Price discovery is a blackbox in economic theory. The efficient market hypothesis, implied by the rational expectations paradigm, assumes that all relevant information is impounded into asset prices instantly and costlessly. Yet, that simplifying assumption implies an impossibility: it means that no agent in the economy has any incentive to undertake any effort to uncover information relevant to the price of a security. If one is interested in how information actually gets impounded into asset prices, one has to pay attention to how the mechanics of trading structures the process of price discovery. This is the principal explanandum of market microstructure theory.
Market microstructure theory emerged from models of the market marker’s inventory optimization problem. The question there was: how does a market maker choose bid-ask prices to manage the risks and other costs of holding inventory? This literature originated with Garman (1976). Market microstructure in the modern sense, as concerned above all with the problem of the incorporation of asymmetric information or privately-held information into asset prices, begins with Kyle (1985). (In Empirical Market Microstructure (2003), Hasbrouck tells us, ‘”Albert S.” [Kyle] is pronounced “Pete”.’) Kyle (1985) begins by asking:
How quickly is new private information about the underlying value of a speculative commodity incorporated into market prices? How valuable is private information to an insider? How does noise trading affect the volatility of prices? What determines the liquidity of a speculative market?Albert S. “Pete” Kyle. “Continuous Auctions and Insider Trading,” 1985.
All of these questions remain central to microstructure theory. In the generic schema of market microstructure theory, a monopolistic or competitive market maker, who may be risk neutral or risk averse, trades with two types of traders: informed investors, who observe a private signal that contains predictive information on the future value of an asset, and uninformed investors or noise traders, who do not observe any such signal and trade randomly. The main problem of market microstructure theory is one of asymmetric information — the market maker cannot tell one from the other. By being ready to buy and sell the asset at quoted bid ask prices, ie, by providing liquidity, she runs the risk of being adversely selected against. That is, she runs the risk of making a loss by trading with an informed investor at prices she will come to regret.
Kyle (1985) calls the holder of private information on the future value of the security, an insider. The term insider is accurate for the holder of privileged information in Kyle (1985) because in that model the informed trader is an information monopolist — no one else observes the true signal. In particular, market makers do not observe the signal. This last observation is true more generally of the theory and real asset markets. Indeed, as Prado notes in his magnum opus, Advances in Financial Machine Learning (2018), “microstructural information can only be defined and measured relative to the predictive power of market markers.” In effect, an informed investor is one who has access to some kind of superior technology or insider information that gives him greater predictive power about the future value of an asset than marker makers.
Market microstructure theory is applied game theory — it models the strategic interaction of these different player types. The market maker wants to detect the presence of informed investors and the latter want to evade detection. The central theorem of the theory is that informed investors use the presence of noise traders to mask their identity. They stagger their trade to conceal their intentions; they use volume to hide from the market makers. But as they trade, they reveal their presence. For unlike noise trading, that just gives random kicks to asset prices that dissipate over time, informed trading brings asset prices closer to their fundamental value. The rate at which information is impounded into asset prices depends on the strategic interaction of these different player types, their risk aversion, and the degree of competition among market marker on the one hand and among informed traders on the other. The authoritative treatment of the theory is Maureen O’Hara’s Market Microstructure Theory (1997).
David Easley and coauthors have theoretically derived and empirically estimated the probability of informed trading (PIN), which is the fraction of order flow accounted for by informed traders and thus the risk of adverse selection faced by market markers; and its more sophisticated, high-frequency version, volume-synchronized probability of informed trading (VPIN). These third generation estimands require fine-scale information on order flow, which we do not have. What we do have is open source volume and price data on some highly liquid markets at the daily frequency. That will allow us to compute two measures of market liquidity, giving us some idea of where informed traders should and do operate without revealing their presence.
The measures we have in mind are Kyle’s lambda and Amihud’s lambda; both measure market illiquidity. Kyle’s lambda is the elasticity of returns against net order flow or signed volume (volume times the sign of the return). It measures the price impact of trading. Amihud’s lambda is the elasticity of absolute returns against volume, which can be computed from time series price and volume data. We obtain price and volume data on E-mini SP500 futures from Quandl (code: CHRIS/CME_ES1). We obtain price and volume data on VIX futures from the CBOE’s website. These two futures markets are some of the most liquid markets for systematic risk in the world.
What does price discovery mean in the context of synthetic assets that contain a strong signal of systematic risk — like the VIX or the SP500? Microstructure theory says informed traders in such securities are those who are more informed than market markers — in this case, that they are more informed about systematic risk. Meanwhile, intermediary asset pricing reckons that systematic risk in asset markets is a function of shocks to the risk-bearing capacity of broker-dealers. But this raises a very interesting problem: if systematic risk is a function of dealer balance sheet capacity, then how can there be informed investors who know more about the future value of systematic risk than the dealers themselves? In market microstructure theory, this problem is put in a blackbox: informed investors are exogenously assumed to be more informed about the future value of the risky asset than market makers. So the problem is how to endogenize price discovery in the market for systematic risk. It is an open question.
We first document the volume of order flow in the E-mini SP500 futures market and the VIX futures market. The former market is considerably deeper than the latter. Does this translate into higher market liquidity?
Net order flow in the two markets is displayed next. The volume of transactions in E-mini futures exploded in the 2000s. We do not have data going back that far for VIX futures. But it is reasonable to imagine that the volume of transactions in VIX futures similarly exploded in the high neoliberal period that came to grief in 2008.
The next figure displays scatterplots of returns against net order flow and absolute returns against volume in the two markets for the full sample. By visual inspection, we can see that price impact, as measured by Kyle’s lambda, is larger in the VIX futures market. But this may be an artifact of scaling the two axes. In order to compare apples-to-apples, we robustly standardize both returns and net order flow. We find that Kyle’s lambda, thus suitably normalized, is 2.69 for VIX futures and 3.13 for E-mini futures. Astonishingly, we find that the price impact in the shallower VIX futures market is thus lower than the same in the much deeper market for E-mini futures. Market liquidity is not the same thing as market depth!
Looking at Amihud’s lambda, similarly normalized, is 0.61 for VIX futures and 0.57 for E-mini futures. This contradicts the results obtained from Kyle’s lambda. But still, even though the E-mini futures market is more liquid by this measure, the difference is slight. In fact, since the standard error of the difference of means is the square root of the sum of squared standard errors of the means, we can test whether these estimates are significantly different from zero. We find that the difference in Kyle’s lambda is significant (z = 4.55), while the difference in Amihud’s lambda is not (z = -1.15). So, counterintuitively, the deeper E-mini futures market is less liquid than the shallower VIX futures market. Table 1 reports our estimates.
|Table 1. Estimates of market liquidity in two futures markets.|
|Source: Quandl, CBOE, author’s computations. Both response and feature have been robustly standardized to have zero mean and unit variance. Estimates in bold are significant at the 1 percent level.|
We next examine the time-variation in our measures of market liquidity. Using Kyle’s lambda, we find that liquidity in both markets was very high in 2017, during the so-called Trump reflation trade. But market liquidity collapsed in 2020 with the coronavirus shock. Moreover, it collapsed by more in the E-mini SP500 futures market. There is also the intriguing pattern that the E-mini market was more liquid than the VIX futures market until 2016, and less thereafter.
Using Amihud’s lambda, we find the same liquidity collapse in 2020, with liquidity contracting more in the E-mini SP500 futures market than the VIX futures market. By this measure, 2020 was the only year in which liquidity was higher in the latter.
Although the evidence is not unambiguous, our estimates suggest that, even though the E-mini SP500 futures market has much greater depth, the VIX futures market is more liquid. In light of market microstructure theory, this suggests that informed investors prefer to trade in the VIX futures market to better mask their presence from market makers. If that is the case, then the tail wags the dog: innovations in systematic risk are first impounded into VIX futures prices, and then into SP500 futures prices, even though the underlying of the former is derived from the latter.
These observations assume the existence of traders more informed about systematic risk than market makers. But how can such traders exist at all? How can anyone know more about the state of the world — the growth rate of balance sheet capacity — than the dealers themselves, who at least have partial information, in the sense that they know the degree of slack of their own risk constraints in real time than anyone else?
One potential path forward is suggested by the work of Nina Boyarcheno, one of the sharpest knives in the NY Fed’s drawer, and coauthors, on information sharing by dealers. Although the concern there is on dealers sharing order flow information with other dealers and across the table with their clients, one can see how buy side speculators may acquire information on aggregate balance sheet capacity from multiple dealers at the same time by making them compete against each other. That may explain why and how informed investors in markets for systematic risk in the strict sense — those who can predict innovations in systematic risk better than the dealers themselves — can exist at all.