Volatility and returns: Evidence from China†

• Published date: 01 December 2021
• Author: Yeguang Chi,Xiao Qiao,Sibo Yan,Binbin Deng
• Date: 01 December 2021
• DOI: http://doi.org/10.1111/irfi.12336

ORIGINAL ARTICLE

Volatility and returns: Evidence from China

†

Yeguang Chi

1

| Xiao Qiao

2

| Sibo Yan

3

| Binbin Deng

4

1

Graduate School of Management, The

University of Auckland, Auckland,

New Zealand

2

City University of Hong Kong, Kowloon

Tong, Hong Kong

3

University of California, Los Angeles,

California

4

Compass Lexecon, Chicago, Illinois

Correspondence

Xiao Qiao, City University of Hong, Hong

Kong.

Email: xiaoqiao@cityu.edu.hk

Abstract

Size, value, and momentum factors and industry portfolios in

the Chinese A-share stock market tend to have higher returns

in the months following high volatility. Due to this positive

relationship between lagged volatility and returns, volatility-

managed portfolios of Moreira and Muir (Volatility-managed

portfolios. Journal of Finance,72,1611–1644), which reduce

portfolio exposure when volatility is high, are spanned by the

original portfolios and do not improve the investor's opportu-

nity set. Volatility-scaled portfolios, which increase portfolio

exposure in volatile times, are not spanned by the original

portfolios and expand the investor's opportunity set. The

investor's mean–variance frontier shifts into more desirable

regions when volatility-scaled portfolios are included.

KEYWORDS

portfolio choice, return forecasting, volatility management

JEL CLASSIFICATION

G10; G11; G12; G15

There is strong theoretical basis to believe risk and return are positively related. Risk-averse investors value higher

returns and lower volatility, so risky investments must offer higher returns in equilibrium. In his groundbreaking work

on Modern Portfolio Theory,Markowitz (1952, 1959) demonstrates how investors can quantifytheir risk–return trade-

off by measuring portfolio expected returns against portfolio volatility. Since Markowitz, asset pricing theory and

empirics have largely been built around measuring and testing various forms of risk–return trade-offs. Modern asset

pricing modelsoften imply that in equilibrium, investors must takeon additional risk if they wanthigher returns.

The empirical evidence between risk and return is less clear. In its most basic form, a positive risk–return trade-

off implies higher volatility is associated with higher returns. Although there is a large literature on this topic,

†

We thank Ram Yamarthy for helpful comments. The views expressed are those of the individual authors and are not necessarily the views of Compass

Lexecon (“Compass”), its management, its affiliates, or its other professionals. This article is not an offer to sell or a solicitation of an offer to buy any

investment product or services offered by Compass. Compass does not guarantee the accuracy or completeness of the information contained herein, and

any information provided by third parties has not been independently verified by Compass. All errors are our own.

Received: 15 March 2020 Revised: 23 July 2020 Accepted: 17 October 2020

DOI: 10.1111/irfi.12336

© 2020 International Review of Finance Ltd

International Review of Finance. 2021;21:1441–1463. wileyonlinelibrary.com/journal/irfi 1441

evidence of a positive risk–return trade-off has been mixed. Campbell and Hentschel (1992) and French, Schwert,

and Stambaugh (1987) find a positive relationship between conditional expected returns and conditional variance,

whereas Campbell (1987) and Glosten, Jagannathan, and Runkle (1993) find a negative relationship. Contradictory

empirical results may be partially attributed to different research designs, but may also reflect a weak relationship

buried in noisy data. Whereas much of the existing literature focuses on the U.S. markets, we turn our attention to

the Chinese A-share stock market.

Established in 1991, China's A-share stock market has gone through rapid development. It has become the

second-largest stock market in the world with a market capitalization of $5 trillion by August 2016 (Chen &

Chi, 2018). While the Chinese stock market shares some similar characteristics as other large economies (Carpenter,

Lu, & Whitelaw, 2015), it does have its unique institutional features. For example, according to official statistics from

both the Shanghai and Shenzhen stock exchanges, more than 80% of the trading volume can be attributed to retail

investors. In contrast, institutional investors dominate trading in the U.S. stock market. As retail and institutional

investors may have different goals and can behave differently, asset prices may be impacted in different ways in a

retail-dominated market compared to an institution-dominated market.

Our paper investigates the empirical relationship between volatility measures and returns for China's A-share

stock market. We document a key empirical fact about volatility and returns: there is a positive relationship between

lagged volatility and future returns. Figure 1 illustrates this positive risk–return trade-off for the A-share value-

weight market portfolio. We compute a time series of monthly realized volatility using daily observations. We then

sort the volatility time series into five buckets, and we track the portfolio returns in the following month. In the most

volatile quintile, the annualized average return in the following month is 20%, the highest across all quintiles. In the

least volatile quintile, the annualized average return in the following month is −7%, the lowest of all quintiles. The

intermediate quintiles have average returns somewhere between the two extreme quintiles.

The Chinese evidence stands in sharp contrast to the U.S. evidence shown by Moreira and Muir (2017), where

expected returns show a lack of variation across the five volatility buckets for the U.S. value-weight market portfolio.

For China's A-share stock market, higher volatility appears to be associated with higher future returns. We also find

that lagged change in volatility to be positively associated with future returns. These patterns hold for market

returns, Fama and French (1992) factors, momentum (Carhart, 1997), and 63 industry portfolios defined by the

Global Industry Classification Standard (GICS) level-3 code.

A positive relationship between lagged volatility and returns has important implications for using volatility as a

portfolio management tool. Moreira and Muir (2017) demonstrate that for the U.S. stock market, scaling portfolio

returns inversely proportional to lagged variance produces higher Sharpe ratios and large alphas relative to the origi-

nal portfolios. Because volatility positively forecasts returns in the Chinese A-share stock market, the Moreira and

FIGURE 1 Volatility quintiles, value-

weight Chinese A-share stock market.

We sort monthly realized volatility of the

value-weight A-share market portfolio

into five buckets and track the portfolio

volatility and returns for the following

month. Average returns and volatility are

annualized. The sample is from January

1998 to December 2017

1442 CHI ET AL.