Impact of arbitrage between leveraged ETF and futures on market liquidity during market crash

Ryuki Hayase; Takanobu Mizuta; Isao Yagi

q-fin.CPMar 6, 2026

Impact of arbitrage between leveraged ETF and futures on market liquidity during market crash

Authors: Ryuki Hayase, Takanobu Mizuta, Isao Yagi

Organizations: Department of Informatics, Graduate School of Engineering, Kogakuin University · SPARX Asset Management Co., Ltd. · Department of Information Science, Faculty of Informatics, Kogakuin University

Abstract

Leveraged ETFs (L-ETFs) are exchange-traded funds that achieve price movements several times greater than an index by holding index-linked futures such as Nikkei Stock Average Index futures. It is known that when the price of an L-ETF falls, the L-ETF uses the liquidity of futures to limit the decline through arbitrage trading. Conversely, when the price of a futures contract falls, the futures contract uses the liquidity of the L-ETF to limit its decline. However, the impact of arbitrage trading on the liquidity of these markets has been little studied. Therefore, the present study used artificial market simulations to investigate how the liquidity (Volume, SellDepth, BuyDepth, Tightness) of both markets changes when prices plummet in either (i.e., the L-ETF or futures market), depending on the presence or absence of arbitrage trading. As a result, it was found that when erroneous orders occur in the L-ETF market, the existence of arbitrage trading causes liquidity to be supplied from the futures market to the L-ETF market in terms of SellDepth and Tightness. When erroneous orders occur in the futures market, the existence of arbitrage trading causes liquidity to be supplied from the L-ETF market to the futures market in terms of SellDepth and Tightness, and liquidity to be supplied from the futures market to the L-ETF market in terms of Volume. We also analyzed the internal market mechanisms that led to these results.

Figures & tables

	No arbitrage trading		Arbitrage trading permitted
	Leveraged ETF	Futures	Leveraged ETF	Futures
Volume	$1370.433$	$361.500$	$1336.933$	$1384.333$
SellDepth	$33.649$	$856.261$	$60.970$	$560.027$
BuyDepth	$164.257$	$855.100$	$162.713$	$934.415$
Tightness	$18.686$	$9.379$	$10.974$	$10.934$

Table 1: Market liquidity indicator values during the erroneous order period in the event of an erroneous order in the leveraged ETF market

	No arbitrage trading		Arbitrage trading permitted
	Leveraged ETF	Futures	Leveraged ETF	Futures
bestsell	$4816.153$	$10\,005.410$	$4940.756$	$9940.757$
bestbuy	$4797.467$	$9996.033$	$4929.782$	$9929.823$

Table 2: Best bid and best ask prices during the erroneous order period when an erroneous order occurs in the leveraged ETF market

	No arbitrage trading		Arbitrage trading permitted
	Leveraged ETF	Futures	Leveraged ETF	Futures
Best Bid Price	2.53044	2.532407	1.523627	5.494221
1 tick down	3.107011	3.147141	2.883839	7.781648
10 ticks down	3.200591	5.862466	3.142820	8.539460
20 ticks down	3.299328	7.956378	3.280504	9.025146
30 ticks down	3.353885	8.589546	3.349862	9.247427

Table 3: Number of orders by number of ticks during the erroneous order period when an erroneous order occurs in the leveraged ETF market

	No arbitrage trading		Arbitrage trading permitted
	Leveraged ETF	Futures	Leveraged ETF	Futures
Volume	$68.600$	$8025.533$	$2508.433$	$7425.400$
SellDepth	$173.503$	$120.479$	$20.255$	$157.807$
BuyDepth	$170.828$	$811.344$	$183.352$	$814.255$
Tightness	$5.309$	$24.343$	$17.517$	$17.594$

Table 4: Market liquidity indicator values during the erroneous order period in the event of an erroneous order in the futures market

	No arbitrage trading		Arbitrage trading permitted
	Leveraged ETF	Futures	Leveraged ETF	Futures
bestsell	$5002.437$	$9552.983$	$4695.787$	$9695.771$
bestbuy	$4997.128$	$9528.640$	$4678.270$	$9678.177$

Table 5: Best bid and ask prices during the erroneous order period when an erroneous order occurs in the futures market

	No arbitrage trading		Arbitrage trading permitted
	Leveraged ETF	Futures	Leveraged ETF	Futures
Best Bid Price	1.812732	4.858940	3.190081	4.134082
1 tick down	1.652858	7.717149	3.521053	7.626708
10 ticks down	3.249156	7.843822	3.593917	7.803561
20 ticks down	3.494964	7.945150	3.679266	7.940020
30 ticks down	3.753843	8.033650	3.732040	8.070982

Table 6: Number of orders by number of ticks during the erroneous order period when an erroneous order occurs in the futures market

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 2: Price time series under the following conditions: no erroneous orders or arbitrage transactions, erroneous orders present but no arbitrage transactions, erroneous orders and arbitrage transactions present but no rebalancing transactions, or erroneous orders, arbitrage transactions, and rebalancing transactions present

Figure 3: Price movements of leveraged ETFs and futures with misorders, arbitrage, and rebalancing ( $S_{0}=50000$ ). Although both the left and right vertical axes span a $1000$ range, the initial price of the leveraged ETF is $5000$ , half that of the futures, at $10000$ . Therefore, a $2$ -fold change in the leveraged ETF will cause the graphs to overlap.

Figure 4: Incorrect orders placed, no arbitrage, and the decline in leveraged ETFs when $S_{0}$ is altered with arbitrage, along with the sell volume resulting from leveraged ETF rebalancing.

Figure 5: Incorrect orders placed, no arbitrage, and the decline in futures when $S_{0}$ is altered with arbitrage, along with the sell volume resulting from leveraged ETF rebalancing.

Figure 6: Mechanism of market disruption when leveraged ETFs become too large ( $S_{0}\geq 100000$ )

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Abstract

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