Illiquidity transmission from spot to futures markets

• Author: Erik Theissen,Paolo Krischak,Olaf Korn
• Date: 01 October 2019
• Published date: 01 October 2019
• DOI: http://doi.org/10.1002/fut.22043

J Futures Markets. 2019;39:1228–1249.wileyonlinelibrary.com/journal/fut1228

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© 2019 Wiley Periodicals, Inc.

Received: 22 August 2017

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Accepted: 14 June 2019

DOI: 10.1002/fut.22043

RESEARCH ARTICLE

Illiquidity transmission from spot to futures markets

Olaf Korn

1,2

*

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Paolo Krischak

1

*

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Erik Theissen

2,3

*

1

Faculty of Business and Economics,

University of Goettingen, Goettingen,

Germany

2

Centre for Financial Research Cologne

(CFR), Cologne, Germany

3

Finance Area University of Mannheim,

Mannheim, Germany

Correspondence

Erik Theissen, University of Mannheim,

68161 Mannheim, Germany.

Email: theissen@uni-mannheim.de

Abstract

We develop a model of illiquidity transmission from spot to futures markets that

formalizes the derivative hedge theory of Cho and Engle (1999). The model

shows that spot market illiquidity does not translate one to one to the futures

market but, rather, interacts with price risk, liquidity risk, and the risk aversion

of the market maker. The model’s predictions are tested empirically with data

from the stock market and markets for single‐stock futures and index futures.

The results support our model and show that the derivative hedge theory

provides an explanation for the liquidity link between spot and futures markets.

KEYWORDS

futures markets, illiquidity, liquidity risk

JEL CLASSIFICATION

G10; G13

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INTRODUCTION

Spot and futures markets are closely related because prices are exposed to a common risk factor. For the liquidity of

both markets to be linked is therefore a natural conjecture. This link is relevant to investors, exchange operators, and

regulators alike. Investors seek to follow a strategy that minimizes their illiquidity costs and exchange operators try to

attract these investors. Regulators need to understand illiquidity spillover and contagion effects to assess the impact of

regulatory measures, such as short‐sale bans, on the liquidity of both markets.

Surprisingly little is known about the relation between spot market liquidity and futures market liquidity. There are two

opposing views. The first argues that the two markets are substitutes, while the alternative view argues that they are

complements. If substitution dominates, some investors will migrate from one market to the other if the relative costs in the

two markets change. This results in an inverse relation between spot market liquidity and futures market liquidity, the so‐

called substitution hypothesis. Subrahmanyam (1991) develops a model of such migration effects, arguing that

the introduction of stock index futures lowers the liquidity of the corresponding spot markets because uninformed traders

move to the futures market to avoid adverse selection costs.

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Jegadeesh and Subrahmanyam (1993) investigate the liquidity

of the Standard & Poor’s 500 stocks around the introduction of the Standard & Poor’s 500 index futures contract and find

evidence in support of an inverse liquidity relation between the equity and futures markets. However, Choi and

Subrahmanyam (1994) do not find a similar effect upon the introduction of the Chicago Board of Trade (CBT’s) Major

Market Index futures. Complementary empirical evidence in favor of substitution is provided by Benzennou, ap Gwilym,

and Williams (2018). They analyze single‐stock futures (SSFs; traded on the London Stock Exchange) written on stocks listed

*Olaf Korn, Paolo Krischak, and Erik Theissen contributed equally to this study.

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Berkman, Brailsford, and Frino (2005) provide empirical support for the hypothesis that asymmetric information is low in index futures markets.

on NYSE Euronext. During the 2008–2009 short‐sale ban for the underlying stocks (an event that negatively affected liquidity

in the stock market) the liquidity of the corresponding SSFs contracts is found to improve.

The idea that spot and derivatives markets are complements was first formulated for option markets. Cho and Engle

(1999) propose what they call the derivative hedge theory. It is based on the argument that an illiquid spot market

increases the hedging costs of market makers in the options market, causing the liquidity in the two markets to move in

parallel. Kaul, Nimalendran, and Zhang (2004), Engle and Neri (2010), Wei and Zheng (2010), Goyenko, Ortahanlai,

and Tang (2015), and Guillaume (2015) provide empirical support for a positive relation between spot market liquidity

and options market liquidity. The empirical results of Battalio and Schultz (2011) and Grundy, Lim, and Verwijmeren

(2012) point in the same direction. They investigate how the 2008 short‐sale ban for certain stocks in the United States

affected the corresponding options markets and find that the liquidity in the options market was lower during the ban.

The potential liquidity linkage of spot and derivatives markets via market makers’hedging costs has not been investigated

for futures so far. This is quite surprising because futures are very important risk management tools (Bodnar, Hayt, &

Marston,1998; Gay, Nam, & Turac, 2002). Moreover, futures play an important role in the price discovery process, as shown

by Fleming, Ostdiek, and Whaley (1996) and Chen and Gau (2009). According to these studies, the relative rates of price

discovery in spot, futures, and options markets are closely related to trading costs; and the linkage of trading costs in spot and

futures markets is exactly what we study in this paper. It is not only the importance of futures markets that makes it

interesting to investigate the derivative hedge theory for futures. There are good reasons why empirical evidence for options

might not transfer to futures. First, since stocks and futures are both linear instruments, they should be closer substitutes for

each other than stocks and options, giving potentially more support to the substitution hypothesis. Second, the pricing of

futures and options is different, which affects the risk management strategies of market makers. Options require a dynamic

hedging strategy, whereas linear instruments can be handled via static hedges. The requirement to hedge options

dynamically is why the empirical literature on the derivative hedge theory distinguishes between initial hedging costs and

rebalancing costs. As Goyenko et al. (2015) show, rebalancing costs can be the dominant ones. Because no rebalancing costs

accrue in the futures market, it is an open issue whether we find a similar illiquidity transmission for futures than for

options. Finally, the role of spot market volatility in the process of illiquidity transmission is likely to be different for futures

as compared to options. For both instruments, volatility affects market makers’inventory risk. However, volatility is more

closely intertwined with the pricing process of options, making it likely that volatility plays a more important role as a

moderating variable for option illiquidity than for futures illiquidity.

Our paper is the first one to investigate the derivative hedge theory for futures. Its first contribution is

the development of a theoretical model of the illiquidity transmission from spot to futures markets that formalizes the

derivative hedge theory. The model shows that the illiquidity of the spot market does not translate one to one to the

futures market but, rather, interacts with liquidity risk, price risk, and the risk aversion of the market maker. Our model

provides hypotheses on the drivers of futures market illiquidity. These hypotheses are tested in an empirical study,

which is the second contribution of the paper. We use data from the stock market and the market for SSFs and find

support for the hypotheses derived from our model. Our results thus indicate that the derivative hedge theory is

important for the understanding of the liquidity link between spot and futures markets.

In a first set of robustness checks, we consider different control variables. The results indicate that asymmetric

information provides a further empirically important connection between stock illiquidity and futures illiquidity.

However, even after controlling for asymmetric information, the effects identified by our inventory‐based model are still

highly significant. In a further robustness check, we repeat the empirical analysis using data from the market for stock

index futures. Again we find support for the predictions of our model. However, for index futures, we also find evidence

that is consistent with the existence of a substitution effect.

Our paper is related to the empirical and theoretical literature showing that spot market illiquidity has an impact on

hedging strategies and derivative prices. In an empirical investigation, Roll, Schwartz, and Subrahmanyam (2007) show that

the liquidity of the spot market affects the effectiveness of futures arbitrage and has an impact on the futures basis. Karakaya

(2014), Choy and Wei (2016), Kanne, Korn, and Uhrig‐Homburg (2016), and Christoffersen, Goyenko, Jacobs, and Karoui

(2018) provide empirical evidence on a link between spot market illiquidity and option prices. Liu and Yong (2005), Cetin,

Jarrow, Protter, and Warachka (2006), and Lai and Lim (2009) study the pricing and hedging of options when the spot asset

is not perfectly liquid, which is in the same spirit as our theoretical model for the futures market. Moreover, our theoretical

model is related to the literature on the effects of demand pressure and market makers’inventory risk on derivatives prices,

such as the works of de Roon, Nijman, and Veld (2000), Bollen and Whaley (2004), Gârleanu, Pedersen, and Poteshman

(2009), Jankowitsch, Nashikkar, and Subrahmanyam (2011) and Muravyev (2016). Our study of liquidity builds on a

demand‐based pricing model that delivers a whole price impact function for the futures market.

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