Mispricing: failure to capture the risk preferences dependent on market states

Abstract

This paper explores the mispricing relative to the capital asset pricing model through an equilibrium model. We find that both the strong risk preference dependent on good market states and strong risk aversion dependent on bad market states can produce high mispricing. Choosing the China stock market, the largest emerging market dominated by individual investors and known for its volatile nature in a short history as our sample, the empirical results also support our theoretical findings. Overall, our paper sheds light on the mispricing caused by the investor’s risk preference reference-dependent on market states.

Appendix

• Return: The return of stock i in month t is defined as the logarithmic return including reinvestment of cash dividend on the stock in that month.

• VOL: The total volatility (VOL) of stock i in month t is defined as the standard deviation of daily returns within month t,

  $$ VOL_{{i,t}} = \sqrt {\text{Var} (R_{{i,d}} )} , $$

  (A1)

  where $R_{{i,d}}$ is the return on stock i on day d.

• Price: The price of stock i in month t is defined as the closed price of the stock on the last trading day in that month.

• Volume: The volume of stock i in month t is defined as the natural logarithm of total RMB trading volume of the stock in that month.

• Size: The size of stock i in month t is measured by the natural logarithm of the market value of equity (the closed price of the stock on the last trading day in that month times shares outstanding in thousands of RMB at the end of month t).

• Short-term reversal: Following Jegadeesh (1990), the reversal variable for each stock in month t is defined as the return on the stock in month t − 1.

• Momentum: Following Jegadeesh and Titman (1993), the momentum for each stock in month t is defined as the cumulative return on the stock over the previous five months starting two months ago, i.e., the cumulative return from month t − 6 to month t − 2.

• Illiquidity: Following Amihud (2002), we measure the illiquidity for each stock in month t as the ratio of the absolute monthly stock return to the respective RMB trading volume in that month,

  $$ Illiquidity_{{i,t}} = \frac{{\left| {R_{{i,t}} } \right|}}{{Volume_{{i,t}} }}, $$

  (A2)

  where $R_{{i,t}}$ is the return on stock i in month t, $Volume_{{i,t}}$ is the respective monthly trading volume in RMB.

• Turnover: The turnover of stock i in month t is calculated as the ratio of the number of shares traded to the number of shares outstanding in that month.

• Idiosyncratic volatility: Follow Ang et al. (2006), the idiosyncratic volatility (IVOL) of stock i in month t is defined as the standard deviation of daily residuals in a regression of the stock’s daily returns on the market factor in that month,

  $$ R_{{i,d}} - r_{{f,d}} = \alpha _{{i,t}} + \beta _{{i,t}} (R_{{m,d}} - r_{{f,d}} ) + \varepsilon _{{i,d}} , $$

  (A3)

  where $R_{{i,d}}$ is the return on stock i on day d, $r_{{f,d}}$ is the risk-free rate on day d, and $R_{{m,d}}$ is the market return on day d.

  $$ IVOL_{{i,t}} = \sqrt {\text{Var} (\varepsilon _{{i,d}} )} . $$

  (A4)

• Institutional ownership: In China’s stock market, the institutional investors include funds, qualified foreign investors, securities companies, insurance companies, social security funds, trust companies, financial companies, banks, non-financial listed companies, and other institutions. We take the sum of the shareholding proportions of these institutions as the institutional ownership (IO) and use quarterly IO as monthly IO for this quarter due to data disclosure restrictions.