Positive Return–Volatility Correlation and Short Sale Constraints: Evidence from the Chinese Market

• Published date: 01 February 2018
• Author: Hong Luo,Liang Wu,Zhiming Fu
• DOI: http://doi.org/10.1111/ajfs.12204
• Date: 01 February 2018

Positive Return–Volatility Correlation and

Short Sale Constraints: Evidence from the

Chinese Market*

Liang Wu

The School of Economics, Sichuan University, China

Hong Luo

The School of Economics, Sichuan University, China

Zhiming Fu**

The School of Economics, Sichuan University, China

Received 19 January 2017; Accepted 9 September 2017

Abstract

The market price is a convex function of information when short sales are constrained. Bor-

rowing constraints limit investors to bidding up the price. The two effects imply an asym-

metric return–volatility correlation (RVC) when information shifts. We build a model to

show that: (i) short selling decreases RVC, while margin trading increases RVC; (ii) RVC

increases with disagreement; and (iii) RVC increases with returns. The Chinese stock market

is ideal for the empirical test because only certain stocks are eligible for short selling and

margin trading in the slow policy adoption process. We obtain evidence to support the theo-

retical predictions correlation.

Keywords Positive return–volatility correlation; Anti-leverage; Short sale constraints; Margin

trading

JEL Classification: C46, C58, G14

*Partial financial support from the Fundamental Research Funds for the Central Universities

under grant number skyb201403 and 201506 is gratefully acknowledged. Financial support

from National Social Science Foundation of China (16CJL042) is gratefully acknowledged.

The authors are very grateful to the associate editor and the referees for their constructive

suggestions and their proposed corrections to improve this paper. We also would like to

acknowledge that our research was supported by the National Natural Science Foundation of

China Project Numbers 71742004 and 71673194.

**Corresponding author: The School of Economics, Sichuan University, Chengdu 610065,

China. Tel: +86-28-8541-2504, Fax: +86-28-8547-0032, email: ZhimingFu@scu.edu.cn.

Asia-Pacific Journal of Financial Studies (2018) 47, 132–157 doi:10.1111/ajfs.12204

132 ©2018 Korean Securities Association

1. Introduction

It has been shown theoretically by Miller (1977) and empirically verified by Fig-

lewski (1981), Jones and Lamont (2002), and Boehme et al. (2006) that when inves-

tors have divergent opinions, short sale constraints can cause the overpricing of an

asset. The underlying intuition is that when short sales are constrained, excessively

optimistic investors bid the asset price up to an unreasonable level, forcing other

investors to sit out and preventing negative opinions from being expressed.

The above studies focuse on the impact of short sale constraints on the price level,

which is a somewhat static feature of the market. If we believe that the market price is

driven by information

1

then a dynamic picture of Miller’s (1977) story of the impact

of short sale constraints when investors have heterogeneous beliefs is that when mar-

ket information is bullish, the optimistic group bids up the price, while the pes-

simistic group is crowded out, which amplifies the price-increasing effect of bullish

information. When the market information is bearish, both groups can participate,

and the price reflects an averaged, less biased opinion, cushioning price decreases.

The magnitude of price change would be asymmetric when the information is bullish

versus bearish, leading to a positive return–volatility correlation (RVC).

There are other market frictions that can interact with short sale constraints.

2

During the run-up phase of the market, short sale constraints are binding when the

price is far greater than the pessimistic group’s evaluation. In the meantime, the opti-

mistic group could face credit constraints when the market valuation is bid up by

them. The two offsetting forces, short sale constraints and borrowing constraints,

could be binding at the same time. The conjecture that optimistic investors could bid

up the price is based on the assumption that they are sufficiently financed. It has been

shown both theoretically and empirically that borrowing constraints have an under-

pricing effect (Yuan, 2005, 2006). It would be interesting to study their interactions to

determine whether the RVC is positive or negative. In this paper, we incorporate the

short sale and borrowing constraints into one model to study their impacts on the

return–volatility relationship.

Xu (2007) formalized the idea of an asymmetric price response to information

in a setting in which two groups of heterogeneous investors observe the same public

information but disagree about its precision. High precision investors consider the

information more certain than low precision investors and thus have a higher pos-

terior evaluation of the risky asset when the information is bullish. The price

reflects the biased up evaluation of the high precision investors, which goes bac k to

Miller’s (1977) theory of overpricing. However, when the information is less bullish

1

The information can be news or something regarded as information interpreted by investors

from market trading activities.

2

Cen et al. (2013) studied the interaction of two offsetting forces: disagreement and senti-

ment. Cen et al. (2017) suggested that short-sale constraints are more likely to be binding

when investors underreact to bad news.

Return-Volatility Correlation

©2018 Korean Securities Association 133