volatility handbook final

8/19/2019 Volatility Handbook Final

1/49

EQUITY DERIVATIVE

GLOBAL

Volatility HandbookAn Explanation of Basic Concepts, Strategies for Hedging and

Enhancing Portfolio Return, and Compilation of Selected Prior

Volatility Research

I. Introduction to Volatility

II. Volatility Concepts and Terminology

III. Trading Volatility

IV. Derivatives Trading Regulation and Market Structure

James J. Hosker1.212.526.7460

[email protected]

Amit Dholakia1.212.526.0885

[email protected]

February 2002

http://www.lehman.com


2/49

Volatility Handbook

2 February 2002

Derivatives: The Key to Risk Management

There comes a point when a market observer begins to see beyond buy and sell, long

and short, black and white and perceives a more refined picture of the equity universe.

Degrees of bullishness and bearishness appear, and the observer wishes to align these

views with appropriately corresponding strategies. The risk of owning a stock outright

might seem too great or the leverage not enough. It is at this point that the observer canmake use of derivative instruments.

This guide is intended to be one building block in an education on derivatives. It is

meant as an introduction and a reference. Topics are discussed with the goal of

providing a working understanding. Readers are encouraged to access the Lehman

Brothers catalog of research to gain a more thorough understanding of individual topics.

A derivative is a financial instrument whose value is determined by an underlying asset or

benchmark. Assets and benchmarks range from corn crops, to the S&P 500, to the

Florida hurricane season. In short, derivatives can be tied to just about anything thatproduces measurable results. This report is primarily concerned with equity and equity-

based index derivatives, although the concepts are directly applicable to all types of

derivatives.

Originally, the term “derivative” applied only to transactions based upon an underlying

asset in which no money changed hands at the initiation of the contract. Forwards,

futures and swaps are examples of such instruments. Over time, the term derivative has

become associated with such products as options and exchange-traded funds and such

techniques as program trading. The common link between all of these concepts is that

they are a means of customizing risk exposure to match a view of the underlying. It isthis dynamic ability that makes derivatives extremely relevant in fashioning customized

payoffs and in controlling investment risk.

Understanding volatility is basic to an understanding of derivative securities. In this

handbook, we describe and develop the concept of volatility, discuss option strategies to

implement specific market views, and allude to pertinent derivative trading regulation and

market conventions that govern option trading. Finally, we provide a selected list of our

prior introductory research in this area.


3/49

Volatility Handbook

February 2002 3

Table of Contents

Derivatives: The Key to Risk ManagementDerivatives: The Key to Risk ManagementDerivatives: The Key to Risk ManagementDerivatives: The Key to Risk Management ........................................................................................................................................................................................................................ 2222

DefiDefiDefiDefinitions of Volatilitynitions of Volatilitynitions of Volatilitynitions of Volatility ............................................................................................................................................................................................................................................................................................................................ 6666

Historical Volatility ...........................................................................................6

Implied Volatility ..............................................................................................6

Option Premiums: Paying for Potential .................................................................7

Single Stock and Equity Index DerivSingle Stock and Equity Index DerivSingle Stock and Equity Index DerivSingle Stock and Equity Index Derivatives: Futures and Optionsatives: Futures and Optionsatives: Futures and Optionsatives: Futures and Options............................................................................................................ 8888

Description of Equity Index Futures......................................................................8

Description of Equity Options ............................................................................9

Factors Affecting Option Pricing .......................................................................10

Comparison of Futures and Options .................................................................11

Interpreting Implied VolatilityInterpreting Implied VolatilityInterpreting Implied VolatilityInterpreting Implied Volatility .................................................................................................................................................................................................................................................................................... 14141414

Term Structure of Implied Volatility ....................................................................14

Strike Structure (or Skew) of Implied Volatility ......................................................15

Real-Time Implied Volatility Market Indicators......................................................19 Volatility Cones .............................................................................................21

Option Strategies to Trade VolatilityOption Strategies to Trade VolatilityOption Strategies to Trade VolatilityOption Strategies to Trade Volatility ................................................................................................................................................................................................................................................ 24242424

New Developments in Equity Derivatives: The ExchaNew Developments in Equity Derivatives: The ExchaNew Developments in Equity Derivatives: The ExchaNew Developments in Equity Derivatives: The Exchange Traded Fund (ETF)nge Traded Fund (ETF)nge Traded Fund (ETF)nge Traded Fund (ETF)........................................ 28282828

Investment Strategies Using Exchange-Traded Funds ............................................28

Conclusion ................................................................................................... 35

List of Available ETF’s on Selected Indices..........................................................36

CostCostCostCost----Effective Trading: A Look at NasdaqEffective Trading: A Look at NasdaqEffective Trading: A Look at NasdaqEffective Trading: A Look at Nasdaq----100 Derivative Products100 Derivative Products100 Derivative Products100 Derivative Products.................................................................................... 39393939

Market and Exchange DetailsMarket and Exchange DetailsMarket and Exchange DetailsMarket and Exchange Details ................................................................................................................................................................................................................................................................................ 44444444


4/49

Volatility Handbook

4 February 2002

This page intentionally left blank.


5/49

Volatility Handbook

February 2002 5

Section 1: Introduction to Volatility


6/49

Volatility Handbook

6 February 2002

Definitions of Volatility

Historical Volatility

In statistical terms, volatility is defined as the standard deviation of expected returns. It

reflects the degree to which an asset’s value changes relative to its mean over a given

number of observations. Finally, volatility measures the degree of variability, not the

direction of the change.

In the case of securities, volatility measures the degree of price fluctuation over a specific

period of time. Historical or realized volatility is a backward-looking measure that

attempts to quantify an asset’s price fluctuation over a given time frame in the past.

Realized volatility is calculated according to the following formula:

Realized Volatility =Realized Volatility =Realized Volatility =Realized Volatility =1

)(1

2

n

M X

n

i

i

where: Xi = observation

M = sample mean

n = number of observations

Realized volatility aims to analyze historical price fluctuation to anticipate future

performance.

Implied Volatility

Implied volatility is a forward-looking measure of the expected volatility level that is

implicit in option prices. An option-pricing model, such as the Black-Scholes model, candetermine a theoretical price for an option using other parameters to characterize the

underlying asset. The calculated price can be used to determine a theoretical level of

option implied volatility.

Volatility has value. An option on a highly volatile underlying security will tend to have a

high implied volatility as well. High volatility in the underlying asset is desirable to an

option buyer, because the option has a greater likelihood of expiring in-the-money, but

the buyer will have to pay for this volatility in the form of a higher premium. Conversely,

the rich premium associated with options on a volatile asset may be desirable to an

option seller who looks to absorb the premium by selling the option, thereby trading on aview that volatility will eventually decrease.

While historical volatility is calculated based on an asset’s prior price fluctuations,

implied volatility, which gauges the market’s perception of a contract’s volatility, attempts

to quantify a range for an asset’s future volatility. Examining the sensitivity of implied

volatility to changes in option expiration and strike price provide valuable insights for

structuring an option strategy. Term structure, or implied volatility examined over short- to


7/49

Volatility Handbook

February 2002 7

long-term expirations, reveals the option market’s expectations for volatility going

forward. As mentioned above, a highly volatile underlying asset has a greater

probability of reaching far in-the-money and out-of-the-money (OTM)1 strikes before

expiration, because its price tends to fluctuate in a very wide range. Strike structure

reflects the option market’s assessed probability that different option strike levels will be

reached by an underlying asset before expiration. Underlying asset volatility is a keycomponent in determining strike structure, as highly volatile underlying assets are more

likely to reach far in-the-money and out-of-the-money strikes. We explore term and strike

structure in greater detail in Section 2.

Option Premiums: Paying for Potential

Option premiums have two separate components: intrinsic value and time value.

Intrinsic value is the amount of profit that can be collected by buying an option and

exercising it immediately. For a call option, this is the amount by which the price of the

underlying asset currently exceeds the option strike price. If a call option’s underlyingasset value exceeds its strike price, the call is said to be in-the-money (ITM). If the call

strike is currently greater than the price of the underlying, then the call option has no

intrinsic value and is an (OTM) option. Conversely, put options, which give the holder

the right to sell the underlying asset at the strike price, are in-the-money when the option

strike exceeds the current underlying asset price.

Although an option may not currently have intrinsic value, which is true of all out-of-the

money options by definition, the option is still has time value as it is valid until the

expiration date, by which time the underlying asset value may have changed to a level

that makes option exercise profitable. It is in the time value component of the option

premium that implied volatility plays its role.

For equity calls and puts, further out-of-the-money options tend to have higher implied

volatility compared to near-the-money strike options. The further an option is out-of-the-

money, the more exclusively its price is based upon volatility. This makes sense when

thought of in terms of the underlying asset. If Call ABC on stock XYZ is $15 out-of-the-

money, what is it worth? To determine an accurate option premium, we first need to

answer another question: what is the likelihood that the call will ever be in-the-money? If

the price of the underlying stock is extremely volatile, then the chance of the call being in-

the-money will be greater. Implied volatility will reflect this probability, and the call

premium will be higher than it would have been if the underlying stock were less volatile.

1 We use the following conventions to refer to option strike prices throughout this document: ATM = at-the-money, ITM = in-the-money, OTM = out-of-the-money

Term and Strike Structure of

Implied Volatility


8/49

Volatility Handbook

8 February 2002

Single Stock and Equity Index Derivatives: Futures and Options

Description of Equity Index Futures

Futures and options are two basic examples of derivative products, financial instruments

whose value is dependent upon an underlying variable that is often a traded asset, such

as a stock or an equity index. Futures contracts are normally traded on an exchange,

which allows for standardization in contract specifics such as size, expiration and

delivery method. Within the equity market, futures are generally available on indices and

some exchange-traded funds2 (ETF’s), but are not commonly offered for individual

equities. Liquidity in futures contracts is generLiquidity in futures contracts is generLiquidity in futures contracts is generLiquidity in futures contracts is generally concentrated in the nearestally concentrated in the nearestally concentrated in the nearestally concentrated in the nearest----termtermtermterm

month (the closest expiration from the present)month (the closest expiration from the present)month (the closest expiration from the present)month (the closest expiration from the present), which causes investors wishing to

maintain their current futures position to “roll” it forward to the next expiration. As

expiration approaches and futures roll activity picks up, the spread between the nearest-

term contract and the next closest expiration, known as the calendar spreadcalendar spreadcalendar spreadcalendar spread, becomes

an important profit-and-loss consideration. We provide the formula for calculating the

price of a futures contract on an equity index, and illustrate its use as a hedging vehicle.

Equity Index Futures Price CalculationEquity Index Futures Price CalculationEquity Index Futures Price CalculationEquity Index Futures Price Calculation3333

FFFF0000 = S= S= S= S0000 * e* e* e* e(r(r(r(r –––– q) * Tq) * Tq) * Tq) * T

where FFFF0000: futures price

SSSS0000: current index level

rrrr: continuously compounded risk-free rate

qqqq: annual index dividend yield. Since indices contain many stocks that usually

provide dividends at different times, we make the simplifying assumption thatthe index can be treated as an asset with a continuous dividend yield.

TTTT: time to expiration

Equity index futures are particularly effective tools to hedge risk in diversified portfolios.

Assuming that the maturity of the futures contract is the same as the duration of the

required hedge, the optimal amount of futures contracts needed to hedge depends on

three criteria: the dollar amount of the portfolio, the portfolio beta relative to the market

and the dollar amount of assets that underlies each futures contract. Generally, a portfolio

with a higher beta will require more futures contracts to hedge.

2 A complete introduction to ETF’s is available in Section 3.2.3 As defined in: Hull, John C., Options, Futures and Other Derivatives, 4th Edition, 2000. Prentice-HallInc.

Futures Roll or Calendar Spread


9/49

Volatility Handbook

February 2002 9

Calculating Number of Futures Contracts for HedgCalculating Number of Futures Contracts for HedgCalculating Number of Futures Contracts for HedgCalculating Number of Futures Contracts for Hedgeeee4444

# of contracts needed =# of contracts needed =# of contracts needed =# of contracts needed = * PDV/AV* PDV/AV* PDV/AV* PDV/AV

where: : portfolio beta relative to market

PDVPDVPDVPDV: portfolio dollar value

AVAVAVAV: asset value underlying each futures contract

As the formula shows, the number of futures contracts required to hedge increasesAs the formula shows, the number of futures contracts required to hedge increasesAs the formula shows, the number of futures contracts required to hedge increasesAs the formula shows, the number of futures contracts required to hedge increases

with portfolwith portfolwith portfolwith portfolio volatility (i.e., beta) even if the dollar value of the portfolio does notio volatility (i.e., beta) even if the dollar value of the portfolio does notio volatility (i.e., beta) even if the dollar value of the portfolio does notio volatility (i.e., beta) even if the dollar value of the portfolio does not

change.change.change.change.

Our comprehensive Handbook of World Equity Index Futures in Section 3 of this

publication provides a list of available index future, trading regulations, contract

specifications and exchange information.

Description of Equity Options5

Equity options, derivative instruments offered on individual stocks, baskets of stocks,

indices and ETF’s, are commonly traded on exchanges and in the more unofficial over-

the-counter (OTC) market. At the most basic level, there are two types of optionsAt the most basic level, there are two types of optionsAt the most basic level, there are two types of optionsAt the most basic level, there are two types of options:

Call Option:Call Option:Call Option:Call Option: Gives the holder the right to buy the underlying asset by a certain

expiration date for a certain strike price.

Put Option:Put Option:Put Option:Put Option: Gives the holder the right to sell the underlying asset by a certain

expiration date for a certain strike price.

ExchangeExchangeExchangeExchange----traded options have standardized expiration dates and strike prices, buttraded options have standardized expiration dates and strike prices, buttraded options have standardized expiration dates and strike prices, buttraded options have standardized expiration dates and strike prices, butcustomized options can be created and traded in the OTC market.customized options can be created and traded in the OTC market.customized options can be created and traded in the OTC market.customized options can be created and traded in the OTC market. European options

can be exercised only on the expiration date, whereas the more flexible American

options can be exercised at any time up to expiration. Depending on the underlying

asset, exercised options can be settled through delivery of cash or an equivalent amount

of the asset itself (called physical settlement).

4 As defined in: Hull, John C., Options, Futures and Other Derivatives, 4th Edition, 2000. Prentice-HallInc.5 IBID


10/49

Volatility Handbook

10 February 2002

Factors Affecting Option Pricing

There are five parameters (or variables) that affect the price of an option. Option

sensitivity to each parameter is measured by taking the partial derivative of the underlying

asset’s return function with respect to that particular variable. Each option parameter is

conventionally represented through a Greek letter and summarized in Figure 1.

Figure 1: Parameters Affecting Option Pricing

Delta (Delta (Delta (Delta ()))) Change in option price resulting from an incremental change in the price of theunderlying asset. An option’s delta is a function of the underlying asset price and thefunction of the underlying asset price and thefunction of the underlying asset price and thefunction of the underlying asset price and theoption strike priceoption strike priceoption strike priceoption strike price. Delta is positive for long call options and negative for long putoptions.

Gamma (Gamma (Gamma (Gamma ()))) Change in option price resulting from an incremental change in Delta. Measures theMeasures theMeasures theMeasures thesensitivity (or convexity) of delta relative to the change in the underlying assetsensitivity (or convexity) of delta relative to the change in the underlying assetsensitivity (or convexity) of delta relative to the change in the underlying assetsensitivity (or convexity) of delta relative to the change in the underlying assetprice.price.price.price. The value of Gamma is higher for at-the-money, short-dated options.

Theta (Theta (Theta (Theta ()))) Change in option price with respect to time reChange in option price with respect to time reChange in option price with respect to time reChange in option price with respect to time remaining till expiration.maining till expiration.maining till expiration.maining till expiration. Thetaincreases as time to expiration decreases. One day before expiration, the value ofTheta is equal to the value of the underlying asset at that time. At expiration itself, thevalue of Theta is zero.

Vega (V)Vega (V)Vega (V)Vega (V) Change in optionChange in optionChange in optionChange in option price with respect to volatility of the underlying asset value.price with respect to volatility of the underlying asset value.price with respect to volatility of the underlying asset value.price with respect to volatility of the underlying asset value.Vega increases as time to expiration increases and is higher for at-the-money strikes.

Rho (Rho (Rho (Rho ()))) Change in option price resulting from an incremental change in the risk Change in option price resulting from an incremental change in the risk Change in option price resulting from an incremental change in the risk Change in option price resulting from an incremental change in the risk----freefreefreefreefinancing rate.financing rate.financing rate.financing rate. Rho is positive for long call options and negative for long put options.

Source: Options, Futures and Other Derivatives – 4 th Edition by John C. Hull

Within the equity universe, dividends paid out by an underlying stock or index, which

lower the asset price on the ex-dividend date, have a negative effect on the value of call

options and a positive effect on the value of put options. The following table summarizes

the effects of each parameter on the option price (or option premium).

Figure 2: How Option Prices are Affected by an Increase in Parameter Value

Increase inIncrease inIncrease inIncrease in European CallEuropean CallEuropean CallEuropean Call European PutEuropean PutEuropean PutEuropean Put American CallAmerican CallAmerican CallAmerican Call American PutAmerican PutAmerican PutAmerican PutUnderlying AssetPrice + - + -Strike Price - + - +Time to Expiration ? ? + +Underlying AssetVolatility + + + +Risk-free FinancingRate + - + -Dividends - + - +Source: Options, Futures and Other Derivatives – 4 th Edition by John C. Hull

In most cases, increasing the time to expiration will increase the premium of European

calls and puts, due to higher time value, but the dividend payment, which can lower the

stock price, makes the overall effect ambiguous. The early exercise feature of American

options makes the possibility of dividend payment immaterial, as the holder would simply

exercise prior to the scheduled payment date.


11/49

Volatility Handbook

February 2002 11

Comparison of Futures and Options

Futures and options are similar in their derivative nature, availability of standardized

contract conventions, and sensitivity to time. There is one important difference between

the two: A futures contract is binding with respect to the underlying asset, whereas an

option contract is not. An investor may enter into a futures contract without costAn investor may enter into a futures contract without costAn investor may enter into a futures contract without costAn investor may enter into a futures contract without cost, butbutbutbut

he is bound to buy or sell the underlying asset at the contracted price within thehe is bound to buy or sell the underlying asset at the contracted price within thehe is bound to buy or sell the underlying asset at the contracted price within thehe is bound to buy or sell the underlying asset at the contracted price within thespecified delivery periodspecified delivery periodspecified delivery periodspecified delivery period. Conversely, optoptoptoptions give the holder the right to buy or sellions give the holder the right to buy or sellions give the holder the right to buy or sellions give the holder the right to buy or sell

an underlying asset, but the holder can choose whether or not to exercise that right,an underlying asset, but the holder can choose whether or not to exercise that right,an underlying asset, but the holder can choose whether or not to exercise that right,an underlying asset, but the holder can choose whether or not to exercise that right,

or let the option expire. There is a cost to acquiring an option, which is known asor let the option expire. There is a cost to acquiring an option, which is known asor let the option expire. There is a cost to acquiring an option, which is known asor let the option expire. There is a cost to acquiring an option, which is known as

the option premium paid by the buyer.the option premium paid by the buyer.the option premium paid by the buyer.the option premium paid by the buyer. Finally, we compare the payoffs from long and

short positions in equity futures and options positions in Figure 3.


12/49

Volatility Handbook

12 February 2002

Figure 3: Payoffs from Equity Futures and Equity Options Contracts

Long Future Position Payof f

Asset Price at

M aturity

Delivery Price

Short Future Position Payoff

Delivery Price

Asset Price a

M aturity

Long Call Option Position Payoff

O ption

P rem ium P aid

Strike P rice

Plus P rem ium

Short Call Option Position Payoff

Option Prem ium

Collected

Strike Price

Plus P rem ium

Long Put Option Position Payoff

Option

Prem ium Paid

Strike P rice

M inus Premium

Short Put Option Position Payoff

Option P rem ium

Collected

Strike P rice

M inus Prem ium

Source: Lehman Brothers

It is evident that options offer investors more flexible ways to limit downside risk while

maintaining upside profit potential. In Section 3, we discuss the benefits of options

strategies that use combinations of calls and puts to translate market and volatility views

into trading positions.

Futures have linear payoffs where a

long position has unlimited upside

and a short position has unlimited

downside.

Long option positions offer the

upside benefit of futures with much

lower risk. The downside risk of

buying an option is limited to the

premium paid. Conversely, shorting

a call option (without a position inthe underlying) can cause unlimited

risk, which is mitigated slightly by

the premium collected from the sale.

Shorting a put option also provides

a premium and has limited risk to

the point where the underlying asset

loses all value.


13/49

Volatility Handbook

February 2002 13

Section 2: Volatility Concepts and Terminology


14/49

Volatility Handbook

14 February 2002

Interpreting Implied Volatility

Two important characteristics of implied volatility are its variation patterns over time,

called term structureterm structureterm structureterm structure, and across strike prices (strike structure)(strike structure)(strike structure)(strike structure). In this section, we

provide comprehensive definitions of both concepts, and illustrate their significance to

option pricing and strategy. It is important to remember that term and strike structure

involve the implied volatility measure, which means that both gauge market perception offuture volatility levels across time and strike, respectively.

Term Structure of Implied Volatility

Term structure characterizes option value over time and helps determine the idealTerm structure characterizes option value over time and helps determine the idealTerm structure characterizes option value over time and helps determine the idealTerm structure characterizes option value over time and helps determine the ideal

time horizon over which atime horizon over which atime horizon over which atime horizon over which a strategy may be executed.strategy may be executed.strategy may be executed.strategy may be executed. Conventionally, the term

structure is charted from the nearest month expiration, which provides the clearest

indication of the market’s volatility expectations. Figure 4 shows the daily implied

volatility of 3-month, 6-month and 1-year option contracts on the S&P 500 in 2001. The

3-month contract in Figure 4 shows the greatest variability, while the 1-year contract is

the least variable, suggesting the tendency of implied volatility to revert to its mean valueover the long term. Intuitively, long-term mean reversion is an appropriate characteristic of

implied volatility. Implied volatility forecasts become less accurate as the time frame for

the forecast increases. While even short-term volatility forecasts cannot account for all

possible driving factors, uncertainty is large enough to eliminate any forecasting

accuracy for longer-term implied volatility. Conventionally, the best possible estimate for

longer-term implied volatility is its average value over time.

Figure 4: S&P 500 Implied Volatility Term Structure in 2001

15.0%

17.5%

20.0%

22.5%

25.0%

27.5%

30.0%

1 / 2 / 0 1

2 / 2 / 0 1

3 / 2 / 0 1

4 / 2 / 0 1

5 / 2 / 0 1

6 / 2 / 0 1

7 / 2 / 0 1

8 / 2 / 0 1

9 / 2 / 0 1

1 0 / 2 / 0 1

1 1 / 2 / 0 1

1 2 / 2 / 0 1

3-mth 6-mth 1-yr

Source: Lehman Brothers, Bloomberg

Implied volatility measures market

perceptions of volatility.

Importance of the near-termcontract.

Shorter-term contracts arealso the most variable. As

volatility is measured over

longer terms, it tends to revert

to its mean value.


15/49

Volatility Handbook

February 2002 15

The following graph shows the term structure of S&P 500 implied volatility over the short

and long terms. We examine only atWe examine only atWe examine only atWe examine only at----thethethethe----money (ATM) strikes, keeping the optionmoney (ATM) strikes, keeping the optionmoney (ATM) strikes, keeping the optionmoney (ATM) strikes, keeping the option

delta at each strike level constant to isolate the effects of term structure.delta at each strike level constant to isolate the effects of term structure.delta at each strike level constant to isolate the effects of term structure.delta at each strike level constant to isolate the effects of term structure.

Mathematically, term structure differentials measure the slope at any point along the term

structure curve, and can indicate changes in the option market’s expectations for volatility

over the long and short term. For example, if the market begins to expect increasedvolatility in the S&P 500 in the near term, the implied volatility of 1-month and 3-month

contracts will rise relative to longer-term contracts. If expectations are that volatility will not

rise beyond a few months, the term structure might be flatter for longer-dated contracts.

Expectations of higher near-term implied volatility will cause the term structure differential

between 1-year and 3-month implied volatility (shown in the lower table in Figure 5) to

decrease.

Figure 5: Term Structure of At-the-Money Implied Volatility of the S&P 5006

Current Avg SD SD Units Postive/Negative Slope

0.7% 1.1% 2.0% -0.18 Normal

Current Avg SD SD Units Postive/Negative Slope

-0.2% 1.4% 1.7% -0.97 Fairly Negative

TermStructure of ATMImpl Vol

10%

15%

20%

25%

30%

35%

Current 19.5% 19.9% 20.2% 19.9% 19.9% 19.9% 20.0% 20.7% 21.3%

One Week Ago 21.3% 18.3% 19.1% 19.2% 19.4% 19.7% 19.9% 20.9% 21.7%

One Month Ago 16.4% 20.2% 20.4% 20.6% 21.0% 20.9% 21.1% 21.5% 22.2%

3-Yr Avg +2 SD 27.6% 26.9% 26.9% 27.1% 27.3% 27.9% 28.5% 29.5% 30.1%

3-Yr Avg -2 SD 14.8% 16.9% 17.6% 17.9% 18.3% 18.5% 18.6% 19.3% 20.1%

1-Mth 2-Mth 3-Mth 4-Mth 6-Mth 9-Mth 1-Yr 2-Yr 3-Yr

3-Mth - 1-Mth TermSlope of Impl Vol

1-Yr - 3-Mth TermSlope of Impl Vol

Source: Lehman Brothers, Bloomberg

Strike Structure (or Skew) of Implied Volatility

The strike price of an option affects its sensitivity to price changes in the underlying asset,

a relationship characterized by the option parameter Delta. The option premium

associated with a certain strike price is a function of the implied volatility of the

underlying asset. As mentioned earlier, volatility is the only option parameter not

observed or calculated, but is instead implied by the theoretical market price of the

option, which is derived through a theoretical pricing model such as the Black-ScholesModel. Each market-maker, however, has a different perception of future volatility,

which results in various levels of implied volatility that is observable in the market for any

given option contract. The divergence in implied volatility levels allows us to reasonably

6 Graph shows a snapshot of term structure as of Feb 5, 2002. For a daily update of global index termstructure, contact your Lehman Brothers sales representative.

Term structure reveals the

option market’s expectations

for future volatility over time.

Term structure differentials

measure the slope at anypoint along the curve.


16/49

Volatility Handbook

16 February 2002

infer that the options market, while relying on some theoretical pricing model as a starting

point, does not consider that model to be completely efficient.7

The general shape of implied volatility skew, often called a “volatility smile,” indicates the

market’s belief that large movements in stock price occur with more regularity than a

theoretical pricing model would predict, making OTM options more valuable.Consequently, implied volatility of some single stock options that follow this pattern is

lowest for the ATM strikes, and increases as strikes are set further out-of-the-money on

both the call and put side, since large price movements are also almost equally likely in

either direction.8 Figure 6 shows the generic strike structure of implied volatility, which

has an equal likelihood of large price movements in either direction.

Figure 6: Strike Structure of Implied Volatility for Single Stocks (Volatility Smile)


7 Natenberg, Sheldon, Option Volatility and Pricing, 1994. McGraw-Hill & Co.8 The “volatility smile” effect is observed only for some single stocks and is not a feature of index options,which exhibit negative skew. We compare and contrast index option skew patterns with the “smile”pattern in the following pages.

Strike structure of single stockoptions.

For single stocks, implied

volatility increases for further

OTM strike prices. The

“volatility smile” shape shows

that option markets believelarge stock movements are

likely events, which makes

OTM options valuable, and

that price movements are

almost equally likely to occur

in either direction (strike

structure is similar for single

stock call and put options).

ATM StrikeImplied Volatility

Implied volatility increasesfor OTM puts

Implied volatility increasesfor OTM calls


17/49

Volatility Handbook

February 2002 17

Implied volatility strike structure for equity index options usually does not follow the same

pattern as described above for some individual stock options, due to subtle differences in

the way the market views the likelihood of large price swings occurring for stocks versus

indices. As Figure 7 illustrates, equity index options exhibit a downward sloping strikeequity index options exhibit a downward sloping strikeequity index options exhibit a downward sloping strikeequity index options exhibit a downward sloping strike

structure that is highest for the OTM strikes and decreases as the strikestructure that is highest for the OTM strikes and decreases as the strikestructure that is highest for the OTM strikes and decreases as the strikestructure that is highest for the OTM strikes and decreases as the strike prices moveprices moveprices moveprices move

inininin ----thethethethe----money.money.money.money. This strike structure pattern is known as negative skew, which shows anunderlying market belief that a price swing to the downside is much more likely than to

the upside. We define strike prices as a percentage of the underlying asset value

(thereby making the 100% strike equivalent to the ATM strike).

Figure 7: Implied Volatility Strike Structure of 3-Month S&P 500 Options9

Current Avg SD SD Units Steep/Flat Indicator

5.7% 5.1% 1.1% 0.54 Fairly Steep

Current Avg SD SD Units Steep/Flat Indicator

6.6% 8.1% 2.7% -0.56 Fairly Flat

3-Month Strike Structure of Impl Vol

10%

15%

20%

25%

30%

35%

40%

Current 31.6% 25.9% 20.2% 16.9% 14.2%

One Week Ago 29.6% 24.2% 19.1% 15.9% 13.2%

One Month Ago 30.8% 25.2% 20.4% 17.3% 16.2%

3-Yr Avg +2 SD 38.6% 32.6% 26.9% 22.6% 21.2%

3-Yr Avg -2 SD 26.1% 21.6% 17.6% 14.8% 13.2%

80%Strike 90%Strike 100%Strike 110%Strike 120%Strike

3-Month 90% - 100%Strike Skew of Impl Vol

1-Month 90%- 100%Strike Skew of Impl Vol


Strike Structure Differences BetweStrike Structure Differences BetweStrike Structure Differences BetweStrike Structure Differences Between Single Stock Options and Equity Index Optionsen Single Stock Options and Equity Index Optionsen Single Stock Options and Equity Index Optionsen Single Stock Options and Equity Index Options

We have thus far concluded that strike structure of implied volatility is determined by

market perception of the likelihood of large price movements in either direction. When

the market views large upside and downside moves as being equally likely, implied

volatility skew takes on a balanced “volatility smile” shape. The negative skew of index

option implied volatility means that the market believes that index prices are much more

likely to swing down than up., but why? Two reasons have been offered 10:

Stock markets and sectors have a larger downside correlation than upside

correlation (i.e., stocks tend to drop together in falling markets more often thanthey increase together in rising markets)

9 Graph shows a snapshot of 3-month strike structure as of Feb 5, 2002. For a daily update of globalindex strike structure, contact your Lehman Brothers sales representative.10 Natenberg, Sheldon, Option Volatility and Pricing, 1994. McGraw-Hill & Co.

Indices are thought to have a

greater probability of

downside price movements,

which is expressed in the

negative skew of index

option implied volatility.

The differentials shown on theright describe the slope of the

curve between the 90% and

100% strike. A steep slope

indicates a large drop in

implied volatility between the

strike prices.

Strike structure of equity index

options

Why does index option strike

structure differ from singlestock option strike structure?


18/49

Volatility Handbook

18 February 2002

Stock index options are very commonly used to hedge long equity portfolios,

making demand for put options much higher than call demand, and consequently

raising index put premiums relative to call premiums. Asymmetrically high put

demand and put premiums will skew put implied volatility to the downside for

index options.

We explore the arguments for greater index downside skew:

Extensive prior research has suggested an asymmetric correlation in equity sector returns

during bull and bear markets.11 Specifically, sector correlation is higher during periods of

negative return12, which leads to different volatility implications for single stocks and

indices. Figure 8 plots the average downside and upside inter-sector correlation for nine

market sectors13 and the S&P 500 index option implied volatility from October 1995 to

October 2001.

Figure 8: Average Sector Index Downside and Upside Correlations from October1995 to October 2001

0.2

0.4

0.6

0.8

1.0

1 0 / 2 7 / 9 5

1 / 2 7 / 9 6

4 / 2 7 / 9 6

7 / 2 7 / 9 6

1 0 / 2 7 / 9 6

1 / 2 7 / 9 7

4 / 2 7 / 9 7

7 / 2 7 / 9 7

1 0 / 2 7 / 9 7

1 / 2 7 / 9 8

4 / 2 7 / 9 8

7 / 2 7 / 9 8

1 0 / 2 7 / 9 8

1 / 2 7 / 9 9

4 / 2 7 / 9 9

7 / 2 7 / 9 9

1 0 / 2 7 / 9 9

1 / 2 7 / 0 0

4 / 2 7 / 0 0

7 / 2 7 / 0 0

1 0 / 2 7 / 0 0

1 / 2 7 / 0 1

4 / 2 7 / 0 1

7 / 2 7 / 0 1

1 0 / 2 7 / 0 1

Market Downside Upside


As we stated in our earlier analysis, the graph in Figure 8 suggests that average upside

and downside sector correlation move together except in periods of low or high option

implied volatility, such as October 1997 and August 1998 (Southeast Asian Crisis and

Russian debt crisis respectively), when downside correlation spikes.

11 See Longin F. and B. Solnik, 2001, “Extreme Correlation of International Equity Markets,” Journal ofFinance, 56, 649-676.12 See “Not All Momentum Sectors are Created Equal,” in November 12, 2001, issue of The Outlook .13 From a prior analysis conducted on November 12, 2001. The nine sector indices are Banks (BKX),Biotechnology (BTK), Consumer Staples (CMR), Cyclicals (CYC), Pharmaceuticals (DRG), HighTechnology (MSH), Semiconductor (SOX), Broker/Dealer (XBD) and Utilities (UTY). Our analysis used a22-day period (calendar month) to calculate inter-sector correlation. The average inter-sector correlation isa 22-day moving average of the 36 pair-wise inter-sector correlations.

During periods of high market

implied volatility, which is

associated with falling returns,

market correlation is higher than on

the upside. This asymmetry in market

correlation causes the negative

implied volatility skew present in

index options.

High implied volatility andhigh downside correlation


19/49

Volatility Handbook

February 2002 19

Indices exhibit asymmetric return distributions that are historically skewed to the negative

tail. Furthermore, these distributions also have a higher level of kurtosis than exhibited by

a normal distribution.14 Examined together, negatively biased asymmetry and higher

kurtosis imply that indices, as empirical research would suggest, have more downside

risk than a single stock. The discrepancy between index and single stock option strike

structure volatility occurs on the put side, precisely because of the greater index tendencyfor downside moves. This perceived asymmetric downside index tendency raises the

value of OTM index puts and lowers the value of ITM puts. Single stock ITM puts have

similar premiums to OTM puts, because markets perceive single stocks to have a

relatively equal chance of moving significantly up or down.

While term structure is useful in identifying the ideal time horizon to execute a strategy,

skew can help identify the appropriate strike prices based on market expectation of

relative volatility. For example, the strike structure in Figure 7 drops more steeply from the

OTM strikes leading up to the ATM strike than it does after, which indicates that the

market expects higher volatility (and higher premiums) on that portion of the skew curve.

Real-Time Implied Volatility Market Indicators

The Chicago Board Options Exchange (CBOE) offers real-time indices that track short-

term index implied volatility on the S&P 100 (OEX) and the Nasdaq-100 (NDX).

VIX Index (shows implied volatility of S&P 100) 15

The VIX was developed in 1993 as an indicator of market implied volatility, and is often

regarded by technical analysts as a contrary market indicator, meaning it moves

inversely with the market. Since it measures implied volatility, VIX increases as the market

declines (showing higher implied volatility) and vice versa. Low VIX levels signify lowimplied volatility and relatively complacent markets. Extremely high VIX levels indicate

high anxiety, risk and uncertainty in the options market and generally coincide with a

continued decline in stock prices.

VXN Index (shows implied volatility of Nasdaq-100)16

Similar to the VIX, the VXN Index gauges implied volatility on the Nasdaq-100,

providing investors with a real-time volatility barometer for the technology universe.

Compared to the VIX, which tracks the relatively more stable S&P 100 index, the VXN

shows the higher implied volatility inherent in technology stocks.

14 Kurtosis measures how much of a distribution’s variability lies at the extremes (i.e., the thickness of thetails).15 The VIX index replicates the payoff of a hypothetical ATM option expiring in 30 days. The option iscomposed of eight puts and calls on the underlying OEX weighted by time to expiration and the ATMstrike price.16 Uses NDX options and the same construction methodology as the VIX.


20/49

Volatility Handbook

20 February 2002

A Note on Contrary Market Indicators

It is important to clarify the relationship between VIX and VXN levels and market activity.

Implied volatility, as earlier defined, is the volatility implicit in option prices, and has an

inverse relationship to the market. Implied volatility is notnotnotnot reflective of the size of price

swings, but of the implied risk associated with the stock market.17 As mentioned before,

sector risk (and hence market risk) has an asymmetric negative bias, which means thatmarket declines are associated with higher overall levels of risk and higher implied

volatilities. For evidence of rising implied volatility in risky markets, we can look no further

than the VIX and VXN spike in Figure 9 caused by the additional risk that the events of

September 11 injected into the markets. Put option implied volatility is the most likely to

rise in a falling market as investors seek protection; the spike in put activity also causes

premiums to rise.

Figure 9: Daily 2001-2002 VIX and VXN Volatility Index Levels

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

1 / 2 / 0 1

2 / 2 / 0 1

3 / 2 / 0 1

4 / 2 / 0 1

5 / 2 / 0 1

6 / 2 / 0 1

7 / 2 / 0 1

8 / 2 / 0 1

9 / 2 / 0 1

1 0 / 2 / 0

1

1 1 / 2 / 0

1

1 2 / 2 / 0

1

1 / 2 / 0 2

2 / 2 / 0 2

V o l a t i l i t y ( % )

VIX Level VXN Level


QQV Index (shows implied volatility of options on the Nasdaq-100 ETF)

The Nasdaq-100 Index Tracking Stock (ticker symbol QQQ) is the most popular

example of a relatively new investment vehicle known as an exchange traded fund

(ETF).18 The QQV Index (quoted on the American Stock Exchange) was developed inSeptember 2000 to track the implied volatility of options on the QQQ. The methodology

is similar to that used by the CBOE in calculating the VIX and VXN.

17 From the CBOE website (www.cboe.com)18 ETF’s are introduced and described in Section 3.2.

The VIX and VXN indices

developed by the CBOE

track implied volatility of the

S&P 100 and Nasdaq-100

respectively. The two are

regarded as barometers of

implied volatility in the

options markets.


21/49

Volatility Handbook

February 2002 21

Volatility Cones

Just as term and strike structure display market perceptions of implied volatility, volatility

cones show technical and momentum trends in historical volatility over time. The volatility

cone in Figure 10 condenses implied and realized index volatility data, and shows near-

term volatility spread trends to make an effective trading tool.

Figure 10: S&P 500 Implied and Realized Volatility Cone and Near-term VolatilitySpreads19

Realized Volatility Cone &Current ATMImplied Vol

0%

10%

20%

30%

40%

Min Realized 9.1% 11.0% 12.9% 13.2% 17.0% 17.2% 17.9% 19.2% 17.3%

Max Realized 35.5% 30.6% 28.6% 27.1% 26.0% 24.1% 23.1% 21.8% 21.7%

Avg Realized 19.8% 20.2% 20.4% 20.4% 20.7% 21.0% 21.0% 20.5% 19.8%

Current Realized 17.6% 16.4% 15.8% 17.0% 19.6% 18.7% 20.8% 21.4% 20.5%

Current Implied 20.9% 20.9% 20.8% 20.5% 20.4% 20.3% 20.4% 21.1% 21.7%

1-Mth 2-Mth 3-Mth 4-Mth 6-Mth 9-Mth 1-Yr 2-Yr 3-Yr

Near-TermATMImplied Vol &Realized Vol

10%

15%

20%

25%

30%

35%

40%

45%1-Mth Realized Vol

Near-ATMImpl Vol

Vol Spread (Near-ATMImpl - 1 Mth-Realized)

-15%

-10%

-5%

0%

5%

10%

15%

20%

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

Vol Sprd 3-Yr Avg Vol Sprd3-Yr Avg Vol Sprd -2 SD 3-Yr Avg Vol Sprd +2 SD Near-ATMImpl Vol


Profitable relative volatility trades can be executed on discrepancies between implied

and realized volatility or current and historical levels of realized volatility. Cones are also

useful tools to compare relative volatility levels of two stocks or indices. The shape of a

volatility cone illustrates the long-term mean reverting property of volatility. The cone is

widest for the near-term expirations, which are susceptible to the widest fluctuations, but

the range narrows as the time horizon is extended.

19 Graph provides a snapshot of S&P 500 historical and implied volatility as of February 6, 2002.Contact your Lehman Brothers Sales Representative for current levels.

A volatility cone is useful in

identifying trading

opportunities caused by

discrepancies in realized and

implied volatility levels.


22/49

Volatility Handbook

22 February 2002

This page intentionally left blank.


23/49

Volatility Handbook

February 2002 23

Section 3: Trading Volatility


24/49

Volatility Handbook

24 February 2002

Option Strategies to Trade Volatility

Most investors have a view on a single stock, sector or index and how they think its price

will vary over a given future time frame. Options are an efficient and cost-effective way

to implement trading positions designed to profit on an investor’s views on the market.

There are two basic factors that should help determine an appropriate s trategy:There are two basic factors that should help determine an appropriate s trategy:There are two basic factors that should help determine an appropriate s trategy:There are two basic factors that should help determine an appropriate s trategy:

View on the Underlying Asset:View on the Underlying Asset:View on the Underlying Asset:View on the Underlying Asset: What factors does the investor believe will drive

the value of a stock or index over a given time period in the future? These could

be fundamental factors or technical/momentum driven factors.

Current and Future Volatility Levels:Current and Future Volatility Levels:Current and Future Volatility Levels:Current and Future Volatility Levels: How high or low are current implied and

realized volatility levels relative to each other? How high is current realized

volatility relative to past levels of realized volatility?

In Figure 11 below, we show appropriate option strategies to implement various views

on underlying asset price movement and volatility levels.

Figure 11: Option Strategies for Expectations of Momentum and Volatility

Expect Price IncreaseExpect Price IncreaseExpect Price IncreaseExpect Price Increase Expect Price StabilityExpect Price StabilityExpect Price StabilityExpect Price Stability Expect Price DecreaseExpect Price DecreaseExpect Price DecreaseExpect Price Decrease

Expect IncreasedExpect IncreasedExpect IncreasedExpect IncreasedVolatilityVolatilityVolatilityVolatility

Buy Calls Buy Straddles orStrangles

Buy Puts

Expect StableExpect StableExpect StableExpect StableVolatilityVolatilityVolatilityVolatility

Bullish Spread Strategies Long-Short Strategies Bearish Spread Strategies

ExpectExpectExpectExpectDecreasedDecreasedDecreasedDecreasedVolatilityVolatilityVolatilityVolatility

Sell Puts Sell Straddles orStrangles

Sell Calls


The basic strategies outlined above can be combined to capitalize on current marketconditions. We outline the mechanics of the basic strategies and possible combinations

to profit from expected market and volatility movements in Figure 12.


25/49

Volatility Handbook

February 2002 25

Figure 12: Basic Description of Basic Option Strategies

StrategyStrategyStrategyStrategyNameNameNameName

Strategy ComponentsStrategy ComponentsStrategy ComponentsStrategy Components Possible UsesPossible UsesPossible UsesPossible Uses

Buy Calls Buying Calls Strongly bullish – risks entire premium for upsidemovement in underlying, uses less capital thanbuying the underlying outright. Potential entry

strategy.Sell Calls Sell calls with no position inunderlying stock

Extremely bearish – unlimited risk potential sincethere is no existing position in the underlying asset.

CallOverwriting

Selling calls with an existinglong position in underlying

Income strategy/Exit strategy – either take inpremium or sell off long position at a favorableprice. Strategy can also be accomplished bysimultaneously buying the underlying asset andselling calls to finance the purchase.

Buy Puts Buying Puts Strongly bearish – a low cost short or insuranceagainst loss on long position.

Sell Puts Selling Puts Strongly bullish – entry strategy or potential incomestrategy. The risk is a potentially forced longposition if sold put is exercised.

Call Debit

Spreads

Sell high strike call, buy lower

strike call

Moderately bullish – willing to risk capital for

limited upside with less risk than outright callbuying.

Call CreditSpread

Buy high strike call, sell lowerstrike call

Moderately bearish – seek to take in premium withlimit to potential loss

Put DebitSpreads

Buy high strike put, sell lowerstrike put

Moderately bearish – willing to risk capital fordownturn in underlying but not to the degree ofoutright put buying

Put CreditSpread

Sell high strike put, buy lowerstrike put.

Moderately bullish – seek to take in premium withlimit to potential loss

Long Straddle Buy a put and a call at thesame strike price.

See movement in underlying away from strike, butnot sure of the direction

Short Straddle Sell a put and a call at thesame strike price.

See little movement in underlying away from thestrike in either direction.

Long Strangle Buy a put and a call at

different strikes (call strikehigher, put lower)

See movement in underlying away from range

between strikes. Cheaper than long straddle butmore risky.

Short Strangle Sell a put and a call atdifferent strikes (call strikeabove, put below)

See price of underlying remaining within the rangebetween strikes until expiration. Less risky thanshort straddle, but less profitable.

Collar Buy an out-of-the-money putand sell an out-of-the-moneycall.

A collar is designed to protect a long position inthe underlying. The insurance put is financed, atleast partially, by the selling of the call, whichrepresents the upside potential of the underlying.


Selecting Appropriate Strike Prices for Out-of-the-Money Options

The option strategies above are each combinations of call and put options with different

relative strike prices If a desired strategy recommends buying or selling OTM strike

options, the appropriate strike price is critical. Option premiums decrease as strike prices

get further out-of-the-money, reflecting the lower probability that the strike price will be hit

before expiration. We outline a methodology for choosing OTM strike prices and the

trade-off between income (cost) and downside protection (upside potential):


26/49

Volatility Handbook

26 February 2002

Buying OTM Options:Buying OTM Options:Buying OTM Options:Buying OTM Options: Strike price should be set at a level where the investor believes

the premium paid is worth the potential upside and the probability that it will be reached.

Sell OTM Options:Sell OTM Options:Sell OTM Options:Sell OTM Options: Strike price should be set at the investor’s optimal trade-off between

current income and protection. Defensive-minded investors will likely opt to collect a

lower premium by selling a further OTM option in return for the added protectionprovided by the higher strike.

We provide graphical illustrations of the payoffs of the basic options strategies described

above in Figure 13.

Figure 13: Illustrations of Option Strategy Payoffs

Call Overwriting

Collar Strategy

Call Debit Spread Call Credit Spread


27/49

Volatility Handbook

February 2002 27

Put Debit Spread

Put Credit Spread

Long Straddle

Short Straddle

Long Strangle Short Strangle



28/49

Volatility Handbook

28 February 2002

New Developments in Equity Derivatives: The Exchange Traded Fund (ETF)20

An ETF is a hybrid security that is traded on an exchange, like a single stock, but

provides the returns from owning a portfolio of stocks. The portfolio could represent

either an entire market (such as the S&P 500, or the Nasdaq-100, Russell 3000, the

FTSE 100 etc.), a sector or industry of the market (Internet, Telecommunication, Financial

services, Energy, Technology, Real Estate, etc.) or even a selected basket of stocks.Although the current ETF’s track or replicate well-known market indices, plans are under

way to introduce ETF’s that represent any actively traded portfolio of stocks.

ETFs have grown in popularity since their origin in 1993. The first ETF, called Standard

and Poor’s Depository Receipts (SPDRs, known21 as “spiders”), tracks the performance of

the S&P 500 index much like a mutual fund. With a current estimated asset base of

about $20 billion, it has more than 100 million shares outstanding. By far the dominant

ETF on the market today, SPDR’s have more than 40% of the market share of all ETF

assets, and institutions own nearly 40% of SPDR shares.

Another widely popular ETF tracks the Nasdaq 100 index and trades under the ticker

symbol QQQ. Launched in March 1999,22 QQQ’s have quickly become one of the

most actively traded securities on any of the U.S. stock exchanges. Currently, the

QQQ’s have two-thirds the assets of SPDR’s (approximately $11 billion) but trade nearly

twice the average daily dollar volume of the latter. On average, QQQ’s traded slightly

over 70 million shares a day in 2001, making them one of the most liquid securities

traded on any exchange.

Investment Strategies Using Exchange-Traded Funds

Part of the excitement surrounding the introduction of ETF’s is due to the facilitation of newinvestment strategies they make possible. It is a well known fact that asset allocation

decisions are significant determinants of superior investment performance. ETF’s that

represent aggregated units of the market (sectors, styles, sizes, etc.) are ideally suited to

implement asset allocation decisions. In what follows, we establish the need for asset

allocation strategies to achieve superior returns and to forecast asset returns In addition

to asset allocation, we list potential investment strategies executed efficiently with ETF’s.

ETF’s and Futures Contracts

Equity asset managers that are benchmarked to a major index have alternative methods

of investment to achieve the performance of their benchmark. The obvious approach isto own the stocks in the benchmark index in a portfolio that is weighted according to the

benchmark's weighting methodology. However, real world issues such as index

20 See “Exchange-Traded Funds: Where the Market i s a Stock,” September 15, 2000 publication byLehman Brothers Equity Derivatives & Quantitative Research.21 SPDRs are managed by State Street Global Investors.22 QQQs are managed by the Bank of New York.

What is an ETF?

Brief History of ETF’s

ETF enabled investmentstrategy


29/49

Volatility Handbook

February 2002 29

changes, cash management, dividends, corporate actions, redemptions and trading

costs precipitate inefficiencies in this simple approach. For instance, when the asset

manager receives cash from dividends paid, he should transform that cash position into

index exposure. The job of managing an index portfolio becomes quite dynamic since

he is receiving dividends with regularity and simultaneously managing cash inflows or

outflows. Couple the cash management issues with changes in the benchmark fromreconstitutions and M&A activity and things can get pretty complicated. Fortunately, for

some index managers, they have the ability to use other methods to obtain performance

exposure to his or her benchmark. Namely, the fund manager can use futures contracts,

exchange traded funds and options to make his job more efficient. However, many

index managers are prohibited by the fund's bylaws from trading in derivative products.

For these managers, ETFs are a ”non-derivative” solution.

Because of their lower transaction costs and minimal margin requirements, equity index

futures can play an important role for the index manager. An index manager that

requires exposure to a benchmark index can make the appropriate investment in the

futures contract. Then the asset manager can either roll into the next futures contract as

time passes or let the position expire and invest in the actual stocks. Historically, the

futures contract was ideal for obtaining index exposure for extended periods of time,

however more recent times have seen the cost of holding a futures position for an

extended period of time become more costly.

This cost is called the calendar spread and is measured as the annualized spread of the

roll cost of closing the near futures contract and opening a position in the next futures

contract versus the current risk free rate. If the calendar spread trades at fair value the

roll cost is zero. If the calendar spread is trading over the fair value the investor incurs

roll cost, however, the calendar spread can trade cheap which is a benefit. Figure 14

illustrates that the calendar spread trade has generally traded rich since 1995.

Figure 14: S&P 500 Calendar Spread 1988-2001

- 3 . 5

- 3 . 0

- 2 . 5- 2 . 0

- 1 . 5

- 1 . 0

- 0 . 5

0 . 0

0 . 5

1 . 0

1 . 5

A u g - 8 7

A u g - 8 8

A u g - 8 9

A u g - 9 0

A u g - 9 1

A u g - 9 2

A u g - 9 3

A u g - 9 4

A u g - 9 5

A u g - 9 6

A u g - 9 7

A u g - 9 8

A u g - 9 9

A u g - 0 0



30/49

Volatility Handbook

30 February 2002

Our analysis looks at the costs that an investor would incur for both products if the

investor were to hold the investment for one year. The breakdown of the costs is asThe breakdown of the costs is asThe breakdown of the costs is asThe breakdown of the costs is as

follows:follows:follows:follows:

ETFETFETFETF cccc = C + B/A= C + B/A= C + B/A= C + B/A ssss + AF+ AF+ AF+ AF

FutFutFutFut cccc = C + B/A= C + B/A= C + B/A= C + B/A ssss + R+ R+ R+ R rrrr

Where:

C = Commission cost (round trip or buy + sell)

B/As = Impact cost reflected as the bid/ask spread

AF = Advisor fee for the ETF

Rr = Roll cost

The costs that are common to both the ETF and the futures contract are commissions and

the bid/ask spread. However, these costs are very different for each product. It is well

known that the commission cost associated with futures contracts are very low when

compared to the notional size of a transaction. We use an estimate of $15 a contract,

which currently amounts to 0.4 basis points. Commissions for the ETF are higher, we

assume a rate of 6 cents per share, or currently 4 basis points. The bid/ask spread also

favors the futures contract. For our analysis we use a bid/ask spread of 0.5 index

points, or in terms of dollars, 0.5 multiplied by $250 (or $125 per contract or 4 basis

points). The bid/ask spread for the ETF is 10 cents, or 8 basis points. The figures used

for both commissions and the bid/ask spreads are provided by Lehman Brother’s trading

desk.

The unique cost to each product is where the separation occurs. The unique cost of the

ETF is the advisor fee and the unique cost of the future is the roll cost.

The ETF is a managed trust for which the investment advisor of the trust charges a fee.

This fee is typically comprised of management fees, distribution fees and other fees. The

S&P 500 exchange traded funds have the lowest fees of all existing ETFs. The advisor

fee charged by the iShares S&P 500 index fund is 9 basis points, and the S&P 500

SPDR carries a fee of 12 basis points. We use the lower of the two fees for our cost

analysis.

The cost of holding a future for any length of time that requires the contract holder to

enter into a calendar spread trade. The roll cost is the premium an investor pays for

selling the futures contract that is closest to maturity while simultaneously buying the futures

contract with the next-closest maturity. Investors that were long June 2001 S&P 500

futures contracts and wanted to continue holding a long position in S&P 500 futures

contracts had to roll into the September 2001 contracts by executing a calendar spread

trade prior to the expiration of the June 2001 contract.


31/49

Volatility Handbook

February 2002 31

Figure 15 shows the scenario of an investor with a one-year holding period. We use

100 futures contracts to establish the notional amount of this trade to be roughly $30

million. The comparison shows a dramatic difference in cost for a buy and hold investor.

The roll cost of the future dominates the analysis, and tilts the scales in favor of the ETF.

However, the roll cost is not a certain cost. The roll cost of 25 basis points used in this

analysis is the average daily roll cost in the four weeks leading up to contract expirationas measured in the last four quarters. The roll cost is a variable, and could even be

negative under certain market conditions.

Figure 15: One-Year Holding Period Costs of Futures versus ETFs

S&P 500 FutureS&P 500 FutureS&P 500 FutureS&P 500 Future S&P 500 ETFS&P 500 ETFS&P 500 ETFS&P 500 ETF

Position 100 Contracts @ $304,625 each 250,103Notional Amount ($) $30,462,500 $30,462,545

Cost Category

Annual Commission $15 a contract or $1500 * 4 or$6,000

6 cents a share or $15,006

Bid/Ask Spread .5 * $250 * 100 contracts or 12,500 .10 * 250,103 or 25,010

Management Fees N/A .0009 * 30,462,545 or 27,416 yearly

Roll Cost 25 bps or $76,156 yearly N/A

Total Cost for OneYear Holding Period

94,656 67,432

Total Cost/Notional 0.31% 0.22%


Option Strategies for ETF Holders

ETF investors can implement a variety of option-based strategies that can potentially

enhance returns and lower risk on their ETF investment. Listed options are not available

for all available ETFs, but some of the more liquid ETFs do have listed options. For

investors that wish to implement an option strategy on ETFs that do not have listed options

available, they can implement their strategy with OTC (over the counter) options.

Additionally, OTC options might provide further flexibility and customization for investors

over and above what is provided by the listed market.

Here we present a few strategies that involve options and a position held in an ETF. The

common theme in the strategies is to provide the investor that has a directional view

(bullish or bearish) with potentially yield enhancing strategies that can also lower the

overall risk taken in the position. Figure 16 is a table of ETFs trading in the United States

that have listed option contracts.


32/49

Volatility Handbook

32 February 2002

Figure 16: U.S. ETF’s with Listed Options

Fund NameFund NameFund NameFund Name SymbolSymbolSymbolSymbol Average Daily Option VolumeAverage Daily Option VolumeAverage Daily Option VolumeAverage Daily Option Volume

Nasdaq-100 Index Tracking Stock QQQ 66,112

Biotech HOLDRs BBH 8,243

Semiconductor HOLDRs SMH 2,809

Oil Services HOLDRs OIH 1,176

iShares S&P 100 Index Fund OEF 713Pharmaceutical HOLDRs PPH 243

Internet HOLDRs HHH 238

Internet Architecture HOLDRs IAH 96

Telecommunications HOLDRs TTH 94

iShares Russell 2000 Index Fund IWM 88

Total Stock Market VIPERs Index Fund VTI 83

iShares Russell 2000 Growth Index Fund IWO 81

Wireless HOLDRs WMH 55

Internet Infrastructure HOLDRs IIH 42

Regional Bank HOLDRs RKH 27

Utilities HOLDRs UTH 24

Retail HOLDRs RTH 24

B2B Internet HOLDRs BHH 24

iShares Russell 1000 Index Fund IWB 20

Market 2000+ HOLDRs MKH 18

FORTUNE e-50 Index Fund FEF 10

Europe 2001 HOLDRs EKH 5

iShares Russell 2000 Value Index Fund IWN 3


Call Overwrite Strategy

An investor that currently holds a long position in a security and is neutral to moderately

bullish, can consider the call overwrite strategy to enhance yield on his/her investment.The strategy is designed to increase the investor's return if the long position is neutral over

the period until the option's maturity. The investor collects the option premium of the

written call option and maintains his/her long position if the option expires out of the

money. The investor will outperform the simple long position without call overwriting in

all cases except where the underlying rises above the written call's strike price plus the

collected premium at maturity. In this case, the option writer will have the ETF called

away" which means that the holder of the option is exercising his or her right to purchase

the ETF at the designated strike price. The writer of the option must satisfy the option

holder by selling the ETF to the option holder at the designated strike price. The investor

who implemented the call overwrite strategy has a positive return for the period, but willunderperform a simple long position if his ETF is called away. Hence, a buy write

strategy is not the strategy of choice if one is very bullish. It is often a strategy employed

by asset managers who are mandated to invest in a class of stocks that are neutral or

under-performing. For instance, value managers in 1998 and 1999 and growth

managers in 2000 were well positioned to undertake a call overwrite strategy.


33/49

Volatility Handbook

February 2002 33

Figure 17: Profit/Loss Diagram of Call Overwrite Strategy

5 0 %

6 0 %

7 0 %

8 0 %

9 0 %

1 0 0 %

1 1 0 %

1 2 0 %

1 3 0 %

1 4 0 %

1 5 0 %

Equity Price

P r o f i t & L o

s s

L on g Q s

Long Qs & W r ite

ATM Cal ls


Put Overwrite Strategy

A feature of exchange-traded funds is the ability to short on a down tick. Additionally,

market makers will often quote an ETF transaction as a principal trade. Hence, in a

declining market, ETF investors can quickly hedge certain market/sector exposures by

entering into a short position in a declining market at a known price. Upon examining

short interest levels for SPDR’s and QQQs, we see their popularity as defensive hedges.

Figure 18: QQQ Short Interest - July 1999 to July 2001

0

20

40

60

80

100

120

140

J u l - 9

9

O c t

- 9 9

J a n - 0 0

A p r - 0

0

J u l - 0

0

O c t

- 0 0

J a n - 0 1

A p r - 0

1

J u l - 0

1

0%

100%

200%

300%

400%

500%

600%

Short Int erest Ra tio Q QQ Short Int erest

Short Interest



34/49

Volatility Handbook

34 February 2002

Figure 19: SPYs Short Interest - July 1999 to July 2001

0

5

10

15

20

25

30

35

J u l - 9

9

O c t

- 9 9

J a n - 0 0

A p r

- 0 0

J u l - 0

0

O c t

- 0 0

J a n - 0 1

A p r

- 0 1

J u l - 0

1

0%

100%

200%300%

400%

500%

600%

S ho rt In te re st R atio S PY S ho rt In te re st

S hort Interest


The put overwrite strategy is very similar to the call overwrite strategy, but differs in oneway: the investor is bearish and holds a short position in the ETF (the underlying). The

investor writes put options against the ETF short position and expects to collect the

premium if the ETF price is above the written puts strike price when the option expires.

The only scenario in this strategy that will under-perform the simple short position is when

the ETF price falls below the strike price of the written put option, less the collected

premium. Figure 20 illustrates the profit and loss scenario at expiration. Otherwise, the

put overwrite strategy will outperform a simple short position.

Figure 20: Profit/Loss Diagram of Put Overwrite Strategy

8 0 %

9 0 %

1 0 0 %

1 1 0 %

1 2 0 %

Equity Price

P r o f i t & L

o s s

S hor t Qs

S h ort Qs & W rite

Ou t-of-Money P uts



35/49

Volatility Handbook

February 2002 35

Conclusion

Presuming returns can be forecast, ETF’s are a cost-efficient way to implement strategies

or views at the sector level. Prior to the creation of ETF’s, investment managers had to

trade in portfolios of securities to gain exposure to the relevant size, style or sectors. This

caused higher transaction cost—both in trading and management of those portfolios—in

the implementation of active asset allocation strategies. We highlighted the majorbenefits of ETF’s: lower transaction costs, breadth of asset class coverage, transparency

in pricing and liquidity.

We also presented a list of potential investment strategies for which the ETF’s would

prove to be ideal instrument of execution. For these reasons, we believe ETF’s are likely

to show increasing acceptance globally in the near future. The impending introduction of

ETF’s in the world of actively managed funds (and hedge funds) can only increase their

acceptance and broad appeal as an instrument of asset allocation strategies. Below we

provide lists of index ETF’s available by asset class, sector and geographic region.


36/49

Volatility Handbook

36 February 2002

List of Available ETF’s on Selected Indices

Figure 21: List of Currently Available ETF’s Related to Style (Growth/Value) Asset Class

TickerTickerTickerTicker NameNameNameNameOutstandingOutstandingOutstandingOutstandingShares (m)Shares (m)Shares (m)Shares (m)

Assets (m)Assets (m)Assets (m)Assets (m)AvgAvgAvgAvgBid/AskBid/AskBid/AskBid/Ask

SpreadSpreadSpreadSpread

AverageAverageAverageAverageDollarDollarDollarDollar

VolumeVolumeVolumeVolume

InceptionInceptionInceptionInceptionDateDateDateDate

Advisor FeeAdvisor FeeAdvisor FeeAdvisor Fee

IVW iShares S&P 500/Barra Growth 0.95 86.30 0.50% 1,246,375 5/26/00 0.25%

IVE iShares S&P 500/Barra Value 0.70 43.99 0.74% 1,981,290 5/26/00 0.18%

IJK iShares S&P Midcap 400/Barra Growth 0.25 36.44 0.40% 269,892 7/28/00 0.25%

IJJ iShares S&P Midcap 400/Barra Value 0.25 19.32 0.68% 109,023 7/28/00 0.25%

IJT iShares S&P SmallCap 600/BarraGrowth

0.20 17.54 0.65% 302,457 7/28/00 0.25%

IJS iShares S&P SmallCap 600/Barra Value 0.20 14.37 0.68% 256,443 7/28/00 0.25%

IWF iShares Russell 1000 Growth 0.50 44.77 0.53% 1,464,657 5/26/00 0.20%

IWD iShares Russell 1000 Value 0.45 25.84 0.83% 1,628,253 5/26/00 0.20%

IWO iShares Russell 2000 Growth 0.35 29.12 0.81% 3,596,446 7/28/00 0.25%

IWN iShares Russell 2000 Value 0.35 37.71 0.59% 588,526 7/28/00 0.25%

IWZ iShares Russell 3000 Growth 0.25 17.72 0.58% 28,616 7/28/00 0.25%

IWW iShares Russell 3000 Value 0.25 18.35 0.68% 22,258 8/4/00 0.25%

Source: Bloomberg

Note: Average Bid/Ask Spread and average dollar volume is calculated over the last 30 days. Additionally, outliers areeliminated from the average calculation. All funds mentioned above are managed by Barclays Global Advisors Ltd.

Figure 22: Currently available ETF’s related to size (large/medium/small) asset class

TickerTickerTickerTicker NameNameNameName OutstandingOutstandingOutstandingOutstandingShares (m)Shares (m)Shares (m)Shares (m) Assets (m)Assets (m)Assets (m)Assets (m)

AvgAvgAvgAvg

Bid/AskBid/AskBid/AskBid/AskSpreadSpreadSpreadSpread

Average DollaAverage DollaAverage DollaAverage DollarrrrVolumeVolumeVolumeVolume InceptionInceptionInceptionInceptionDateDateDateDate Advisor FeeAdvisor FeeAdvisor FeeAdvisor Fee

SPY S&P 500 Depositary Receipt 118.92 17,957 0.50% 660,989,952 1/29/93 0.12%

QQQ Nasdaq-100 Shares 128.95 12,677 0.82% 1,644,067,456 3/10/99 0.18%

MDY S&P 400 Mid-Cap Dep Recpt 27.46 2,704 0.98% 55,934,068 5/4/95 0.25%

IVV iShares Trust -S&P 500 11.85 1,788 0.30% 37,165,872 5/19/00 0.09%

DIA Diamonds Trust Series I 13.75 1,534 0.18% 75,368,688 1/20/98 0.18%

IWB iShares Trust - Russell 1000 3.40 274 0.56% 520,743 5/19/00 0.15%

IJH iShares S&P Midcap 400 2.30 247 0.45% 7,339,662 5/26/00 0.20%

IWM iShares Russell 2000 2.25 238 0.51% 9,733,797 5/26/00 0.20%

IJR iShares S&P SmallCap 600 0.40 44 0.44% 1,296,404 5/26/00 0.20%

IWV iShares Russell 3000 0.40 33 0.58% 762,961 5/26/00 0.20%IYY iShares Total Market 0.15 11 0.67% 737,789 6/16/00 0.20%

Source: Bloomberg

Note: Average Bid/Ask Spread and average dollar volume is calculated for the last 30 days. A

volatility handbook final

Documents