12th Artificial Economics Conference 201620-21 September 2016 in Rome

Analysis of the Impact of Leveraged ETF
Rebalancing Trades on the Underlying Asset
Market Using Artificial Market Simulation(proceedings) http://ae2016.it/public/ae2016/files/ssc2016_Mizuta.pdf

Isao Yagi

Kanagawa Institute of Technology

Takanobu Mizuta

SPARX Asset Management Co., Ltd.

Mail: mizutata[at]gmail.com
HP: http://www.geocities.jp/mizuta_ta/

It should be noted that the opinions contained herein are solely those of the authors and do
not necessarily refrect those of SPARX Asset Management Co., Ltd.

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1(1) Introduction(2) Artificial Market Model(3) Simulation Results(4) Summary & Future Works

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2

(1) Introduction(2) Artificial Market Model(3) Simulation Results(4) Summary & Future Works

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3ETF = Exchange Traded Funds is an investment fundtraded on stock exchanges, much like stocks.
A Leveraged ETF is designed to deliver several times the return of its
benchmark index (future), e.g. S&P 500, Euro Stoxx 50, FTSE 100, Nikkei 225.

Leveraged ETF

Value

Index (Future)

Leveraged ETF (x2)14013012011010090807060

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15days
Actually, Leveraged ETF has to trade the index
on daily to maintain its leverage (Rebalance).

4

Rebalance to maintain its leverage
For example, when the index returns are +10% on day 1 and -10% on day 2
The Leverage is twice (x2)
Index
Days

(a) Return0
12+10%-10%

Leveraged ETF (x2)
is Designed as(b) Return= 2x(a)+20%-20%

Leveraged ETF (x2) Holding
Index (future) Value(c) Value
Will be by (b)(d) Shouldhave = 2x(c)

$100
+20%
$120
-20%
$96

x2x2x2(e) Will be (f) Rebalanceby (a)= (d)-(e)$200 +10%$200
$240
$220
$192 -10%$216

So, leveraged ETF

buy the index when its price goes up
sell the index when its price goes down

+20
-24

This leads

Momentum
Trading

This momentum trading Rebalance concern some people,
This Rebalance makes Financial Market Unstable?
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Previous Studies for Leveraged ETF
Many Empirical Analysis
For examples,
Cheng and Madhavan(2009): “In USA market, the index moves 1% in one
day, the volume of rebalancing trading of a leveraged ETF may account for
16.8% of total trading in the index at the close of trading on that day.”
Deshpande et. al.(2009): “Leveraged ETFs accounted for a mere 0.0079%
of trading in the S&P 500.”
Trainor Jr. (2010): “Examined the impact of leveraged ETF rebalancing on
the volatility of the S&P 500 but was unable to draw any firm conclusions.”
These shows

Very Different Results about an Impact on the Financial Market
In actual markets, there are

So many factors cause price formation. An empirical study
cannot isolate the direct effect of leveraged ETFs.
6Therefore, In this Study,
We built an Artificial Market Model (Agent Based Model forFinancial Market) to investigate the market impact of leveraged
ETF rebalancing on the index price formation.
• There are no previous study investigating the market impact of leveraged
ETF using an Artificial Market Simulation.
• Our model is based on the model of Yagi et. al. (2010).

Strong Advantages: Artificial Market Simulations canisolate the direct effect of leveraged ETFs.
analyze micro process and give us new knowledge.
treat situations have never occurred.
(e.g. There are more Leveraged ETFs than current)7(1) Introduction(2) Artificial Market Model(3) Simulation Results(4) Summary & Future Works

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8Ground Design

This area is only modeled (treated)

NormalAgents
10,000
Trading

Index (future)
Markete.g. S&P500, Euro Stoxx 50,
FTSE 100, Nikkei225
Rebalance
Trading

Trading

Leveraged ETF
Market

The Leveraged
ETF Agent
Only oneNot modeled(Not treated)9Normal Agents
We modeled Normal Agents as 3 kinds of agents, fundamentalists,Chartists and Noise traders.

4,500Fundamentalists
expects a positive return when the market price is lower than theFundamental Price (externally given and constant), and vice versa.
4,500
Chartists
Market followers mode: an agent expects a positive return when historicalmarket return (moving average) is positive, and vice versa.
Contrarians mode: an agent expects a positive return when historicalmarket return is negative, and vice versa.
1,000
Noise Tradersorders to buy, sell, and wait with equal probabilities.
Learning Process
Fundamentalists and Chartists learn some parameters of high-performance
agents and switch mode.

Exactly same as Yagi et. al.(2010)10Fundamentalists and Chartists* Fundamentalists
Fundamental Price > Market Price  expect Positive return
Fundamental Price < Market Price  expect Negative return* Chartists (Market followers mode)
Historical return > 0  expect Positive return
Historical return < 0  expect Negative return
Chartists(Market followers mode)

Fundamental
Price

Fundamentalist

MarketPrice11

Price Determination ModelCall Market (Batch Auction)

100Price8060

BUY (Bid)

Market Price40 (Trade Price)

SELL (Ask)
Trading
Volume2000

Supply Curve
Cumulative number ofShares that sellers want
to sell over this price

50
100
Cumulative number of Shares

Demand Curve
Cumulative number ofShares that buyers wantto buy under this priceIn a call market, buy and sell orders are grouped together and thenexecuted at specific times (rather than executed one by one continuously).
We determine Market Price and Trading Volume at the crossing point of12
supply and demand curves.

The Leveraged ETF AgentOur Original Model

The leveraged ETF ONLY does Rebalance Trading.

Immediately Before
leveraged ETF ordering

After it ordered

8080604020

BUY (Bid)

50SELL (Ask)

500Price

100Price

10060

BUY (Bid)
SELL (Ask)

604020700050
100
Cumulative number of Shares

050100
Cumulative number of Shares

The leveraged ETF orders after all Normal Agents ordered.
It determines rebalance trading using the temporary market price, 50 (Left).
If it need buying 20 shares, it makes buy 20 shares order at very high price.
The order changes Supply and Demand Curve (Right).
The market price is changed to 60 (from 50).
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The price difference, 10 is the market impact of the rebalance.

(1) Introduction(2) Artificial Market Model(3) Simulation Results(4) Summary & Future Works

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Search Parameter
We investigated how the leverage ETF impacts market prices,relationship between size (total value) of the leverage ETF and themagnitude of the market impact.
We executed simulations for several size of the leveraged ETF.
We defined the size of leveraged ETF as

Total Value of the leveraged ETF / Total Value of all Normal agentsand the size is changed to 0.1%, 1%, 10%, 15%, 16%, 17%This is Search Parameter.

Note that in our proceeding we tried on greater number of parameters, however here we
only show important results for simplicity.

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Volatility, stylized facts
Volatility = Standard Deviation of Returns
Kurtosis = Kurtosis for Return distribution

Size (Total Value of the leveraged ETF/ Total Value of all Normal agents)
NO Leveraged ETF 0.1% 1%
10%
15%
16%
17%
1.13 1.18 1.4 1.47 1.39 6.42 29.5
4.64 4.34 2.56 6.29 19.2 15.8 3.41

Volatility(%)
Kurtosis

Autocorrelationof the squared
rate of return

Lag
123
4
5

0.52
0.71
0.52
0.65
0.53

0.49
0.70
0.50
0.64
0.51

0.38
0.72
0.42
0.66
0.44

0.39
0.64
0.35
0.52
0.31

Stable(small volatility)

0.56
0.45
0.31
0.21
0.13

0.48 -0.49
0.48 0.79
0.27 -0.55
0.28 0.73
0.11 -0.60

Unstable(large volatility)

There is clearly the threshold for stable or unstablemarket between 15%-16%16Market Impact Volatility Ratio
We defined the Market Impact Volatility Ratio (MIVR)= market impact (averaged absolute market impact / market price)/ Volatility (in the case of no leveraged ETF)

No. of Orders(a) Market Impact (%)
Volatility (%)[MIVR] Market Impact
Volatility Ratio = (a) / (*1)

Size (Total Value of the leveraged ETF/ Total Value of all Normal agents)
NO Leveraged ETF 0.1%
1%
10%
15% 16% 17%0872
88
90 6,34157,617
0 0.00493 0.0396 0.0539 0.0785 2.18 12.5
1.13 (*1)
1.18
1.4 1.47 1.39 6.42 29.5
0 0.00434 0.0349 0.0476 0.0692 1.92

StableVery Small Impact

11Unstable
Large Impact

MIVR is very important Key Parameter
MIVR < 1: Stable, MIVR > 1: Unstable
Market is Destabilized when Market Impact > Volatility
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Possible Mechanism

Market Prices
ImpactedMarket Prices
Without Impact

Market Impact < Volatility

Volatility

Prices remain within theNormal Volatility Range

StableMarket Impact

within the normal volatility range

FundamentalPricethe market impact do NOT amplify volatilityMarket Impact > Volatility
Unstable: Destabilize
Financial Market
Recovering to Fundamental Price> normal Volatility range
AmplifiedVolatility
Market ImpactVolatility Range wider
market impact amplify
volatility range

pushed out prices outer the normal volatility range
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(1) Introduction(2) Artificial Market Model(3) Simulation Results(4) Summary & Future Works

You can download this presentation material fromSlide Share http://www.slideshare.net/mizutata/20160921.pdf http://www.geocities.jp/mizuta_ta/20160921.pdf

19Summary* We built an artificial market model (a kind of agent basedmodel) to investigate the impact of leveraged ETF rebalancing
on the index price formation.
* We found that Market Impact (MI) per Volatility (V) is very
important Key Parameter, MI < V: Stable, MI > V: Unstable.
* We showed the possible Mechanism of Destabilizing Market.

Future Works* search the threshold more precisely, 15%-16% is true?
* discuses Mechanism of Destabilizing Market more deeply* do Empirical Study focusing the relationship between
Market Impact and Volatility20

That’s all, thank you!!
References-- Proceedings of this presentation -http://ae2016.it/public/ae2016/files/ssc2016_Mizuta.pdf-- Empirical Studies -* M. Cheng and A. Madhavan, “The Dynamics of Leveraged and Inverse ExchangeTraded Funds,” Journal ofInvestment Management, vol. 7, no. 4, 2009.
* M. Deshpande, D. Mallick, and R. Bhatia, “Understanding Ultrashort ETFs,” Barclays Captital Special Report,Jan. 2009.
* W. J. Trainor Jr., “Do Leveraged ETFs Increase Volatility,” Technology and Investment, vol. 1, 2010.
-- Artificial Market Model: Base Model --* I. Yagi, T. Mizuta, and K. Izumi, “A study on the effectiveness of short-selling regulation in view of regulation
period using artificial markets,” Evolutionary and Institutional Economics Review, vol. 7, no. 1, pp. 113–132,
2010. http://link.springer.com/article/10.14441%2Feier.7.113#-- Artificial Market Model: Brief Review focusing our studies -* T. Mizuta, “A Brief Review of Recent Artificial Market Simulation (Multi-Agent Simulation) Studies for Financial
Market Regulations and/or Rules,” SSRN Working Paper Series, 2016. http://ssrn.com/abstract=2710495

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