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Setting the futures margin with price limits: the case for single-stock futures

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Abstract

Price limits are artificial boundaries established by regulators to establish the maximum price movement permitted in a single day. We propose using a new censoring method that incorporates the effect of price limits on the futures price distribution and investigates how to set an appropriate daily margin level using single-stock futures in Taiwan. We compare our estimations with those obtained using the method in Longin (J Bus 69:383–408, 1999). The results show that (1) the margin levels derived from the Longin method, which ignore price limits in the estimation, are lower than those in our censoring method; and (2) the legal margin for single-stock futures set at 13.5 % by the Taiwan Futures Exchange to avoid default risk appears to be too high.

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Notes

  1. The censoring method originated from the area of reliability engineering. The main concept of this method is to recover each of censored data to its conditional expected value. Thus, the censoring method results in augmented observations with censored data as “pseudo-complete” data.

  2. In the 1980s, the Commodity Futures Trading Commission and the Securities and Exchange Commission were unable to decide which one would have the regulatory authority over single-stock futures. After the Commodity Futures Modernization Act of 2000 (CFMA) came into effect, the ban on single-stock futures was lifted and the two agencies were directed to regulate single-stock futures jointly using a jurisdiction-sharing plan. As a result, single-stock futures began trading on November 8, 2002.

  3. See www.futuresindustry.com.

  4. For example, the TAIFEX sets 7 % price limit on its stock index futures. However, this index futures will never hit the 7 % lower and upper bound unless all underlying stocks hit the price limit. Thus, the situation with actual prices hitting the price limits rarely occurs. TAIFEX stock index futures can be an example. The censoring technique is not appropriate to estimate the stock index futures margins.

  5. The number of underlying securities for trading single-stock futures was 117 in 2011, 213 in 2012, and 233 in 2013.

  6. The NT$:US$ exchange rate fluctuates between NT$29.18 and NT$30.09 per US$.

  7. The single-stock futures markets in Hong Kong and the United States had low liquidity and trading volume in their first year of trading.

  8. See the TAIFEX annual report for 2013. The average daily trading volume in single-stock futures increased to 38,341 contracts in 2014.

  9. For example, TAIFEX sets the ratio of an initial margin to contract value at about 5–6 % for equity index futures, but 13.5 % for single-stock futures.

  10. The futures exchange may set the price limits too wide for the price limit hits.

  11. In their later paper, Cotter and Longin (2006) conclude that daily margin levels estimated with high-frequency data are consistently higher than daily margin levels directly obtained from daily price changes. They find that the intraday dynamics should be a key component in margin setting.

  12. The extreme value theory shows that the distribution for extremes observed over a long time period is largely independent of the parent distribution (see Longin 1999). This feature helps us ignore the fact that individual stock (and single-stock futures contract) has its unique return distribution.

  13. The extreme value theory (EVT) shows that the distribution for extremes observed over a long time period is largely independent of the parent distribution (see Longin 1999). This feature helps us ignore the fact that individual stock (and single-stock futures contract) has its unique return distribution. In the Longin (1999) method, the parameters embedded in the nonlinear equations are solved numerically. We use the Newton–Raphson iterative method to obtain the location, the scale parameters, and the tail index in the EVT.

  14. Broussard (2001) uses a discarding data approach (i.e., deleting the censoring data that hit the price limit) to compare the distribution estimated with and without the violating incidents. We also follow the discarding data approach to estimate the EVT parameters in Taiwan’s single-stock futures market. The results (available upon request) are similar to those of Longin (1999). Meanwhile, following  Chou et al. (2014) definition, α2  and β2  are location parameters;  α1 and β1 are  scale parameters; α0 and β0 are usually called the tail indices and determine the types of limiting distributions.

  15. In Table 4, the estimated futures margins with and without price limits are obtained by averaging out equally the estimated margin for each stock futures contract. For comparison, we also calculate the future margins by taking a market-value-weighted approach to find average futures margin. Because the smaller firms are more likely to be volatile than large firms and may require higher margins, it is intuitive to show that the future margins estimated based on equally-weighted approach will be larger than market-weighted average across contracts. For simplicity, we only report the empirical results by the equally-weighted approach.

  16. We compare the initial margin for other futures trading on the TAIFEX and we find that the ratio of an initial margin to the contract value at about 5–6 % for the stock index futures (with daily trading volume of 99,838 contracts in 2014), compared to 13.5 % for single-stock futures (with daily trading volume of 38,341 contracts in 2014).

  17. Table 2 indicates that the percentage of upper-limit hits is 1.28 % and that of lower hits is 1.03 % in the total sample. The result indicates that during our sample period the frequency of the positive extreme price movements is higher than that of the negative extreme price movements.

  18. Currently, the TAIFEX sets a 7 % daily price limit on its single-stock futures contracts, and the initial margin is set as futures contract value multiplies the risk price coefficient, which is set at 13.5 % for all single-stock futures. The risk price coefficient must at least cover 99.9 % of the range of one-day price change. But, in light of our futures margin estimation method, there is no theoretical support for the current futures margin policy adopted by the TAIFEX, which is quite subjective and arbitrary.

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Authors and Affiliations

  1. Department of Finance, Chang Jung Christian University, Tainan, Taiwan

    Chen-Yu Chen

  2. Department of Finance, National Kaohsiung First University of Science and Technology, Kaohsiung, Taiwan

    Jian-Hsin Chou

  3. School of Business Administration, University of Missouri-St. Louis, St. Louis, MO, USA

    Hung-Gay Fung & Yiuman Tse

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  1. Chen-Yu Chen
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  2. Jian-Hsin Chou
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  3. Hung-Gay Fung
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  4. Yiuman Tse
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Correspondence to Yiuman Tse.

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Chen, CY., Chou, JH., Fung, HG. et al. Setting the futures margin with price limits: the case for single-stock futures. Rev Quant Finan Acc 48, 219–237 (2017). https://doi.org/10.1007/s11156-015-0548-7

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