Can you measure market fear?

March 28, 2011

Donald MacKenzie is again in the news. A recent article by Gillian Tett draws on MacKenzie’s work to make sense of the recent success of a sophisticated financial instrument. (Thanks to Martha Poon, illustrious ex-blogger, for the lead.)

Tett’s article asks fundamental questions about the recent success of the Vix index, a proprietary product of the Chicago Board Options Exchange.

In recent days, the level of the Vix, which measures the implied volatility of S&P 500 options, jumped to 31, before falling back to below 20 yesterday. But what is more noteworthy is that trading in this index – dubbed the “fear gauge” – has exploded as investors try to speculate on volatility or protect themselves.

The Vix, which is seven years old and has become a moneymaker for the Exchange, may soon be licensed for individual stocks. So: in addition to a “fear gauge” for the entire market, a fear gauge for Apple, a fear gauge for IBM, and so on. But is that a good thing? The question is a classic one for the social studies of finance. And as Tett rightly points out, the benefits of having an extra instrument need to be weighted against the potential reactivity:

In theory, this could potentially be very beneficial for the market. After all, the more liquidity that exists in any product, the more accurate prices are likely to be (…) But as sociologist Donald Mackenzie points out in his book An Engine Not a Camera, when new financial measures and models emerge, they do not simply offer a “snapshot” of activity, they can drive behaviour and change it too (…)

The potential problem is indeed intriguing. Banks have already began to integrate the Vix index in other products such as exchange traded notes. As Tett puts it, “does the existence of another hedging tool smooth adjustments or can a ‘fear’ gauge create more fear?”

Can it indeed? The question provides sociologist of finance with an excellent opportunity to explore the ways in which it can do so — and what to do about it.

Counter-performativity and resonance

One possibility is that the index could prove to be counter-performative. It is a complex measure of an invisible magnitude, “implied volatility.” As the index is increasingly diffused, the diffusion could undermine the premises on which the index rests.

Another disaster scenario is one in which traders get their volatility estimates wrong. If, for instance, traders miss a key factor and thereby underestimate future volatility, their measure of implied volatility will be mistaken. The Vix will still capture “implied” volatility. But that would just magnify the traders’ mistake, and hide it behind a number. And because the Vix is increasingly integrated into other products, the price of equities could easily start dropping. This situation of “resonance” is what David Stark and I explore in our recent paper.

As the Vix becomes a modern deity — more and more encrusted into products, and an increasingly fat cash cow at the CBOE, the innocent gauge will give employment to more and more people. Extra regulators will be needed to keep an eye for spurious increases in the Vix that might percolate into stock prices, government bonds and even house prices. In the private sector, options arbitrageurs in hedge funds will revere the name of Robert Whaley, the academic that brought the index to life. Arbs will be best placed to exploit mispricings in the price of volatility, and their job of master guardians of the fear gauge will become ever more interesting, lucrative — and unpopular.

23 Responses to “Can you measure market fear?”

  1. Yuval Says:

    Daniel thanks! This is a really nice story, but the big potential risk that comes from embedding VIX into composite contract does not come, as far as I can tell, from the potential ‘simple’ counter-performativity that it may induce, but from a more specific ‘performative’ risk. A quick explanation: the VIX provides a prediction of the volatility of the S&P index over the next 30-day period. This calculation, in turn, is based on the assumption of put-call parity (see the calculation of F, the ‘Forward index level’ in page 5, here: http://www.cboe.com/micro/vix/vixwhite.pdf). Put-call parity, however, assumes that options are exercised *at* the date of expiry and not before and this assumption fit much more a market that trades European-style options than American-style options. Moreover (and this is the cruncher), the more volatile the S&P index is, the more likely it is that investors would exercise their options ahead of time. Therefore, the more volatile the S&P is, the less accurate the VIX is going to be. This last statement, of course, assumes that the VIX market would follow its intended purpose: to hedge/speculate on volatility. However, VIX would become embedded in other contracts in such a way that the dominant trading goals would be different, and then all bets are off, as they say.

  2. danielbeunza Says:

    This is very interesting but I’m not sure I agree with the last part of your argument. You argue that integrating the index in non-hedging instruments will undermine its core assumption that the options are used for hedging, as in put-call parity. But this won’t typically be the case, as the instrument (e.g. an ETF) is not necessarily involved in trading options.

    • Yuval Says:

      Fine, if the EFTs’ main use is not to hedge or speculate on the S&P volatility (or something that follows this volatility) then there is less reason to assume that VIX would undermine its own accuracy.

  3. Tom Nugent Says:

    A few points:

    (1) You cannot buy the VIX index, only VIX futures & options on those VIX futures. It is the VIX future that will typically be embedded in structured products. You pay to go long volatility (upward sloping VIX term structure), and you typically loose money being long volatility (negative volatility risk premium).

    The exceptions to this is a market crash – when the VIX and to a lesser extent the future will pay of royally. So one way to see the VIX is as the price of crash insurance. More formally a kurtosis (fat tail) trade. Given a time varying risk premium, cost of carry etc. – it is typically an expensive form of insurance.

    (2) You “other disaster scenario” is way off the mark. The VIX is the vega weighted average of the near month(s) S&P 500 index options implied volatility. It is calculated on a 30 day constant maturity. So the VIX right now (its calculated every 15 seconds in the trading day) is the S&P 500 index options expectation of what S&P volatility will be over the next 30 days (annualised).

    No more, no less. It is a price. That price is determined by the willingness of traders to write options versus the bid for those options. If you think it is rich – you sell it. Cheap – buy it. Your expectations scenario is just bizarre. (I will not even go into your diffusion statement that precedes it – but I hope you get better.)

    (3) A more interesting point is that realised volatility is typically less than implied volatility for matching periods. That is sellers of implied volatility (investment banks / hedge funds) tend to make money – while buyers of volatility (Joe Citizen) tend to lose money. (Black Swans excluded – but Joe Citizen still pays for that).

    Buying the VIX is an expensive (faddish?) way of insuring against tail risk.

  4. danielbeunza Says:

    Tom — your critique is not factually wrong, but because you misunderstood my original post, it does not really engage with it.

    To begin with, my understanding of diffused, as in ’embedded in other contracts’, is different from your understanding of diffusion (you seems to think about it, judging from his reaction, in terms of Jump Diffusion process – see the following: http://en.wikipedia.org/wiki/Jump_diffusion).

    More importantly, you missed my point about the VIX being an ‘amplifier’ of traders’ actions: they buy and sell futures on the S&P500 and this determines the VIX. If the traders mis-estimate risks then the VIX would replicate this wrong estimation in the markets where VIX-based contracts are traded. This is what I’m saying. So I don’t understand why you think my proposed scenario is bizarre.

  5. Tom Nugent Says:

    FYI –

    (1) It is the S&P index option strip(s) pricing that are used to calculate the VIX, not the futures.

    (2) You appear to fundamentally misunderstand the pricing process. A fundamental approach interprets the market price of a security as the discounted value of future expected cash flows. Given the currently available information set. As events unfold, volatility is a process not an event, either the discount rate used, or the expectation set will change, or both. Thus the price changes. That does not mean that the original price that embeds those original expectations was “wrong”. Only with hindsight can one definitively state that risk estimates where optimistic / pessimistic. At the time they were “correct”. Thus you scenario remains bizarre.

    (3) The VIX is simply a calculation, using a model free implied volatility technology, that accounts for the volatility skew seen particularly in the index option markets. As stated, the data for the calculation arises in the S&P index options market. The trading volume in the S&P index options markets dwarfs the trading volume in the VIX futures. In your amplification assertion you are mistaking the tail for the dog.

    (4) I could take you through a VIX futures trade in which the trader “mis-estimates risk“. Given the mark to market, margin collateralised mechanics of this market place, a mis-estimate of risk leads to rapid and sustained capital loss. The trader expires, but the VIX continues to accurately reflect the market cost of crash insurance at a given point in time.

    (5) Yuval’s stab at put call parity is plucky but misguided. Without going into the detail, they are cash settled, you do not physically take delivery of the VIX. They are not exercised but bought or sold at any time in their term. Thus the idea that as they as Euro style options, their value can become detached from their underlying security or index is also just so wrong as to be bizarre.

  6. danielbeunza Says:

    Tom — I continue to disagree with your points 2-4.These points go at the heart of the problem of resonance — which you still don’t get.

    So let’s start with point (2). While it is true that pricing is about the future and therefore uncertain, it can certainly be wrong. If I say the probability of rain tomorrow is 1% and it rains, I’m not wrong. But if my pricing model is based on three scenarios and it’s missing a crucial fourth scenario and then that scenario takes place, e.g., a black swan, then I was certainly wrong. Ask the Japanese.

    The problem of resonance takes in this context. Traders are able to see the consensus estimate by backing out “implied” volatility from option prices. If a vast majority of traders miss a key scenario, then the implied volatility will be wrong. The problem then is that this inaccurate volatility estimate will reassure each individual trader that s/he is right, possibly leading them to double up the bet.

    To put it simply, while everyone is in the dark, mistakes do not spread. Once traders start to see what each other is doing, a new risk arises.

    Resonance differs from your points 3 and 4 in the following. First, the model I’m referring to is not the VIX but whatever model traders use to gauge future volatility. Second, if a single trader gets his estimates wrong the VIX won’t budge, of course. But if many simultaneously do, as when there is an unprecedented event coming up, then the entire index will be inadequate.

  7. Tom Nugent Says:

    From the top:

    (1) While it is true that pricing is about the future and therefore uncertain, it can certainly be wrong.

    It is only “wrong” ex post, with the benefit of 20-20 hindsight. Indeed it is a market truism that the “consensus is always wrong.” Again you fail to apprehend what information a price impounds, and the process by which this occurs. A price is constantly evolving to discount new information as it arises, and at a point in time that price is “right” given the current information set. That information set changes (expectations, discount rates etc) then the price changes. This does not mean that the prior price was “wrong”. The information set may be incomplete, be stochastic , or embed elevated sentiment. But you can only make that judgement ex post. Note you can buy at current prices (spot) or those in the future, given current expectations. It is facile to talk about trading the VIX at last months price!

    Question: What is the “correct” level for the VIX right now? Where would you go to find it? What criteria would you use, right now, to say it is wrong? In our imperfect world – what is the current “best” estimate? Hint: look at the CBOE pricing page. We are all wise after the event.

    (2) If I say the probability of rain tomorrow is 1% and it rains, I’m not wrong.

    Last night the VIX closed at 18.16%. This means that over the next 30 days the S&P index is expected to move up/down by 5.2%. (18.16 / Ö12)

    That is, index options are priced with the assumption of a 68% likelihood (one standard deviation) that the magnitude of the S&P 500’s 30-day return will be less than 5.2% (up or down). Or that with a 32% likelihood that the 30D return will be more than 5.2% up/down. If that does not happen is the VIX wrong?

    (3) But if my pricing model is based on three scenarios and it’s missing a crucial fourth scenario and then that scenario takes place, e.g., a black swan, then I was certainly wrong. Ask the Japanese.

    Again, ex ante and ex post is getting conflated here. Prices can only discount the current information set on which expectations are based. Markets make a stab at “known unknowns” – like macro or earnings releases etc. “Unknown unknowns” (Knightian uncertainty) are by definition are not part of this data set. Taleb defines his Black Swan as an outlier “outside the realm of regular expectations”. Not being able to predict the unpredictable does not make you wrong. A failure to account for its possibility defines you as stupid, (and poor). So you price in that “tail risk” – as evidenced by the negative skew and positive kurtosis of the (risk neutral) implied volatility probability density function.

    (4) If a vast majority of traders miss a key scenario, then the implied volatility will be wrong.

    No. Again, conflating ex ante / ex post information sets. At the time the implied volatility estimate is the best there is, see question (1) Note: implied vol contains some information regarding future realised vol, but it typically overstates experienced realised vol.

    (5) To put it simply….

    Seems like your resonance is a reworking of the Herding phenomena. “Crowded trade” seems to sum it up. In a market crash – correlation goes to 1. There is no heterogeneity of view, the market(s) are all one way.

    But if many simultaneously do, as when there is an unprecedented event coming up, then the entire index will be inadequate.

    Did you think before / reflect after writing this? Think of a time line, before the event, during the event, after the event. What will the index do over each of these phases? Or is it related to the stream of consciousness with which you ended your original piece?

  8. danielbeunza Says:

    Tom:

    I’m going to start by addressing your last comment.

    >Did you think before / reflect after writing this? Think of a time line, before >the event, during the event, after the event. What will the index do over each >of these phases? Or is it related to the stream of consciousness with which >you ended your original piece?

    I am sorry, but this tone is inappropriate and I will not tolerate it. Meaning: I (as the editor of the blog) will not accept any more comments from you, or anybody, that use this aggressiveness. Confrontation is good. Attack is excessive.

    Now, on the problem of Knightian uncertainty and the possibility to be wrong. If the future is unknown, can a claim about the future ever be wrong? I argue it can. Can someone else know that it is wrong? No, this can only be ascertained retrospectively (as you point out). But that is besides the point for the problem of resonance. The key to my argument is that the possibility of being wrong exists. It matters because if it is true that market actors influence one another, then we should ask whether mistakes can spill over from one fund to the next, and how they might do so.

    Now, is resonance like herding? It is not. In fact, it is the opposite. In the classic formulation (Banerjee 1992), you have the following setup (p. 798):

    “There are two restaurants A and B that are next to each other and it is known that the prior probabilities are 51 percent for restaurant A being the better and 49 percent for restaurant B being better. People arrive at the restaurants in sequence, observe the choices made by the people before them, and decide on one or the other of the restaurants. Apart from knowing the prior probabili- ties, each of these people also got a signal which says either that A is better or that B is better (of course the signal could be wrong). It is also assumed that each person’s signal is of the same quality.

    Suppose that of the 100 people, 99 have received signals that B is better but the one person whose signal favors A gets to choose first. Clearly, the first person will go to A. The second person will now know that the first person had a signal that favored A, while her own signal favors B. Since the signals are of equal quality, they effectively cancel out, and the rational choice is to go by the prior probabilities and go to A.

    The second person thus chooses A regardless of her signal. Her choice therefore provides no new information to the next person in line: the third person’s situation is thus exactly the same as that of the second person, and she should make the same choice and so on. Everyone ends up at restaurant A even if, given the aggregate information, it is practically certain that B is better.”

    The difference between resonance and herding is simple. In herding, people use the social cue of what others are doing as a replacement for their own decision-making. In resonance, people use social cues as a way to check their own model. If there is disagreement, they go back and search for more information. They don’t just blindly follow the rest.

    In herding the problem arises when people do not take their own private signals into account. In resonance, the problem arises when people get a similar spurious signal and they find confirmation in the fact that others are doing the same.

    Resonance, in short, is the flip side of herding.


  9. Hey Daniel, I have a conceptual question. I was just wondering if you had come across Morris and Shin’s 2002 paper on the “Social Value of Public Information” (see here: http://www.jstor.org/stable/3083261)

    They develop a concept that’s similar to resonance, but is also slightly different. They examine a situation in which traders *know* the fundamental value of an asset, but are incentivized to coordinate around each other’s actions instead (a bubble would be an example of this).

    Would a bubble be an example of resonance? And if so, under what circumstances?

    Or does resonance require that people are somehow ignorant of the fundamentals, and this is reinforced by the feedback loop created by the models/cognitive tools they use?

  10. danielbeunza Says:

    Taylor — thanks for pointing me to the paper. I read it with great interest and got some good points out of it.

    The scenario examined by Morris and Shin is different from ours. It is a beauty contest or social construction situation, while the scenario that Stark and I looked at is one where the final payoffs do not depend on the perception of others. This makes all the difference. Resonance, in our view, takes place when the reflexivity of the traders is led astray by the price mechanism.

    By contrast, Morris and Shin do not have reflexive traders, because they traders are cynics that only care about what others believe. If you are a socialite and live and die by the on-the-spot approval of others, the world is just fashion, and anything that signals a change in trends needs to be acted upon right away. A bad restaurant review in the Michelin guide (even if you know it’s written by an incompetent critic) would mean that you stop going to the place… because you’re not there for the food but to see and be seen. That’s the world of Morris and Shin.

    In the scenario that Stark and I have outlined, it’s only about the quality of the food. Bad incompetent review? Even a better reason to keep going to the restaurant… less crowded, same menu.

    More broadly, Morris and Sheen is another example of how behavioral finance introduces strong arms the social into market dynamics. The asocial homo economicus is now replaced by a shallow socialites. No wonder orthodox economists are aghast. Buy contrast, the challenge, which Stark and I took on, is to introduce the social into valuation without resorting to irreflexiveness.

    In any event, the paper can also be read as a piece on financial communication which as you know is another passion of mine. So, thanks for bringing it to my attention and I hope my comment helps.


  11. I agree with you that providing “symmetric” accounts of success/failure is valuable. But I feel that both scenarios — yours and Morris & Shin’s — are possible, and I think the two might be related, although I’m not sure how.

    The tail-end of the housing bubble was arguably a Morris & Shin-type scenario where many people suspected that residential real estate was over-valued but tried to game the market anyways. But that kind of mutual revelation, where everyone comes to understand that the bubble is probably real, only happens gradually over time. Presumably, when the bubble first starts, people don’t know that it exists.

    I wonder to what extent resonance could explain the *emergence* of a bubble. It would be neat if one could point to a material object — a valuation model for instance — to show how the mis-pricing gets primed.

  12. danielbeunza Says:

    Agreed. Both Morris and Shin and our own scenario are possible. I just would not call M&S a case of resonance.

    As for the real estate bubble, your proposed mechanism is plausible but I would differentiate between professionals and retail buyers. The former include mortgage derivatives traders. In their case, the account that seems to me most plausible is not a beauty contest but the more complex story that Donald tells in his paper. That was probably the lion’s share of the capital being put into housing.

    As for the retail buyers, many of them were probably chasing the trend, as you suggest. But then again, we have very little systematic evidence of what is it that they were doing.

  13. Peter Maas Says:

    As a person who participated in the design of the VIX Futures, I have to voice my support for Tom Nugent’s comments.

    If you look at the dollar volume of S&P options versus the dollar volume of VIX products, you will have a clear picture of which component is the head of the dog and which component is the tail of the dog.

  14. yuvalmillo Says:

    Peter, in the graph attached you’ll find the ratio between VIX options and SPX for July 2010 – April 2011, which is, more or less, the period discussed in the FT story. Sure, SPX volume is still much larger, but the ratio is shrinking. So, I think that the dog’s head and it’s tail maybe are switching places. At least they are having a fight…
    https://socfinance.files.wordpress.com/2011/04/vix_spx_ratio.pdf
    Yuval

    • Peter Maas Says:

      Yuval –

      First – the VIX Futures are equivalent to S&P 500 Options (see the CBOE paper for the methodology). I believe the total $ volume on VIX futures and VIX futures related products is less than 10% of the $ volume on S&P 500 Options.

      Second – VIX options are a volatility of volatility product. S&P options are a volatility product. Both VIX options and S&P options trade at $100 / point. However, the S%P often changes daily by 10 points, while the VIX often changes by 0.1 points. Hence while the volumes differ by a factor of 10, the P/L impact of a typical day’s move differs by 1000.

      Bear in mind that I am comparing products on the basis of the $ impact which is what matters in the market. There is a big difference between 100,000 shares of Google and 100,000 shares of Citigroup.

      Peter

      • yuvalmillo Says:

        Peter, yeah, I was actually following the CBOE methodology when I collected the data in graph. But, I’m not sure exactly what is the argument regarding market impact. Please clarify the point here.

  15. Tom Nugent Says:

    Yuval

    Peter Mass makes atelling point. Also your calculation may ignore the index volumes traded in the Exchange traded funds market. The ETF, the S&P 500 SPDR Trust traded 2.2m contracts in Q1 11 versus 666K for the S&P index options. They are essentially the same thing – are these included in your numbers?

    • yuvalmillo Says:

      Tom, I did not include the ETFs because they usually, as far as I know, play a different role in most people’s portfolios (and clearing is also quite different). But, from a quick glance, the trend is very similar. That said, I still need to see what Peter means exactly in his point.

  16. Tom Nugent Says:

    Yuvalmillo

    If you look at the Options Clearing Corporation’s data (7 APR 11). ETF options volumes are up by 37%. Index options as a group rose by 6% in Q1 11. Within this the SPY (ETF)contracts trade 2.2m per day (S&P Index trade 666K). These are prefered over the S&P contracts as the bid/ask spreads perform better in volatile markets; they move a couple of cents versus much larger bid/ask spreads in the S&P index options. They are a growing feature of institutional portfolios. As such they should be included in the relevant data.

  17. Peter maas Says:

    Yuval – the exercise I suggest is calculating the daily change in value of the open interest in S&P options versus VIX options. I think the relative size of the changes will illustrate my point that the money invested and earned on S&P options dwarfs the amount committed to the VIX.

    Peter

  18. Tom Nugent Says:

    Daniel, Yuval

    Interesting short article on the possible role of vol hedging in mitigating market turbulence:

    “Not All Black Swans are Black Swans
    Is the market is becoming less volatile on pullbacks?”

    by Bernie Schaeffer (Schaeffer Investment Research 22 MAR 11 – available on site)

    Be interested on your take on this?


  19. Daniel and Yuval — According to this post today at FT Alphaville (http://is.gd/snVeHU) the market doesn’t yet have a good modelling approach for valuing Vix futures. Moreover, such an approach might be *impossible* (at least within the relative-value Black-Scholes paradigm) since you can’t replicate the payoffs of holding the Vix with its underlying:

    “While the VIX can be a great tool, and the VIX tradables (like futures and options) are quite liquid to trade, the spot VIX itself cannot be realistically replicated, as the execution/bid-offer costs are too high, and rolling the two strips every single day would be a logistical nightmare.” (qtd here: http://is.gd/BvqIeZ)

    Given that, it seems like a 1987-style feedback loop is pretty unlikely.

    I’d be interested to hear your thoughts.


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