Towards Evology a Market Ecology Agent-Based Model of US Equity Mutual Funds

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Towards Evology: a Market Ecology Agent-Based Model of US Equity Mutual

Funds

AYMERIC VIE,

Mathematical Institute, University of Oxford, UK and Institute for New Economic Thinking at the

Oxford Martin School, University of Oxford, UK

MAARTEN SCHOLL,

Department of Computer Science, University of Oxford, UK and Institute for New Economic

Thinking at the Oxford Martin School, University of Oxford, UK

ALISSA M. KLEINNIJENHUIS,

Stanford University, USA and Institute for New Economic Thinking at the Oxford

Martin School, University of Oxford, UK

JAMES D. FARMER,

Mathematical Institute, University of Oxford, UK, Institute for New Economic Thinking at the

Oxford Martin School, University of Oxford, UK, and Santa Fe Institute, USA

The protability of various investment styles in investment funds depends on macroeconomic conditions. Market ecology, which

views nancial markets as ecosystems of diverse, interacting and evolving trading strategies, has shown that endogenous interactions

between strategies determine market behaviour and styles’ performance. We present Evology: a heterogeneous, empirically calibrated

multi-agent market ecology agent-based model to quantify endogenous interactions between US equity mutual funds, particularly

Value and Growth investment styles. We outline the model design, validation and calibration approach and its potential for optimising

investment strategies using machine learning algorithms.

CCS Concepts:

•Applied computing →

Economics;

•Computer systems organization →

Heterogeneous (hybrid) systems;Self-

organizing autonomic computing.

Additional Key Words and Phrases: agent-based model, calibration, nance, investment, market ecology, mutual funds, validation

ACM Reference Format:

Aymeric Vie, Maarten Scholl, Alissa M. Kleinnijenhuis, and James D. Farmer. 2022. Towards Evology: a Market Ecology Agent-

Based Model of US Equity Mutual Funds. In Benchmarks for AI in Finance Workshop. ACM, New York, NY, USA, 20 pages. https:

//doi.org/10.1145/nnnnnnn.nnnnnnn

1 INTRODUCTION

1.1 Motivation

Research question. One key nancial topic of discussion is the Value vs Growth debate. Does Value, focusing on

stocks trading for less than their intrinsic or book value, beat Growth, investing in fast-growing companies, over the

long term? What investment styles can prot-driven machine learning search nd in a multi-fund simulation?

Motivation. A rst piece of the answer is undoubtedly macroeconomic and monetary conditions. The last ten years in

nancial markets have seen the Growth investment style signicantly outperform Value. One common reason to justify

this performance is the protability of Growth investing in low-interest rates environments. Growing companies rely on

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not

made or distributed for prot or commercial advantage and that copies bear this notice and the full citation on the rst page. Copyrights for components

of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to

redistribute to lists, requires prior specic permission and/or a fee. Request permissions from permissions@acm.org.

Manuscript submitted to ACM

arXiv:2210.11344v2 [cs.MA] 25 Oct 2022

ICAIF ’22, November 2022, New York, USA Vie et al.

borrowing to fuel their expansion. Hence low-interest rates facilitate this growth. With the recent rising interest rates,

and the 2022 bear market particularly aecting tech stocks, those growth prospects appear less favourable and suggest

a comeback of the Value style. Outside of those external factors, does Value and Growth performance depend on more

endogenous factors such as their respective shares of invested wealth and market composition? Can Value/Growth

returns cycles emerge from the endogenous interaction of those dierent investment styles? Over the last 30 years,

this rotation of winners visible in Figure 2in the appendix resembles the oscillations and cycles typically observed in

population dynamics. The theory of market ecology [

–

] borrows concepts from ecology and biology to

study nancial markets. Trading strategies are analogous to biological species: they exploit market ineciencies and

compete for survival or prot. [

] has highlighted the nature of interactions between common trading strategies and

the strong density dependence of their returns for stylised trading styles. We here propose to expand this agent-based

approach more quantitatively to investigate the Value/Growth interactions in investment funds. We focus on mutual

funds: investment companies that pool money from shareholders and invest in securities portfolios.

Related work. This research is in the continuity of the rich area of nancial agent-based models and market selection

with heterogeneous beliefs [

]. For example, several ABMs have recently been introduced for market-making

optimisation [

], understanding ash crashes [

] and providing sophisticated nancial architectures for trading

training [

]. We attempt to develop the complementary approach of market ecology [

] by focusing on the ecological

interactions between the dierent types of agents and strategies.

Signicance. This research topic participates in an active area of debate with a novel approach. We describe how

some particular results of the market ecology model provide a new, exciting challenge for optimising investment

styles using machine learning algorithms. Such simulation-based training can account for interactions and density

dependence eects that could be signicant and overlooked by traditional time-series training. However, its importance

is not limited to the world of nancial investment professionals. In the US alone, according to the Investment Company

Institute, more than 102 million individuals and an estimated 48% of households own mutual fund shares [

]. The

total retirement market assets in the US represent 39 trillion dollars, of which more than 12 trillion are invested in

mutual funds. Net sales of regulated open-end funds surged in 2021, with investors placing more than 3 billion dollars

in the sector, which holds an increasing share of worldwide equity and debt securities (27%). Any currently unknown

endogenous dynamics at play within the market fund ecosystem thus carry actual, high-magnitude economic impact.

1.2 Stylised facts of US equity mutual funds

Developing a more quantitative agent-based model of the mutual fund industry requires laying down the characteristics

of the system we are trying to model. One of the critical elements of validation of the model is its correspondence

to the key attributes of real regulated funds. At year-end 2021, more than 34 trillion US$ were invested in open-end

funds, which issue new shares and redeem existing shares on demand. This broad category with total net assets of 34

trillion dollars includes mutual funds (27 trillion) and exchange-traded funds (ETFs, 7.2 trillion) but also unit investment

trusts (95 billion) and closed-end funds (309 billion). The US contain more than 8,800 mutual funds and 2,800 ETFs. The

Investment Company Institute 2022 Fact Book [

] describes the total aggregate assets under management and the

number of funds of each type. We discuss modelling approaches (few aggregate agents vs many agents) and present

some mutual fund data in the appendix.

Towards Evology: a Market Ecology Agent-Based Model of US Equity Mutual Funds ICAIF ’22, November 2022, New York, USA

2 MODEL

We consider a population of

𝑛

investment funds, which trade shares of a single representative asset and cash. Every

period-day

𝑡

, the funds can buy, sell and short-sell shares of the asset in constant supply. Asset shares pay daily dividends

𝛿(𝑡)

following an autocorrelated Geometric Brownian Motion. Cash yields an interest rate

𝑟

paid daily. We build over

the model of [

], with notable improvements in empirical calibration. We show an example simulation run in the

appendix.

Initialise Trading signal Demand

Market clearing

Dividends/interest

Solvency

InvestmentTerminate

For 𝑇max periods

After 𝑇max periods

Fig. 1. Visual summary of the model components.

2.1 Trading strategies and signals

Like real markets, our nancial market model features a diverse sample of stylised versions of the most common

funds’ trading strategies [

]. The previous section outlined the main results from the ICI data [

], which suggests

including Value and Growth funds, possibly divided by their cap, in the model. For the current version of the model in

development, we include three styles: Value, Noise trading and Momentum (trend following). Value investors (VI) form

heterogeneous subjective valuations

𝑉𝑖

of the asset based on discounted sums of dividends. Noise traders (NT) trade on

a similar valuation perturbed by a mean-reverting Ornstein Uhlenbeck process

𝑋(𝑡)

, mimicking exogenous sentiment

dynamics. We calibrate the parameters of the Ornstein Uhlenbeck process to match empirical excess volatility [

Trend followers (TF) trade on the existence of trends in the asset price over various time horizons. Agents’ trading

strategies are represented by their trading signals 𝜙(𝑡).

𝜙NT

𝑖(𝑡)=log2(𝑋𝑖(𝑡)𝑉𝑖(𝑡)/𝑝(𝑡))(1)

𝜙VI

𝑖(𝑡)=log2(𝑉𝑖(𝑡)/𝑝(𝑡))(2)

𝜙TF

𝑖(𝑡)=log2(𝑝(𝑡−1)/𝑝(𝑡−𝜃𝑖))(3)

2.2 Asset demand

The funds’ daily trading signals are inputs of the excess demand function for the asset [

]. The excess demand function

expresses the demand of the fund for the asset as a function of the unknown price

𝑝(𝑡)

. Fund wealth

𝑊

is the sum of

agent cash, present value of asset shares and liabilities. Our demand function features maximum leverage

𝜆

and strategy

aggression

𝛽

. Our demand function simply represents an investor with asset position

𝑆(𝑡)

and budget

𝜆𝑊 (𝑡)

spending

a share ˜

𝜙(𝑡)of her budget on the asset, and 1−˜

𝜙(𝑡)on the cash [22,23].

ICAIF ’22, November 2022, New York, USA Vie et al.

𝐷(𝑡, 𝑝 (𝑡)) =˜

𝜙(𝑡)𝜆𝑊 (𝑡)

𝑝(𝑡)−𝑆(𝑡)(4)

For

𝜙(𝑡)=tanh(𝛽𝜙 (𝑡))

: the

tanh

function smooths and bounds the trading signal in the range

[−

]

, so that the

demand never exceeds the agent budget including leverage. This demand function is continuous, allows short-selling,

and enforces deleveraging & margin calls1, and always deliver orders that respect the budget constraint.

2.3 Market-clearing

The market-clearing process nds the price for which the sum of the funds’ demands equals the xed asset supply

𝑄

demand matching supply [

]. This is equivalent to the market-clearing procedure of nding the root of the aggregate

excess demand function [

]. The market-clearing condition here is thus:

Í𝑖𝐷𝑖(𝑡, 𝑝 (𝑡)) =𝑄

. While many nancial

agent-based models use limit-order books (LOBs), our focus here is on long timescales from decades to centuries, while

those models focus on intraday dynamics. We do not exclude using LOBs in this model’s future but believe that market

clearing is sucient for our time horizon.

2.4 Dividends, interest and investment flows

After computing the clearing price, funds execute the resulting demand orders. Agents receive capital gains: the

dividends

𝛿(𝑡)

and interest

𝑟

corresponding to their new positions. The actions of external investors play an essential

role in the wealth dynamics of mutual funds. Depending on the performance of the funds, external investors can choose

to redeem their shares or buy new fund shares. Our model models those inows and outows in the investment module

according to empirical data on fund ows.

2.5 Solvency

Funds with negative wealth enter bankruptcy and exit the market. An administrator slowly liquidates their shares. The

wealthiest fund will split into several identical, equal-sized entities to ll the vacant spot. This mechanism keeps the

number of funds and asset shares constant and limits market perturbations due to insolvencies.

3 CALIBRATION AND VALIDATION

Calibration and validation of agent-based models (ABMs) are crucial [

]. A common criticism of ABMs is that they

often have too many parameters and risk being unrealistic. Our validation includes three main targets. The rst is for

the model to reproduce the stylised nancial properties of asset returns [

]. The second is to model realistic fund

ows. The third is for the fund agents to be consistent in various properties with the empirical data on mutual funds

[

]: their number/size, returns, and investment styles. While we achieve the rst two, more work is necessary to satisfy

the latter, as we detail in the appendix.

3.1 Reproducing stylised facts of financial markets

Generating the so-called nancial “stylised facts” is a popular requirement for validating nancial ABMs. Our model

reproduces the main stylised facts of asset prices [

]. Our log prices display intermittency. The log price returns do

Previous designs of the demand function in our model tended to generate huge short positions. Because of the embedded deleveraging, i.e. reduction of

short positions in case of price increase, this demand function over the simulation test run gives an average short position size equivalent to

1.03%

asset supply. This level is in line with the top10 NASDAQ stocks (

1.17%

of oat on average). If leverage increases, the short ratio increases to riskier stock

levels.

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TowardsEvology:aMarketEcologyAgent-BasedModelofUSEquityMutualFundsAYMERICVIE,MathematicalInstitute,UniversityofOxford,UKandInstituteforNewEconomicThinkingattheOxfordMartinSchool,UniversityofOxford,UKMAARTENSCHOLL,DepartmentofComputerScience,UniversityofOxford,UKandInstituteforNewEconomicThinkingatth...

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