Volatility And Liquidity

Dan Amiram

Columbia Business School – Accounting, Business Law & Taxation

Balazs Cserna

University of Frankfurt

Ariel Levy

Technion-Israel Institute of Technology – The William Davidson Faculty of Industrial Engineering & Management

June 15, 2015

Columbia Business School Research Paper No. 15-62

Abstract:

The positive relation between stock return volatility and illiquidity has long been documented. We revisit this relationship using recent developments in the literature and decompose total volatility into its jump and diffusive components. This investigation yields several new insights. We find that the positive relation between total volatility and illiquidity is exclusively driven by the jump component. In contrast, we find a negative relation between diffusive volatility and illiquidity, even though this component is what is commonly perceived as volatility. We show that this negative relation is driven by the positive association between diffusive volatility and trading activity. Our findings extend the understanding of liquidity and liquidity risk and have implication to market microstructure and disclosure policies.

Volatility And Liquidity – Introduction

The relationship between asset liquidity and return volatility has been studied extensively both theoretically and empirically. Market microstructure theories predict that higher return volatility increases illiquidity (e.g., Stoll, 1978a). A simplified description of the mechanism behind these theories is that market-makers, who must hold the stock, bear higher inventory risk for more volatile stocks. These theories are supported by numerous empirical studies that have confirmed the predicted positive relation between illiquidity and return volatility (e.g., Stoll 1978b, 2000; Amihud and Mendelson, 1989; Bao and Pan, 2013).

However, treating volatility as a uniform measure with a homogeneous impact on liquidity overlooks the subtle, yet potentially important, structure of total volatility. More realistic developments in the asset pricing literature treat stock returns as a jump-diffusion process, that is, as a combination of a continuous Brownian motion component and a discontinuous jump component. Consequently, this approach implies that the total return variance is an aggregate outcome of two separate sources that have very different characteristics. While volatility patterns generated by a discontinuous jump process arise from infrequent, large, isolated “surprise” price changes, the diffusive volatility arises from smooth and more “expected” small price changes. The overall volatility is merely the integration of these two types of volatility.

This literature has also emphasized, as we discuss in detail below, three additional facts. First, jumps in prices are di¢ cult to hedge, unlike diffusive changes. Second, jumps are mainly driven by information events. Third, diffusive volatility is associated with increased trading, while jump volatility is not. These three facts directly relate to the two channels affecting illiquidity, as illiquidity is theoretically driven by inventory risk and information adverse selection. This gives rise to our research question: Do the jump and diffusive components of total volatility have the same effect on liquidity? Alternatively stated, does the structure of volatility matter for liquidity in addition to raw levels of volatility?

The centrality of liquidity to the functioning of capital markets underscores the importance of understanding the separate impacts each volatility component has. For example, targeting the reduction of jump volatility as opposed to diffusive volatility would require the implementation of a different set of regulatory policies. While jumps are mostly attributed to new information that dramatically affects prices, diffusive volatility may be attributed to noise trading. Therefore, if it is primarily the jump-driven volatility component that affects illiquidity, implementing accounting policies that encourage more continuous information disclosure may make sense to increase liquidity, rather than policies targeting noise trading, such as restricting short-selling or lending securities.

Moreover, understanding how each volatility component impacts liquidity is important for the understanding of asset pricing as prior studies have shown that liquidity risk significantly affects expected returns (e.g., Pastor and Stambaugh, 2003; Acharya and Pederson, 2005; Brunnermeier and Pederson, 2009). As suggested below, jump and diffusive volatilities have different correlations with illiquidity. Since these studies show that it is the correlation between firm-specific and market liquidity or market return that drives liquidity risk, this implies that jump and diffusive volatility components have different implications for liquidity risk. That is, the extent to which different volatility components have different effects on liquidity has direct consequences to liquidity risk as well.

There are at least four reasons why the jump volatility component could have a more dominant effect on liquidity compared to the diffusive component. The first is associated with the inventory risk dimension of liquidity. Market-makers bear the risk of price changes to their stock inventories, which they must maintain. Therefore bid-ask spreads are set to compensate them for bearing this inventory risk (e.g., Stoll 1978a; Amihud and Mendelson, 1980; Ho and Stoll, 1981; Ho and Stoll, 1983). Nevertheless, in a diffusive environment, market-makers can control their potential losses, update their inventory portfolios, and fix “stop-loss” rules in a more flexible and gradual manner compared to a trading environment that exhibits infrequent dramatic price changes. That is, jumps impose a more restrictive set of risk management tools and stopping rules compared to diffusive price changes.

Volatility

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