Unveiling Contemporaneous Relations Between Jump Risk and Cross Section of Stock Returns

• Author: Krishna Prasanna,Saranya Kshatriya
• DOI: http://doi.org/10.1111/irfi.12235
• Published date: 01 September 2020
• Date: 01 September 2020

Unveiling Contemporaneous

Relations Between Jump Risk and

Cross Section of Stock Returns

SARANYA KSHATRIYA AND KRISHNA PRASANNA

Department of Management Studies, Indian Institute of Technology Madras,

Chennai, India

ABSTRACT

This study analyzes the impact of time varying jump risk on aggregate

returns. We, in particular, examine the pricing of jump size and intensity

components in the cross section of stock returns for four Asian markets. We

use stochastic volatility model with jumps to estimate jump size and inten-

sity. Fama–MacBeth regression results indicate that both jump size and

intensity have statistically significant effect on expected returns. A one stan-

dard deviation increase in jump intensity beta lowers the expected annual

returns by 1% for Japan, 2% for China, 5% for India, and 7% for South

Korea. The results are consistent even after controlling for the Fama and

French three factors, firm size, and liquidity proxies.

Accepted: 8 August 2018

I. INTRODUCTION

Risk-based models, such as the capital asset-pricing model (Treynor 1961;

Sharpe 1964; Lintner 1965a, 1965b; Mossin 1966) and Fama and French three-

factor models (Fama and French 1993), have gained prominence in financial

asset pricing literature. Since then, market value (size), book-to-market equity

(BTM) ratio, and market risk are considered to be the three predominant risk

factors that explain the cross section of asset returns. However, in light of

recent financial crises and economic cycles, the stock returns are observed to be

sensitive to market crashes, discontinuities, and infrequent drastic price move-

ments (Cremers et al. 2015). Moreover, these discontinuities, otherwise referred

to as jumps, in the returns have a substantial impact on pricing (Merton 1973;

Cox and Ross 1976). Hence, the present study investigates the effects of these

jumps on the cross section of stock returns.

The financial literature contemplates that jump risk varies over time (Bates

1991; Santa-Clara and Yan 2010). Prior studies indicate that the classic asset

pricing models are not sufficient to explain the variation in expected returns

when the price patterns exhibit discontinuities, momentum, and reversals

(Cakici et al. 2015). Hence, this study investigates the sensitivity of investors to

© 2018 International Review of Finance Ltd. 2018

International Review of Finance, 20:3, 2020: pp. 581–604

DOI: 10.1111/irfi.12235

the jump risk and examines whether jump risk gets discounted in the price dis-

covery process.

The importance of jumps in the financial arena of risk management, hedg-

ing, and investment decisions has been well established. Prices for options vary

abruptly during market crashes (Bates 2000). A substantial premium is required

to compensate for the time-varying jump risk (Pan 2002). Nevertheless, there

are few studies on understanding the role of the jump risk in asset pricing, par-

ticularly in the context of emerging Asian markets. Ignoring jump risk would

lead to misspecification bias in factor-based models and thus affect hedging and

diversification decisions. Given this context, this study embeds a jump compo-

nent as a separate risk factor into the asset pricing model to analyze its impact

on equity returns.

Naik and Lee (1990) conceptualized the theoretical importance of jump risk

while pricing options. Andersen et al. (2002) and Huang and Wu (2004), have

highlighted the importance of jumps in US markets using S&P 500 index return

data and SPX option data respectively. Chang et al. (2013) suggested that the

market price of jump risk is positive, while Cremers et al. (2015) observed it to

be negative. The sensitivity of stock returns to jumps might vary based on the

magnitude and direction of jump (Bates 2008). Most of these prior studies

either explored the impact of jumps on option pricing or used proxy of jump

risk while investigating the contemporaneous relation.

Hence, we estimated the realized jump intensity and size of each stock using

stochastic volatility model with jumps (SVJ) and analyzed the impact of time-

varying jump risk. We examine the pricing of jump size and intensity compo-

nents in the cross section of stock returns for four Asian markets: India, China,

South Korea, and Japan. The actual jump frequency and size of each constitu-

ent stock of BSE500, KOSPI200, TPX1000, and SSE Composite indices, totaling

2310 stocks, were estimated every year over a period of 11 years from January

1, 2005 to December 31, 2015. The jump intensity is computed from the

obtained size and frequency of the stock.

Following Fama and French (1993), we obtained the jump size factor by tak-

ing the difference between the high and low portfolios constructed based on

jump size. Similarly, we ascertained the jump intensity risk factor. We

employed a Fama and MacBeth (1973) regression to identify the aggregate

impact of intensity and size of the jumps on the cross section of asset returns.

Our empirical results indicate that both jump size and intensity have statisti-

cally significant effects on expected returns. A one standard deviation increase

in jump intensity beta lowered the annualized returns by 1% for Japan, 2% for

China, 5% for India, and 7% for South Korea. However, the effect of jump size

on Japanese markets is observed to be insignificant. Consistent with the theory,

stocks with higher sensitivity to jumps have lower expected returns. This

implies that jumps carry significant negative market price. The results are con-

sistent even after controlling for Fama–French three factors, firm size, and

liquidity proxies.

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