An Interaction Between a Leveraged ETF and Futures in a Crash Investigated by an Agent-Based Model

From 2010's, investors that invest leveraged exchanged-traded funds (L-ETFs) are increasing. L-ETFs is listed funds try to track amplified returns of a stock index prices, e.g., S&P 500 index. L-ETFs are listed themselves, however, it has not enough been investigated how sharply falling of L-ETFs affects futures contracts tracking the stock index (following we just call “futures”) markets. In this study, the artificial market model (an agent-based model for financial market) was built by adding a market in which a L-ETF itself is traded and adding a erroneous orders leading turmoil implemented to the prior model. We investigated that sharply falling of the futures or the L-ETF affects the another market and effects of rebalancing trades of the L-ETF. In the result, the erroneous orders to the L-ETF leads that market prices of the L-ETF fall, but the arbitrage-trades reduce the fall. Liquidity of the futures is consumed to prevent the fall of the L-ETF. This means that liquidity of the futures is used as hidden liquidity of the L- ETF. In the case that the erroneous orders to the futures, the futures can gain only a less liquidity from the L- ETF that has a less liquidity, then this leads not to reduce falling so much. In real financial market, this means that investors of L- ETFs have great benefit by gaining much liquidity of futures, on the other hand, investors of futures do not have so benefit by gaining low liquidity of L-ETFs. We also found the rebalance-trades make enlarge the fall of market prices. A previous study showed that when a L-ETF impacts market prices more than their volatility the L-ETF should additionally rebalance-trade, and then market prices fall again and this leads to continue the loop. Our this result is consistent with the previous study.