Giovanni Cespa and Thierry Foucault
Illiquidity Contagion and Liquidity Crashes
Review of Financial Studies | Volume 27, Issue 6 (Jun 2014), 1615–1660

Liquidity (the impact of trades on prices) fluctuates over time and these fluctuations are correlated across assets (see Holden-Jacobsen-Subrahmanyam (FTiF 2014) for a survey). This correlation (“co-movement in liquidity”) is a source of non-diversifiable risk and this risk is priced (see, for instance, Acharya-Pedersen (JFE 2005) or Pastor-Stambaugh (JPE 2003)). There are yet very few theories explaining why liquidity co-moves across assets. We provide such a theory.

Learning from prices leads to interconnected liquidity

Liquidity suppliers (e.g., market makers) specialized in one asset often learn information from observing the price of related assets because asset prices contain information (Grossman-Stiglitz (AER 1980). Consider for instance a market maker in a stock part of the S&P500 index. This market maker will follow prices of futures on the S&P500 index or ETF on the same index because these prices contain information on risk factors common to the stock and these indexes. Similarly, the market maker in a bond or a stock of a given firm will extract information from prices of CDS written on this firm.

Liquidity suppliers in one asset, say X, face therefore less uncertainty when price movements of other assets are more informative. In this case, they bear less inventory risk and can provide liquidity at better terms. Price informativeness in turn depends on liquidity. Indeed, at a relatively high frequency, price movements are due both to news about fundamentals and demand shocks. For instance, a large sell market order pressures prices downward because liquidity suppliers require a compensation to take additional risk (see Hendershott-Menkveld (JFE 2014). As liquidity suppliers gradually unwind their position, this price pressure disappears. Price movements like this, due to transient demand or supply shocks, do not contain information on fundamentals and make prices noisy. The signal-to-noise ratio in prices is therefore smaller when the noise due to transient price pressures is higher, that is, when illiquidity is higher (see Ait-Sahalia-Yu (Arxiv 2009) for empirical evidence).

Thus, when liquidity suppliers learn from the prices of other assets, the liquidity of different assets is interconnected: The liquidity of one asset is higher when the liquidity of other assets is higher because their prices are then more informative. We formalize this interconnection and analyze its implications.

Interconnected liquidity leads to contagion, amplification, and fragile liquidity

Interconnected liquidity generates liquidity spillovers. Consider Figure 1. An exogenous increase in the illiquidity of asset Y (e.g., a decrease in the risk bearing capacity of liquidity suppliers in this asset) triggers a drop in the informativeness of the price of this asset and thereby a drop in the liquidity of asset X, as if illiquidity was contagious. In turn, this reduces the informativeness of the price of asset X, which can reinforce the drop in liquidity for asset Y. This feedback loop can significantly amplify the initial drop in liquidity of assets Y and X, through a multiplier effect.

1: Liquidity spillovers and price informativeness
cespa-foucault-1
The liquidity of one asset affects the liquidity of another asset, which in turn again affects its own liquidity.

There exist situations in which the multiplier can be very large: a small initial shock to the liquidity of one asset can ultimately trigger a very large drop in liquidity of all assets. For instance, in the paper, we provide examples in which a 1% decrease in the risk tolerance of liquidity suppliers in asset Y triggers a very large percentage increase in the illiquidity of assets X and Y while such a shock would have negligible effects if dealers in each asset were not learning from each others' prices (see Table 1 in our RFS paper). Market liquidity can therefore be very fragile when market makers learn from other asset prices: a small increase in the illiquidity of one asset can ultimately generate a very large increase in the illiquidity of all assets. Thus, the model suggests the possibility of liquidity crashes, that is, market wide evaporations of liquidity, in the absence of noticeable changes in the economic environment, very much as was observed during the 2010 “flash crash.”

Implications of broader price dissemination

In our theory, liquidity spillovers and co-movements are due to cross-asset learning: liquidity suppliers in one asset learn from prices of other assets. This mechanism has several implications. First, changes in market structure (e.g., market transparency) or regulations (e.g., a short-sale ban) that directly affect the liquidity of one asset class should also indirectly affect the liquidity of other classes, if dealers in the latter use prices of the former as a source of information. For instance, in 2002, the National Association of Securities Dealers began reporting transaction prices for a subset of corporate bonds (“eligible bonds”). Hence, prices of these bonds became easier to observe for market makers acting in related assets, e.g., other corporate bonds or stocks of eligible bonds' issuers. Bessembinder-Maxwell-Venkataraman (JFE 2006) show that the liquidity of eligible bonds increased with reporting of their prices. Consistent with our model, this improvement propagated to non-eligible bonds (see Bessembinder-Maxwell-Venkataraman (JFE 2006)) and issuers' stocks (see Yin (IJEF 2011)).

Our theory also implies that the size of liquidity co-movements between assets should be stronger when access to information about asset prices is easier. Figure 2 shows the co-movement between two assets X and Y as a function of the fraction of dealers in asset X with information on the price of Y for specific parameters of our model. When more liquidity suppliers in asset X can observe the price of asset Y (e.g., because the market of this asset is more transparent or because of progress in information technologies), liquidity co-movements between the two assets become stronger. The reason is that the multiplier effect associated with the feedback loop highlighted in Figure 1 is larger.

2: Liquidity comovements and price dissemination
cespa-foucault-2
When more liquidity suppliers in asset X can observe the price the asset Y, liquidity comovements between the two assets become stronger.

Funding liquidity or cross-asset learning?

Funding liquidity (i.e., capital constraints) shocks and wealth effects for liquidity suppliers have been proposed as possible sources of covariation in liquidity (see Gromb-Vayanos (JFE 2002), Brunnermeier-Pedersen (RFS 2009), and Kyle-Xiong (JF 2001)). These mechanisms and the cross-asset learning channel described in our paper are not mutually exclusive. In reality, they could therefore work in tandem to generate comovements in liquidity. Their relative importance should vary according to the frequency at which comovements in liquidity are measured: shocks to liquidity suppliers' capital are more likely to play a role at relatively low frequency (daily, weekly, or monthly) whereas the cross-asset learning channel should play out even (and maybe predominantly) at high frequency (intra-daily). In any case, our cross-asset learning mechanism has implications distinct from other theories of comovements in liquidity. These could be used to test whether this channel plays a role in liquidity comovements beyond and above other possible channels.

Conclusion

Asset prices are signals and the informativeness of these signals increases with asset liquidity. In turn asset liquidity increases with the amount of information that liquidity suppliers can learn from prices. This joint determination of price informativeness and liquidity generates a feedback loop whereby small shocks affecting the liquidity of one asset can have large effects on the liquidity of all assets. This is a source of co-movement in liquidity and market fragility.


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