Tail risk aversion and backwardation of index futures

Abstract

We show that tail risk aversion, proxied by the skewness risk premium implied from the SSE 50 ETF options market, explains a significant proportion of the unusually deep backwardation of index futures during the 2015 Chinese stock market crash, while traditional factors such as non-synchronous trading, spot return, volatility and liquidity, all fail to explain the backwardation. These empirical results imply that investors' concern over the crash risk causes speculators to charge a high ‘insurance premium’ on hedgers. On the other hand, short-sale constraints, namely high security borrowing costs and other barriers, prevent reverse arbitrage such that the deep backwardation of index futures persists.

Keywords:

• Futures basis
• Skewness risk premium
• Tail risk aversion

JEL Classifications:

• G13
• G14

Acknowledgments

We thank two anonymous Quantitative Finance referees, for constructive suggestions that significantly improved the paper. We also thanks the participants of the Xiamen University-Tianjin University Forum on Quantitative Finance and Risk Management, the 1st Greater China Finance Symposium at Xiamen University, and the annual China Finance Research Conference at Tsinghua University, where earlier versions of this paper were presented. We have benefited from comments and suggestions by Qi Liang, Wei Zhang, Zongwu Cai, Yinggang Zhou, Xiaoyan Zhang, Qunzi Zhang. We are solely responsible for any remaining errors and omissions.

Disclosure statement

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

Supplemental data

Supplemental data for this article can be accessed online at http://dx.doi.org/10.1080/14697688.2024.2330612.

Notes

1 Besides being a proxy of tail risk premium, the SRP is also used as proxy of uncertainty, e.g. Feunou et al. (2018) or fears, e.g. Bollerslev and Todorov (2011). In both studies, tail risk premium, uncertainty and fears have the same implication. In this paper, the term of tail risk premium is used.

2 iVIX is a model-free SSE 50 ETF option implied volatility index which is similar to the CBOE VIX. It has not been published since 22nd February 2018.

3 We use the SRP to measure the tail risk (uncertainty) premium. This approach is easier to calculate than that in Bollerslev and Todorov (2011). Particularly, the SRP avoids separating the jump and diffusion parts from spot returns under both risk neutral measure and physic measure, which is necessary in Bollerslev and Todorov (2011).

4 The relative spread of spot, $R{S}_s^i$, is calculated by $R{S}_{s,t}^i=\frac{1}{N}\sum _{j=1}^N\left(\frac{1}{K}\sum _{k=1}^K\frac{\mathrm{Bi}{d}_k^j-\mathrm{As}{k}_k^j}{P_t^j}\right)$, where $i\in \{\mathrm{CSI}500,\mathrm{CSI}300,\mathrm{SSE}50\}$, $\mathrm{Bi}{d}_k^j$ and $\mathrm{As}{k}_k^j$ are bid and ask prices of index i's component stock j at intraday time k of date t, respectively. $P_k^j$ is the middle point of bid and ask price of component stock j at time k. N is the number of component stocks in index i and K is the number of samples for price within each intra-day. The relative spread of futures, $R{S}_{f,t}^i$, is calculated by $R{S}_{f,t}^i=\frac{1}{K}\sum _{k=1}^K\frac{\mathrm{Bi}{d}_k^i-\mathrm{As}{k}_k^i}{P_k^i}$, $\mathrm{Bi}{d}_t^i$ and $\mathrm{As}{k}_t^i$ are bid and ask prices of futures contract i at time k, respectively. $P_k^i$ is the middle point of bid and ask price of futures contract i at time k.

5 Technical details of the derivation of IRF can be found in White et al. (2015) for reference and codes in this paper are available on the website of the journal.

6 Our results are robust to substituting the $\widehat{\mathrm{Basis}}$ and the original basis for $\widetilde{\mathrm{Bward}}$.

7 These results may seem in contrast with those from the VAR analysis in which this relationship is insignificant. It may be related to that the explainability of liquidity to backwardation depends on market conditions which has not been considered in the one stage regression.

8 These results are reported in the Appendix.

9 According to Cao and Li (2020), China's MTSL (margin trading and security lending) remains unbalanced with MT: SL balance at 97:3, mainly due to limited eligible stocks/lenders/order types; and high fees for stock lending. The industry stock lending rate is around 8%, a bit higher than the margin financing rate. In addition, security lending business in China is rather restricted, both because brokers face large hedging costs for their security pools so that there is a limited supply of securities, and because there are substantial communication/negotiation costs between brokers and typical clients. All of these short-sale constrains help generate a wide no-arbitrage interval on index futures bases, resulting in the ‘persistency’ of deep backwardation.

10 Anecdote has it that a few market investors replicate short positions from option portfolios, but soon the regulatory body forbids this kind of behavior.

11 The CFTC classifies traders of commodity futures into business positions and speculative positions, and the former can be grouped into hedging positions.

Additional information

Funding

Liang's research is supported by Natural Science Foundation of China (Grant No. 71871087 and 71971077), Humanities and Social Science Fund of Ministry of Education of China (Grant No. 17YJC790089) and Natural Science Foundation of Hunan Province, China (Grant No. 2019JJ40026). Han's research is supported by Natural Science Foundation of China (NSFC project no. 71471153).