difficult at the close because riskbecomes a big driver as traders seek to close out their position. So if we hada market structure – and I do not know what it would be – where pricediscovery was more uniform in quality over the trading day, we would notsee the volatility patterns that you have shown us.SCHWARTZ: Yes. I would say yes to that. Holly, how would I answerRich’s market structure question?HOLLY STARK17 [From the Floor]: I think that was a set up for Bob tomake the case for call auctions at both the open and the close.SCHWARTZ: Call auctions? That is a wonderful idea (laughter).BENNETT: I thank our panelists, and I thank the audience for a gooddiscussion.
16
Richard Repetto is currently Associate Director at Sandler O’Neill & Partners, LP. At thetime of the conference, he was a Managing Director at Putnam Lovell.
17
Holly Stark is Principal and Director of Trading at Kern Capital Management.
CHAPTER 2: INTRA-DAY VOLATILITY:FRIEND OR FOE?Moderator – David Krell, President and CEO, International Securities ExchangeThomas Cardello, Managing Director, Morgan StanleyAvner Wolf, Chairman, Department of Economics and Finance, Zicklin School ofBusiness, Baruch College, CUNY
DAVID KRELL: We are very fortunate to have two panelists in thissession who are experts in the field of volatility. This panel is, therefore,balanced, unlike the previous panel, which consisted mostly of academics.Here we have a 50/50 balance between the practitioner community and theacademic community. Thomas Cardello, managing director at MorganStanley, is in charge of the automated market-making department. He is alsoinvolved in market making in the U.S. as well as overseas. Our otherpanelist is Professor Avner Wolf, Chairman of the Economics and Financedepartment here at Baruch College. Both of these individuals have hadextensive experience in derivatives trading. It is a pleasure for me to be themoderator of this panel.First, I would like to meander a little bit beyond the discussion that Boband I had talked about. Our primary objective on this panel is to talk aboutintra-day volatility. In the options business, we are very much concernedabout volatility in general. If I can present an overview of volatility first,and some definitions of volatility, then we can get to the real topic, theessence of what we would like to talk about this morning – the impact ofmarket volatility on market quality.In the options business, as you well know, all of the theoretical optionpricing models include six basic factors. Five of them are pretty wellknown. They are the underlying stock price, the exercise price, time tomaturity, interest rates and dividends. All five of these factors are known atthe outset. The sixth factor is volatility. Volatility is the one that we spendmost of our time thinking about, dreaming about, and analyzing.
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A Trading Desk’s View of Market Quality
What do we mean by ‘volatility?’ What do we mean by ‘impliedvolatility?’ We can use any one of the various models – Black-Scholes18, thebinomial19, or any of the derivatives thereof – and solve for what we call‘implied volatility.’ I selected AOL as an example. Look at Exhibit 21.
Exhibit 21. AOL 2001 Implied Volatility Index (30 Day)
18
A model used to calculate the value of an option, by considering the stock price, strikeprice and expiration date, risk-free return, and the standard deviation of the stock’s return.
19
An option pricing model in which the Underlying asset can assume one of only twopossible, discrete values in the next time period for each value that it can Take on in thepreceding time period.
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What we see from this histogram is that, in 2001, the 30-day impliedvolatility from the options price, ranged from about 35% annually to about90% annually. About 2/3 of the time, volatility was between 40% and 50%,and indeed the highest individual bar is about 45%. This is a pretty tightcompression of volatility as we measure it in the options business. We canalso look at the implied volatility and compare it to the historical volatility ofan underlying stock. Exhibit 22 shows an overlay of both the impliedvolatility (in this case it is a solid line), and the historical volatility (a dottedline).
Exhibit 22. AOL 2001-02 Historical and Implied Volatility (30 Day)
In 2001-2002, volatility ranged from a low of about 30% to a high ofabout 90%. It is not surprising that the highs of around 90% occurred in
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A Trading Desk’s View of Market Quality
September 2001.20 The historical volatility deals with what happened in thepast. It measures the previous 30 days. The implied volatility, on the otherhand, is a forecast of what options traders think volatility will be for theremaining life of the option (in this case, about 30 days). Our measure ofhistorical volatility is the variance of stock price returns over a period oftime. Bob, Bob and Deniz discussed this in the previous panel. Wefrequently use a 20- or 30-day time slot, depending on the life span of theoption.That is an option trader’s basic perspective. I would now like to ask ourpanelists their views. Let me turn first to you, Tom. What does volatilitymean to you? Specifically, what does it mean to you as an option trader whoneeds to make markets in 400 different securities and options at any givepoint in time?THOMAS CARDELLO: To provide some perspective, I will first giveyou a brief overview of the operation we run at Morgan Stanley. We operateas an individual department, which makes markets in options worldwide.We trade hundreds of underlyings and make markets in more than 50,000derivatives on those underlyings. We are currently handling between 5%and 7% of U.S. national market option volume.So, from our perspective, what is good volatility and what is badvolatility?Good volatility is when I am long and the implied volatility is going up.Bad volatility is when I am long and the implied volatility is going down.What is most important vis-à-vis volatility is that there are two aspects to it.One, which the previous panel alluded to, is the microstructure of theunderlying asset. There is an implied transaction cost for the underlying thatcauses volatility in the underlying price. It is influenced by the number ofposted shares available and the number of shares the customer wants to buyor sell. The other volatility is the implied volatility that is in the options. Inorder for us to trade, a good market is one where market impact is not veryhigh. If I see an underlying market with a bid of 1 and an offer of 1 ½7, Ineed to know whether I can hit that bid or take that offer. So, to me, goodvolatility versus bad volatility means the efficiency with which I can executeat a price that is displayed in the market.KRELL: Avner, what does it mean to you?AVNER WOLF: I would like to elaborate on the issue of impliedvolatility. Sometimes it seems that we use the term and do not understandwhat it means. Implied volatility is typically measured with the use of theBlack-Scholes option-pricing model. Instead of plugging a volatility20
The tragic events of September 1, 2001 created fear and uncertainty in the market. Krellpicks up this theme later in the session.
Chapter 2: Intra-Day Volatility: Friend or Foe?
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estimate into Black-Scholes to find the price of an option, the market priceof the option is plugged into the formula and a value for volatility is ‘backedout.’ The value that is backed out is the value that is implied by the BlackScholes formula, given the market price of the option.David, I would like to mention something that you alluded to in passing.It is something that I emphasize in my teaching. The volatility that we use inoptions pricing does not reflect what happened yesterday. Rather, it is theexpected standard deviation of a stock’s rate of return between now and theexpiration date of the option. Volatility is not something that we can takefrom history. I gave a presentation in Chicago a number of years ago, and atrader came up to me and proposed that I become his partner if I could comeup with a model to forecast and quantify volatility, (laughter) which is veryhard.The title of our session is ‘Volatility: Friend or Foe.’ I would like tomention Bob’s presentation, and try to come up with a definition. It seemsto me that good volatility has to do with market information. When newinformation comes to the market and sparks trading, it generates goodvolatility. Prices should adjust to new information. But if the volatility werethe result of market imperfections and transaction costs, I would call it badvolatility. This is an academician’s definition. But please understand thatthis academician clearly sympathizes with what you perceive as good andbad volatility from your perspective as a trader.KRELL: I want to make sure that, when we talk about volatility in theoptions or derivatives business, it is understood that we are not talking aboutBeta. Beta is a relative measure of performance. Beta measures theperformance of a given stock against a broad based index, such as the S&P500 or the NYSE composite index. In the options business, we measure theabsolute volatility of that underlying component. We only look at thereturns and the variance (or standard deviation) of those returns. I think thatis considerably different than what you in the academic community, or in theequities world, might think about variability of returns.I will mention one thing that pertains to the discussion in the previouspanel. Paul Bennett talked about different views of market quality. Lastyear, the SEC requested comment letters pertaining to the proposed rule thatPaul Bennett mentioned, Rule 11Ac 1-5. We sent a comment letter to theSEC. It was a tongue-in-cheek comment letter where we created a phantomairline called Fly by Night Airline. Fly by Night had the cheapest fares.However, it only flew between 1 a.m. and 5 a.m. It had a poor safety record.It had a departure and arrival timeliness of 0. It had very poor terminalservice. No food or drink was available, and you had to rent your seat beltfrom them at an additional cost (laughter). Do you want to fly on that kindof an airline?
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A Trading Desk’s View of Market Quality
If the government forced you to go to the cheapest provider, is that thebest for you as a consumer? That is the underlying question we are allfacing in our businesses today. Is the cheapest cost the best for you at anygiven point in time? The previous panel talked about price, liquidity, speed,service, transaction costs, transparency and anonymity. These are allcomponents of what is important to certain people at certain points in time.And yet, while price may be an overwhelming desire at some points in time,for large traders it may not be the only component that is important. Justmeasuring bid-ask spread differentials is not enough. We have to go beyondthat price to see what is driven by the desires, the objectives, of users.I have another question. Does volatility mean revert intra-day? Does ittrend?CARDELLO: Yes, volatility exhibits strong mean reversion.21 Thequestion is, how do you exploit that mean reversion? There are twovolatilities that exhibit mean reversion – the historical volatility of theunderlying object, and the implied volatility. They both seem to mean revertduring the day, but the interesting thing is that they by no means move inlock step with each other. If you have noticed, one may revert back to itsvalue earlier in the day. The other might not follow.KRELL: Avner, any observations?WOLF: The study described by Bob Wood, Bob Schwartz and DenizOzenbas, showed clearly that there is some kind of pattern of short-termvolatility, at least intra-day volatility. I am not so sure about long-termvolatility. I would agree with you, Tom, that there is some kind of meanreversion structure to volatility. There is also a lot to study with respect tovolatility, both historical and implied. How do the two work together inhelping us to predict future numbers? I want to emphasize one other issue.The question you asked me earlier, what does volatility tell you, or whatdoes it mean to you? I looked at your numbers in Exhibit 21 for AOL (seepage 36). It was what, about 45% for 30 days volatility?KRELL: Yes.WOLF: Just think what that means. AOL was trading around 50 for along time. Fifty percent volatility means that, within one year, the pricecould go up from 50 to 75, or go down to about 33. That is what volatilitytells you on an annual basis. I can use the normal distribution to get an ideaabout the annual price range of the underlying stock price. So the volatilityconveys information that may be used in options as well as in equity trading.21
Mean reversion (reversion back to the mean) refers to reversal behavior. Namely, when avariable deviates from its mean (is either higher or lower), it tends to reverse direction andrevert back to its mean (average) value.
Chapter 2: Intra-Day Volatility: Friend or Foe?
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It suggests what the average investor thinks about the range of stock priceswithin a given period (one month, three months, six months, one year, etc).KRELL: Good. I have some more questions. First, how do youmeasure volatility?CARDELLO: How we measure volatility is again two fold. The naïveway is to model the returns generation process of the underlying stock.Volatility would be the second moment of the returns distribution that I ammodeling. The other way is to look at the option prices, describe the processthat defines an option’s price, and back out the implied second moment.Generally, you end up with two different measurements.The interesting thing is that, as the previous panel said, there is an awfullot of noise in these measures. Getting back to your other question about thereversion of volatility during the day, I again note that there is an awful lotof noise in these measurements. Something as simple as changing the timeframe for measurement can give you different answers.WOLF: If there is a stock or an option that is not traded on an exchange,you cannot use implied volatility. I hope everyone understands this. Thereis no way to use Black-Scholes to estimate the implied volatility since thereis no price that is disseminated throughout the day. You need to do yourown calculations and estimation of the volatility. If it is an exchange tradedoption, where prices are available, I would typically use what the optionsmarket tells me the volatility is. This is the easiest way to get informationfrom the market.KRELL: Over what period of time do you measure volatility? Is it aspecific period?WOLF: When it comes to options, I would typically use 30 days to threemonths. What is the highest volume of options traded? One-year options?Half-hour options? No. It is typically one-month, two-month, or threemonth options. This would be my guideline for the length of time I woulduse to study volatility.KRELL: Is volatility inherently good or bad, generically?WOLF: I will answer with a story. Years ago I attended a conference atColumbia University. There was a big discussion between a Nobel PrizeLaureate, Kenneth Arrow, and a yet to be Nobel Prize Winner, MyronScholes. The topic was, ‘Is Volatility Good or Bad, or Do We NeedVolatility?’ Without volatility, there would be no market. If we lived in aworld of certainty, there would be no interest on our part in trading anything.Information would mean nothing. Volatility is necessary for markets. Thequestion once more is, what is bad, and what is good. I gave you my answerbefore.KRELL: Tom, any comments?
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A Trading Desk’s View of Market Quality
CARDELLO: I think that volatility, per se, is neither good nor bad.What matters is the costs involved in transacting. You can have two marketsthat each have a measurable volatility of 40%, and bid-ask spreads ofequivalent magnitude. What matters is whether you can actually execute inreasonable size on the bid and offer that is displayed in that market. If I canonly trade 200 shares at any one time in one of the markets, and in the otherI can trade 100,000 shares at any one time, the second market is going to bemuch more conducive, not only to higher volumes, but to more orderlymarkets. In the first market, where you can easily transact only 200 shares ata time, your transaction costs for doing 100,000 are going to be much larger.ROBERT WOOD22 [From the Floor]: Back to your comment on howyou calculate volatility. When you are calculating it as a second moment,you are implicitly assuming that the first moment is stationary.CARDELLO: No. Why do you say that? I have to ask a question toanswer a question (laughter).WOOD [From the Floor]: Because you are assuming that the firstmoment is stationary when you are calculating deviations from the mean.CARDELLO: You have to assume that it is stationary during a certaintime period. If I am calculating volatility over a period of, let us say, 30minutes, yes I have to assume some kind of stationary mean. But I take itduring that short time period.WOOD [From the Floor]: Supposing that, in the 30-minute segment,news arrives that significantly changes the mean expected return for thatcompany over its lifetime. Is that assumption of stationary in the firstmoment justified?CARDELLO: No, not in that particular case. But that is just one reasonwhy measuring volatilities is so noisy. In a prior world, I was anexperimental physicist. If that was a noisy set of data, I would throw outthat particular half-hour period. You have to be very careful about pickingperiods of data. If you are going to do this analysis, do it when the FederalReserve does not come out with any news during that half-hour period.WOOD [From the Floor]: How do you know when you are justified inthe assumption that the first moment is stationary?WOLF: I want to refer to the first study in that area by Fisher Black. Itwas in 1975. Black had discovered that volatility is not fixed.23 This is astrong violation of one of the basic assumptions of his model, which, as youmay know, got his co-authors Myron Scholes and Robert Merton the Nobel22
Robert Wood is Distinguished Professor of Finance at the University of Memphis.
23
See Black, Fisher: “Fact and Fantasy in the Use of Options,” Financial Analysts Journal(July/August 1975) pp. 36-41.
Chapter 2: Intra-Day Volatility: Friend or Foe?
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Prize for options pricing theory. This is a challenge. Most of the modelsthat are currently being used by almost everyone –correct me, David, if I amwrong, even by your exchange – to price options makes the assumption thatvolatility is fixed. Otherwise, you cannot come up with a closed formformula to price options. Everything else is either too slow, or tooinaccurate, or gives results that you cannot interpret.I do not have a clear answer. I do not even think you can use time inBlack-Scholes and find a pattern to the volatility. As you just said, wheninformation comes half an hour later on AOL, or any other company, it maychange your initial assumption about the stationarity of the first moment. Toa degree, your model is flawed. Nevertheless, we keep using Black-Scholes.I would estimate that 90% of the time market users, with some modification,are still using Black-Scholes in one form or another.I would like to allude to another issue. What if we have one stock thattrades, on average, every 10 seconds, and another that trades, on average,once a minute? The question is, can we use implied volatility for both ofthem? Once again, implied volatility is taken from options prices. So, ifyou have a set of stocks with this kind of a delay in trading, you need to lookat the underlying stock. You must also know what the liquidity is in theoptions market. Then ask the question, can implied volatility be used?Sometimes, if there is no liquidity – and, Tom, correct me if I am wrong– the implied volatility means nothing. Perhaps you have bid and askquotes. You still do not know what it means, what price to put into yourBlack-Scholes model for backing out implied volatility.KRELL: That is right. Option traders take that into account. If you havea stock that is trading within a one point range every 10 or 15 minutes,versus one that is trading every 10 seconds, that will be taken into account inthe pricing of that option.CARDELLO: I have a further thought about the stationarity of the mean.I view any given data sample in segments that are piece-wise stationary.That way, I can make an assumption that the mean will be stationary oversmall subsets of the overall data sample. In that way, I can get a statisticalestimate of the second moment of the distribution. It is the shape of thedistribution that you assume is going to be changing. It is going to bevarying over longer periods than the mean. The mean itself varies. The ideais that implied volatility is varying more slowly than the actual price.KRELL: I might point to this chart that is up there (see Exhibit 22 onpage 37) to show you how a traumatic event like Septembereffectedoption pricing, not just for AOL, but for the overall market. Volatility wentup for everyone because of the event. You see that dramatically illustratedhere. The 90% annualized volatility of AOL in September was indicative ofthat.
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A Trading Desk’s View of Market Quality
WOOD [From the Floor]: Our tools for measuring volatility are prettyprimitive. I wish we could do better.KRELL: We agree with that.CARDELLO: Yes, we agree. Absolutely.PAUL DAVIS24 [From the Floor]: To change the subject just a bit.KRELL: It is not in the script.ROBERT SCHWARTZ25 [From the Floor]: That’s volatility (laughter).DAVIS [From the Floor]: We are talking about market quality. I aminterested in knowing how the International Securities Exchange is growing,and how Tom’s desk plays into that. How has having the ISE availablechanged what you do?KRELL: This is a commercial for the ISE (laughter). The ISE is goingto be two years old on May 26, 2002. We trade stock options on about 500individual stocks. Our market share this month is about the highest in ourhistory. Our market share, for the entire market, is about 21%.26Yesterday was an event for us. It was the first day that we traded morevolume than two of our competitors combined. We have been very happyabout the acceptance of our market structure, which is a hybrid. The ISE is ascreen based, agency-auction market. We do not have a floor. We are fullyelectronic. We also have dealers like Tom and Morgan Stanley, and othersas well, who are required to provide liquidity to our marketplace. With that,I will turn it over to Tom and let him share his experience with us.CARDELLO: The market share numbers I quoted were volumesexclusively on the ISE. We have significant national market volume byparticipating primarily on the ISE. We expected, two or three years ago, thatthe markets in this country are likely to go electronic. Because of that, weput tremendous effort into developing a market making capability for theelectronic markets in the U.S. Two years ago, it was a risky decision. Moreand more, it is turning out to be the right decision.One of the most valuable things about being able to transactelectronically worldwide is the immediacy that electronic trading gives. We24
Paul Davis is Senior Managing Director at TIAA-CREF Investment Management.
25
Robert Schwartz is Distinguished Professor of Finance at the Zicklin School of Business,Baruch College, CUNY.
26
The ISE, which is the second largest U.S. options exchange, reported strong gains inFebruary 2003, and according to a published release it was the largest U.S. equity optionsexchange in that month. An analysis of trading volume showed the ISE traded moreequity options than any other U.S. options exchange, and its equity options market sharewas 27%, up 42% from 19% for the same period 12 months earlier. ISE lists 533 optionsclasses.
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find that market impact is significantly lower, largely because we do notextend a free option to specialists or to other market participants during thetime that elapses between when we first put in an order and when we get thatorder filled. And now there are enough participants on the ISE and theelectronic markets for us to start ramping up our sizes.Among the many factors which drive the success of a market, especiallyan electronic market, are the number of participants. Also important is thequality of the participants and the quality of the market makers. We canprovide a significant amount of capital. Consequently, the market impactsuffered by customers and clients is far less when they come to theelectronic market than to an open outcry market. Because of that, we arenoticing that our profitability, our market share, and our market volumes arecontinuing to go up. They are going up by virtue of us providing bettermarkets. I hope that answers your question.KRELL: Just one more slight commercial. We measure some of ourown quality by looking at the spread differential in all of the options wetrade. We trade more than 40,000 different series in these 500 differentnames. Almost 70% of the time we offer the tightest spread. Almost 90%of the time, ISE spreads are equal to or better than the spreads offered in theother four markets. That is another measure of how we think this marketwill evolve, and why we think that we offer a successful model.We provide one other thing that I should note. We have intra-marketcompetition among our dealers. Tom is constantly competing with othermarket makers in our market. This is part of what creates tighter markets andtighter spreads.CARDELLO: One other comment. There are electronic marketstructures other than the ISE. U.S. market structure in the future is notnecessarily going to be identical to the current ISE market structure.However, I suspect that David will be guiding how the broader U.S. marketstructure evolves.WOOD [From the Floor]: What has decimalization done to the noise involatility that you have talked about?CARDELLO: Interesting question.KRELL: Generally, in the options business, we migrated to decimaltrading together with the underlying securities moving to decimal trading.However, we did not move into a penny increment environment. Not yet,anyway. In the options business, we still have a minimum tick of 5 cents.This is our minimum increment in trading.CARDELLO: We trade in both the option and the underlying market.We have observed that decimalization has made the apparent book – thedisplayed market – more real in the stock market. What is the apparentbook? By the apparent book I mean I can trade 100 shares at a 0 spread. I
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A Trading Desk’s View of Market Quality
can trade 500 at a 1-penny spread. I can trade 1,000 at a 2 pennies spread. Ican trade 10,000 at a 4 pennies spread and 100,000 at 6 pennies away.Decimalization has just made that a reality. To trade 100 shares you cannow trade at a spread of 1 cent or less, and you do not have to get to the levelwhere there is a 10,000-share market which may be 6 cents wide.27 I nolonger have to trade 100 shares at the 6-cent spread. I now can trade the 100shares at the narrowest piece. Consequently, decimalization has apparentlynarrowed spreads. But it probably has not done that much to the real marketin terms of being able to get volume at a given price.KRELL: We will open the discussion up to other questions. Anthony?ANTHONY NEUBERGER28 [From the Floor]: I want to return to therelationship between the quality of the underlying market and the quality ofthe options market. There seems to be some belief that a poor underlyingmarket is characterized by excessive volatility, and that, somehow, this isgood for options traders because options traders like volatility. In reality,poor quality in the underlying market makes it much more difficult toarbitrage between the options market and the underlying market. Therefore,the extra volatility which is induced by poor market quality in the underlyingpresumably translates into poor underlying quality in the options market. Iwas wondering to what extent this is what you actually observe.CARDELLO: Two factors come to mind. First, if you have anunderlying security that is uncorrelated (or is only weakly correlated) withany other underlying security, then the illiquidity affects the spreads in theoptions themselves. This is because of the transaction cost inherent inhedging the option. And there is a continued excess transaction costassociated with the dynamic synthesis of the option. If you are going tosynthesize an option – if you are long or short an option – you can hedge thatoption by trading stock against it, according to a prearranged trading strategyin the Black-Scholes model. On the other hand, let there be a highcorrelation between an underlying security that has very low liquidity andanother security that has very high liquidity. For instance, assume that somelow liquidity stock has a high correlation to some high liquidity stock such27
Decimal pricing on the NYSE, for instance, has narrowed spreads. On the negative side,academic studies show that the depth of the market – the number of shares offered at aspecific price – has decreased sharply from the levels in the pre-decimal market. Thereason cited is that investors have more pricing options than under fractional pricing.Decimals have made it cheaper to trade in small quantities of stock but harder to executemuch larger orders.
28
Anthony Neuberger is Associate Dean of the Full-time Masters in Finance Programme atLondon Business School.
Chapter 2: Intra-Day Volatility: Friend or Foe?
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as General Electric. Then I can effectively hedge the option using the highliquidity stock. Because it is liquid, it enables me to put on the position withlower transaction costs. So the answer to your question is, yes-no (laughter).WOLF: The answer, in my view, is very clear. If there is no liquidity inthe underlying stock, there is an accentuated volatility for the underlyingstock. This is an increased volatility for the options trader, and volatility isvery important for options trading. However, as Tom just said, people donot trade options just for the sake of trading and speculating. Someparticipants trade to hedge. You cannot establish the hedge very easily in anilliquid market. In that respect, what you alluded to as bad volatility won’thelp the options market at all.WOOD [From the Floor]: Tom, are you saying that your hedging costshave not been reduced by decimalization?CARDELLO: No, I am saying that the apparent liquidity has notchanged. But if I trade 1000 contracts and my hedge ratio is 20%, I reallyonly need to hedge a certain amount of stock. I will be able to hedge thatstock at a better price if it is within the apparent market.I have to translate that into English. If I trade one option contract on 100shares, the underlying amount that I have to hedge is 20 shares. If, in the oldregime prior to decimalization, that market was 1000 up 6 cents wide, I willbe better off now because I can probably get the 20 shares off at 