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The lifecycle of exchange-traded derivatives
Journal of Commodity Markets xxx (2018) 1–22
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Journal of Commodity Markets journal homepage: www.elsevier.com/locate/jcomm
The lifecycle of exchange-traded derivatives Grant Cavanaugh a,*, Michael Penick b a b
Nephila Climate, 801 Larkspur Landing Circle, Larkspur, CA 94939, USA U.S. Commodity Futures Trading Commission, Office of the Chief Economist, 1155 21st Street, NW, Washington, DC 20581, USA
A R T I C L E
I N F O
JEL classification: Q020 G100
Keywords: Liquidity Trading Derivatives Financialization Bayesian inference Markov model
A B S T R A C T
Using a comprehensive dataset covering most derivatives trades reported to US exchanges since 1954, we present distributional estimates of the rate at which derivative trading volumes rise and fall. Results suggest that the lifecycle of cleared derivatives shifted in the 2000’s. Derivatives with low trading volumes moved to modest volumes with increased probability. Prior to that shift, less popular contracts were likely to remain at low volumes or be delisted altogether. This additional resilience from low levels of trading improved the trajectory of trading volumes for the marginal contract, despite the decade’s launch of a record number of new contracts and historic abundance of rarely traded contracts. The New York Mercantile Exchange, an exchange that shifted abruptly to electronic trading, provides some evidence that this shift was driven by new technology. We present our analysis as a non-stationary Markov model, estimated using Bayesian methods. This approach offers simple summary statistics to inform the launch of a new derivatives contract, organized in a model that describes the dynamics of the derivatives market as a whole. This facilitates distributional comparisons among historical groups of contracts (e.g. across time, exchange, or product type) as well as simulation of new derivatives emerging over time.
1. Introduction What are the chances that a new derivative will reach a sustainable level of liquidity? This is an important question for new contract innovators (Sandor, 1973). It also became an important question for policy makers as the United States crafted and implemented the Dodd-Frank reforms. With the stated aims of improving the stability and transparency of derivatives markets, those reforms envisioned regulatory changes that, according to industry participants, might shift trading activity away from swaps markets in favor of futures markets (Gensler, 2013). A 2011 white paper by the International Swaps and Derivatives Association described this shift and its potential adverse impacts on trading dynamics (ISDA Research Staff and NERA Economic Consulting, 2011). This policy debate was taking place in the absence of up-to-date empirical evidence on the lifecycle of derivatives and how that lifecycle has changed with recent shifts in the underlying structure of derivatives markets. Such shifts include electronic trading, the financialization of commodities markets, and the proliferation of new contracts. Silber (1981) and Carlton (1984) provided some of the first summary statistics on the survival of new futures contracts. Their core conclusions - that most new derivatives fail and that they do so soon after their launch - remained widely cited, when the U.S. Commodity Futures Trading Commission (CFTC) agreed to facilitate more comprehensive research on the subject in response to industry concerns (Gorton and Rouwenhorst, 2004; Hung et al., 2011).
* Corresponding author. E-mail addresses: [email protected] (G. Cavanaugh), [email protected] (M. Penick).
https://doi.org/10.1016/j.jcomm.2018.05.007 Received 27 June 2016; Received in revised form 15 May 2018; Accepted 16 May 2018 Available online XXX 2405-8513/© 2018 Published by Elsevier B.V.
Please cite this article in press as: Cavanaugh, G., Penick, M., The lifecycle of exchange-traded derivatives, Journal of Commodity Markets (2018), https:/doi.org/10.1016/j.jcomm.2018.05.007
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Researchers had previously identified correlates to high trading volumes within niches of the derivatives markets such as the size of the underlying spot market, the volatility of the contract, or the availability of cross-hedges (Black, 1986; Corkish et al., 1997; Brorsen and Fofana, 2001; Hung et al., 2011). There had also been case studies on the failures of individual markets to sustain high trading (Working, 1953; Sandor, 1973; Johnston and McConnell, 1989). Together, those informed theoretical models of the economic optimization process underlying contract innovation and subsequent trading (Cuny, 1993; Duffie and Jackson, 1989; Tashjian and Weissman, 1995; Pennings and Leuthold, 2001). But prior to Gorham and Kundu (2012), there had been few attempts to provide an empirical description of US derivatives trading in decades. Among the important findings in that work were:
• Since 1955, the average contract had a life span (longest stretch of non-zero trading) of six years. • A cluster of the most traded contracts to date were launched in the 1980’s. • US derivatives markets show a tendency toward liquidity-driven monopoly, with the dominant contract accounting for 95 percent of all trading within a product niche. Here we extend that work using a comprehensive dataset on cleared derivatives (futures, options, and swaps reported to the CFTC) augmented with data on historic futures absent from most electronic databases. The primary aim is to provide statistics necessary to inform policy and serve as base-rates for decision-making surrounding the launch or delisting of derivatives contracts (Kahneman and Tversky 1973, 1982; Bar-Hillel, 1980). Those statistics are offerd in the form of a Markov model, which estimates the probability of a contract trading within a ranges of annual volume given the previous year’s volume. This model allows for statistical comparisons of the trajectory of growth and decay of contracts over time and across many contract groups of interest such as exchanges and product categories. Previous studies have proposed many plausible explanations for the success of individual contracts. Our contribution to that literature is providing a full picture of how markets succeed. Our model also allows us to identify clusters of contracts growing (or decaying) at statistically distinct rates. In some cases, those clusters suggest causal factors such as the introduction of electronic trading. 2. Material and methods 2.1. Data The core data used here comes from the Futures Industry Association’s monthly and annual volume reports. These have been compiled since 1954 from exchange data and subsequently made available to the CFTC. To this, we have added monthly volumes reported to the CFTC under the US Commodity Exchange Act. This gives a near complete set of all futures contracts since 1956 (with annual data to 1954) and of regulated agricultural futures contracts back to 1940 (with annual data to 1931). We have also added information on unregulated contracts available in CFTC Annual Reports, historic log books from exchanges available in the CFTC library, and the CFTC’s internal database of futures contracts. The subset of that data used in this analysis covers 22993 total annual observations of 4658 distinct contracts across 42 exchanges; running between 1954 and 2012. Those values are broken down by year in Fig. 1. Including marginal product categories and exchanges provides a picture of the dynamics of the entire market over time and minimizes survivorship bias in the resulting statistics. New contracts or exchanges cannot know a priori which sub sample of the data will best reflect the path of their flagship contracts, so they should benefit from base-rates describing the full derivatives markets. Fig. 2 provides the empirical cumulative distribution function (ECDF) for the longest stretch of non-zero trading across all contracts. For roughly 50 percent of all contracts, the longest stretch of non-zero trading was three years or less. The comparable figure in Gorham and Kundu (2012) was six years, suggesting that the sample does include esoteric derivatives outside of the FIA’s reported futures. These numbers do not necessarily represent the time between launch and delisting. It is not possible to satisfactorily identify delisted contracts in the data. As we describe later, contracts at low trading volumes has been particularly resilient in recent years, so simple definitions of delisting might throw out many contracts that will continue to trade in the future. Also, the merger of exchanges means that many contracts are not in fact delisted when they cease reporting in the database, but are re-listed on new exchanges (Jouzaitis, 1987). Fig. 3 is the ECDF of annual trading volumes by contract for every year in the sample, with an overlay in color highlighting the ECDFs for each decade. In each figure, individual lines represent the ECDFs for a single year. Lines approaching a right angle in the upper left hand corner represent years with more concentrated trading. Each line’s y-intercept represents the percent of all contracts trading at a volume of 0. The ECDF for each year is colored chronologically, with the lines representing the oldest years in the sample in red and the most recent years in purple. In this graphic we see clear patterns in concentration over time. Markets grew more concentrated between the 1950’s and 1990’s with some retrenchment between the 1980’s and 1990’s. That trend reversed sharply in the 2000’s, with the annual ECDFs approaching a right angle. Not surprisingly most contracts trade at low volumes in any given year. However, that masks tremendous difference in the overall distribution of trading across the market. That difference is visible in Fig. 3, but comes into more stark relief in the time series in Fig. 4, displaying the trading volume for the median contract across time. The median contract’s trading volume was many times higher in the 1980’s and 1990’s than at any time before or after. 2
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Fig. 1. Sample summary statistics by year.
Fig. 2. Empirical cumulative distribution function of the longest stretch of non-zero trading for each contract.
Fig. 3 itself highlights one likely cause of the more recent shift - the explosion of innovation during the 2000’s. The ECDFs for the 2000’s are appreciably smoother than those of previous decades, with 2011 looking almost like a continuous function. This smoothness is due to the inclusion of additional contracts. Fig. 1 directly displays the number of contracts with annual reported volume (which is allowed to be zero) in the sample by year. It shows the same explosive trend in innovation discussed in Gorham and Kundu (2012), with over 3000 derivatives contracts reporting in 2011. 2.2. Model Our core results are presented in the form of Markov transition matrices (Markov, 1971). Given a derivative contract’s discrete state of annual trading volume today, it transitions to discrete states of annual trading volume in the following year according to probability vector 𝜃 (Volumelevelyear t+1 |Volumelevelyear t ). For contracts with non-zero trading volumes, the discrete state is equivalent to the common (base 10) logarithm of the annual trading, rounded down to the nearest integer. (For example, annual 3
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Fig. 3. Empirical cumulative distribution function of annual trading volumes by year, highlighted by decade.
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Fig. 4. Median trading volume by year.
trading of 10500 is assigned a volume level that groups it with all contract-years with volume ≥ 10000 and < 100000.) A special discrete state is reserved for annual trading of zero. 𝜃 describes discrete probabilities that can be represented using a Dirichlet distribution, commonly used for the probability of ending up in an exhaustive set of categorical states. This approach treats the underlying probabilities of moving between states of trading volume as randomly distributed parameters, as in equation (1). Volume levelyear t+1 ∣ Volume levelyear t ∼ Categorical(𝜃)
(1)
𝜃 ∼ Dirichlet(xvol level 0 , xvol level 1 , … , xvol level 108 )
This model is estimated using Bayesian methods via statistical modeling packages with standard implementations of a Dirichlet distribution. (Here we used STAN (Carpenter et al., 2016).) Binding the resulting vector 𝜃 for each current volume level provides a transition matrix for a discrete-state Markov model. The matrix describes the probability of moving from any volume level (indicated by the entry’s row) to any other volume level (indicated by the entry’s column). Delisting was not included as a separate state for two reasons. First, the data cannot distinguish between delisted contracts and those with zero trading volumes. Second, in a Markov model that includes a state from which a contract could not recover to non-zero trading (delisting), all contracts would eventually be delisted. With a Markov model, it is possible to multiply a vector describing the probability that a new derivative will start in any given state of trading volume by the transition matrix to produce a vector of probabilities that a new market will be any state over an arbitrary number of years. Multiplying the resulting probability vector by annual trading volumes corresponding to each possible state produces a probability-weighted approximation of the expected trading volume in that arbitrary year. All expected trading volumes are presented here at a ten-year horizon, but the Markov model is flexible in this regard. While a decade is an arbitrary lens for viewing the distributions of historical derivatives markets or making projections of future markets, Fig. 3 suggests that the horizon is sufficient to distinguish between distinct regimes in US derivatives markets. We do not assume that the transition matrix is stationary across time, so the resulting expected value estimates do not describe an equilibrium, only the general direction of the market. Note that the data does not allow us to control for changes in contract size, in circumstances where the re-sized contract continued to be reported identically to the CFTC. However, the focus on the analysis is on the dynamics with which contracts move between levels of liquidity and those levels of liquidity are factors of 10 apart from one another. So in a circumstance where an exchange begins with an annual volume of, for example, 100 and decides to halve its contract size with the hope of boosting volumes to 200, that shift would not register in the model. In circumstances where a one-time shift did push a contract across model levels, it would only register in the year of the change. Change point probabilities. For some research topics, such as the impact of electronic trading on specific exchanges, it is helpful to look at individual transition probabilities as they change year on year. The Markov model estimates stemming from equation (1), provide all the information necessary to determine if subsequent transition parameters are statistically distinct at a given level of probability. To provide more intuitive analysis, we have also presented specific results in the form of a change point model. We have taken blocks of simulated values of specific transition probabilities determined by equation (1), connected them as a time 5
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series, and run them through a Bayesian change point model in R, Erdman and Emerson (2007), based on models described in Barry and Hartigan (1993). For each point in the simulated time series Erdman and Emerson (2007) provides posterior estimates of the mean parameter value (the transition probability) as well as the probability that each point marks a transition between statistical regimes. Prior probabilities on moving between states of annual volume. The parameters x in equation (1) describe the probability of moving to any volume level in the subsequent year given a contract’s current state of trading. When estimating these parameters using Bayesian methods, x requires prior probability estimates. Those priors came from an informal survey of economists at the CFTC. That survey found beliefs corresponding roughly to:
• Probability of regressing one level of trading: Pr(Volumelevelyear t+1 = Volumelevelyear t − 1) = 0.16 • Probability of remaining at the same level of trading: Pr(Volumelevelyear t+1 = Volumelevelyear t ) = 0.63 • Probability of progressing one level of trading: Pr(Volumelevelyear t+1 = Volumelevelyear t + 1) = 0.14 The probability of a contract jumping more than one order of magnitude up or down was assigned a value of 0.01. In edge cases (Volumelevelyear t = 0 and Volumelevelyear t = 108 ) where a move up or down would take the contract below annual trading of 0 or to annual trading ≥ 109 , we combined the probabilities of moving up or down with the probability of remaining in the same state. Informative priors on transition probabilities, x, are preferable to flat or weak priors (equal weighting to the probability of a transition to any state) in this circumstance. Equally weighting all future states of trading biased estimation by assigning sub populations within the dataset (exchanges or product subgroups) with few observations a high baseline probability of jumping to extraordinary levels of trading.
3. Theory/calculation 3.1. Hypotheses about market dynamics adapted to a Markov model Previous literature has proposed hypotheses about derivatives market dynamics, and contract success in particular, that may be restated in the context of the present Markov model. Those hypotheses include:
• Winner-take-all trading: Many studies have suggested that contracts with high historic trading growth tend to sustain that trading in the future, either because they are managing the risk associated with large volatile underlying markets (Carlton, 1984; Tashjian, 1995; Black, 1986; Brorsen and Fofana, 2001; Hung et al., 2011; Corkish et al., 1997) or because there is a first mover effect in derivatives trading that make the first contract to gain some trading volume likely to dominate all future trading in similar risk (Cuny, 1993; Corkish et al., 1997; Gorham and Kundu, 2012). These hypotheses suggest that the Markov model should show high and sustained path dependence, with the probability of remaining in the current state of trading or progressing one level year on year high and the probability of jumping from modest levels of trading low. To the extent that this pattern increases/decreases over time, it may suggest that these hypothesized dynamics are more/less important driving factors. • Relative size of the exchange and the special properties of distinct product groups: Carlton (1984), Gorham and Kundu (2012), and Holder et al. (1999) highlight the relative success of specific exchanges and product groups. The relative variance of Markov transition matrices across exchanges, product groups, and time can show whether, for example, a single exchange is more likely to produce highly traded contracts or if its success, in retrospect, was driven more by factors outside the exchange’s control such as random chance or the era in which it operated. If, for example, the variance of important market dynamics is greater across time than across exchange or product type, then time was a more likely determinant of success than either exchange or product type. • Balance of hedging demand: Cuny (1993) and Duffie and Jackson (1989) propose that optimal contract design involves assessing hedger demand, with the former focused on net (|long − short|) and the latter on aggregate (|long| + |short|) demand balance. This assumes both that the designer is capable of making that assessment at the time they launch a contract, and that their assessment will continue to be valid over some reasonable time horizon. To the extent that the lifecycle of derivatives measured here shifts over time, that shortens the window of validity for this planning. • Correlated contracts: Duffie and Jackson (1989), Tashjian and Weissman (1995), and Pennings and Leuthold (2001) all provide theoretical discussions of an exchange’s decision to launch a new contract that is correlated with their existing contracts. One important input for that discussion is additional empirical information on the marginal cost of launching and servicing new contracts. The Markov model presented here can reveal growth dynamics that are suggestive of marginal costs being a binding consideration in the innovation of exchanges. To the extent that marginal costs are a constant and constraining consideration for exchanges, contract innovation is more likely to remain steady, tied to the underlying growth of the economy. An optimizing exchange might also shy away from correlated contracts, as proposed in Duffie and Jackson (1989), Tashjian and Weissman (1995), and Pennings and Leuthold (2001). Periods with explosive contract innovation (and more correlated contracts) hint at low marginal cost to new contracts. Such periods might follow the introduction of new technology.
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Table 1 Median estimates of transition matrix between volume states on full sample - with annual trading volume state in year t denoted by row, trading volume state in year t denoted by column.
4. Results 4.1. General market patterns and path dependence Table 1 presents the median estimates of transition probabilities across the full sample. They show high baseline path dependence and suggest a few important thresholds for market dynamics. Among contracts with an annual volume at or above 100, the single most likely outcome is to remain at their present state of trading year on year (see the diagonal of Table 1.) This pattern becomes more pronounced at higher levels of trading. This is consistent with the hypothesis that there are powerful network effects sustaining trading of already-popular contracts. Having reached annual trading in the 10000’s, a full collapse becomes relatively unlikely (4 percent.) In fact, the probability of progressing or regressing more than one level is below 10 percent. By contrast, less-traded contracts are jumpy. The probability of skipping a level of trading (high or low) raises to 49 percent for contracts trading in the double digits. Despite the clear path dependence, transitioning to higher trading levels never gets easy. At or above annual trading of 1000, the lower off-diagonal of the matrix is always higher than the upper off-diagonal, meaning that the marginal contract is always more likely to fall back in its trading than to progress forward.
Fig. 5. Expected volume of 10,000 simulated contracts after ten years, conditional on trading dynamics, grouped by exchange.
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Fig. 6. Expected volume of 10,000 simulated contracts after ten years, conditional on trading dynamics, grouped by product type.
4.2. The relative importance of time, exchange, and product type in determining the prospects for the marginal contract Previous studies suggested that individual exchanges, product categories, or decades might be particularly well-suited to producing blockbuster trading. But which is more influential to the marginal contract’s trading? The Markov model in equation (1) can answer one form of that question: which is more likely to produce higher or lower expected trading volumes over some horizon, a specific exchange/product category/decade or a randomly chosen exchange/product category/decade? Figs. 5–7 provide expected trading volumes for a marginal contract across individual exchanges, decades, and product subgroups against their randomly assembled benchmarks. To calculate those figures, we initialize trading based on each sub population’s historic probability of starting in each state, then multiplied that by ten randomly drawn transition matrices for that sub population. Finally, we multiplied each state by the lower bound of each trading range (zero, 1, 10, etc.) and summed the resulting vector. We repeated that procedure 10000 times for each sub population. In Figs. 5–7, as well as all of the similar graphics to follow, the median estimate of the posterior predictive distribution is noted by a dot, the 50 percent probability interval is in color, and the 95 percent high density interval (HDI) in black. The HDI is analogous to a frequentist 95 percent confidence interval insofar as it provides a standardized basis for assessing distributional differences. In this case, simulated sub-populations (such as samples across time or
Fig. 7. Expected volume of 10,000 simulated contracts after ten years, conditional on trading dynamics, grouped by trading decade.
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product category) whose HDIs (black lines) do not overlap are statistically distinct at the 95 percent probability level. The most important results of this exercise are:
• Most exchanges and product categories are indistinguishable (show overlapping HDIs) from their random benchmarks and from one another. Due to the large number of these sub populations, those trivial results were excluded from Figs. 5 and 6.
• While some of the largest exchanges are probabilistically distinct from one another, they are not distinct from a randomly selected exchange. The CME’s failure to distinguish itself is particularly interesting since Gorham and Kundu (2012) found that the CME lead other major exchanges in mean volume in the 5th year of trading, mean lifetime volume, and their approximations of present value discounted fee generation. • There were two notable exceptions to that pattern among exchanges: – The single-stock futures traded on OneChicago which showed particularly low expected trading volumes over ten years. – The two registered exchanges in the IntercontinentalExchange group, marked ICE and ICEU, likely have higher expected trading volumes than most other exchanges.
• Interest rates and natural gas were distinctly successful while single-stock futures and exchange traded weather were notably unsuccessful.
• The expected trading volume after 10 years for a contract has varied substantially across time, jumping up or down from decade to decade.
• While many decades were distinct from one another, only the 1980’s looks to be a particularly auspicious time for the marginal contract.
• The period between 1980 and 2010 was particularly volatile for market dynamics. The marginal contract rose to higher trading in the 1980’s, plummeted in the 1990’s, and recovered to the middle of that range in the 2000’s.
• In the 2000’s, low volume contracts tended to rise to modest levels of trading balancing any fall in the probability of reaching the highest trading levels.
4.3. Market dynamics over time Figs. 8–10 show probabilities of individual contracts moving between volume levels in a given year t (indicated by the row of estimates) and volume levels in year t + 1 (indicated by the column of the estimate) based on draws from the posterior predictive distribution of the model described by equation (1). As before, the dots in the figure indicate median parameter estimates, the colored band indicates the 50 percent probability range, and the black line indicates the 95 percent probability range. Despite the volatility in Fig. 7, no decade shows meaningful deviation from the general story that emerges from Table 1. There was substantial inertia, keeping contracts at their current level of trading and this inertia is stronger at both the highest and lowest levels of trading. Weakening path dependence in the 2000’s. However, the degree to which the transition matrix supports the story in Table 1 (as well as Silber (1981) and Carlton (1984)), changed remarkably in the 2000’s (See the top rows of Fig. 8.). The inertia trapping less-traded contracts is lower than in previous decades, with the median probability of a contract at an annual volume of zero remaining at zero falling to 70 percent (Fig. 11). While zero volume contracts remained unlikely to rise to higher volume levels in absolute terms, contracts with no current trading were not doomed to remain untraded as in the past. (Their 95 percent probability interval for remaining untraded was lower in the 2000’s than in recent decades. That probability interval did not overlap with those from recent decades, suggesting the difference holds with high probability.) How did contracts recovering from zero trading perform? While a year without trading no longer trapped contracts in the 2000’s, the decade did not see a complete reversal of conventional wisdom about trading volumes. Untraded contracts remained very unlikely to become blockbusters. Contracts were more likely to jump from an annual trading volume of 0 to trading volumes between 10 and 1000 than in previous decades (See top row of Fig. 8.). The 2000’s stands out as a period where there was tremendous contract innovation (see Fig. 1.) Most of that innovation produced no trading in any given year (see Fig. 3.) But in a clear break with the past, the derivatives markets of the 2000’s were relatively likely to subsequently use a contract that had gone without trading for a year. This further obscures our ability to identify candidates for delisting from trading volumes alone. Blockbuster contract trading by decade. If derivatives markets changed to encourage innovation in the 2000’s, did the market also change in its ability to create and sustain blockbuster contracts, those with the highest levels of annual trading volumes? Having reached annual trading volumes in the 10’s or 100’s (row 1, column 4 of Fig. 9), contracts in the decade of the 2000’s were again substantially more likely to continue increasing their trading volume in the 2000’s than in the 1980’s or 1990’s. Only after reaching trading volumes in the 1000’s (row 2, column 5 of Fig. 9) did the probability of an individual contract progressing to higher levels of annual trading volume fall roughly back within the same range as those from previous decades. In general, in the 2000’s contracts moved up to annual trading in the 1000’s with an ease not seen in previous decades. Some of the flexibility gained for contracts at lower levels of trading may have come at the expense of contracts at mid to high levels of trading. Contracts trading in the 10000’s were 8 percent more likely to fall back to lower levels of annual volumes in the 2000’s than in previous decades, a difference that holds with high probability (row 3, column 5 of Fig. 9). However, Fig. 7
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Fig. 8. Transition matrix for Markov model of derivatives contract moving between states of annual trading volume by decade: low initial trading.
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Fig. 9. Transition matrix for Markov model of derivatives contract moving between states of annual trading volume by decade: moderate initial trading.
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Fig. 10. Transition matrix for Markov model of derivatives contract moving between states of annual trading volume by decade: high initial trading.
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Fig. 11. Probability of remaining at annual volume of zero from year to year by decade.
indicates that this retrenchment was not enough, on balance, to lower the prospects of a new contract over the course of ten years. Interestingly, no decade provided the marginal contract with a distinct advantage in moving across the important threshold of 10000, discussed above. 4.4. The introduction of electronic trading The shifts in the lifecycle of derivatives in the 2000’s are consistent with the hypothesis that electronic trading made trading activity more mobile across derivatives markets and substantially cut the costs of launching and sustaining a derivatives contract. However, given the myriad changes to the structure of US exchanges that took place during the 2000’s, it is difficult to isolate the
Fig. 12. Bayesian change point probability run on 1000 random samples per year of the NYMEX’s probability of remaining at volume level 100 year on year. Black line shows change point probability. Colored points show posterior mean estimates.
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Fig. 13. Bayesian change point probability run on 1000 random samples per year of the NYMEX’s probability of remaining at volume level 1000 year on year. Black line shows change point probability. Colored points show posterior mean estimates.
influence of electronic trading by looking at trading on a decade by decade basis alone. Instead, we need to look at the individual exchange level for a circumstance where electronic trading was introduced suddenly. That was the case for the New York Mercantile Exchange (generally called NYMEX, but registered as NYME in CFTC databases and in various graphics here), which abruptly switched from open-outcry to electronic trading in 2006. This transition was followed closely by the NYMEX’s merger with the Chicago Mercantile Exchange (CME), announced in March 2008 and finalized September 2009. Since that merger may have also changed the exchange’s dynamics (new systems and network effects might change transition probabilities), it is helpful to compare the NYMEX to the Chicago Board of Trade (CBT), another large exchange that also merged with the CME (announced in October 2006 and finalized in January 2008) and might show similar transition dynamics if the CME’s systems and scale are driving trading volume. The CBT’s transition matrices (Figs. 17–19) show no consistent trends in post-merger years relative to the earlier years in the sample. To the extent that the CBT shows any post-merger trend, it stems from 2010, an especially volatile year for the CBT, where many contracts advanced to trading in the tens of thousands and a particularly large percentage fell back from annual volumes in the tens of thousands. The CME merger did not drive trading dynamics in any particular direction and/or to a degree that overrode other factors, as might be expected if the CME held the special advantage over other exchanges hinted at by summary statistics of the exchange’s success (Gorham and Kundu, 2012). By contrast, the NYMEX, does show a trend in its transition probabilities which predates, and is uninterrupted by, the CME merger. Sometime in the latter half of the decade, the trading levels 10 through 10000 become sinks for NYMEX contracts (Fig. 15). The probability of staying at these levels year on year increases gradually, shown in row three of Fig. 14, all rows of Fig. 15, and row 1 of Fig. 16). Figs. 12 and 13 show these dynamics in greater detail in the form of a Bayesian change point model run on posterior simulations of the key parameters. Following noisy years at the beginning of the decade, year on year transitions are distinct, indicated by a clear spike in the change point probability between blocks of 1000 annual simulations. This happens while mean parameter estimates show a general upward trend over the latter half of the decade. 2007, the first year of fully electronic trading, is statistically distinct from 2006. But given the general volatility of these parameters over time, this should be taken only as modest evidence in favor of the hypothesis that the transition to electronic trading is a causal factor. Meanwhile, the probability of rising to higher levels of trading falls on the NYMEX. At levels 100000 and above, contracts showed a time trend with falling back more likely at the expense of them staying put or rising (row 1, columns 6 through 8 and row 2, columns 7 columns 7 through 9 of Fig. 15). The pattern on the NYMEX is an exaggerated form of one we see in the 2000’s across markets: contracts rise easily from low to modest trading while falling more easily from high to modest trading. It accelerated on over a window in time that is consistent with the hypothesis that electronic trading played a determining causal factor. Meanwhile, the same trend is not present on the CBT, which like the NYMEX, merged with the CME over this period and consequently helps us to tease apart the influence of the CME itself. These parallel trends favor electronic trading as a causal factor in derivatives trading over the decade as a whole and they echo the earlier finding that time is generally a more effective lens for distinguishing different market regimes than exchange. 14
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Fig. 14. NYME’s transition matrix for Markov model of derivatives contract moving between states of annual trading volume by year: low initial trading.
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Fig. 15. NYME’s transition matrix for Markov model of derivatives contract moving between states of annual trading volume by decade: moderate initial trading.
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Fig. 16. NYME’s transition matrix for Markov model of derivatives contract moving between states of annual trading volume by decade: high initial trading.
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Fig. 17. CBT’s transition matrix for Markov model of derivatives contract moving between states of annual trading volume by year: low initial trading.
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Fig. 18. CBT’s transition matrix for Markov model of derivatives contract moving between states of annual trading volume by decade: moderate initial trading.
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Fig. 19. CBT’s transition matrix for Markov model of derivatives contract moving between states of annual trading volume by decade: high initial trading.
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5. Conclusions In this article we have presented an analysis of trading volumes for derivatives reported to exchanges in the United States. In addition to providing comprehensive summary statistics on derivatives markets, we have also modeled the lifecycle of derivatives, the dynamics with which trading in a given contract across time, exchanges, and product categories. Starting in the 2000’s the lifecycle of derivatives changed in ways that run counter to heuristics that emerged from earlier studies. While a larger percentage of contracts had little or no volume in any given year of the 2000’s, contracts did not fail at the high rates noted in previous analyses. Instead, they remained at low levels of trading until they were needed, transitioning back into active trading with greater probability than in previous decades. This flexibility was important enough that it effectively buoyed the prospects for the marginal contract during a period when the number of new contracts exploded and the likelihood of blockbuster contracts waned. Trading data covering the NYMEX, an exchange that introduced electronic trading suddenly, provides support for the hypothesis that these shifting dynamics were driven by the introduction of electronic trading. While a small handful of exchanges and product types showed a consistent tendency toward elevated or diminished trading, the vast majority were indistinguishable from their peers. This suggests that retrospective explanations of contract success or failure are likely to overemphasize the role of a specific exchange or product type. By contrast, successive decades show remarkable volatility in the prospects for a marginal contract. The 1980’s in particular was a period well distinguished from a randomly chosen decade, with very high expected trading volumes for new contracts. Despite the diversity of market dynamics across time and some exchanges/product groups, the winner-take-all nature of derivatives markets noted in previous literature remains relatively constant. Across exchanges, product types, and decades the single most likely outcome for a contract year on year is that it will remain where it was trading. This is the same incumbency bias noted in previous literature. Our analysis also affirms the common observation that it is unusual for a contract to experience initial popularity and to crash subsequently (Johnston and McConnell, 1989). After reaching a trading volume in the tens of thousands, the probability that a contract will have annual trading volume of zero in the subsequent year drops appreciably. We presented these results in the form of a Markov model. That framework for looking at derivatives trading facilitates quick distributional comparisons across various contract groupings (e.g. decade and exchange). It also allows for subsequent research to extend our results to many basic questions about derivative markets beyond the scope of this article. For example, a quick examination of the Markov models produced here suggests that trading volumes do not follow a normal or log-normal random walk over time, as the dynamics of trading vary greatly conditional on starting volume. Furthermore, switches to higher and lower levels of trading are often not symmetric. In particular, an outright crash to zero trading volume appears more likely than would be predicted by a symmetrically distributed random walk. Empirical extensions of this work might incorporate data from bilateral trading. In the 1990’s and 2000’s trading that might have historically taken place on a futures market moved to over-the-counter markets. Many of those trades were eventually reported to an exchange (“swaps-to-futures” trades) and, hence, included in this analysis. But the most bespoke transactions remained bilateral. In some cases that data on bilateral transactions would yield distinct trade dynamics from those presented here. For example, the market for highly customized weather risk management has continued to grow even as exchange traded weather derivatives have been delisted (Evans, 2016). Theoretical extensions might focus on the nature of derivatives as economic goods. With very low marginal costs and high network effects, derivatives resemble many of the economic goods where use and distribution have been transformed by the internet. For example, the weakening path dependence and explosive rates of innovation detailed here bare a qualitative similarity to those observed in the market for digital music (Anderson, 2006).
References Anderson, Chris, 2006. The Long Tail: Why the Future of Business Is Selling Less of More. Hyperion Books. Bar-Hillel, Maya, 1980. The base-rate fallacy in probability judgments. Acta Psychol. 44 (3), 211–233. Barry, Daniel, Hartigan, John A., 1993. A Bayesian analysis for change point problems. J. Am. Stat. Assoc. 88 (421), 309–319. Black, D.G., 1986. Success and Failure of Futures Contracts: Theory and Empirical Evidence. New York University. Graduate School of Business Administration. Salomon Brothers Center for the Study of Financial Institutions, New York. Brorsen, B.W., Fofana, N.F., 2001. Success and failure of agricultural futures contracts. J. Agribus. 19 (2), 129–146 The Agricultural Economics Association of Georgia. Carlton, D.W., 1984. Futures markets: their purpose, their history, their growth, their successes and failures. J. Futures Mark. 4 (3), 237–271 Wiley Online Library. Carpenter, Bob, Gelman, Andrew, Hoffman, Matt, Lee, Daniel, Goodrich, Ben, Betancourt, Michael, Brubaker, Michael A., Guo, Jiqiang, Li, Peter, Riddell, Allen, 2016. Stan: a probabilistic programming language. J. Stat. Software 20, 1–37. Corkish, Jo, Holland, Allison, Vila, Anne, 1997. The Determinants of Successful Financial Innovation: an Empirical Analysis of Futures Innovation on Liffe. Cuny, C.J., 1993. The role of liquidity in futures market innovations. Rev. Financ. Stud. 6 (1), 57–78 Soc Financial Studies. Duffie, D., Jackson, M.O., 1989. Optimal innovation of futures contracts. Rev. Financ. Stud. 2 (3), 275–296. Erdman, Chandra, Emerson, John W., 2007. Bcp: an R package for performing a Bayesian analysis of change point problems. J. Stat. Software. 23 (3), 1–13, http:// www.jstatsoft.org/v23/i03/. Evans, Steve, 2016. Barney Schauble, Nephila Capital on Weather Risks as Ils Assets. Artemis.bm August 23, 2016 http://www.artemis.bm/blog/2016/08/23/barneyschauble-nephila-capital-on-weather-risks-as-ils-assets/. Gensler, Gary, 2013. Testimony of Gary Gensler, Chairman, Commodity Futures Trading Commission before the U.S. Senate Banking, Housing and Urban Affairs Committee, Washington, Dc. february http://www.cftc.gov/PressRoom/SpeechesTestimony/opagensler-131. Gorham, Michael, Kundu, Poulomi, 2012. A half-century of product innovation and competition at U.S. Futures exchanges. Rev. Futures Mark. 20, 105–140 (july). Gorton, G., Rouwenhorst, K.G., 2004. Facts and Fantasies about Commodity Futures. National Bureau of Economic Research.
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Holder, M., Tomas, M., Webb, R., 1999. Winners and losers: recent competition among futures exchanges for equivalent financial contracts. Deriv. Q. 6 (2), 19. Hung, M.W., Lin, B.H., Huang, Y.C., Chou, J.H., 2011. Determinants of futures contract success: empirical examinations for the Asian futures markets. Int. Rev. Econ. Finance 20 (3), 452–458 Elsevier. ISDA Research Staff, NERA Economic Consulting, 2011. Costs and Benefits of Mandatory Electronic Execution Requirements for Interest Rate Products. Discussion Paper 2. International Swaps; Derivatives Association https://www2.isda.org/attachment/MzczMw==/ISDA%20Mandatory%20Electronic%20Execution%20 Discussion%20Paper.pdf. Johnston, E.T., McConnell, J.J., 1989. Requiem for a market: an analysis of the rise and fall of a financial futures contract. Rev. Financ. Stud. 2 (1), 1–23 Soc Financial Studies. Jouzaitis, C., 1987. Rice Market Goes Snap, Crackle, Pop. Chicago Tribune October 12, 1987 http://articles.chicagotribune.com/1987-10-12/business/8703170257_ 1_rice-futures-marketing-loan-program-trading. Kahneman, Daniel, Tversky, Amos, 1973. On the psychology of prediction. Psychol. Rev. 80 (4), 237 American Psychological Association. Kahneman, Daniel, Tversky, Amos, 1982. Evidential Impact of Base Rates. Judgement Under Uncertainty: Heuristics and Biases. Cambridge University Press, pp. 153–160. Markov, Andrey, 1971. Extension of the Limit Theorems of Probability Theory to a Sum of Variables Connected in a Chain. Reprinted in Appendix B of: R. Howard. Dynamic Probabilistic Systems, vol. 1. Markov Chains. John Wiley & Sons, Inc. Pennings, J.M.E., Leuthold, R., 2001. Introducing new futures contracts: reinforcement versus Cannibalism. J. Int. Money Finance 20 (5), 659–675 Elsevier. Sandor, Richard L., 1973. Innovation by an exchange: a case study of the development of the plywood futures contract. J. Law Econ. 16 (1), 119–136 The University of Chicago Law School. Silber, W.L., 1981. Innovation, competition, and new contract design in futures markets. J. Futures Mark. 1 (2), 123–155 Wiley Online Library. Tashjian, E., 1995. Optimal futures contract design. Q. Rev. Econ. Finance 35 (2), 153–162 Elsevier. Tashjian, E., Weissman, M., 1995. Advantages to competing with yourself: why an exchange might design futures contracts with correlated payoffs. J. Financ. Intermediation 4 (2), 133–157 Elsevier. Working, H., 1953. Futures trading and hedging. Am. Econ. Rev. 3 (3), 314–343 JSTOR.
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Contents lists available at ScienceDirect
Journal of Commodity Markets journal homepage: www.elsevier.com/locate/jcomm
The lifecycle of exchange-traded derivatives Grant Cavanaugh a,*, Michael Penick b a b
Nephila Climate, 801 Larkspur Landing Circle, Larkspur, CA 94939, USA U.S. Commodity Futures Trading Commission, Office of the Chief Economist, 1155 21st Street, NW, Washington, DC 20581, USA
A R T I C L E
I N F O
JEL classification: Q020 G100
Keywords: Liquidity Trading Derivatives Financialization Bayesian inference Markov model
A B S T R A C T
Using a comprehensive dataset covering most derivatives trades reported to US exchanges since 1954, we present distributional estimates of the rate at which derivative trading volumes rise and fall. Results suggest that the lifecycle of cleared derivatives shifted in the 2000’s. Derivatives with low trading volumes moved to modest volumes with increased probability. Prior to that shift, less popular contracts were likely to remain at low volumes or be delisted altogether. This additional resilience from low levels of trading improved the trajectory of trading volumes for the marginal contract, despite the decade’s launch of a record number of new contracts and historic abundance of rarely traded contracts. The New York Mercantile Exchange, an exchange that shifted abruptly to electronic trading, provides some evidence that this shift was driven by new technology. We present our analysis as a non-stationary Markov model, estimated using Bayesian methods. This approach offers simple summary statistics to inform the launch of a new derivatives contract, organized in a model that describes the dynamics of the derivatives market as a whole. This facilitates distributional comparisons among historical groups of contracts (e.g. across time, exchange, or product type) as well as simulation of new derivatives emerging over time.
1. Introduction What are the chances that a new derivative will reach a sustainable level of liquidity? This is an important question for new contract innovators (Sandor, 1973). It also became an important question for policy makers as the United States crafted and implemented the Dodd-Frank reforms. With the stated aims of improving the stability and transparency of derivatives markets, those reforms envisioned regulatory changes that, according to industry participants, might shift trading activity away from swaps markets in favor of futures markets (Gensler, 2013). A 2011 white paper by the International Swaps and Derivatives Association described this shift and its potential adverse impacts on trading dynamics (ISDA Research Staff and NERA Economic Consulting, 2011). This policy debate was taking place in the absence of up-to-date empirical evidence on the lifecycle of derivatives and how that lifecycle has changed with recent shifts in the underlying structure of derivatives markets. Such shifts include electronic trading, the financialization of commodities markets, and the proliferation of new contracts. Silber (1981) and Carlton (1984) provided some of the first summary statistics on the survival of new futures contracts. Their core conclusions - that most new derivatives fail and that they do so soon after their launch - remained widely cited, when the U.S. Commodity Futures Trading Commission (CFTC) agreed to facilitate more comprehensive research on the subject in response to industry concerns (Gorton and Rouwenhorst, 2004; Hung et al., 2011).
* Corresponding author. E-mail addresses: [email protected] (G. Cavanaugh), [email protected] (M. Penick).
https://doi.org/10.1016/j.jcomm.2018.05.007 Received 27 June 2016; Received in revised form 15 May 2018; Accepted 16 May 2018 Available online XXX 2405-8513/© 2018 Published by Elsevier B.V.
Please cite this article in press as: Cavanaugh, G., Penick, M., The lifecycle of exchange-traded derivatives, Journal of Commodity Markets (2018), https:/doi.org/10.1016/j.jcomm.2018.05.007
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Researchers had previously identified correlates to high trading volumes within niches of the derivatives markets such as the size of the underlying spot market, the volatility of the contract, or the availability of cross-hedges (Black, 1986; Corkish et al., 1997; Brorsen and Fofana, 2001; Hung et al., 2011). There had also been case studies on the failures of individual markets to sustain high trading (Working, 1953; Sandor, 1973; Johnston and McConnell, 1989). Together, those informed theoretical models of the economic optimization process underlying contract innovation and subsequent trading (Cuny, 1993; Duffie and Jackson, 1989; Tashjian and Weissman, 1995; Pennings and Leuthold, 2001). But prior to Gorham and Kundu (2012), there had been few attempts to provide an empirical description of US derivatives trading in decades. Among the important findings in that work were:
• Since 1955, the average contract had a life span (longest stretch of non-zero trading) of six years. • A cluster of the most traded contracts to date were launched in the 1980’s. • US derivatives markets show a tendency toward liquidity-driven monopoly, with the dominant contract accounting for 95 percent of all trading within a product niche. Here we extend that work using a comprehensive dataset on cleared derivatives (futures, options, and swaps reported to the CFTC) augmented with data on historic futures absent from most electronic databases. The primary aim is to provide statistics necessary to inform policy and serve as base-rates for decision-making surrounding the launch or delisting of derivatives contracts (Kahneman and Tversky 1973, 1982; Bar-Hillel, 1980). Those statistics are offerd in the form of a Markov model, which estimates the probability of a contract trading within a ranges of annual volume given the previous year’s volume. This model allows for statistical comparisons of the trajectory of growth and decay of contracts over time and across many contract groups of interest such as exchanges and product categories. Previous studies have proposed many plausible explanations for the success of individual contracts. Our contribution to that literature is providing a full picture of how markets succeed. Our model also allows us to identify clusters of contracts growing (or decaying) at statistically distinct rates. In some cases, those clusters suggest causal factors such as the introduction of electronic trading. 2. Material and methods 2.1. Data The core data used here comes from the Futures Industry Association’s monthly and annual volume reports. These have been compiled since 1954 from exchange data and subsequently made available to the CFTC. To this, we have added monthly volumes reported to the CFTC under the US Commodity Exchange Act. This gives a near complete set of all futures contracts since 1956 (with annual data to 1954) and of regulated agricultural futures contracts back to 1940 (with annual data to 1931). We have also added information on unregulated contracts available in CFTC Annual Reports, historic log books from exchanges available in the CFTC library, and the CFTC’s internal database of futures contracts. The subset of that data used in this analysis covers 22993 total annual observations of 4658 distinct contracts across 42 exchanges; running between 1954 and 2012. Those values are broken down by year in Fig. 1. Including marginal product categories and exchanges provides a picture of the dynamics of the entire market over time and minimizes survivorship bias in the resulting statistics. New contracts or exchanges cannot know a priori which sub sample of the data will best reflect the path of their flagship contracts, so they should benefit from base-rates describing the full derivatives markets. Fig. 2 provides the empirical cumulative distribution function (ECDF) for the longest stretch of non-zero trading across all contracts. For roughly 50 percent of all contracts, the longest stretch of non-zero trading was three years or less. The comparable figure in Gorham and Kundu (2012) was six years, suggesting that the sample does include esoteric derivatives outside of the FIA’s reported futures. These numbers do not necessarily represent the time between launch and delisting. It is not possible to satisfactorily identify delisted contracts in the data. As we describe later, contracts at low trading volumes has been particularly resilient in recent years, so simple definitions of delisting might throw out many contracts that will continue to trade in the future. Also, the merger of exchanges means that many contracts are not in fact delisted when they cease reporting in the database, but are re-listed on new exchanges (Jouzaitis, 1987). Fig. 3 is the ECDF of annual trading volumes by contract for every year in the sample, with an overlay in color highlighting the ECDFs for each decade. In each figure, individual lines represent the ECDFs for a single year. Lines approaching a right angle in the upper left hand corner represent years with more concentrated trading. Each line’s y-intercept represents the percent of all contracts trading at a volume of 0. The ECDF for each year is colored chronologically, with the lines representing the oldest years in the sample in red and the most recent years in purple. In this graphic we see clear patterns in concentration over time. Markets grew more concentrated between the 1950’s and 1990’s with some retrenchment between the 1980’s and 1990’s. That trend reversed sharply in the 2000’s, with the annual ECDFs approaching a right angle. Not surprisingly most contracts trade at low volumes in any given year. However, that masks tremendous difference in the overall distribution of trading across the market. That difference is visible in Fig. 3, but comes into more stark relief in the time series in Fig. 4, displaying the trading volume for the median contract across time. The median contract’s trading volume was many times higher in the 1980’s and 1990’s than at any time before or after. 2
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Fig. 1. Sample summary statistics by year.
Fig. 2. Empirical cumulative distribution function of the longest stretch of non-zero trading for each contract.
Fig. 3 itself highlights one likely cause of the more recent shift - the explosion of innovation during the 2000’s. The ECDFs for the 2000’s are appreciably smoother than those of previous decades, with 2011 looking almost like a continuous function. This smoothness is due to the inclusion of additional contracts. Fig. 1 directly displays the number of contracts with annual reported volume (which is allowed to be zero) in the sample by year. It shows the same explosive trend in innovation discussed in Gorham and Kundu (2012), with over 3000 derivatives contracts reporting in 2011. 2.2. Model Our core results are presented in the form of Markov transition matrices (Markov, 1971). Given a derivative contract’s discrete state of annual trading volume today, it transitions to discrete states of annual trading volume in the following year according to probability vector 𝜃 (Volumelevelyear t+1 |Volumelevelyear t ). For contracts with non-zero trading volumes, the discrete state is equivalent to the common (base 10) logarithm of the annual trading, rounded down to the nearest integer. (For example, annual 3
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Fig. 3. Empirical cumulative distribution function of annual trading volumes by year, highlighted by decade.
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Fig. 4. Median trading volume by year.
trading of 10500 is assigned a volume level that groups it with all contract-years with volume ≥ 10000 and < 100000.) A special discrete state is reserved for annual trading of zero. 𝜃 describes discrete probabilities that can be represented using a Dirichlet distribution, commonly used for the probability of ending up in an exhaustive set of categorical states. This approach treats the underlying probabilities of moving between states of trading volume as randomly distributed parameters, as in equation (1). Volume levelyear t+1 ∣ Volume levelyear t ∼ Categorical(𝜃)
(1)
𝜃 ∼ Dirichlet(xvol level 0 , xvol level 1 , … , xvol level 108 )
This model is estimated using Bayesian methods via statistical modeling packages with standard implementations of a Dirichlet distribution. (Here we used STAN (Carpenter et al., 2016).) Binding the resulting vector 𝜃 for each current volume level provides a transition matrix for a discrete-state Markov model. The matrix describes the probability of moving from any volume level (indicated by the entry’s row) to any other volume level (indicated by the entry’s column). Delisting was not included as a separate state for two reasons. First, the data cannot distinguish between delisted contracts and those with zero trading volumes. Second, in a Markov model that includes a state from which a contract could not recover to non-zero trading (delisting), all contracts would eventually be delisted. With a Markov model, it is possible to multiply a vector describing the probability that a new derivative will start in any given state of trading volume by the transition matrix to produce a vector of probabilities that a new market will be any state over an arbitrary number of years. Multiplying the resulting probability vector by annual trading volumes corresponding to each possible state produces a probability-weighted approximation of the expected trading volume in that arbitrary year. All expected trading volumes are presented here at a ten-year horizon, but the Markov model is flexible in this regard. While a decade is an arbitrary lens for viewing the distributions of historical derivatives markets or making projections of future markets, Fig. 3 suggests that the horizon is sufficient to distinguish between distinct regimes in US derivatives markets. We do not assume that the transition matrix is stationary across time, so the resulting expected value estimates do not describe an equilibrium, only the general direction of the market. Note that the data does not allow us to control for changes in contract size, in circumstances where the re-sized contract continued to be reported identically to the CFTC. However, the focus on the analysis is on the dynamics with which contracts move between levels of liquidity and those levels of liquidity are factors of 10 apart from one another. So in a circumstance where an exchange begins with an annual volume of, for example, 100 and decides to halve its contract size with the hope of boosting volumes to 200, that shift would not register in the model. In circumstances where a one-time shift did push a contract across model levels, it would only register in the year of the change. Change point probabilities. For some research topics, such as the impact of electronic trading on specific exchanges, it is helpful to look at individual transition probabilities as they change year on year. The Markov model estimates stemming from equation (1), provide all the information necessary to determine if subsequent transition parameters are statistically distinct at a given level of probability. To provide more intuitive analysis, we have also presented specific results in the form of a change point model. We have taken blocks of simulated values of specific transition probabilities determined by equation (1), connected them as a time 5
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series, and run them through a Bayesian change point model in R, Erdman and Emerson (2007), based on models described in Barry and Hartigan (1993). For each point in the simulated time series Erdman and Emerson (2007) provides posterior estimates of the mean parameter value (the transition probability) as well as the probability that each point marks a transition between statistical regimes. Prior probabilities on moving between states of annual volume. The parameters x in equation (1) describe the probability of moving to any volume level in the subsequent year given a contract’s current state of trading. When estimating these parameters using Bayesian methods, x requires prior probability estimates. Those priors came from an informal survey of economists at the CFTC. That survey found beliefs corresponding roughly to:
• Probability of regressing one level of trading: Pr(Volumelevelyear t+1 = Volumelevelyear t − 1) = 0.16 • Probability of remaining at the same level of trading: Pr(Volumelevelyear t+1 = Volumelevelyear t ) = 0.63 • Probability of progressing one level of trading: Pr(Volumelevelyear t+1 = Volumelevelyear t + 1) = 0.14 The probability of a contract jumping more than one order of magnitude up or down was assigned a value of 0.01. In edge cases (Volumelevelyear t = 0 and Volumelevelyear t = 108 ) where a move up or down would take the contract below annual trading of 0 or to annual trading ≥ 109 , we combined the probabilities of moving up or down with the probability of remaining in the same state. Informative priors on transition probabilities, x, are preferable to flat or weak priors (equal weighting to the probability of a transition to any state) in this circumstance. Equally weighting all future states of trading biased estimation by assigning sub populations within the dataset (exchanges or product subgroups) with few observations a high baseline probability of jumping to extraordinary levels of trading.
3. Theory/calculation 3.1. Hypotheses about market dynamics adapted to a Markov model Previous literature has proposed hypotheses about derivatives market dynamics, and contract success in particular, that may be restated in the context of the present Markov model. Those hypotheses include:
• Winner-take-all trading: Many studies have suggested that contracts with high historic trading growth tend to sustain that trading in the future, either because they are managing the risk associated with large volatile underlying markets (Carlton, 1984; Tashjian, 1995; Black, 1986; Brorsen and Fofana, 2001; Hung et al., 2011; Corkish et al., 1997) or because there is a first mover effect in derivatives trading that make the first contract to gain some trading volume likely to dominate all future trading in similar risk (Cuny, 1993; Corkish et al., 1997; Gorham and Kundu, 2012). These hypotheses suggest that the Markov model should show high and sustained path dependence, with the probability of remaining in the current state of trading or progressing one level year on year high and the probability of jumping from modest levels of trading low. To the extent that this pattern increases/decreases over time, it may suggest that these hypothesized dynamics are more/less important driving factors. • Relative size of the exchange and the special properties of distinct product groups: Carlton (1984), Gorham and Kundu (2012), and Holder et al. (1999) highlight the relative success of specific exchanges and product groups. The relative variance of Markov transition matrices across exchanges, product groups, and time can show whether, for example, a single exchange is more likely to produce highly traded contracts or if its success, in retrospect, was driven more by factors outside the exchange’s control such as random chance or the era in which it operated. If, for example, the variance of important market dynamics is greater across time than across exchange or product type, then time was a more likely determinant of success than either exchange or product type. • Balance of hedging demand: Cuny (1993) and Duffie and Jackson (1989) propose that optimal contract design involves assessing hedger demand, with the former focused on net (|long − short|) and the latter on aggregate (|long| + |short|) demand balance. This assumes both that the designer is capable of making that assessment at the time they launch a contract, and that their assessment will continue to be valid over some reasonable time horizon. To the extent that the lifecycle of derivatives measured here shifts over time, that shortens the window of validity for this planning. • Correlated contracts: Duffie and Jackson (1989), Tashjian and Weissman (1995), and Pennings and Leuthold (2001) all provide theoretical discussions of an exchange’s decision to launch a new contract that is correlated with their existing contracts. One important input for that discussion is additional empirical information on the marginal cost of launching and servicing new contracts. The Markov model presented here can reveal growth dynamics that are suggestive of marginal costs being a binding consideration in the innovation of exchanges. To the extent that marginal costs are a constant and constraining consideration for exchanges, contract innovation is more likely to remain steady, tied to the underlying growth of the economy. An optimizing exchange might also shy away from correlated contracts, as proposed in Duffie and Jackson (1989), Tashjian and Weissman (1995), and Pennings and Leuthold (2001). Periods with explosive contract innovation (and more correlated contracts) hint at low marginal cost to new contracts. Such periods might follow the introduction of new technology.
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Table 1 Median estimates of transition matrix between volume states on full sample - with annual trading volume state in year t denoted by row, trading volume state in year t denoted by column.
4. Results 4.1. General market patterns and path dependence Table 1 presents the median estimates of transition probabilities across the full sample. They show high baseline path dependence and suggest a few important thresholds for market dynamics. Among contracts with an annual volume at or above 100, the single most likely outcome is to remain at their present state of trading year on year (see the diagonal of Table 1.) This pattern becomes more pronounced at higher levels of trading. This is consistent with the hypothesis that there are powerful network effects sustaining trading of already-popular contracts. Having reached annual trading in the 10000’s, a full collapse becomes relatively unlikely (4 percent.) In fact, the probability of progressing or regressing more than one level is below 10 percent. By contrast, less-traded contracts are jumpy. The probability of skipping a level of trading (high or low) raises to 49 percent for contracts trading in the double digits. Despite the clear path dependence, transitioning to higher trading levels never gets easy. At or above annual trading of 1000, the lower off-diagonal of the matrix is always higher than the upper off-diagonal, meaning that the marginal contract is always more likely to fall back in its trading than to progress forward.
Fig. 5. Expected volume of 10,000 simulated contracts after ten years, conditional on trading dynamics, grouped by exchange.
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Fig. 6. Expected volume of 10,000 simulated contracts after ten years, conditional on trading dynamics, grouped by product type.
4.2. The relative importance of time, exchange, and product type in determining the prospects for the marginal contract Previous studies suggested that individual exchanges, product categories, or decades might be particularly well-suited to producing blockbuster trading. But which is more influential to the marginal contract’s trading? The Markov model in equation (1) can answer one form of that question: which is more likely to produce higher or lower expected trading volumes over some horizon, a specific exchange/product category/decade or a randomly chosen exchange/product category/decade? Figs. 5–7 provide expected trading volumes for a marginal contract across individual exchanges, decades, and product subgroups against their randomly assembled benchmarks. To calculate those figures, we initialize trading based on each sub population’s historic probability of starting in each state, then multiplied that by ten randomly drawn transition matrices for that sub population. Finally, we multiplied each state by the lower bound of each trading range (zero, 1, 10, etc.) and summed the resulting vector. We repeated that procedure 10000 times for each sub population. In Figs. 5–7, as well as all of the similar graphics to follow, the median estimate of the posterior predictive distribution is noted by a dot, the 50 percent probability interval is in color, and the 95 percent high density interval (HDI) in black. The HDI is analogous to a frequentist 95 percent confidence interval insofar as it provides a standardized basis for assessing distributional differences. In this case, simulated sub-populations (such as samples across time or
Fig. 7. Expected volume of 10,000 simulated contracts after ten years, conditional on trading dynamics, grouped by trading decade.
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product category) whose HDIs (black lines) do not overlap are statistically distinct at the 95 percent probability level. The most important results of this exercise are:
• Most exchanges and product categories are indistinguishable (show overlapping HDIs) from their random benchmarks and from one another. Due to the large number of these sub populations, those trivial results were excluded from Figs. 5 and 6.
• While some of the largest exchanges are probabilistically distinct from one another, they are not distinct from a randomly selected exchange. The CME’s failure to distinguish itself is particularly interesting since Gorham and Kundu (2012) found that the CME lead other major exchanges in mean volume in the 5th year of trading, mean lifetime volume, and their approximations of present value discounted fee generation. • There were two notable exceptions to that pattern among exchanges: – The single-stock futures traded on OneChicago which showed particularly low expected trading volumes over ten years. – The two registered exchanges in the IntercontinentalExchange group, marked ICE and ICEU, likely have higher expected trading volumes than most other exchanges.
• Interest rates and natural gas were distinctly successful while single-stock futures and exchange traded weather were notably unsuccessful.
• The expected trading volume after 10 years for a contract has varied substantially across time, jumping up or down from decade to decade.
• While many decades were distinct from one another, only the 1980’s looks to be a particularly auspicious time for the marginal contract.
• The period between 1980 and 2010 was particularly volatile for market dynamics. The marginal contract rose to higher trading in the 1980’s, plummeted in the 1990’s, and recovered to the middle of that range in the 2000’s.
• In the 2000’s, low volume contracts tended to rise to modest levels of trading balancing any fall in the probability of reaching the highest trading levels.
4.3. Market dynamics over time Figs. 8–10 show probabilities of individual contracts moving between volume levels in a given year t (indicated by the row of estimates) and volume levels in year t + 1 (indicated by the column of the estimate) based on draws from the posterior predictive distribution of the model described by equation (1). As before, the dots in the figure indicate median parameter estimates, the colored band indicates the 50 percent probability range, and the black line indicates the 95 percent probability range. Despite the volatility in Fig. 7, no decade shows meaningful deviation from the general story that emerges from Table 1. There was substantial inertia, keeping contracts at their current level of trading and this inertia is stronger at both the highest and lowest levels of trading. Weakening path dependence in the 2000’s. However, the degree to which the transition matrix supports the story in Table 1 (as well as Silber (1981) and Carlton (1984)), changed remarkably in the 2000’s (See the top rows of Fig. 8.). The inertia trapping less-traded contracts is lower than in previous decades, with the median probability of a contract at an annual volume of zero remaining at zero falling to 70 percent (Fig. 11). While zero volume contracts remained unlikely to rise to higher volume levels in absolute terms, contracts with no current trading were not doomed to remain untraded as in the past. (Their 95 percent probability interval for remaining untraded was lower in the 2000’s than in recent decades. That probability interval did not overlap with those from recent decades, suggesting the difference holds with high probability.) How did contracts recovering from zero trading perform? While a year without trading no longer trapped contracts in the 2000’s, the decade did not see a complete reversal of conventional wisdom about trading volumes. Untraded contracts remained very unlikely to become blockbusters. Contracts were more likely to jump from an annual trading volume of 0 to trading volumes between 10 and 1000 than in previous decades (See top row of Fig. 8.). The 2000’s stands out as a period where there was tremendous contract innovation (see Fig. 1.) Most of that innovation produced no trading in any given year (see Fig. 3.) But in a clear break with the past, the derivatives markets of the 2000’s were relatively likely to subsequently use a contract that had gone without trading for a year. This further obscures our ability to identify candidates for delisting from trading volumes alone. Blockbuster contract trading by decade. If derivatives markets changed to encourage innovation in the 2000’s, did the market also change in its ability to create and sustain blockbuster contracts, those with the highest levels of annual trading volumes? Having reached annual trading volumes in the 10’s or 100’s (row 1, column 4 of Fig. 9), contracts in the decade of the 2000’s were again substantially more likely to continue increasing their trading volume in the 2000’s than in the 1980’s or 1990’s. Only after reaching trading volumes in the 1000’s (row 2, column 5 of Fig. 9) did the probability of an individual contract progressing to higher levels of annual trading volume fall roughly back within the same range as those from previous decades. In general, in the 2000’s contracts moved up to annual trading in the 1000’s with an ease not seen in previous decades. Some of the flexibility gained for contracts at lower levels of trading may have come at the expense of contracts at mid to high levels of trading. Contracts trading in the 10000’s were 8 percent more likely to fall back to lower levels of annual volumes in the 2000’s than in previous decades, a difference that holds with high probability (row 3, column 5 of Fig. 9). However, Fig. 7
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Fig. 8. Transition matrix for Markov model of derivatives contract moving between states of annual trading volume by decade: low initial trading.
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Fig. 9. Transition matrix for Markov model of derivatives contract moving between states of annual trading volume by decade: moderate initial trading.
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Fig. 10. Transition matrix for Markov model of derivatives contract moving between states of annual trading volume by decade: high initial trading.
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Fig. 11. Probability of remaining at annual volume of zero from year to year by decade.
indicates that this retrenchment was not enough, on balance, to lower the prospects of a new contract over the course of ten years. Interestingly, no decade provided the marginal contract with a distinct advantage in moving across the important threshold of 10000, discussed above. 4.4. The introduction of electronic trading The shifts in the lifecycle of derivatives in the 2000’s are consistent with the hypothesis that electronic trading made trading activity more mobile across derivatives markets and substantially cut the costs of launching and sustaining a derivatives contract. However, given the myriad changes to the structure of US exchanges that took place during the 2000’s, it is difficult to isolate the
Fig. 12. Bayesian change point probability run on 1000 random samples per year of the NYMEX’s probability of remaining at volume level 100 year on year. Black line shows change point probability. Colored points show posterior mean estimates.
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Fig. 13. Bayesian change point probability run on 1000 random samples per year of the NYMEX’s probability of remaining at volume level 1000 year on year. Black line shows change point probability. Colored points show posterior mean estimates.
influence of electronic trading by looking at trading on a decade by decade basis alone. Instead, we need to look at the individual exchange level for a circumstance where electronic trading was introduced suddenly. That was the case for the New York Mercantile Exchange (generally called NYMEX, but registered as NYME in CFTC databases and in various graphics here), which abruptly switched from open-outcry to electronic trading in 2006. This transition was followed closely by the NYMEX’s merger with the Chicago Mercantile Exchange (CME), announced in March 2008 and finalized September 2009. Since that merger may have also changed the exchange’s dynamics (new systems and network effects might change transition probabilities), it is helpful to compare the NYMEX to the Chicago Board of Trade (CBT), another large exchange that also merged with the CME (announced in October 2006 and finalized in January 2008) and might show similar transition dynamics if the CME’s systems and scale are driving trading volume. The CBT’s transition matrices (Figs. 17–19) show no consistent trends in post-merger years relative to the earlier years in the sample. To the extent that the CBT shows any post-merger trend, it stems from 2010, an especially volatile year for the CBT, where many contracts advanced to trading in the tens of thousands and a particularly large percentage fell back from annual volumes in the tens of thousands. The CME merger did not drive trading dynamics in any particular direction and/or to a degree that overrode other factors, as might be expected if the CME held the special advantage over other exchanges hinted at by summary statistics of the exchange’s success (Gorham and Kundu, 2012). By contrast, the NYMEX, does show a trend in its transition probabilities which predates, and is uninterrupted by, the CME merger. Sometime in the latter half of the decade, the trading levels 10 through 10000 become sinks for NYMEX contracts (Fig. 15). The probability of staying at these levels year on year increases gradually, shown in row three of Fig. 14, all rows of Fig. 15, and row 1 of Fig. 16). Figs. 12 and 13 show these dynamics in greater detail in the form of a Bayesian change point model run on posterior simulations of the key parameters. Following noisy years at the beginning of the decade, year on year transitions are distinct, indicated by a clear spike in the change point probability between blocks of 1000 annual simulations. This happens while mean parameter estimates show a general upward trend over the latter half of the decade. 2007, the first year of fully electronic trading, is statistically distinct from 2006. But given the general volatility of these parameters over time, this should be taken only as modest evidence in favor of the hypothesis that the transition to electronic trading is a causal factor. Meanwhile, the probability of rising to higher levels of trading falls on the NYMEX. At levels 100000 and above, contracts showed a time trend with falling back more likely at the expense of them staying put or rising (row 1, columns 6 through 8 and row 2, columns 7 columns 7 through 9 of Fig. 15). The pattern on the NYMEX is an exaggerated form of one we see in the 2000’s across markets: contracts rise easily from low to modest trading while falling more easily from high to modest trading. It accelerated on over a window in time that is consistent with the hypothesis that electronic trading played a determining causal factor. Meanwhile, the same trend is not present on the CBT, which like the NYMEX, merged with the CME over this period and consequently helps us to tease apart the influence of the CME itself. These parallel trends favor electronic trading as a causal factor in derivatives trading over the decade as a whole and they echo the earlier finding that time is generally a more effective lens for distinguishing different market regimes than exchange. 14
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Fig. 14. NYME’s transition matrix for Markov model of derivatives contract moving between states of annual trading volume by year: low initial trading.
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Fig. 15. NYME’s transition matrix for Markov model of derivatives contract moving between states of annual trading volume by decade: moderate initial trading.
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Fig. 16. NYME’s transition matrix for Markov model of derivatives contract moving between states of annual trading volume by decade: high initial trading.
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Fig. 17. CBT’s transition matrix for Markov model of derivatives contract moving between states of annual trading volume by year: low initial trading.
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Fig. 18. CBT’s transition matrix for Markov model of derivatives contract moving between states of annual trading volume by decade: moderate initial trading.
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Fig. 19. CBT’s transition matrix for Markov model of derivatives contract moving between states of annual trading volume by decade: high initial trading.
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5. Conclusions In this article we have presented an analysis of trading volumes for derivatives reported to exchanges in the United States. In addition to providing comprehensive summary statistics on derivatives markets, we have also modeled the lifecycle of derivatives, the dynamics with which trading in a given contract across time, exchanges, and product categories. Starting in the 2000’s the lifecycle of derivatives changed in ways that run counter to heuristics that emerged from earlier studies. While a larger percentage of contracts had little or no volume in any given year of the 2000’s, contracts did not fail at the high rates noted in previous analyses. Instead, they remained at low levels of trading until they were needed, transitioning back into active trading with greater probability than in previous decades. This flexibility was important enough that it effectively buoyed the prospects for the marginal contract during a period when the number of new contracts exploded and the likelihood of blockbuster contracts waned. Trading data covering the NYMEX, an exchange that introduced electronic trading suddenly, provides support for the hypothesis that these shifting dynamics were driven by the introduction of electronic trading. While a small handful of exchanges and product types showed a consistent tendency toward elevated or diminished trading, the vast majority were indistinguishable from their peers. This suggests that retrospective explanations of contract success or failure are likely to overemphasize the role of a specific exchange or product type. By contrast, successive decades show remarkable volatility in the prospects for a marginal contract. The 1980’s in particular was a period well distinguished from a randomly chosen decade, with very high expected trading volumes for new contracts. Despite the diversity of market dynamics across time and some exchanges/product groups, the winner-take-all nature of derivatives markets noted in previous literature remains relatively constant. Across exchanges, product types, and decades the single most likely outcome for a contract year on year is that it will remain where it was trading. This is the same incumbency bias noted in previous literature. Our analysis also affirms the common observation that it is unusual for a contract to experience initial popularity and to crash subsequently (Johnston and McConnell, 1989). After reaching a trading volume in the tens of thousands, the probability that a contract will have annual trading volume of zero in the subsequent year drops appreciably. We presented these results in the form of a Markov model. That framework for looking at derivatives trading facilitates quick distributional comparisons across various contract groupings (e.g. decade and exchange). It also allows for subsequent research to extend our results to many basic questions about derivative markets beyond the scope of this article. For example, a quick examination of the Markov models produced here suggests that trading volumes do not follow a normal or log-normal random walk over time, as the dynamics of trading vary greatly conditional on starting volume. Furthermore, switches to higher and lower levels of trading are often not symmetric. In particular, an outright crash to zero trading volume appears more likely than would be predicted by a symmetrically distributed random walk. Empirical extensions of this work might incorporate data from bilateral trading. In the 1990’s and 2000’s trading that might have historically taken place on a futures market moved to over-the-counter markets. Many of those trades were eventually reported to an exchange (“swaps-to-futures” trades) and, hence, included in this analysis. But the most bespoke transactions remained bilateral. In some cases that data on bilateral transactions would yield distinct trade dynamics from those presented here. For example, the market for highly customized weather risk management has continued to grow even as exchange traded weather derivatives have been delisted (Evans, 2016). Theoretical extensions might focus on the nature of derivatives as economic goods. With very low marginal costs and high network effects, derivatives resemble many of the economic goods where use and distribution have been transformed by the internet. For example, the weakening path dependence and explosive rates of innovation detailed here bare a qualitative similarity to those observed in the market for digital music (Anderson, 2006).
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