will rise above $120 andthat the call with the 120 strike will move in-the-money. If this isn’t entirely clear yet, don’t worry; it will make more sense by the conclusionof this chapter.
THE CBOE VOLATILITY INDEXThe CBOE Volatility Index ($VIX) is a good starting point for a discussionof volatility. It is probably the most widely watched tool for tracking market volatility, but also the least understood. The VIX is an index based onthe current prices of S&P 500 Index ($SPX) options. To be specific, thevalue of the index represents the expected volatility priced into optionson the S&P 500 Index. The CBOE uses a mathematical formula to compute the volatility index using a basket of SPX options contracts. The VIXis then broadcast to the financial markets throughout the trading day on areal-time basis. Punch the symbol $VIX into a quote machine and you’llget the latest readings.What is expected volatility? Expected volatility and implied volatility are two measures of volatility that are computed using optionspricing models. These volatility measures are factored into currentoption prices and reflect consensus expectations about future volatilityof the underlying index. In this case, the VIX reflects expectations regarding the S&P 500 Index.When the volatility index rises, it means that SPX traders believevolatility will increase going forward. It that sense, the VIX represents aconsensus forecast about future volatility in the S&P 500 Index, and therefore in the U.S. stock market. During periods of market uncertainty andworry—and when the S&P 500 Index declines sharply—VIX tends to jumphigher, which is why it is sometimes referred to as the market’s “feargauge.” In contrast, when the market trades quietly or makes a steadymove higher, VIX tends to fall.Figure 12.2 shows the movement of the VIX and the SPX from thesummer of 1998 to 2003. During market declines, including the S&P 500Index’s tumble in the fall of 1998, the volatility index will jump higher;when the SPX trades in a range or trends higher, the VIX will edgelower. Hence, there is an inverse relationship between the VIX and theS&P 500 Index.
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FIGURE 12.2 S&P 500 Index and VIX (Source: www.ProﬁtSource.com)
IMPLIED VOLATILITYWhile the VIX measures expected volatility of the S&P 500 Index, strategistscan create similar volatility graphs for any stock, index, or exchange-tradedfund. These charts are called implied volatility (IV) charts and are computed using an options-pricing model. Most of options-pricing models arebased on the Black-Scholes formula, which was introduced at roughly thesame time as the launch of the Chicago Board Options Exchange (1973). We(and Optionetics.com Platinum software) use the Bjerksund-StenslandAmerican option model. It is a variant of the original Black-Scholes model.When a model is used to compute the volatility priced into an optionscontract, the result is known as implied volatility. The VIX is such an example and is constructed using a basket of options. The same thing can beaccomplished with any options contract. For example, if I know that theSMH is trading at $35.25 and the SMH January 35 call option is trading for$2.25 a contract, I can plug that information into a model and compute theIV of that option.More on Option Pricing ModelsIf you are interested in the mathematics behind the option model, a goodbook on the subject is Option Volatility and Pricing, by S. Natenburg (BurrRidge, IL: Irwin Professional Publishing, 1994). Another is The VolatilityCourse, by George Fontanills and Tom Gentile (New York: John Wiley &Sons, 2004). The Bjerksund-Stensland American option model is discussedin The Complete Guide to Option Pricing Formulas, by E. Haug (New York:McGraw-Hill, 1998).
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For the less mathematically inclined, these models or formulas mayseem cumbersome, but in fact the formula is relatively easy to computeand can be created in most programmable calculators. The simplest wayis to use a computer, which can handle the computation with ease. However, many web sites and brokerage firms offer implied volatility data andcharts. Therefore, unless the reader is an adventurous type and reallywants to learn the math, knowing the formula isn’t really necessary.The most important factor to consider when looking at impliedvolatility is what it tells us about option premiums. Since volatility is a factor in computing options prices, IV tells us whether option premiums arecheap or expensive. Recall that VIX tends to rise when the S&P 500 Indexbecomes more volatile. This tells us that SPX option premiums are increasing to reflect expectations about future volatility. Alternately, whenVIX falls, it is a sign that S&P 500 Index options are becoming cheaper.The Black-Scholes Option Pricing ModelFischer Black and Myron Scholes’ work in developing what is now knownas the Black-Scholes option pricing model led to a Nobel Prize. Since theoriginal formula was published in 1973, other models have been developed, but virtually all of them are based on the ﬁrst Black-Scholes model.Options traders use these models to compute theoretical option valuesand implied volatility. The formula is complex. Fortunately, options pricing calculators based on the formula are available at many online brokersand options-related web sites at no cost. For example, the Chicago BoardOptions Exchange (CBOE) offers a free options pricing calculator on itsweb site (www.cboe.com).
Let’s consider another example. Let’s say the OEX is trading for 570 inearly January and the February 570 call with 45 days left until expirationis quoted for $17 a contract. If this information is plugged into an optionspricing model the model will compute the IV. In this case, the impliedvolatility is 20 percent. Table 12.1 shows how the value of calls and puts
TABLE 12.1 Changes in IV Affect Options Premiums (OEX = 570 on January 3)Implied Volatility
OEX February 570 Call
OEX February 570 Put
10%15%20%25%30%
8.9013.0017.0021.4025.50
7.8011.9016.1020.2024.40
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will change as the implied volatility of the options changes. All else beingequal, the greater the IV, the higher the option premium.VegaVega is the option Greek that captures the change in the options premiumrelative to each one-point change in implied volatility. If an options contract has a vega of 0.05, it will increase in value by $0.05 for every 1 percentage increase in IV.
ACTUAL OR HISTORICAL VOLATILITYWhile implied volatility measures expectations about future volatility, historical (or actual) volatility is a measure of past price changes in a stockor index. It’s a look in the rearview mirror, so to speak.There are a variety of ways to view past or historical volatility. Oneexample, the OHLC chart, discussed earlier. Strategists can also watch thedaily point moves in the index. If the index is beginning to make largerpoint moves, it is becoming more volatile. Table 12.2 shows the average
TABLE 12.2 Average Daily Moves, November 2004 toDecember 2005Month
SPX
Dow
NASDAQ
November
5.60
48.37
12.79
December
4.90
47.46
11.00
January 2005
7.16
59.27
18.56
February
6.41
56.71
12.99
March
5.86
52.81
11.15
April
9.30
83.24
18.87
May
6.24
57.83
11.17
June
4.61
42.31
10.18
July
6.05
55.32
12.25
August
5.52
49.14
12.61
September
5.20
49.50
10.79
October
9.13
68.97
18.86
November
5.16
39.12
10.92
December
4.32
39.53
11.23
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FIGURE 12.3 VIX from November 2004 to December 2005 (Source: www.ProﬁtSource.com)
daily moves in the major exchanges during the year ended December2005. The most volatile month was April 2005. However, the trend wasclearly toward declining volatility. For example, in November and December 2004, the average daily moves in the Dow were 48.4 and 47.5 points,respectively. However, one year later, the average daily move was lessthan 40 points during those two months.The VIX will react to the changes in the market’s actual volatility.Figure 12.3 shows the changes in the volatility index during the sametime frame as Table 12.2. Notice that the most volatile months in Table12.2 are April and October, which corresponds with the two spikes thatoccur in Figure 12.3. This is a familiar pattern throughout the index markets, namely, when an index begins to see increasing daily price swings,the options premiums will begin to “price in” the greater volatility and IVwill rise.
AVERAGE TRUE RANGEThe ATR indicator discussed in Chapter 9 can also be used to gauge thevolatility of an index. Developed by Welles Wilder and introduced in his1978 book, New Concepts in Technical Trading Systems (McLeansville,
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FIGURE 12.4 Rising Volatility and ATR (Source: www.ProﬁtSource.com)
NC: Trend Research, 1978), this indicator defines the true range (TR) asthe greatest of these three measures:1. The current high minus the current low.2. The current high minus the previous close.3. The current low minus the previous close.
In general, if the difference between the high and low of the day islarge, it will be used as the True Range. In instances when the differencebetween the current day’s high and low is relatively small, one of the othertwo methods will typically define the TR.The average true range is simply an average of the TRs over time. Fourteen days is a common time frame when using averaging the true ranges. Obviously, computing TR is a cumbersome task without the aid of computer. Inaddition, the best way to view ATR is over a period of time alongside a stockchart. An example of ATR alongside the AMEX Airline Index appears in Figure 12.4. Notice that during periods of high volatility—seen as large verticalbars and a fluctuating price chart—ATR rises. This occurs whether the pricemovement is higher or lower. Volatility doesn’t care about direction.
BOLLINGER BANDSBollinger bands, developed by John Bollinger, have become one of themost widely used measures of volatility among traders today. As with theATR, Bollinger bands are best viewed graphically and the indicator is not
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Number of Students
practical to compute by hand. But the math is discussed here in order toget a better understanding of how the indicator works.Bollinger bands use both moving averages and standard deviations.Recall from earlier chapters that a moving average is simply the averageof an index price over a period of time. For instance, if at the end of sixtrading days an index closes at $400, $440, $500, $480, $500, and $520, thefour-day moving average at the end of the fifth day is $480, or ($440 + $500+ $480 + 500) ÷ 4. It is important to note that as each new day is added tothe moving average, the last price is removed. This means that in the previous example, the four-day moving average at the end of the sixth dayequals ($500 + $480 + $500 + $520) ÷ 4, or $500. Moving averages are mostoften used over a period of 20, 50, or 200 days.Bollinger bands use the moving average as an input along with thestandard deviation. In order to understand how the bands work, it is important to understand what standard deviations tell us. A standard deviation is defined as the variability of the distribution of stock or indexprices. According to statistics, roughly 68 percent of a data set will bewithin one standard deviation of its mean. Two standard deviations contain 95 percent of the price data.To illustrate, consider the bell curve in Figure 12.5. The chart represents
F
D
C
Grades
FIGURE 12.5
A Bell Curve with Standard Deviations
B
A
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FIGURE 12.6 XAL with Bollinger Bands (Source: www.ProﬁtSource.com)
the grades received on a high school history exam. The first standard deviation of grades will fall somewhere around a grade of C, which is the averageor mean. Thus, 68 percent of the grades fall between C– and C+. The nextstandard deviation contains Bs and Ds. It is between a D– and a B+ where95 percent of the grades given on the exam fall (two standard deviationsfrom both sides of the mean, or C). And finally, there are only a couple of Asand one or two Fs. They lie beyond two standard deviations of the mean.An important difference between the Bollinger bands and the historytest example is that Bollinger bands are moving standard deviations. Theindicator considers the two standard deviations above and below themoving average. After each new trading day, the oldest price is droppedand replaced with the new data.As the security’s price changes through time, the bands will becomewider and narrower as the stock’s volatility increases or decreases. This iswhat makes the Bollinger bands a unique visual gauge of a stock’s volatility. When movement in the index is less volatile, the bands come together.When the movement of the index becomes more hyperactive and volatile,the bands will diverge, or widen. Figure 12.6 shows the changes in theBollinger bands on the airline index. Often, the bands will narrow and become tight ahead of a major move higher or lower. This is sometimesknown as a Bollinger band breakout.
STATISTICAL VOLATILITYWhile ATR and Bollinger bands are useful chart indicators, statisticalvolatility (SV) is the mostly widely used gauge of historical or actual
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volatility among options traders. Using the closing price of the stock or index over a fixed number of trading days, the SV is computed as the annualized standard deviation of prices over a period of days. High standarddeviations are generally associated with higher risk, or higher volatility,investments. A higher standard deviation reflects a higher level of variability in the distribution of stock prices—in other words, greater volatility.In practice, rather than using the simple standard deviation, mostcomputations of statistical volatility use the lognormal distribution ofstock returns. Understanding the math is not that important becausemany services offer statistical volatility information at no cost; nevertheless, the math is presented here for those who might be interested. In financial theory, it is assumed that the logarithms of stock prices arenormally distributed, but not the prices themselves. Therefore, to compute historical volatility, the logarithm of prices will take the place of Pand Pi. The most common way of computing statistical volatility is shownin the accompanying box.Computing the Standard Deviationn
∑ (P − P )
2
i
σ2 =
i =1
σν=P
n −1
wherePi = the stock price over a range of n daysP = the average stock price over n daysn = number of daysν = volatility
Similar to implied volatility, SV is expressed as a percentage. For instance, an index with a 20-day SV of 25 percent has been more volatilethan an index with a 20-day SV of 15 percent during the referenced period.An index with a 100-day SV of 10 percent and a 9-day SV of 30 percent hasseen an increase in volatility during the past 20 days. In this case, its longterm (100-day) SV is much less than its short-term (9-day) SV.Some software programs now allow us to apply statistical volatilitygraphs to charts. Figure 12.7 shows the 20-day statistical volatility plottedalongside the price action of the AMEX Airline Index. Similar to the ATRindicator, this SV indicator doesn’t distinguish between volatile moveshigher or lower. Volatility is a measure of the speed of movement of theunderlying index and says nothing about direction.
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FIGURE 12.7 XAL with SV Indicator (Source: www.ProﬁtSource.com)
THE RELATIONSHIP BETWEEN IMPLIEDAND HISTORICAL VOLATILITYStatistical volatility is a rearview mirror look at past price volatility. Implied volatility reflects expectations about future volatility. Consequently,SV and IV for the same underlying index should be similar much of thetime. If IV is considerably higher than its historical volatility, it is a signthat the market is pricing in or bracing for an increase in volatility goingforward. This will often happen, for example, ahead of an earnings report.Figure 12.8 shows a spike in implied volatility in Marvell Technology(MRVL) ahead of an earnings report in August 2004.It is not unusual to see IV rise ahead of a known event. In the indexmarket, a spike like the one in Figure 12.8 is not likely. Nevertheless, sincethe market is forward looking, IV will often move higher in anticipation ofspecific events like political elections or economic data releases.For options traders, understanding trends with respect to the impliedvolatility of an underlying asset is important because it can help determine (1) what the market expects in terms of future volatility, and (2)whether the premiums are relatively cheap or expensive. The optionsmarket is relatively efficient, and increases in IV are often followed byincreasing volatility.Sometimes, however, the options market is wrong and implied volatility is out of whack with reality. For example, although the IV chart indicated that MRVL might make a volatile move following its earnings reportin August 2004, it did not. As a result, implied volatility came crashingdown—a phenomenon known as volatility crush. (See Figure 12.9.)
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FIGURE 12.8 MRVL Implied Volatility Spike, August 2004 (Source: www.Optionetics.com Platinum)
FIGURE 12.9 MRVL Volatility Crush (Source: www.Optionetics.com Platinum)
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How does one know if IV is too high or low? Without a crystal ball,there is no way to clearly discern the future, but there are ways to get ageneral idea. First, the strategist will want to look at the longer-term IVchart in order to find the average or normal range for implied volatility.For example, it is clear from Figure 12.8 that the IV of Marvell was outsideof its normal range in August 2004. Second, the strategist will want to consider long-term trends with respect to statistical volatility. Is SV rising orfalling? Are there seasonal patterns?Computing Theoretical ValuesEarlier we introduced the Black-Scholes options-pricing model. The mostcommon way to use this model is to take the options premium and various inputs (price of the underlying index, strike price of option, days leftuntil expiration, and the current risk-free rate) to compute the impliedvolatility of the option.The model can also be used to compute the theoretical value of theoption. To do so, the strategist will enter the SV of the underlying assetand solve for the option premium.• If the theoretical value of the option is less than the actual optionvalue (SV < IV), the options might be too expensive.• If the theoretical value is greater than the current market price of theoption (SV > IV), the options are perhaps undervalued.
Finally, looking at statistical volatility compared to implied volatilitycan give you a better sense of whether option premiums are cheap or expensive. If IV is much higher than the underlying index’s actual or statistical volatility, it could be a sign that the premiums are too high.In sum, volatility can be measured in several ways. The VIX is probably the most widely used gauge of market volatility, and it tracks the expected volatility priced into S&P 500 Index options. The same analysis canbe duplicated for any options contract, and each options contract has aunique level of implied or expected volatility. That level of implied volatility will, in turn, tell the strategist whether that options contract is relatively cheap or expensive. If IV is high on a historical basis, the optionsare expensive. If IV is low, the options are cheap. As a result, when looking at IV, the strategist will want to do three things:1. Understand the index’s historical volatility (SV) over time.2. Understand the index’s implied volatility (IV) over time.3. Compare IV to SV.
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VOLATILITY BY SECTORThe VIX and other volatility indexes are used to track the expected volatility of the major averages, but the strategist will sometimes want to take acloser look at the trends within specific sectors or industry groups. TheSelect Sector SPDR Funds offer a relatively easy way to view volatility bysector. Recall that the SPDRs are a group of nine funds created aroundspecific industry groups including technology, utilities, and energy. In addition, options are listed on each of these ETFs. Therefore, just as VIX isused to track the implied volatility of the S&P 500 Index, traders can trackthe volatility of the SPDR funds to view trends related to specific sectors.As noted earlier, technology stocks were the most volatile five or sixyears ago, when the CBOE launched the VXN and the AMEX created theQQV Index. That has since changed; by most measures, energy-relatedstocks have been the most volatile in recent years. Shares of oil, naturalgas, and oil-drilling companies have been trading in reaction to volatilityin the commodities to which they are closely linked: crude oil, heating oil,and natural gas.Table 12.3 shows the volatility of the various Select Sector SPDRs inearly October 2005. The 20-day SV of the energy fund jumped to 30.4 percent, or nearly double the levels seen two months ago. Meanwhile the IV alsorose, to 30.5 percent, which was almost perfectly in line with the fund’sactual volatility. So the data supports the premise that energy stocks
TABLE 12.3 Volatility by Sector, as of October 2005
Select SectorSPDR
Symbol
20-dayStatisticalVolatility(SV)
ImpliedVolatility(less than30 days)
ImpliedVolatility(30–60day)
Energy
XLE
30.40%
30.50%
31.50%
Utilities
XLU
18.30%
18.20%
16.90%
Consumer Discretionary
XLY
14.10%
18.40%
18.50%
Basic Materials
XLB
13.10%
20.30%
20.50%
Financials
XLF
12.90%
12.70%
14.80%
Information Technology
XLK
11.00%
16.50%
16.00%
Industrials
XLI
10.90%
17.80%
16.80%
Consumer Staples
XLP
9.60%
11.20%
12.60%
S&P 500 Index
SPX
9.60%
14.70%
13.60%
Health Care
XLV
8.20%
14.20%
14.20%
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were by far the most volatile of the funds evaluated. Judging by the relatively high IV in the energy fund, that trend was expected to continue inthe future.Utilities were also becoming volatile. In this table, the Select SectorUtility Fund (XLU) October options currently have an IV of 18 percent.Outside of utility and energy stocks, the market was trading relatively quietly at that time. The SV was low in the health care, technology, and consumer staples sectors. Financials and technology were also showingrelatively low levels of actual volatility. However, relative to actual levelsof volatility, the IV of some of the funds (XLY, XLB, and XLI) was high,which was a sign that these groups were expected to see greater volatilityover the next 30 to 60 days.
VOLATILITY SKEWSVolatility skew occurs when different options contracts on the same underlying asset have different levels of IV. For instance, if the XYZ January2007 options have implied volatility of 40 percent and the XYZ January2009 options have implied volatility of 20 percent, a volatility skew exists.Why? Because the shorter-term options have a much higher level of IVcompared to the longer term options. Additionally, skews may occur between different time frames, between calls and puts, and between different strikes.Volatility skews can develop under several circumstances: when amarket experiences a strong uptrend or downtrend, in fast-moving markets with sizeable volume, when there is a gap move due to news or apanic-type atmosphere, or when the market expects some event to causegreater volatility in the short term rather than the long term.A time skew is identified by different levels of implied volatility onstock options with the same (or possibly different) strike prices, but different expiration months. This is sometimes called a calendar skew because it affects options with different months remaining until expiration(and can therefore be exploited by employing a calendar spread).Another skew that occurs, although not as often, is when there is adifference in the IV of calls and puts on the same index. Sometimeswhen there is a flurry of put activity, the implied volatility in the putswill increase relative to that of the calls due to the increase in demand.However, large differences between implied volatility of puts and callson exchange-traded funds will lead to risk-free arbitrage opportunities.For instance, if the IV of the QQQQ puts is lower than the calls, astrategist could buy shares, buy puts, and sell calls. This is known as a
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conversion. (See the box on the following page for more informationabout conversions and reversals.) Arbitrageurs will continue thisprocess until the IVs return to their normal values.Price skews occur when the implied volatility differs across the strikeprices of options, on the same underlying index with the same expirationmonths. There are two types: forward and reverse volatility skews. In aforward volatility skew, higher-strike options have higher IV and lowerstrike options have lower IV. In a reverse volatility skew, lower-strike options have higher IV and higher-strike options enjoy lower IV. If a forwardvolatility skew occurs, the trader may want to look at potential put ratiobackspreads; if a reverse volatility skew occurs, the trader may want tolook at potential call ratio backspreads.Reverse price skews almost always exist in the cash index market.Since the stock market crash of 1987, options with a lower strike pricehave higher implied volatility than those with higher strike prices. Theout-of-the money options are more expensive than the at-the-money andin-the-money options. In addition, the puts have modestly higher IV thanthe calls.For instance, if the SPX is trading near 1,045, the implied volatilities ofthe puts and calls might look similar to Table 12.4. The greater IV in theout-of-the-money puts implies that the market has priced in a greaterchance of a move lower rather than higher. But, in fact, history has shownthat the opposite is more likely to happen. The market is more likely torise in the long term. The reason for this skew is subject to debate, but
TABLE 12.4 SPX Reverse SkewCalls IV
Strike Price
Puts IV
10.7
1200.0
12.8
10.8
1205.0
12.5
10.8
1210.0
12.4
10.8
1215.0
11.9
10.7
1220.0
11.9
10.6
1225.0
11.4
10.4
123