The Inelastic Market Hypothesis - A Microstructural Interpretation

We attempt to reconcile Gabaix and Koijen’s (GK) recent Inelastic Market Hypothesis (IMH) with the order-driven view of markets that emerged within the microstructure literature in the past 20 years. We review the most salient empirical facts and arguments that give credence to the idea that market price fluctuations are mostly due to order flow, whether informed or non-informed. (Page 1)

We discuss several empirical results suggesting that the lion’s share of volatility is due to trading activity. We argue that the IMH holds for all asset classes, beyond the case of stock markets considered by GK. (Page 1)

Traditionally, market prices are considered to reflect the fundamental value (of a stock, currency, commodity, etc.), up to small and short-lived mispricings. In this way, a financial market is regarded as a measurement apparatus that aggregates all private estimates of an asset’s true (but hidden) value and, after a quick and efficient digestion process, provides an output price. In this view, private beliefs should only evolve because of the release of a new piece of information that objectively changes the value of the asset. (Page 1)

This Platonian view of markets is fraught with a wide range of difficulties that have been the subject of thousands of academic papers in the last 40 years. The most well-known of these puzzles is the excess volatility puzzle [1, 2]: prices move around too much to be explained solely in terms of fluctuations of the fundamental value. (Page 1)

After accepting the presence of non-rational agents, the next conceptual step is to accept that all trades (informed or random, large or small) possibly contribute to long-term volatility. This corresponds to a paradigm change: instead of fundamental value determining prices, the main driver of price changes is the order flow itself — whether informed or random, trades will move prices. This is the order-driven view of markets, that progressively emerged in the last 20 years, motivated by several empirical facts obtained using microstructural data [11–19], to be recalled below. (Page 2)

In fact, calibrating – say – self-exciting Hawkes models on data leads to the conclusion that a very large fraction (¦ 80%!) of market activity and volatility is self-generated, rather than exogenous [24–26]. (Page 2)

Based both on an empirical analysis of the long-term price response to funds’ order flow and on an equilibrium model of the holdings of mandate-constrained investment firms, the authors argue quite convincingly in favour of the order-driven scenario and debunk many dissenting arguments based on the traditional lore. The central result of GK is that buying (or selling) 1$ of an individual stock on average increases (decreases) the market capitalisation of that stock by M$ in the long run, with M ≈ 1 even for uninformed trades. Buying the market as a whole (i.e. the index or a basket of stocks) has an even larger impact, with M ≈ 5. (Page 2)

The aim of this paper is to discuss how the price adjustment actually unfolds, and why recent measures of price impact at the daily time scale, when correctly interpreted, are quantitatively compatible with GK’s value of the multiplier M. We believe that our reconciliation of high-frequency liquidity (i.e. the realm of microstructure) and low-frequency equilibrium (i.e. quarterly or longer, as studied by GK) is quite remarkable and gives strong credence to the order-driven/inelastic theory of markets. (Page 2)

Buy trades (i.e. market orders hitting the ask) tend to push the price up and sell trades (i.e. market orders hitting the bid) tend to push the price down. This is price impact and is an all-too-familiar reality for traders who need to buy or sell large quantities of an asset. To these traders, price impact is tantamount to a cost, because the impact of their earlier trades makes the price of their subsequent trades worse on average. (Page 2)

2. Price impact is a reaction to order-flow imbalance. This is the order-driven view, which asserts that even if a trade reflected no information in any reasonable sense, then price impact would still occur and contribute to the long-term volatility. (Page 3)

In the first story, trades reveal private information about the fundamental value, creating a so-called price discovery process. In the second story, the act of trading itself impacts the price. In this case, one should remain agnostic about the information content of the trades, and should therefore speak of price formation rather than price discovery. (Page 3)

In fact, traders or trading algos do not execute large trades via single market orders, but instead split up their trades into many small pieces. These pieces are executed incrementally, using market orders, limit orders, or both, over a period of several minutes to several days. (Page 3)

The main conclusion here is that even relatively small metaorders cause surprisingly large impact. In fact, the GK multiplier measured in that regime would be uncannily high: taking T = 1 day, σT = 2.5% (a typical value for single stocks, corresponding to an annual volatility of ≈ 40%) and Q = 1%VT = 5 10−5M leads to I(Q, T) ≈ 1.25 10−3 or M = 25. However, since impact is proportional to p Q and not Q, GK’s multiplier is meaningless in the regime T Tm. As we will discuss in section 4, the square-root impact contribution is mostly transient, while the permanent part (which survives for T Tm) is linear and characterized by M of order unity, as indeed found by GK. (Page 4)

Since the mid-nineties, several stories have been proposed to account for the square-root impact law. The first attempt, due to the Barra Group [36] and Grinold & Kahn [37] argues that the square-root behaviour is a consequence of market-markers being compensated for their inventory risk (see also [38]). (Page 4)

Finally, Tóth et al. [41] proposed an alternative theory based on a dynamical description of supply and demand, called the Latent Liquidity Theory (LLT). This approach, developed further in several papers [42–48], provides a natural statistical interpretation for the square-root law and its apparent universality. It also makes further predictions, in particular concerning the decay of impact once the metaorder has been executed [44, 46]. This is a piece of information that turns out to be crucial for recovering GK’s multiplier at long times, about which the theories recalled above make substantially different predictions compared to LLT (Page 5)

Finally, let us make an important remark: a very nice feature of the LLT is that any round trip incurs a positive cost, see [44] for a proof. To wit, trading impact prices, but there is no way to construct an arbitrage strategy out of this effect, since getting out of position would lead to a net loss. (Page 6)

Within the order-driven view of markets, high-frequency traders and market makers only seek to exploit short-term statistical arbitrage opportunities, without any long-term view about fundamental value. By doing so, such traders activity makes prices unpredictable and simply propagate the high-frequency value of volatility to long time scales. (Page 8)

From a microstructural point of view, each trade can be characterized as “active” (consuming liquidity) or “passive” (providing liquidity). This distinction breaks the symmetry at high frequencies, and allows one to define a meaningful order imbalance, as the sum of active buy trades minus the sum of active sell trades. It is this imbalance that reflects an aggregate “urge” to buy or sell and that mechanically impacts prices, whether or not this urge is justified by a genuine piece of information about future value. Ultimately, the GK multiplier M will turn out to be the low frequency stigma of the asymmetry between active and passive trades. (Page 9)

The aim of this paper was to relate Gabaix and Koijen’s Inelastic Market Hypothesis [27] to the orderdriven view of markets that emerged within the microstructure literature in the past 20 years. We reviewed the most salient empirical facts and arguments that give credence to the idea that market price fluctuations are mostly due to order flow, whether informed or non-informed: trades impact prices, even on the long run. We focused in particular on the Latent Liquidity Theory (LLT) of price impact, and argued that the underlying mechanism for what GK call inelasticity is the dynamics of private estimates of asset value, which tend to realign around the market price over some finite memory time that we called Tm. (Page 10)

The macro-finance implications of the inelastic market hypothesis are important and have been thoroughly discussed in GK’s paper [27], in particular the idea that governments could buoy the stock market by investing in equities [60]. (Page 10)

If order flow is the dominant cause of price changes, “information” is chiefly about correctly anticipating the behaviour of others, as Keynes envisioned long ago, and not about fundamental value. The notion of information should then be replaced by the notion of correlation with future returns, induced by future flows. For example, when all market participants interpret a positive piece of news as negative and sell accordingly, the correct move for an arbitrageur is to interpret the news as negative, even if doing so does not make economic sense. (Page 10)

The idea that it is the order-flow that must be predicted, even if uninformed, resonates well with the intuition of finance professionals and allows one to understand why statistical regularities might exist and be exploited by quant firms. Indeed, flow data is quite popular among statistical arbitrage funds. The order-driven paradigm also allows one to resolve some paradoxes, like for example that it is surprisingly easier to find predictive signals for large cap. stocks than for small cap. stocks, probably because the former are more actively traded and that the order flow reveals more statistical regularities. The 2007 quant crunch and other recurrent deleveraging spirals are also extreme consequences of the impact of order flow on prices [62–64]. In conclusion, we hope that the present reformulation of the Inelastic Market Hypothesis in terms of mechanistic and measurable microstructural effects will shed a complementary light on the origin of financial market fluctuations, and possibly hammer a final nail into the coffin of the Efficient Market Hypothesis. (Page 10)