How does leverage in stock market influence the margin of stock index futures?

ABSTRACT

In this article, we propose a margin-setting model under the assumption of extreme stock price changes. Specifically, extreme stock price changes are caused by the positive feedback effect of leverage and market impact. By introducing these factors into the futures price changes through a cost-of-carry model for setting the margin of stock index futures, we find that leverage and market impact in stock market are positively correlated with the margin.

KEYWORDS:

• Margin of stock index futures
• leverage
• market impact
• portfolio rebalance

JEL CLASSIFICATION:

• G15
• G23
• G33

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ The assumption 2 of our model looks like the one adopted in Equation 2 of page 7, the research of Obizhaeva (2008). The only difference is the value of the price impact parameter (denoted by λ in the original research) which depends on the authors’ research focus. The research focus of the original paper is to estimate the price impact parameter which can be found in page 20: ‘The unconditional estimate of the price impact λ is equal to 0.31 for a total sample. Therefore, on average, 1% of the average daily volume has the price impact equal to 0.31% of the daily return standard deviation. The estimates of λ range from 0.25 to 0.93, if different sub-samples are considered’. However, we do not care about the true value of the parameter, as long as the market impact remains linear so we can get closed-form solutions, so here we simply set the market impact parameter to 1.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [project no. 71273169].