Persistent noise, investors’ expectations, and market meltdowns

Giovanni Cespa, Xavier Vives

Since capital flows to and from hedge funds are strongly related to past performance, an exogenous liquidity shock can trigger a vicious cycle of outflows and declining performance. Therefore, ‘noise’ trades – usually thought of as erratic – may in fact be persistent. Based on recent research, this column argues that there can be multiple equilibria with different levels of liquidity and informational efficiency, and that the high-information equilibrium can under certain conditions be unstable. The model provides a lens through which to interpret the ‘Quant Meltdown’ of August 2007 and the recent financial crisis.

The recent financial crisis has revived interest in the question of what triggers crashes and meltdowns in financial markets. An important reason for abrupt and large price dislocations is the lack or ‘slow motion’ of arbitrage capital (Duffie 2010) that weakens the risk-bearing capacity of liquidity providers.

We suggest that there is an alternative explanation based on expectations dynamics in the presence of persistent market noise.

In the market:

There are traders who operate on the basis of public and private information.

Their actions are persistent across time and tend to anchor asset prices to the fundamentals.

There are traders who act on motives unrelated to information, such as hedging, or the need for liquidity (‘noise’ traders).

Their trades are generally thought to be erratic. They reduce the extent to which price movements reflect the real value of the asset.

The question that arises seems therefore to be a rather empirical one, that is:

How can we estimate the amount of noise in asset prices?

The problem is not easy to solve, since the motives that drive traders’ decisions are often unknown to other traders in the market, as well as to outside observers. In principle, an order to sell given by a fund to satisfy savers who need to liquidate their positions can be mistaken for the decision to unwind a position at a profit, prompted by information about the asset’s fundamentals.

However, there are conditions in which trading decisions can to some extent be safely ascribed to liquidity needs. A case in point is the behaviour of funds that face huge redemption orders from their investors (Coval and Stafford 2007). The idea is that, pressed with the need to satisfy investors’ orders, funds liquidate their positions without looking too much at market conditions, thereby trading as uninformed investors.

The next step in the logic is to connect this behaviour with the evidence that capital flows to and from funds are strongly related to past performance (Chevalier and Ellison 1997).

Plainly this can induce a vicious cycle.

An exogenous shock (such as, for example a large redemption order) leads funds to liquidate their positions;

This negatively affects their performance, which subsequently feeds back to additional outflows from the fund (Lou 2012).

A vivid example of this dynamic is offered by the ‘Quant Meltdown‘ episode, when some of the most profitable hedge funds steadily unwound their positions during the second week of August 2007 (Khandani and Lo 2011).

Taken as a whole, this mechanism suggests that ‘noise’ trades, far from being erratic across time, can actually display persistence. Does this apparently innocuous feature of uninformed orders change in some way our understanding of the way asset prices reflect information about fundamentals?

New research

This is the starting point of a recent paper (Cespa and Vives 2014) in which we explore the effect of persistent liquidity trading on asset prices. We show that persistence in uninformed orders, when coupled with the short horizons that informed traders usually exhibit, causes co-movement in investors’ behaviour in terms of their response to private information. This may yield multiple situations with self-fulfilling expectations, and has important implications for the informational content of equilibrium prices, as well as for return volatility and the liquidity of the market.

Suppose that fundamentals information and persistent liquidity trading – ‘noise’ for short – affect asset prices. In these conditions, any news that accrues to our information set about one of these factors affects our present and, crucially, past understanding of the other factor. This means that dynamic learning involves reconsidering the assessment investors have made about the relative impact of noise trading and fundamentals at the early stages of the trading game, under the lenses of newly gathered information. We refer to this backward-looking expectation revision mechanism as ‘retrospective’ inference.

Here is how retrospective inference works. Consider a two-period setup and suppose that in the first period dealers receive a sell order from investors with unknown trading motives. In order to absorb it, they mark the price down for two reasons:

First, the order may come from informed investors, who know the asset is overvalued.

Second, independently from the investors’ trading motives, absorbing the order increases the dealers’ asset inventory, exposing them to a potentially larger loss when they rebalance it one period ahead, at a random (possibly much lower) price.

Suppose now that in the next trading round a new order to sell arrives. How should dealers interpret this renewed selling pressure? Due to persistence, a first possibility is that noise trading is the main driver of both orders. However, it could as well be that informed traders have taken advantage of the price dislocation created by (a large buy order from) noise traders, so that fundamentals information is a strong driver of one, or both orders. Which among these alternatives is more likely to arise? The answer turns out to crucially depend on dealers’ opinion about the first order.

Suppose first-period dealers trust the order they face to be mostly information-driven. In this case, the bulk of the price adjustment to fundamentals information must occur in the first period. But then, in the second period the asset is no longer likely to be very much overvalued. This lowers the odds that the new sell order comes from informed investors, while increasing the chances of noise trading. But if noise trading is driving the current order, due to persistence, its impact in the first period must have been underestimated. Equivalently, dealers’ previous assessment of the fundamentals must have been too low and, working retrospectively, dealers revise up their expectation of the asset. As a result, the usual, inventory-driven downward price adjustment is now mitigated by the retrospective inference-operated expectation correction, and the order commands a mild price change. But if dealers in the first period envisage a small future price adjustment, they see their increased exposure to the asset as less risky, and therefore are willing to accommodate the sell order at better terms, supplying more liquidity. This implies a milder price impact of noise trades that allows fundamentals information to prevail. In this case, a high-liquidity equilibrium, in which prices are driven by fundamentals, arises.

Of course, if dealers are instead convinced that the initial order was mostly driven by noise/liquidity trades, they attribute the new sell order to informed speculation. This means that probably the effect of liquidity trading in the first period was smaller than they previously thought, which leads them to revise downwards their expectation of the asset payoff. This reinforces the downward price adjustment they require as compensation for their increased exposure to the asset, magnifying the total price change. As a result, first-period dealers are now less willing to accommodate the order. In this case, the equilibrium level of liquidity is instead low, and noise/liquidity trading is the main price driver.

Thus, retrospective inference teaches us that when the demand for an asset is driven by different – information- and non-information-motivated – persistent factors, a given order to sell (or buy) can have a large or small impact, depending on investors’ opinions about the drivers of the asset demand. Equivalently, the market can hover in a high-liquidity, high-informational-efficiency state, or be mired in a low- liquidity, poor-informational-efficiency trap. What determines which state prevails?

Concluding remarks

Our results show that the high-liquidity equilibrium can be fragile. For example, if public information about the asset is scant, investors over-rely on the information they extract from the orders they observe, and the retrospective inference loop becomes very strong. As a consequence, the high-liquidity equilibrium becomes unstable. In this case, only the noise-driven equilibrium, in which the price impact of trades is large, survives. Of course, in such a situation, liquidity provision is a very profitable, albeit very risky, activity. Interestingly, some authors (Nagel 2012) find that during the recent financial crisis ‘contrarian’, liquidity-providing strategies that loaded on losers and shorted winners turned out to be highly profitable. If we couple this with the observation that public information on the financial health of important players became abruptly scarce during the financial crisis (see e.g. Gorton and Metrick 2010), our paper provides a narrative of the crisis that emphasises the importance of public information provision. Through the lenses of our model, a paucity of reliable public information may have reduced the risk-bearing capacity of the market, relegating most of the economy to the low-liquidity equilibrium.

The low-liquidity equilibrium also prevails when the demand of noise traders becomes more volatile. In this case, the loop weakens, and the high-liquidity equilibrium disappears. This observation illuminates the Quant Meltdown of August 2007. Indeed, when several hedge funds started unwinding their holdings (arguably for non-informational reasons), the price impact of trades jumped. According to Khandani and Lo (2011), a lack of arbitrage capital (together with the rising importance of high-frequency trading for market making) was largely responsible for the meltdown. An alternative interpretation derived from our model is that the large increase in price impact was due to an increase in the volume (and volatility) of noise trading which fostered a switch from the high-liquidity to the low-liquidity equilibrium.

References

Cespa, G and X Vives (2014), “Expectations, Liquidity, and Short-Term Trading”, CEPR Working Paper 8303.

Chevalier, J and G Ellison (1997), “Risk Taking by Mutual Funds as a Response to Incentives”, Journal of Political Economy, 105(6): 1167–1200.

Coval, J and E Stafford (2007), “Asset Fire Sales (and Purchases) in Equity Markets”, Journal of Financial Economics, 86: 479–512.

Duffie, D (2010), “Asset Price Dynamics with Slow-moving Capital”, Journal of Finance, 65(4): 1237–1267.

Gorton, G and A Metrick (2010), “Haircuts”, Federal Reserve Bank of St. Louis Review, 92(6): 507–519.

Khandani, A and A Lo (2011), “What Happened to the Quants in August 2007? Evidence from Factors and Transactions”, Journal of Financial Markets, 14: 1–46.

Lou, D (2012), “A Flow-based Explanation for Return Predictability”, Review of Financial Studies, 25(12): 3457–3489.

Nagel, S (2012), “Evaporating Liquidity”, Review of Financial Studies, 25(7): 2005–2039.