The impact of trading restrictions and margin requirements on stock index futures

• Author: Jun Tong,Tianxiang Wang,Jianqiang Hu,Wenwei Hu
• Date: 01 July 2020
• Published date: 01 July 2020
• DOI: http://doi.org/10.1002/fut.22111

J Futures Markets. 2020;40:1176–1191.wileyonlinelibrary.com/journal/fut1176

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© 2020 Wiley Periodicals, Inc.

Received: 19 September 2018

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Accepted: 22 February 2020

DOI: 10.1002/fut.22111

RESEARCH ARTICLE

The impact of trading restrictions and margin

requirements on stock index futures

Jianqiang Hu

1

|Tianxiang Wang

1

|Wenwei Hu

2

|Jun Tong

3

1

School of Management, Fudan University, Shanghai, China

2

School of Management Studies, Shanghai University of Engineering Science, Shanghai, China

3

School of Management, Zhejiang University of Technology, Hangzhou, China

Correspondence

Jun Tong, School of Management,

Zhejiang University of Technology, 310014

Hangzhou, China.

Email: tongjunsh@yahoo.com

Funding information

National Natural Science Foundation of

China, Grant/Award Numbers:

71720107003, 71571048

Abstract

Stock index futures in Chinese market have consistently diverged from their

theoretical values. In this paper, we try to provide some explanations by

proposing an equilibrium model. Although the model itself does not provide

analytical solutions, it enables us to conduct extensive numerical studies and

compare them with our empirical results on two major Chinese market

indices, CSI300 and SSE50. Our results show that the divergence of stock index

futures prices from their theoretical values may be due to various trading and

regulatory constraints, such as position limits and margin requirements, which

play significant roles in Chinese market.

KEYWORDS

margin requirement, market liquidity, position limit, stock index futures

1|INTRODUCTION

It has been observed in many empirical studies that stock index futures prices are frequently divergent from and are in

many instances below their theoretical values. This problem was interpreted first by Zeckhauser and Niederhoffer

(1983) as the result of convenience of short selling in the futures market and its fast reaction to new information relative

to the stock market, followed by Kawaller, Koch, and Koch (1987), Chan (1992), Pizzi, Economopoulos, and O'Neill

(1998), and Ersoy and Çıtak (2015) along a similar line. On the other hand, Cornell and French (1983a,1983b)

considered it to be the consequence of taxing rather than market inefficiency, although they also pointed out that

prohibiting short sales is another significant factor driving the futures price down because it impedes the arbitrage

trading and attracts investors to the futures market. This viewpoint was empirically supported by Puttonen (1993), Pope

and Yadav (1994), and Fung and Draper (1981) who tested various markets, although it has been pointed out recently

by Jarrow, Protter, and Pulido (2015) that under a no‐arbitrage framework, the trading of futures may not be able to

overcome the constraint on short sales in the stock market. However, despite these earlier works, there are still very few

analytical models available in the literature to analyze the impact of market inefficiency and liquidity caused by trading

and regulatory constraints on the pricing of stock index futures.

Our work in this paper is an attempt in this direction. In fact, our work is especially motivated by a phenomenon

observed in recent years in the Chinese market: Stock index futures prices have significantly and consistently deviated

from their theoretical values since their introduction to the Chinese market in 2010.

In Figure 1, we depict the difference between the futures price of Chinese stock index CSI300 and its spot price (as a

percentage w.r.t. the spot price) during 2010–2019. We can see from Figure 1that from 2010 to early 2015, the price of

CSI300 futures was significantly above the spot price during several portions of that time period while it became

significantly lower than its spot price for the majority of the time after early 2015. We believe that this phenomenon is

mainly due to stringent limits and constraints that Chinese regulators impose on their futures and equity markets (such

as high margin requirement, low position limit, and short‐selling restriction) and some dramatic changes they made

during the periods of market turbulence. It is clear that these stringent regulations significantly increase trading costs

and reduce market liquidity, hence distort asset prices. As a result, we see stock index futures significantly diverge from

their theoretical values.

Up to this date, the cost‐of‐carry model proposed by Cornell and French (1983a,1983b) is still the most commonly

used method to calculate the theoretical value or fair price of futures. In the cost‐of‐carry model, the futures price is

derived based on a no‐arbitrage portfolio which depends on the spot price of the underlying index, the risk‐free interest

rate, the dividend yield, and the time to maturity. It simply views a futures contract as a forward contract, for example,

see Cox, Ingersoll, and Ross (1981) and Kamara (1984). Despite its popularity, the cost‐of‐carry model has one severe

shortcoming: It assumes that financial markets are perfect in that any arbitrage strategy can be carried out, while in

reality there are various trading and regulatory constraints in the markets which can prevent some arbitrage strategies

from being realized.

In this paper, we propose an equilibrium model to study how trading and regulatory constraints may affect stock

index futures prices. These constraints include a short‐selling restriction on stocks and a margin requirement on futures

trading. Our model is very different from the cost‐of‐carry model. It has a similar setup to that of the early work by

Jarrow (1980) with a few exceptions:

1. It allows stock index futures as a type of asset available to investors.

2. It allows position limits on stocks, with both lower and upper limits on the amount of each stock that every investor

can own.

3. It allows margin requirements for both short‐selling stocks and trading futures.

With this model, we are able to show that stock index futures prices can be influenced by various factors, in

particular, by position limits (e.g., no short selling on stocks) and margin requirements. In general, we show that stock

index futures prices would deviate from their fair (theoretical) values due to these restrictions and requirements. For

example, we show that if short selling is not allowed for stocks, then the stock index futures price would be lower than

FIGURE 1 Basis of CSI300 during 2010–2019 [Color figure can be viewed at wileyonlinelibrary.com]

HU ET AL.

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