Empirical Pricing Kernel and Option-Implied Risk Aversion in China 50 ETF

ABSTRACT

Based on an analysis of the China 50 ETF options and their underlying assets, we measure the empirical pricing kernel and implied risk aversion. By employing a Markov-switching GARCH model, the estimated results show a monotonically decreasing pricing kernel under a high-volatility regime and a U-shaped pricing kernel under a low-volatility regime. The implied risk aversion is inversely S-shaped under both high- and low-volatility regimes. However, the implied risk aversion under the low-volatility regime has a wide range. Investors’ risk aversion perspective helps explain patterns of pricing kernels and risk aversion estimates. Finally, we find that implied risk aversion is predictive of short-term (excess) market returns based on in-sample and out-of-sample tests.

KEYWORDS:

• Pricing kernel
• Option-implied risk aversion
• pricing kernel puzzle
• MSGARCH
• option on the China 50 ETF

JEL:

• G10
• G12
• G13

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Supplementary Material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/1540496X.2022.2089559

Notes

1. The literature review on empirical pricing kernel and option-implied risk aversion can be found in the online Appendix.

2. Similar to Note 1.

3. There is literature to support the representativeness of the use of China 50 ETF data. For example, Li (2021) also used this as an indicator to measure the risk sentiment of the market. We thank the Subject Editor’s suggestion on this.

4. This approach was first adopted by Mehra and Prescott (1985) in exploring the stock premium puzzle. They calibrated the market data with a representative investor of a power utility function. The resulting risk aversion coefficient was too high compared with the estimated aversion coefficient based on the survey. Kocherlakota (1996) and Mehra (2006) also used such methods. Benth, Groth, and Lindberg (2010) calibrated the market data with a representative investor of an exponential utility function.

5. According to Banz and Miller (1978), Breeden and Litzenberger (1978), and Cox and Ross (1976), all investors are assumed to be risk-neutral. Then the expected return of all assets, including options, will be set to the risk-free rate. Then, the risk-neutral probability distribution can be estimated through the options on the market and the price of the market portfolio. Finally, the empirical pricing kernel can be obtained by comparing two estimates of probability distribution functions.

6. Referring to the rule of thumb in Silverman (1986), the bandwidth of a Gaussian kernel density estimator is set to $\frac{1.8\sigma }{\sqrt[5]{10,000}}$, where $\sigma$ is the standard deviation of the annualized stock return based on the exponential level simulation data.

7. Instead of relying on parametric assumptions, in nonparametric methods, people could use option prices data to estimate the points of risk-neutral probability distributions directly (e.g., Aït‐Sahalia and Lo 1998; Figlewski 2008; Jackwerth 2004; Rosenberg and Engle 2002).

8. The details of deriving risk-neutral distributions can be found in the online Appendix.

9. For ease of presentation, the results of the MSGARCH model, the risk-neutral and physical probability density functions, and implied volatility of SSE 50 ETF index are relegated to the online Appendix.

10. We present the estimated results of the predictability of excess stock returns of investors’ risk aversion for options within the four-week term. Similar results can be obtained for the two- and six-week terms and are available from the authors upon request.

11. We thank the Editor in Chief’s suggestion of demanding us to report out-of-sample prediction analyses, which can cross-check the results of investors’ risk aversion with the MSGARCH model from the in-sample test.

12. The detailed definition of these statistics can be found in the online Appendix.