The assessment of stock volatility has attracted increasing attention among academic researchers. Market stock volatility is associated with future investment opportunities for firms. Market volatility can affect the value of a firm’s shares. Therefore, firms respond by raising more capital by issuing shares or by using their stocks as leverage to buy firms or acquire competitors. It is believed that investors, financial analysts, and portfolio managers are aware of the volatility in stock investment. Previous researchers have proposed various measures of volatility. Altman and Schwartz [
23] define the uncertainty of stock price movement as a volatility measure. Pinches and Kinney [
24] also employ basic historical volatility measure (i.e. daily standard deviation of stock returns). In addition, volatility is measured by implied volatility presented in an option pricing model [
25,
26]. Volatility cannot be observed directly; thus, it is necessary to employ a reasonable proxy for it when conducting financial studies.
Researchers have continuously discussed and argued about the relation between an asset’s volatility and its return. French et al. [
27] use the Autoregressive Conditional Heteroskedasticity in Mean (ARCH-M) model of Engle et al. [
28] and find a positive relation between expected return and stock market volatility in the U.S. stock market from January 1928 to December 1984. Goyal and Saretto [
29], based on the U.S. equity option market data from 1996 to 2005, show that the volatility risk premium, the difference between individual implied volatility and historical volatility, is positively related to option returns. A positive relation between returns and volatility is also observed by subsequent researchers [
30,
31,
32,
33,
34]. By contrast, other studies show a negative relation or insignificant estimates [
35,
36,
37,
38,
39]. For example, Glosten et al. [
39] observe a negative relationship between returns and stock volatility during 1951 to 1989 by using the modified Generalized Autoregressive Conditional Heteroskedasticity in Mean (GARCH-M) model. More recently, Ang et al. [
3] have found that innovation in market volatility has a negative risk price of approximately −1% per annum for a sample of the U.S. market from 1986 to 2000 by using the Chicago Board Options Exchange Volatility Index as a proxy for market volatility. Da and Schaumburg [
40] use a sample of the U.S. market to examine the pricing of volatility across asset classes. They find that market-volatility factor can price different assets such as portfolios of stocks, stock options, and corporate bonds. Consistent with the previous study, significant negative volatility risk premiums are observed in the stock and option markets, with the premium for corporate bonds also negative but not significant because corporate bond returns were volatile during the period covered. However, the magnitude of the risk premium is similar across different assets, thereby supporting the contention that the market volatility is a pricing factor in asset pricing model. The results of Cremers et al. [
41] in the U.S. market between 1988 and 2011 also show that volatility risk factor is negatively priced in the cross-section of stock returns. This relationship is examined in the context of the BRIICKS (Brazil, Russia, India, Indonesia, China, South Korea, and South Africa) economies by Sehgal and Garg [
42]. They find low premiums for portfolios with high market volatility in Brazil, South Korea, and Russia. However, significantly positive risk premiums are found for Indonesia and South Africa. In India and China, no significant risk premiums are reported. With a sample of 17 international stock markets from December 1992 to December 2007, Dimitriou and Simos [
43] find a significantly negative relationship between stock volatility and expected returns in most markets, except Austria, Belgium, and Luxemburg by using a semiparametric specification for the conditional variance. Using the GARCH-M model in four of China’s stock exchanges, Lee et al. [
44] find no evidence of a relationship between volatility and expected return. In the context of emerging financial markets, De Santis and Imrohoroǧlu [
45] do not find any relation between expected stock returns and volatility in each country. However, they detect a risk-reward relation in the Latin American markets when they generalize their model and assume international integration. Using GARCH in the mean estimations, Shin [
46] find a positive but insignificant relation between expected stock returns and volatility in emerging markets. Chiang and Doong [
47] find significant relationships between stock volatility and returns in four out of the seven Asian stock markets by following the method suggested by French et al. [
27]. In summary, the role of market volatility factor in asset pricing test remains controversial.
A better approach than the one-factor model for market return volatility is the two-component volatility specification [
5,
6,
7,
8,
9,
10,
11,
12]. For instance, Alizadeh et al. [
7] identify two factors in the volatility models. Specifically, they argue that there are two factors, one highly persistent and slowly moving, the other rapidly moving. The two-factor stochastic volatility models are also investigated in the option pricing literature [
13,
48,
49]. For example, for the valuation of European options, Christoffersen et al. [
13] present a new model with two long- and short-term components of the volatility of returns. In the Hong Kong stock market, Ané [
14] suggests that a model including short- and long-term volatility components significantly improves the goodness-of-fit over the traditional single model. Adrian and Rosenberg [
15] also decompose market volatility into short- and long-term components to further support the relationship between returns and volatility. Based on U.S. stock market data from 1963 to 2005, they find that both volatility components have significantly negative risk prices. Specifically, the short-term volatility has a risk price of −2.25% per annum, and the long-term volatility has a risk price of −24.24% per annum. Yang and Copeland [
16] also apply the decomposition of market volatility to the UK stock market to examine whether the short- and long-term volatilities are priced in the cross-section of stock returns and to estimate the prices of these components. Their study asserts that the short- and long-term volatility components are also negatively priced. By contrast, using the two-component model, Guo and Neely [
17] confirm a positive relationship between volatility risk and returns based on international stock market data from 1974 to 2003. Zhu [
18] decompose volatility into a volatile component and a persistent component to examine the relation between volatility and returns. By analyzing data from 10 Asia-Pacific stock markets—eight Asian and two Oceanian stock markets—the volatile component is found to have a significant positive relation with returns. By contrast, the persistent component is not significantly priced in the respective stock markets.
Based on this stream of literature, two components of market volatility can be priced in the cross-section of stock returns. Therefore, this study examines the pricing of two components of market volatility risk in the Korean stock market to fill the gap in the literature. We decompose market volatility into short- and long-term volatility based on the model specification suggested by Adrian and Rosenberg [
15]. However, our study differs from Adrian and Rosenberg [
15] in measuring innovations of the volatility components at a monthly frequency. We construct factors that mimic volatility-component innovations, similar to the method used by Ang et al. [
3], instead of summing innovations over the days of each month.