread. That is, the spread will widen out slightly. To verify this, look at
Table 37-8 again, only now imagine that one is buying the spread for a debit. Note
that the smallest debit is at the lower implied volatility- 9.15 debit with IV at 30%.
If implied volatility were to instantaneously jump to 80%, the spread would widen
out to 11.33 debit. A very quick profit could be had. So there's a difference right away
between a debit call bull spread (which loses money when implied volatility sudden
ly increases) and a debit put bear spread.
Unfortunately, the other major drawback - that the spread doesn't widen out
much if the underlying makes a favorable move - is still true. Figure 37-9 shows a
bear put spread, 30 days hence, for two different implied volatilities. Once again, the
lower-volatility spread widens out more quickly, because both options tend to go to
parity in that case. In fact, one can see on the graph that there is early assignment
risk in the low-volatility case, below a price of about 77 on the stock. That is not a
778 Part VI: Measuring and Trading Volatility
FIGURE 37-9.
Bear put spread profit in 30 days.
1000 IV= 30%
Assignment
Risk
Area
(/)
(/)
0
...J
~ 0
e 70 80 110 120 130 140
a.
ff7
IV= 80%
-1000
'~
Stock
problem, though, since the spread would have widened to its maximum potential in
that case and could just be removed when the risk of early assignment materialized.
When implied volatility remains high, though, the spread doesn't widen out
much, even when the stock drops a lot after 30 days. Since it is common for implied
volatility to rise (even skyrocket) when the underlying drops quickly, the put bear
spread probably won't widen out much. That may not be a psychologically pleasing
strategy, because one won't make the level of profits that he had hoped to when the
underlying fell quickly.
Once again, it seems that the outright purchase of an option is probably superi
or to a spread. In these cases, it is true with respect to puts, much as it was with call
options. Spreading often unnecessarily complicates a trader's outlook.
CALENDAR SPREADS
In the earlier chapter on calendar spreads, it was mentioned that an increase in
implied volatility will cause a calendar spread to widen out. Both options will become
more expensive, of course, since the increase in implied volatility affects both of
them, but the absolute price change will be greatest in the long-term option.
Therefore, the calendar spread will widen. This may seem somewhat counterintu
itive, especially where highly volatile stocks are concerned, so some examples may
prove useful.
Chapter 37: How Volatility Affects Popular Strategies 779
Example: Suppose that XYZ is trading at 100, and one is interested in a calendar
spread in which an August (5-month) call is bought and a May (2-month) call is sold.
For the purpose of this example, it will be assumed that these are both at-the-money
options. First, the vegas of the two options will be examined, assuming that implied
volatility is 40%:
Stock: 100
Implied Volatility:
40% Option
Sell May 100 call
Buy August 1 00 call
Theoretical Price
6.91
11.22
Vega
0.162
0.251
In theory, this spread should be worth 4.31 - the difference in the theoretical
values. Perhaps more important, it has volatility exposure of 0.089 - the difference
between the vega of the long call and that of the short call. Since vega is positive, this
means that an increase in implied volatility will be beneficial to the spread. In other
words, one can expect the spread to widen if implied volatility rises, and can expect
the spread to shrink if implied volatility de


values. Perhaps more important, it has volatility exposure of 0.089 - the difference
between the vega of the long call and that of the short call. Since vega is positive, this
means that an increase in implied volatility will be beneficial to the spread. In other
words, one can expect the spread to widen if implied volatility rises, and can expect
the spread to shrink if implied volatility declines.
The following table can also be constructed, showing the theoretical value of
the spread at various levels of implied volatility. This table makes the assumption that
very little time has passed ( only one week) before the implied volatility changes take
place. It also assumes that the stock is still at 100.
Stock Price: 100
One week ofter the spread hos been established:
Implied Volatility Theoretical Spread Value
20% 2.58
30% 3.52
40% 4.46
50% 5.40
60% 6.33
80% 8.16
100% 12.92
From the above data, it is quite obvious that implied volatility levels have a huge
effect on the value of a calendar spread. The actual initial contribution of time decay
is rather small in comparison. For example, note that if volatility remains unchanged
at 40%, then the spread will have widened only slightly - to 4.46 from 4.31 - after
the passage of one week's time. That is small in comparison to the changes dictated
by volatility expansion or contraction.
780 Part VI: Measuring and Trading Volatility
A common mistake that calendar spreaders make is to think that such a spread
looks overly attractive on a very volatile stock. Consider the same stock as above, still
trading at 100, but for some reason implied volatility has skyrocketed to 80% (per
haps a takeover rumor is present).
Stock: JOO
Implied Volatility: 80%
Coll
May 100 call
June 100 call
Theoretical Value
12.55
16.81
On the surface, this seems like a very attractive spread. There are two months
of life remaining in the May options (and three months in the Junes) and the spread
is trading at 4.36. However, both options are completely composed of time value
premium, and most certainly the June 100 call would be worth far more than 4.36
when the May expires, if the stock is still near 100. The fact that many traders miss
when they think of the calendar spread this way is that the June call will only be
worth "far more than 4.36" if implied volatility holds up. If implied volatility for this
stock is normally something on the order of 40%, say, then it is probably not reason
able to expect that the 80% level will hold up. Just for comparison, note that if the
stock is at 100 at May expiration - the maximum profit potential for such a calendar
spread - the June 100 call, with implied volatility now at 40%, and with one month
of life remaining, would be worth only 4. 77. Thus the spread would only have made
a profit of a few cents (4.36 to 4.77), and if the underlying stock were farther from
the strike price at expiration, there would probably be a loss rather than a profit.
The point to be remembered is that a calendar spread is a "long volatility" play
(and a reverse calendar spread is just the opposite). Evaluate the position's risk with
an eye to what might happen to implied volatility, and not just to where the stock
price might go or how much time decay there might be in the position.
RATIO SPREADS AND BACKSPREADS
The previous descriptions in this chapter describe fairly fully and accurately what
the effect of volatility changes are. More complicated strategies are usually nothing
more than combinations of the strategies presented earlier, so it is easy to discern
the effect that changes in implied volatility would have; just combine the effects on
the simpler strategies. For example, a ratio call write is really just the equivalent of
a straddle sale - a strategy whose volatility ramifications are fairly simple to under
stand.
Ratio spreads, on the other hand, might not be as intuitive to interpret, but they
are fairly simple nonetheless. A call ratio spread is really just the combination of some
Chapter 37: How Volatility Affects Popular Strategies 781
call bull spreads and some naked call options. For example, a call ratio spread might
consist of buying an XYZ July 100 call and selling two XYZ July 120 calls. If one were
to break it down into its components, this spread is really long one XYZ July 100-120
call bull spread, plus an additional naked July 120 call.
We already know that an increase in implied volatility is very detrimental to a
naked call option. In addition, it was shown earlier than an increase in implied volatil
ity actually harms the value of an at-the-money call bull spread. So, for a ratio call
spread, both components are harmed by an increase in implied volatility. Conversely,
a decrease in implied volatility would be beneficial to a ratio spread, but where naked
options are concerned, one should be more mindful of his risk than of this reward.
It was also shown previously that a call bull spread does not widen out much if
the underlying stock makes a quick upward move. The spread won't widen out to its
maximum profit potential until expiration draws nigh or the stock is well above the
upper strike in the spread. This scenario also does not bode well for the ratio call
spread. Suppose that the underlying stock suddenly jumps upward and implied
volatility increases at the same time. That combination is seen quite frequently, espe
cially if the stock were previously "dull" or if there is some sort of active corporate
(takeover) rumor. The call ratio spread will fare miserably under these conditions,
because the increase in stock price certainly harms the naked call position and the
bull spread is not widening out much to compensate for it. In addition, the increase
in implied volatility is working against both components.
The same sort of thing happens with put ratio spreads. They are really the com
bination of a put bear spread plus some additional n


are miserably under these conditions,
because the increase in stock price certainly harms the naked call position and the
bull spread is not widening out much to compensate for it. In addition, the increase
in implied volatility is working against both components.
The same sort of thing happens with put ratio spreads. They are really the com
bination of a put bear spread plus some additional naked put options. If the under
lying falls in price, while implied volatility increases - a very common occurrence in
all markets then the put ratio spread will fare poorly. In fact, implied volatility
sometimes explodes if the underlying falls very rapidly (crashes), so the ratio put
spreader should clearly assess his risk in this light.
In summary, a trader utilizing ratio spread strategies should clearly understand
and attempt to analyze the risks of an increase in implied volatility. This includes not
only assessing the vega risk of the spread, but also using a probability calculator with
some inflated volatility estimates to see just what the chances are of the spread get
ting into real trouble.
BACKSPREADS
A call backspread is merely the opposite of a call ratio spread. Thus, any of the earli
er commentary about how an increase in implied volatility is detrimental to a ratio
spread can be reversed when discussing the backspread. An increase in implied
volatility will be beneficial to a backspread strategy, while a decrease in implied
782 Part VI: Measuring and Trading Volatility
volatility will be slightly harmful to the spread. However, since risk is limited in a
backspread, such a decrease in implied volatility would not have catastrophic conse
quences unless one had overcommitted his funds to one position.
SUMMARY
In general, one can always determine the exposure of his position to volatility by com
puting the vega of this position. However, it is also useful for a strategist to have some
general feeling for how implied volatility will affect his positions and strategies. Thus,
this chapter was designed to point out the most common effects that changes .in
implied volatility will have on the basic types of option strategies. Once one has a
feeling for his exposure to volatility, he can then assess whether an adverse volatility
movement is likely. For example, if an increase in implied volatility would be harm
ful, and the strategist sees that current levels of implied volatility are quite low in
comparison to historical norms, then perhaps he should remove or adjust the posi
tion.
Volatility and the price of the underlying are the two major components
affecting profitability for most option positions. Time decay is only most pertinent
as expiration approaches. Yet, many traders concentrate greatly on potential price
movements of the underlying, often while ignoring what changes in implied volatil
ity could do. That is a mistake, for the most knowledgeable option traders plan for
volatility risk at all times. Understanding and handling that risk can have a positive
effect on an option trader's profits.
The Distribution of
Stock Prices
Much of the work that has been done in statistics and related areas regarding the
stock market has made the assumption that stock prices are distributed normally, or
more specifically, lognonnally. In actual practice, this is usually an incorrect assump
tion. For the option strategist, this means that some of the things one might believe
about certain option strategies having an advantage over certain other option strate
gies might be incorrect. In this chapter, a number of facts concerning stock price dis
tribution will be brought to light, including how it might affect the option strategist.
MISCONCEPTIONS ABOUT VOLATILITY
Statistics are used to estimate stock price movement (and futures and indices as well)
in many areas of financial analysis. Many authors have written extensively about the
use of probabilities to aid in choosing viable option strategies. Stock mutual fund
managers often use volatility estimates to help them determine how risky their port
folios are. The uses are myriad. Unfortunately, almost all of these applications are
wrong! Perhaps wrong is too strong a word, but almost all estimates of stock price
movement are overly conservative. This can be very dangerous if one is using such
estimates for the purposes of, say, writing naked options or engaging in some other
such strategy in which volatile stock price movement is undesirable.
As a review for those not familiar with mathematical distributions, the lognor
mal distribution is what's commonly used to describe stock prices because its shape
is intuitively similar to the way stocks behave - they can't go below zero, they can rise
to infinity, and most of the time they don't go much of anywhere. On top of that, the
distribution's shape is based on the historical volatility of the underlying instrument.
In a lognormal distribution (and normal distribution, too), stocks remain within 3
standard deviations of their current price 99. 7 4% of the time. A standard deviation
783
784 Part VI: Measuring and Trading Volatility
(sigma) is a statistical measure whose absolute distance grows larger with time, and
it is something that can be easily calculated for any individual stock or futures con
tract, using historical prices.
There are great differences between the way stocks really behave and the
assumptions that many mathematical models make about the way stocks theoretical
ly behave. The problem lies in assuming that normal or lognormal distribution pre
dicts stock price movements. Such an assumption does not allow for the occasional
wild days that many stocks, some futures, and the relatively rare index undergo. The
normal distribution pretty much says that a stock can't rise or fall by more than 3 stan
dard deviations. In fact, according to math, the probability of something that behaves
according to the normal distribution ( the "cla