In recent theoretical research, the idea that market returns endogenously affect liquidity has received attention. For example, in Brunnermeier and Pedersen (2005), market makers obtain significant financing by pledging the securities they hold as collateral. A large decline in aggregate market value of securities reduces the collateral value and imposes capital constraint, leading to a sharp decrease in the provision of liquidity. Liquidity dry-ups arise when the worsening liquidity leads to call for higher margins, and feedback into further funding problems. Since this supply of liquidity effect affects all securities, Brunnermeier and Pedersen also predict larger commonality in liquidity following market downturns. Anshuman and Viswanathan (2005), on the other hand, present a slightly different model where investors are asked to provide collateral when asset values fall and decide to endogenously default, leading to liquidation of assets. Simultaneously, market makers are able to finance less in the repo market leading to higher spreads, and possibly greater commonality in liquidity.
Several other recent papers link changes in asset value to liquidity. In Morris and Shin (2003), traders sell when they hit price limits (which are correlated across traders) and liquidity black holes emerge when prices fall enough (the model in analogous to a bank run). Their model emphasizes the feedback effect of one trader’s liquidation decision on other traders. According to Kyle and Xiong (2001), a drop in stock prices leads to reduction in holdings of risky assets because investors have decreasing absolute risk aversion, resulting in reduced market liquidity (see also Gromb and Vayonos (2002) for a model of capital constraints and limits to arbitrage). In Vayanos (2004), investors withdraw their investment in mutual funds when asset prices (fund performance) fall below an exogenously set level. Consequently, when mutual fund managers are close to the trigger price, they care about liquidity, especially during volatile periods. Hence, these theoretical models also emphasize shifts in demand for liquidity with changes in asset prices as liquidation of assets generates more selling pressure. Additionally, some of the above models also suggest cross-sectional differences in the liquidity effects: a drop in asset value has a greater impact on the liquidity of stocks with greater volatility exposure, a phenomenon related to flight to liquidity (see e.g. Anshuman and Viswanathan (2005), Vayanas (2004) and Acharya and Pedersen (2004)).