Does FinTech Democratize Investing?∗

Michael Reher†and Stanislav Sokolinski‡

January 2020

Abstract

We provide evidence that automated asset management affects wealth inequality

by reducing a fixed cost of household investment in risky asset markets: account min-

imums. Using data from a large U.S. robo advisor, we show how an unexpected, 90%

reduction in account minimum shifts the wealth distribution of robo investors leftward

to become more representative of the U.S. population (i.e. more “democratic”). The

reduction increases stock market participation among households from the middle quin-

tiles of the U.S. wealth distribution, raising their risky share by 27 percentage points

and their total return on liquid assets by 2 percentage points, relative to wealthier

households. However, the reduction has no effect on households in the bottom quintile

of the U.S. wealth distribution, suggesting that automation has an ambiguous effect on

wealth inequality by favoring middle class households over both the lower and upper

classes.

Keywords: FinTech, Stock Market Participation, Financial Advice, Inequality

JEL Classification: G11, G24, D3, O3

∗We thank John Campbell, Francesco D’Acunto, Ben Friedman, Jakub Jurek, Iva Kalcheva, AlbertoRossi, Andrei Shleifer, Celine Sun, Boris Vallee, and seminar participants at the California Corporate FinanceConference, CAFR FinTech Workshop, and Harvard’s finance PhD lunch for comments. The views expressedin this paper are those of the authors and do not necessarily reflect the position of Wealthfront Inc.†University of California San Diego, Rady School of Management. Email: mreher@ucsd.edu‡Rutgers Business School, Newark and New Brunswick. Email: ssokolinski@business.rutgers.edu

“The [wealth-management] industry stratifies customers in a manner rather similar to

airlines. ‘High-net-worth’ clients fly business class, picking stocks and chatting in person

with named advisers. Flying private are the ‘ultra-high-net-worth’ individuals, who have

access to venture capital and currency hedges, with exclusive dinners, golf outings and so on

as cherries on top. Cattle class gets no service at all.”

The Economist Magazine, December 2019.

1 Introduction

Wealthy households typically earn a higher return on their liquid assets relative to less-

wealthy households, and this disparity can contribute to growth in wealth inequality (e.g.

Picketty 2014; Campbell 2016; Bach, Calvet and Sodini 2018). The inequality in returns

largely reflects limited participation in risky asset markets, since only 24% of households

outside the top quintile of the U.S. wealth distribution own stocks according to the 2016

Survey of Consumer Finances (SCF). Over the past decade, so-called robo advisers have

sought to tap this market of would-be investors, using automation to manage large numbers

of portfolios at lower per-portfolio cost relative to traditional asset managers.1 Indeed, robo

advisers have become increasingly popular because of their low-cost, personally-customized,

and automatically-rebalanced portfolios (e.g. D’Acunto, Prabhala and Rossi 2019; Loos,

Previtero, Scheurle and Hackethal 2019), with a U.S. market size of $750 billion in 2019 that

is anticipated to reach almost $1.5 trillion by 2023 (Abraham, Schmukler and Tessada 2019).

Does the introduction of robo advice reduce inequality in liquid asset returns by giving

less-wealthy households access to professionally-managed stock portfolios? Robo advisors are

distinguished by their reliance on automation, which lowers their per-portfolio management

costs and enables them to significantly reduce account minimums. Thus, robo advice gives

less-wealthy households access to portfolio management services historically only available to

the very-wealthy and so may reduce inequality, given that many households rely on advisors

1Wealthfront, a leading U.S. robo advisor, describes its founders as seeking to “democratize accessto sophisticated financial advice”. Similarly, in April 2015 the vice president of operations at Betterment,another leading U.S. robo advisor, wrote that the company’s goal was to “democratize sophisticated portfoliomanagement that has traditionally been available only to higher-balance investors”.

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to help them take risk (e.g. Gennaioli, Shleifer and Vishny 2015). On the other hand,

less-wealthy households – especially the poorest – may not benefit from such a reduction in

account minimums if they face additional fixed costs of investing in the stock market, like

acquiring education or financial literacy (e.g. Cole, Paulson and Shastry 2014; Van Rooij,

Lusardi and Alessie 2011).

We provide the first empirical evidence to weigh in on the previous question. Our

setting is an experiment in which a dominant U.S. robo advisor, Wealthfront, unexpectedly

lowered its account minimum from $5,000 to $500. This change was motivated by the

advisor’s philosophy of inclusive investment, as well as its hope that less-wealthy households

will accumulate enough assets to become highly-profitable customers.2 The effect of the

reduction is quite significant for many U.S. households, given that 37% of households have

liquid assets less than $5,000 per the 2016 SCF. We study the consequences of the reduction

using a novel, household-level dataset with details on a household’s liquid assets, investment

activity with the robo advisor, and demographic information.

We have three main findings. First, the reduction leads to a sharp leftward shift in

the wealth distribution of robo investors, making it more representative of the U.S. popu-

lation (i.e. more “democratic”). Second, the reduction significantly increases risky share

and expected return on liquid assets for middle-wealth households, and most of this effect

comes from households who were formerly non-participants in the stock market. Third, the

reduction has no effect on households from the bottom quintile of the U.S. wealth distri-

bution, who have less than $1,000 in liquid assets. Thus, consistent with the predictions

of Philippon (2019), our findings imply that FinTech – namely, robo advice – can partially

democratize investing by giving middle-wealth households access to professionally-managed

stock portfolios.

In more detail, we first document how the reduction in account minimum increases the

share of robo investors from the second and third quintiles of the U.S. wealth distribution,

who have liquid assets between $1,000 and $42,000. In particular, the share of robo investors

2In the words of the company’s then-CEO Adam Nash: “Unlike the many banks and brokerage firmsthat came before us, [we] refuse to build our business by preying on clients with small accounts. . . . Webelieve that, given a fair shake, people bold enough to scrape together the savings for their first investmentaccount will build those accounts over time.”

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from the second wealth quintile (i.e. between $1,000 and $6,000) increases by 42% after the

reduction. The compositional shift coincides exactly with the change in the robo advisor’s

policy, so that our findings do not confound pre-trends in robo investment or competi-

tive pressures within the asset management industry. Leveraging our detailed demographic

information, we further rule out alternative explanations such as targeted advertising or

word-of-mouth effects.

Our core analysis is a difference-in-difference exercise in which we estimate the effect

of the reduction on new robo investors’ risky share and total return on liquid assets. The

“treatment” is the reduction in minimum, and the “treatment exposure” is a household’s

quintile of the U.S. wealth distribution. This approach differences out the effect of time-

varying shocks which influence robo investment but do not depend on a household’s wealth

(e.g. web advertising), and it is robust to including multiple demographic controls, such

as age, income, risk tolerance and state-of-residence. We find that the reduction increases

risky share by 27 pps for households from the second quintile of the U.S. wealth distribution,

relative to households in the two upper quintiles who constitute our control group.

Using the estimates from the previous exercise, we calculate the reduction’s effect on

a household’s total portfolio return, defined as the expected annual return on liquid assets

based on a variety of benchmark asset pricing models (Calvet, Campbell and Sodini 2007).

Importantly, households have very little scope to modify the asset allocation within their

robo portfolio, so that our results do not reflect differential sophistication across investors.

Accordingly, we find that the reduction increases total portfolio return by 2.2 pps for house-

holds in the second quintile of the U.S. wealth distribution, relative to the households in the

two top quintiles. Our results are the same regardless of the asset pricing model used to

calculate expected return, and they are in line with the predictions of canonical models of

portfolio choice. For example, we find a stronger effect among households who score higher

on a risk tolerance questionnaire and among those with relatively-high income, consistent

with the idea that labor income hedges fluctuations in stock returns (e.g. Viceira 2002).

In terms of robustness, we provide evidence that the results indeed reflect an increase

in risky share, rather than liquidation of an unobserved risky position (e.g. a Vanguard

account). For example, we obtain very similar estimates on the subsample of retirement

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accounts (i.e. IRAs). Since cash is presumably the dominant source of funds for retirement

robo accounts – as premature liquidation of a non-robo retirement account would incur a

costly penalty – the similarity in estimates supports the interpretation of our results as an

increase in risky share. Moreover, our results are also robust to whether robo investment

is financed by cash-on-hand, holding the savings rate fixed, versus an increase in savings.

Lastly, we show that new robo investors are less likely to withdraw funds from the advisor

in response to market downturns. This finding suggests that new robo investors hold their

positions long enough to realize the gains in performance documented in our core analysis.

New robo investors consist of two types of households: former stock market non-

participants making a first-time stock investment; and existing stock market participants

who gain access to a professionally-managed portfolio. We conclude by assessing the role of

the former type of household – new stock market participants – in generating our baseline re-

sults. Since we do not observe participation status directly, we impute it from the SCF using

a variety of classification algorithms applied to households’ observed demographic features

(e.g. logistic regression, random forest, and gradient boosting). Accordingly, we find that

78% of new robo investors from the second and third quintiles of the U.S. wealth distribution

did not participate in the stock market before the reduction. Consistent with this finding,

we find that new robo participants disproportionately live in states with lower stock market

participation rates. We therefore conclude that our main results are driven by a switch in

the participation status of former stock market non-participants.

Finally, while the reduction has a large effect on households in the middle quintiles of the

U.S. wealth distribution, it has no effect on households from the bottom quintile, who have

less than $1,000 in liquid assets. This non-result among the poorest households is consistent

with the existence of additional fixed costs of stock market investment, such as acquiring

education or financial literacy. Therefore, we conclude that the introduction of robo advice

has an ambiguous effect on inequality in liquid asset returns. In one direction, it reduces

inequality between middle and upper-wealth households by giving middle-wealth households

access to professionally-managed stock portfolios. In the other direction, it does not appear

to affect lower-wealth households. Our results are thus consistent with robo advice as a

Pareto-improving technological shock with ambiguous distributional effects.

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Related Literature

This article makes three contributions to the literature. First, we provide novel evidence

on the effects of new financial technologies on financial inclusion and inequality. Abraham,

Schmukler and Tessada (2019) and Philippon (2019) argue that robo advisors can reduce

minimum investment requirements, since they save on fixed costs such as advisor compen-

sation or office maintenance. Our study contributes to this nascent literature by providing

direct evidence on how automation-induced reductions in account minimums affect house-

hold investment across the wealth distribution. In particular, our empirical findings support

the theoretical predictions of Philippon (2019), who shows how robo advice may have an

ambiguous effect on financial inclusion and wealth inequality.

Second, we show how the introduction of robo advice can produce significant gains in

household portfolio returns, especially for less-wealthy households who were formerly stock

market non-participants. This set of results makes a contribution to the literature on the

effects of robo advice on investor asset allocation and portfolio returns. The previous work

has shown that automated portfolio selection improves diversification and reduces behavioral

biases in the international samples (e.g. D’Acunto, Prabhala and Rossi 2019; Loos, Previtero,

Scheurle and Hackethal 2019) as well as in the U.S. (Reher and Sun 2019). By contrast, our

study focuses on significantly less-wealthy households who become participants as a result of

the reduction in account minimums. We complement existing research on robo advisors by

highlighting the importance of the extensive margin, as we document welfare gains for new

investors rather than studying improvements in asset allocation among existing investors.

Third, we contribute to a body of papers focused on limited stock market participation,

which spans the asset pricing and household finance literatures. On the asset pricing side, a

number of papers have studied how limited participation may contribute to the equity pre-

mium puzzle (e.g. Mankiw and Zeldes 1991; Vissing-Jørgensen 2002; Gomes and Michaelides

2008; Malloy, Moskowitz and Vissing-Jørgensen 2009). A common feature in many of these

models is a fixed cost of participation in the stock market. We make a novel contribution

to this literature by identifying the effects of a concrete barrier that constrains household

investment: account minimums.3 Unlike the previous work, our barrier to stock market

3Based on a calibration, Haliassos and Bertaut (1995) conclude that account minimums may have a

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participation arises from the supply side and does not directly depend on household char-

acteristics that prevent participation, such as preferences (e.g. Barberis, Huang and Thaler

2006), sophistication (e.g. Grinblatt, Keloharju and Linnainmaa 2011; Christelis, Jappelli

and Padula 2010), and education (e.g. Cole, Paulson and Shastry 2014; Van Rooij, Lusardi

and Alessie 2011). Moreover, our results support the idea that access to asset managers

facilitates investment in risky asset markets, as studied theoretically by Gennaioli, Shleifer

and Vishny (2015) and Garleanu and Pedersen (2018).

The rest of the paper is organized as follows. Section 2 describes the institutional

environment, the dataset, and the experiment. Section 3 studies the effect of the reduction

on the wealth distribution of robo participants. Section 4 studies the effects on risky share

and total portfolio return. Section 5 analyzes the role of changes in stock market participation

in our baseline results. Section 6 concludes. All figures and tables may be found at the end

of the paper. The appendix contains additional material.

2 Data and Experiment

We begin by describing our source of data and providing an overview of the market for

robo advising. Then, we describe the experiment which serves as the paper’s focal point.

We conclude this section with a discussion of summary statistics.

2.1 Source of Data

Our data come from a large U.S. automated financial advisor, Wealthfront, which we will

henceforth refer to as the “robo advisor”. As of March 2018, Wealthfront managed $10 billion

and was among the top 5 largest robo advisors in the U.S. market. Wealthfront offers many

services including tax loss harvesting, long term financial planning, portfolio lines of credit,

and a risk parity fund. Its benchmark product, which is most relevant for this paper, is an

automatically rebalanced portfolio of 10 ETFs across 10 asset classes.4 The portfolio weights

quantitatively small effect on household investment, but they do not actually use data on such minimums.4Strictly speaking, each asset class has a primary ETF and multiple secondary ETFs. The robo advisor

will rebalance toward the secondary ETF if doing so yields a capital loss and thus reduces the client’s taxliability. The 20 ETFs are chosen to track stock market indices (VIG, VTI, VEA, VW), bond market indices

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are determined by a questionnaire which asks the client several questions about her age, liquid

assets, income, demographic background, and response to hypothetical investment decisions.

The client is then assigned to one of 20 possible levels of risk tolerance, which range from 0.5

to 10 in increments of 0.5. Each level of risk tolerance uniquely determines a robo portfolio.

The portfolios weights are chosen as the solution to a mean-variance optimization problem

across the 10 ETFs, taking risk tolerance as a parameter. As summarized in Appendix Table

B2, portfolios designed for higher levels of risk tolerance exhibit higher betas, higher expected

returns, and higher proportions of wealth invested in stocks. To reiterate, these portfolios

are not recommendations, but, rather, they are directly managed by the robo advisor and

thus a client’s sophistication will not affect her performance.

Our main dataset contains a weekly time series of client deposits from December 2014

through February 2016. We observe the date and size of the deposit and whether the deposit

comes from a new client. We also observe the client’s age, annual income, and value of liquid

assets, all of which are self-reported via the robo advisor’s questionnaire and static. Per the

language of the questionnaire, liquid assets include “cash, savings accounts, certificates of

deposit, mutual funds, IRAs, 401ks, and public stocks”.

2.2 Experiment

The experiment occurs on July 5, 2015, when the robo advisor unexpectedly reduced

its account minimum from $5,000 to $500. This reduction is substantial for many U.S.

households: according to the 2016 Survey of Consumer Finances (SCF), 37% of households

have liquid assets less than $5,000. Prior to the reduction, these households lacked access to

an advised portfolio from the robo advisor or any other advisor with an account minimum

above $5,000, setting aside the potential for leverage. The reduction did not coincide with a

change in the fee charged by the advisor, which, at the time, was 0.25 pps for accounts over

$10,000 and zero for smaller accounts. Nor did it coincide with any new product launches or

targeted advertising. Thus, from an econometric perspective, the reduction is an attractive

setting in which to study the effect of account minimums on household investment.

At the time of the reduction, the robo advisor’s major competitors were Betterment and

(LQD, EMB, MUB, TIPS), and other asset classes, namely real estate (VNQ) and commodities (XLE).

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Personal Capital. Two larger wealth managers launched robo advisory services earlier that

year, with Charles Schwab introducing Intelligent Portfolios in March 2015 and Vanguard

launching Personal Advisor Services in May 2015. With the exception of Betterment, these

competitors all require account minimums of at least $5,000, with minimums of $100,000,

$50,000, and $5,000 for Personal Capital, Vanguard, and Schwab, respectively. Betterment

had no account minimum, but charged a $3 service fee on accounts under $10,000 for cus-

tomers who do not auto-invest $100 monthly in their accounts. This fee structure implies

a 7.2% annual management fee for a $500 account and a 36% management fee for a $100

account.5

2.3 Summary Statistics

Table 1 provides summary statistics of the households in the sample over the pre-

reduction and post-reduction periods, defined as the 7 months before or after the week of

the reduction. Prior to the reduction, the median robo investor is 34 years old, earns $130,000

per year, and has liquid assets of $200,000, as shown in panel (a). By contrast, the median

U.S. household has liquid assets of only $17,000, according to the 2016 SCF.6 Thus, prior

to the reduction, robo advice primarily caters to wealthier households. After the reduction,

however, both the wealth and income distributions of robo investors shift to the left, as

summarized in panel (b). For example, the 10th percentile of liquid assets falls from $30,000

to $16,000. Figure 1 visualizes the effect by plotting the empirical wealth distribution, which

exhibits a striking leftward shift after the reduction.

This leftward shift in the wealth distribution reflects an inflow of less-wealthy, new

robo investors, whom we summarize in panel (c). In fact, the median new robo investor

is half-as-wealthy as the median investor prior to the reduction, with liquid assets of only

$100,000 compared to $200,000. Interestingly, the median new robo investor is only 1 year

younger than the median existing investor. This minor difference in age suggests that new

robo investors are less-wealthy in the permanent sense, and not simply because they are

5See the Reuters article “Robo-advisor Wealthfront lowers account minimum to $500” on July 7, 2015.6We define liquid assets in the SCF as the sum of checking accounts, savings accounts, certificates of

deposit, cash, stocks, bonds, savings bonds, mutual funds, annuities, trusts, IRAs, and employer-providedretirement plans.

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at an earlier stage in the life cycle. Finally, new robo investors are less likely to live in

California, the robo advisor’s headquarters, suggesting that the reduction brings in investors

from peripheral markets. We return to the question of geography in detail in Section 5.2.

Finally, panel (d) performs a series of t-tests for the difference in means between the post-

reduction and the pre-reduction samples, all of which lend statistical significance to the

patterns just described.

In sum, we uncover two key observations from the descriptive statistics. First, the

representative robo investor prior to the reduction has significantly higher liquid wealth

than the average U.S. household. Second, the reduction in account minimums is associated

with a large inflow of less-wealthy households, which significantly shifts the entire wealth

distribution of robo investors to the left. The next section studies this compositional effect

in detail.

3 Effect on Robo Wealth Distribution

Next, we assess the extent to which the reduction makes the robo market more repre-

sentative of the U.S. population (i.e. more “democratic”). We consider three hypotheses:

Hypothesis 1 (Frictionless Benchmark) In a frictionless world, the reduction has no

effect on the robo market because households can already invest optimally without access to

a professionally-managed portfolio.7

Hypothesis 2 (Binding Account Minimum) If account minimums are the dominant

constraint on household investment, then we should see an increase in robo participation

from households in the lower and middle segments of the U.S. wealth distribution.8 Under

this hypothesis, households behave according to the predictions of frictionless models, but

their optimal risky investment is sufficiently less than $5,000 that they choose not to invest

under the higher minimum. However, some of them decide to invest after the reduction. In

7Even if households require a minimum investment to open a self-managed brokerage account, the absenceof frictions implies that they can borrow to overcome this minimum.

8Account minimums can constrain household investment if, for example, households require professionalassistance to invest in the stock market, in the spirit of Gennaioli, Shleifer and Vishny (2015).

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particular, as we show in Appendix A, we should see an increase in robo participation for

any household with liquid assets above $500, provided there is reasonable variation in risk

tolerance.

Hypothesis 3 (Additional Frictions) Third, if there are additional frictions which con-

strain household investment, then we should see an increase in robo participation from

households in the middle segments of the U.S. wealth distribution.9 Low-wealth households

may lack the resources − financial or otherwise − to overcome both the account minimum

and the costs associated with these additional frictions. Thus, robo participation may not

increase among the lower segments of the wealth distribution. In this case, we expect the

poorest and the wealthiest households to be only weakly affected by the reduction, whereas

middle-wealth households would be affected the most.

3.1 Baseline Effect

We evaluate the previous hypotheses in Figure 2a, in which we plot the distribution

of robo investors across U.S. wealth quintiles. According to the 2016 Survey of Consumer

Finances (SCF), the first quintile is bounded above by $1,000, representing the poorest

households. The second and the third quintiles are bounded above by $6,000 and $42,000,

respectively, whom we call “middle class” households. Finally, the top two quintiles represent

the wealthiest households, whom we call the “upper class”, with the fourth quintile bounded

above by $211,000.

Three observations stand out in Figure 2a. First, bottom quintile households do not

participate with the robo advisor either before or after the reduction. Second, there is

an increase in robo participation from the second and third quintiles of the U.S. wealth

distribution. Finally, the wealthiest households are only weakly affected. In fact, the share

of households in the top quintile dropped from nearly 50% of the investor population to

nearly 40%.

9Examples of such frictions include the costs − financial or otherwise − of setting up a bank account,which would affect the 7% of the U.S. population that is unbanked (FDIC 2017). Alternative frictions includethe costs of acquiring education or financial literacy (e.g. Cole, Paulson and Shastry 2014; Van Rooij, Lusardiand Alessie 2011).

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We next formally test whether robo participation across the U.S. wealth distribution

significantly changes after the reduction. For each quintile, we estimate a regression of the

form:

Quintileq,i = α + βPostt + ui,t, (1)

where i and t index investor and period; periods are defined as the 7 months preceding or

following the reduction; Quintileq,i indicates whether investor i belongs to quintile q; and

Postt indicates whether t is the post-reduction period. In this regression, the estimate of β

represents the change in the share of robo participants in each quintile following the reduction

in account minimum.

Panel (b) of Figure 2 plots the point estimates of β across quintiles, and the brackets

correspond to a 95% confidence intervals. Consistent with panel (a), the effect of the reduc-

tion on households in the bottom quintile of the wealth distribution is zero. At the same

time, middle-class households increase their robo participation. In particular, the share of

households from the second quintile increases by 42% (1.2 pps), and the share of households

from the third quintile increases by 51% (7.4 pps). These increases in the share of middle-

class households are accompanied by a reduction in the share of households from the fifth

quintile by 9.4 pps, and a statistically-insignificant change in the share of households from

the fourth quintiles.

Collectively, these results suggest that the reduction in account minimums by the robo

advisor partially democratizes access to professional portfolio management, in that middle

class households replace the wealthiest households, but there is no effect on the lower class.

One explanation of this result is that additional frictions constrain stock market investment,

beyond the fixed cost associated with surmounting an account minimum, as postulated in

Hypothesis 3. Another explanation is that account minimums dominate these other frictions,

but reducing the minimum to $500, as opposed to $0, was too modest of a reduction to induce

low-wealth households to invest with the robo advisor, which is consistent with the logic of

Hypothesis 2. For example, if households have an optimal risky share less than 0.5 and

cannot borrow to overcome the minimum, then the non-response of households with less

than $1,000 in liquid assets may be optimal. However, based on a basic calibration of the

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benchmark Merton (1969) model described in Appendix A, moderate levels of risk aversion

imply that we should see a much stronger effect on less-wealthy households than shown

in Figure 2. Thus, we conclude that reducing account minimums partially democratizes

access to professional portfolio management, but, consistent with Hypothesis 3, achieving

full democratization requires addressing additional frictions, such as acquiring education or

financial literacy.

3.2 Robustness

3.2.1 Pre-Trend

An alternative explanation is that the compositional shift reflects pre-trends in robo par-

ticipation across wealth quintiles rather than the effect of the reduction in account minimum.

We address this possibility by plotting the monthly time series of key outcome variables by

wealth quintile. Panel (a) of Figure 3 plots the number of robo investors from the three bot-

tom wealth quintiles and the top two quintiles over time. There are parallel, upward trends

for both sets of wealth quintiles. However, the reduction in minimum is associated with a

sharp increase in the growth in investors from the bottom three quintiles, while growth in

investors from the wealthiest quintiles remains unaffected. There are similar results when

comparing dollar inflows from different groups of investors that are presented in panel (b).

The evidence strongly suggests that the shift in the wealth distribution of robo participants

is driven by the reduction in minimum rather than by different time trends.

3.2.2 Demographic Controls and Dollar Investment

In panel (a) of Appendix Figure B1, we reproduce these results after controlling for the

household’s age and income. This result implies that the change in the wealth distribution

does not simply proxy for a change in the age or income distribution. Panel (b) obtains a

similar result in terms of share of dollar investment, which shows how the extensive margin

effect of an increased share of middle class households is not offset by the intensive margin

effect of their smaller typical investment size, relative to upper class households.

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3.3 Summary

Collectively, the reduction in account minimum changes the wealth distribution of

robo participants primarily by bringing more middle class households into the robo market.

Robo participation rates among the poorest households remain unaffected. Neither do the

wealthiest households respond to the reduction, as these households are unlikely to have been

constrained by the previous account minimum. Thus, the upper two wealth quintiles are a

natural choice of control group in our baseline difference-in-difference exercise, as described

in the next section.

4 Effect on Inequality in Household Returns

Our baseline analysis is a difference-in-difference exercise in which we estimate the effect

of the reduction on new robo investors’ risky share and total portfolio return.

4.1 Identification

We design our identification strategy based on the results presented in Figure 3. These

results suggest that the reduction in minimum causes middle class households to join the robo

advisor while the wealthiest households remains unaffected. In addition, robo participation in

the two groups remain on parallel trends before the shock. Consequently, we can implement

a difference-in-difference approach, where households in the second and the third quintiles

(i.e. middle class) constitute the “treatment group” and the households in the fourth and

the fifth quintiles (i.e. upper class) constitute the “control group”.

We start with the standard difference-in-differences setup,

Yi,t = µi + αPostt + β (Middlei × Postt) + δ (Xi × Postt) + vi,t, (2)

where i indexes household; Middlei indicates whether i belongs to the second and the third

quintiles of the U.S. wealth distribution; Postt indicates whether the we observe the household

after the reduction in minimum; δi are household fixed effects; and Xi is a vector of household

characteristics: age, log income, state fixed effects, and a dummy variable which equals 1

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if the household chose a higher level of risk tolerance than recommended by the advisor’s

algorithm. The sample consists of households who become robo investors after the reduction,

and wealth quintiles are defined using the 2016 SCF.

Since there are two time periods, estimating equation (2) is equivalent to estimating the

following first-differenced equation, which will serve as our baseline:

∆Yi = α + βMiddlei + δXi + ui. (3)

Our parameter of interest in equation (3) is β, which measures a difference in changes in Yi

between robo participants from the middle and the upper classes. Under the following two

assumptions, this parameter equals the effect of the reduction on Yi.

Assumption 1 (Exclusion Restriction) The reduction does not coincide with other shocks

that affect robo investment by household wealth.

E [Middlei × ui|Xi] = 0 (4)

Assumption 2 (Unconstrained Control Group) Households in the upper two wealth

quintiles are unconstrained by the initial account minimum.

Assumption 1 is valid in light of Figure 3 and the nature of the experiment. Namely,

there was no other sigificant change in the business model of the advisor or its robo competi-

tors over the 14 month window of our analysis. Assumption 2 is likely conservative, since the

$4,500 difference between pre and post-reduction minimums equals 10% of the fourth wealth

quintile (i.e. $42,000), which is plausibly large enough to relax a constraint for households

slightly-wealthier than the middle class. Under Assumption 2, β represents the effect of the

reduction in account minimum on Yi, while α and δ capture average and heterogeneous trend

growth, respectively.

4.2 Effect on Risky Share

Our first outcome of interest is the change in the household’s risky share. Calculating

this outcome in our data depends on the source of robo investment, for which there are

14

three posibilities: liquidation of cash-on-hand; liquidation of an outside risky position; or

a reduction in consumption. We start by calculating the household’s change in risky share

across the wealth distribution assuming that households finance robo investments with cash.

This assumption is plausible given that liquidating an outside portfolio would entail capital

gains taxes, and the advisor can only manage portfolios consisting of the specified 10 ETFs

so that a direct transfer would also incur capital gains taxes. Moreover, as shown shortly

in Section 5, over 80% of new investors from the middle class are first-time stock market

participants, so that liquidation of an outside risky position is an unlikely source of funds.

To calculate the change in risky share, we suppose that households have some unobserved

risky share during the pre-reduction period, RS. Then their risky share before the reduction

is

Risky Sharei,0 = RSi. (5)

Ignoring the effects of compounding over the relatively-short sample period, their risky share

after the reduction is equal to

Risky Sharei,1 = RSi +Investmenti,1Liquid Assetsi

, (6)

where Investmenti,1 is the value of deposits by i in the post-reduction period (i.e. t = 1); and

we have used the assumption this investment is financed by cash-on-hand. This assumption

implies that the denominator in equation (6), Liquid Assetsi, does not change over time.

Finally, we can take a difference between post-reduction and pre-reduction risky share,

expressing the change in a household’s risky share as

∆Risky Sharei =Investmenti,1Liquid Assetsi

. (7)

If we relax the assumption that the investment is financed by cash-on-hand and instead

assume that it is financed by an increase the savings rate, then equation (7) becomes

∆Risky Share′

i =Investmenti,1

Liquid Assetsi + Investmenti,1. (8)

15

Our results are similar under this alternative definition, as shown in Table B1 and discussed

shortly. However, the implied increase in savings rate associated with with our results is

implausible compared to empirical savings rate in the SCF, which motivates our baseline

assumption that robo investment is financed by cash-on-hand.

Following from our more general specification (3), we now estimate

∆Risky Sharei = α + βMiddlei + δXi + ui. (9)

and present the results in Table 2. Column (1) presents the baseline specification showing

that middle class households gain an additional 14 pps as a result of the reduction in min-

imums. This effect is statistically significant at the 1% level. The estimated coefficients

remain unchanged when we add household-level control variables in column (2) and state

fixed effects in column (3). Panel (a) of Figure 4 visualizes the effect, using the fact that the

coefficient β from our baseline, first-differenced equation (9) is the same as that from the

original difference-in-difference equation (2). Summarizing, our result suggest that middle

class households significantly increase their holdings of risky assets after joining the robo

advisor.

4.3 Effect on Total Portfolio Return

Our second outcome of interest is the household’s total portfolio return, defined as

the expected annual return on liquid assets. For each household we calculate the change

in portfolio return by combining information on her change in risky share with her robo

portfolio return,

∆Total Returni = ∆Risky Sharei × Risky Returni (10)

where ∆Risky Sharei is the change in risky share; and Risky Returni is a measure of the

return on the robo portfolio.

Our primary measure of Risky Returni is the expected return on household i’s robo

portfolio. We follow Calvet, Campbell and Sodini (2007) and propose an asset pricing model

16

to estimate the expected return for securities in the robo portfolio. Specifically, for each

security k, we estimate

Returnk,t = βFk Ft + εFk,t, (11)

where Ft denotes a column vector of pricing factors in month t; βFk denotes the respective

row vector of loadings; and Returnk,t denotes the monthly return on security k in excess of

the return to cash and net of all fees, including the robo advisor’s 0.25 pps management fee

for accounts above $10,000.

While imposing a model improves the efficiency of expected return estimates relative

to directly measuring them from historical returns, it leads to some bias by imposing an

imperfect model of the return structure. Since the choice of model is somewhat arbitrary

and the degree of bias will depend on the characteristics of the portfolio in question, we

estimate equation (11) separately for several common models indexed by factor vector F .

Our baseline model is the capital asset pricing model (CAPM). As described shortly, the

results are robust to using the Fama and French three-factor model or a five-factor model

augmenting the Fama and French model with global and U.S. bond returns. Given the

estimated loadings βFk from estimating equation (11) for model F , it is straightforward to

compute the expected return on household i’s robo portfolio, Risky ReturnFi .10

We next estimate a specification similar to equation (9) with total portfolio return as a

dependent variable,

∆Total Returni = α + βMiddlei + δXi + ui. (12)

Table 3 presents the regression estimates associated with equation (12), where total return is

calculated using the CAPM. Recalling that upper class households are the “control group”,

the point estimates imply that the reduction increases total return by 1.1 pps per year, and

the effect is significant at the 1% level. Panel (b) of Figure 4 visualizes the effect, showing

10Explicitly, if there are K securities and N factors, then Risky ReturnFi = ωiβFλF , where ωi is a 1×K

row vector of weights across securities; βF is a K ×N matrix of factor loadings; and λF is a N × 1 columnvector of factor risk prices.

17

that, relative to the upper class, middle class households experience a 1.1 pp increase in

total return. In sum, the reduction in account minimum generates welfare implications for

the middle class households and leads to a modest increase in portfolio returns.

4.4 Robustness and Extensions

4.4.1 Heterogeneity within Middle Class

One might expect the effects to vary between the second and third wealth quintiles,

whom we call the “lower middle class” and “upper middle class”, respectively. We estimate

the following regression specification,

∆Yi = α + β0Lower Middlei + β1Upper Middlei + δXi + ui,

where i indexes household;Lower Middlei indicates whether i belongs to the second U.S.

wealth quintile; and Upper Middlei indicates whether i belongs to the third quintile. The

outcome ∆Yi is the change in either the household’s risky share or total portfolio return. As

before, households in the fourth and fifth quintiles constitute our control group.

Figure 5 summarizes the results. Panel (a) shows how the shock increases lower middle

class households’ risky share by 28 pps, and this effect is almost three times larger than

the effect on upper middle class households, which equals 11 pps. Panel (b) shows that this

heterogeneity in risky share translates into substantial heterogeneity in total portfolio return.

While the upper middle class gains 0.9 pps in total return, the lower middle class enjoys a

much larger increase of 2 pps. Table 4 confirms that each of these effects is statistically

significant, and the magnitudes do not vary substantially when we add control variables to

the regression.

Collectively, the evidence reveals significant heterogeneity in the effects of the reduction

within the middle class. In particular, lower middle class households − with liquid assets

between $1,000 and $6,000 − experience a substantially greater improvement in total return

than upper middle class households.

18

4.4.2 Consistency with Models of Portfolio Choice

We next ask whether the effects vary with household characteristics in a way consistent

with standard models of portfolio choice. These models predict that the increase in risky

share should be larger for households with greater risk tolerance and higher labor income,

since labor income hedges fluctuations asset returns (e.g. Viceira 2002). We construct a

dummy variable, Highi, which equals 1 if household i has a relatively-high value of some

characteristic. For income, Highi equals 1 if income is above the 75th percentile, among

robo investors. For risk tolerance, the dummy variable equals one if the household chooses

a higher level of risk tolerance than was initially assigned by the robo advisor’s algorithm.

We then interact this variable with Middlei, estimating the following regression equation,

∆Yi = α + β0Middlei + β1 (Middlei × Highi) + δXi + ui,

Table 5 presents the results. The estimated coefficient on Middlei in column (1) shows

how the reduction increases risky share for middle class households by 13 pps, uncondition-

ally. However, the estimated coefficient on the interaction term implies that households with

middle-wealth but high income increase their risky share by an additional 4 pps. Likewise,

middle-wealth households with a high measure of subjective risk tolerance by an additional

5 pps.

Columns (3) and (4) show how the variation in risky share translates into variation in

total return. Middle-wealth households who also have high income increase their total return

by an additional 0.4 pps over other middle-wealth households, shown in column (3). There is

a similar result among middle-wealth households with high risk tolerance, shown in column

(4). In sum, the effect of the reduction in account minimum on risky share and total return

is larger middle-wealth households when these households also have relatively-high income

and relatively-high subjective risk tolerance, consistent with standard models of portfolio

choice.

19

4.4.3 Evaluating Whether New Robo Investment is Temporary

We next evaluate whether new robo investors persist long enough to realize the gains

estimated in Table 3. This question is particularly relevant during market downturns, since

retail investors tend to lose confidence and reduce their risky holdings in bad times rather

than following the conventional advice to “stay the course” (e.g. Malkiel (2015)).

To examine this question, we first ask how recent stock market performance affects

the probability of withdrawing funds from the robo adviser. Then, we ask whether this

relationship differs new robo participants versus households who participated with the robo

advisor before the reduction. We estimate the regression equation

Probability of Withdrawali,τ = β1Rmτ + β2 (Rm

τ × Newi) + αi + ui,τ , (13)

where i indexes household and τ indexes week; Probability of Withdrawali,τ indicates whether

i withdraws funds from her robo account in τ ; Newi indicates whether she joins after the

reduction; αi are investor fixed effects; and Rmτ is the weekly return on the CRSP value-

weighted return index in excess of the risk free rate, measured as the one month Treasury

yield. The sample is restricted to robo investors as of week τ (i.e. who have set a robo

account by τ , and thus have the option to withdraw funds).

Table 6 reports the results. Column (1) shows how a 1 pp decline in the weekly market

return is associated with a 1.2 pps higher probability of withdrawal. This result is robust to

the inclusion of household fixed effects in column (2). Column (3) shows that the estimated

coefficient on the interaction term is positive and statistically significant at the 10% level.

To interpret, a 1 pp decline in the weekly market return is associated with a 2.5 pps higher

probability of withdrawal for existing robo participants, but only a 0.6 pps higher probability

for new investors (i.e. 2.5 - 1.9). Thus, new robo investors are actually less likely to withdraw

funds from the robo advisor following negative returns on the aggregate market. This result

implies that new robo investors exhbit consistency in their investment strategies, and thus

the gains in performance from Table 3 are not transient.

20

4.4.4 Robustness to Costly-to-Liquidate IRA Portfolios

We now construct a test to evaluate our assumption that robo investment is financed by

cash. This test makes use of our data on nontaxable retirement accounts, namely individual

retirement accounts (IRAs), and the logic is as follows. Suppose households finance their

retirement robo investment using either cash or liquidated risky positions from a non-robo

retirement account. Cash is plausibly the dominant source of funds for retirement robo

investments, since premature liquidation of a non-robo retirement account would incur a

costly penalty. Moreover, the robo advisor can only manage portfolios comprised of the

10 ETFs as previously described, and so it is difficult for households to directly transfer

outside IRA accounts to the robo advisor. Thus, if the baseline results from Table 2 are

borne out among the subsample of retirement accounts, it supports our assumption that

robo investment is predominantly financed by cash-on-hand.

Table 7 reestimates the baseline regression equation (9) on the restricted sample of IRAs.

The baseline estimate from column (1) implies an increase in 12.7 pps in risky share following

the reduction. The effect remains similar when we control for household characteristics in

column (2) and add state fixed effects in column (3). The overall results closely resemble

their counterparts from Table 2. This resemblance lends empirical support to our baseline

assumption that households finance their robo investment through cash-on-hand, versus

through a substitution between different risky positions.

4.4.5 Robustness to Asset Pricing Model

Figure 6 presents the estimated expected returns across a variety of asset pricing models.

The results show that the 3-factor model yields even higher expected annual return of 1.3%,

and augmenting this model with bond factors leads to an expected return of 1.4%. We obtain

similar results when measuring Risky Returni using realized instead of expected return.

5 The Stock Market Participation Channel

Our baseline results reflect a mixture of investment by first-time stock market partic-

ipants and existing participants opening an additional account. In this section, we assess

21

the role of the former channel, increased stock market participation. We adopt two separate

strategies to perform this analysis. First, we impute pre-reduction stock market participation

status of new robo investors by training a machine learning algorithm on the entire sample

of the U.S. households. Second, we assess whether new robo investors are more likely to live

in states with lower stock market participation rates.

The first test indicates that 79% of the middle class households did not participate

in the risky asset market before becoming robo investors. The second test suggests that

new households are more likely to live in states with low stock market participation rates.

Together, these two sets of results provide suggestive evidence that the reduction in account

minimum caused many middle class households to make their first investment in the stock

market.

5.1 New Stock Market Participants by Wealth Quintile

Our first strategy entails imputing a household’s stock market participation status,

where stock market participation is defined as ownership of stocks, mutual funds, a trust, or

an IRA. To ensure robustness of the results, we use a variety of imputation methodologies.

Our preferred methodology is a commonly-used, non-parametric classification algorithm

called a random forest. As described in Liberman et al. (2019), a random forest algorithm

iteratively selects subsets of candidate predictor variables from a master set of predictors and,

using those variables, constructs a regression “tree”. A regression tree iteratively splits the

sample into subsamples according to the candidate predictor variables, where the thresholds

used to split the sample are chosen to maximize in-sample predictive power within each

subsample, called a “leaf”. Once the predictive power ceases to improve, the algorithm stops

splitting the sample, and it then moves to the next tree in the “forest”. The final prediction

is given by averaging the predictions implied by each tree.

Our second methodology is another non-parametric classification algorithm called gra-

dient boosting. This method starts by fitting a tree and iteratively adds new trees in a way

that puts more weight on observations with large prediction errors in a previous tree. While

a random forest algorithm builds a sequence of independent trees, in gradient boosting each

new tree helps to correct errors made by the previously trained tree.

22

We complement the previous methodologies with two parametric approaches: Lasso

regression and ridge regression. Both methods use logistic regression as a baseline model

but apply different penalty terms for regularization purposes. In the case of ridge regression,

the penalty term reduces the magnitude of the regression coefficients that contribute most

to the prediction error. In the case of Lasso regression, these coefficients are optimally set

to zero.

We train each algorithm on the 2016 SCF, and we impute participation status for new,

middle-class robo participants in our sample using observed characteristics in both the SCF

and in our main dataset. These characteristics are the household’s age, income and liquid

assets. While the number of overlapping characteristics appears to be relatively small, we

are still able to achieve high accuracy, especially among the non-parametric methods.

Table 8 and Figure 7 present the results of the exercise. The non-parametric methods

have significantly higher accuracy, indicating that the relationship between household par-

ticipation status and characteristics is highly non-linear. Both random forest and gradient

boosting correctly classify 99% of households’ stock market participation status. These al-

gorithms predict that 78%-79% of new investors in the second and third quintiles of the U.S.

wealth distribution did not hold risky assets before becoming robo investors.11

The results are robust to imputation based on Lasso and ridge regressions. Specifically,

these methodologies correctly classify 74%-75% of households’ stock market participation

status. Both methodologies predict that 98% of new robo investors in the second and third

quintiles of the U.S. wealth distribution were non-participants in the stock market before

joining the robo advisor.

5.2 State Stock Market Participation

In our second strategy, we examine the relationship between the probability of joining

the robo advisor and stock market participation in the domicile state. If new robo partic-

ipants predominantly live in states with low levels of stock market participation, they are

11In our baseline results, we use a weighted sample of the SCF households to account for proper repre-sentation wihtin the U.S. population. If we implement all the machine learning methods within a smallerunweighted sample, we obtain similar results.

23

less likely to already own a brokerage account. As a result, their robo investment is more

likely to represent their first investment in the stock market. We follow Cole et al. (2014)

and use a share of IRS tax returns reporting dividend income as a proxy for the stock market

participation rate in the state.12 We next estimate the regression equation

∆Robo Investori = α + βParticipations(i) + ui, (14)

where i and s index investor and state; ∆Robo Investori indicates whether i becomes a robo

investor after the reduction; and Participations(i) is the share of IRS tax returns reporting

dividend income, a proxy for the stock market participation rate in state s.

Panel (a) of Figure 8 presents a binned scatterplot associated with equation (14). The

figure shows how new robo participants are more likely to come from states with low stock

market market participation. Specifically, a decline of 1 pp in state-level stock market

participation rate is associated with an increase of 1.43 pps in the probability of becoming a

robo investor. This evidence indirectly suggests that new robo participants are more likely

to invest in risky assets for the first time through the robo adviser. Table 9 show the full

regression results, confirming that the effect is significant and robust to the inclusion of

household characteristics.

Finally, as complementary evidence, panel (b) of Figure 8 plots the distribution of the

change in the share of robo investors from each state. It shows how new robo investors

do not come from states associated with a strong financial services sector (e.g. New York,

Massachusetts), which provides suggestive support for the patterns shown in panel (a).

5.3 Summary

Both sets of results in this section suggest that new, middle-class robo investors are

first-time stock market participants, either based on imputed participation status from the

SCF or stock market participation in their domicile state. While these results are more

suggestive than our baseline findings, they highlight the importance of increased stock market

12The 2016 Survey of Consumer Finances does not report any geographical information in the publicdataset.

24

participation as a dominant channel through which the reduction in account minimum affects

risky share and total return.

6 Conclusion

We conclude that a reduction in account minimums by robo advisors can partially

democratize investing by bringing middle class households into risky asset markets. We

arrive at this conclusion by studying an experiment where a large U.S. robo advisor suddenly

reduced its account minimum by a factor of 10. The shock significantly increased risky share

by middle-class households and consequently improved their total return on liquid assets.

Moreover, the results appear to be driven by a subset of households who became stock market

participants because of the reduction.

Our study has two key implications. First, these findings exemplify how advancements

in financial technology can enable more households to reap the benefits of access to financial

markets. In our setting, automation in allows asset managers to manage a large number

of portfolios at a low per-portfolio cost (Philippon 2019). In turn, managers can impose

lower account minimums, allowing less-wealthy households to access professional portfolio

management services. Our study quantifies the effects of such a reduction on a number of

household outcomes, implying that automation in financial services can improve the financial

well-being of many households.

At the same time, automation has an ambiguous effect on inequality. On one hand,

the reduction has a profound effect on middle-class households. On the other hand, the

poorest households do not change their participation status and become robo-investors even

after a very large reduction in account minimum. As a result, long term wealth inequality

may decline between the middle and the upper classes, but it also may increase between

the lower and the middle classes. While high costs of asset management in the form of

account minimums can represent a significant barrier to stock market participation, they do

not appear to be the only barrier, especially for the poorest households. Investigating the

effect of FinTech on barriers such as education or financial literacy is a promising avenue for

future research

25

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27

Figures

Figure 1: Wealth Distribution of Robo Investors

0

.002

.004

.006

Empi

rical

Den

sity

0 100 200 300 400 500Liquid Assets ($'000)

Pre-Reduction Post-ReductionD-Statistic: 0.11 (p = 0.00)

Wealth Distribution of Robo Investors

Note: This figure plots the empirical density of liquid assets for robo investors. The blue solid and red

dashed curves correspond to the 7 months preceding the reduction (Pre-Reduction) and following it (Post-

Reduction), respectively. The D-statistic is based on the Kolmogorov-Smirnov test for equality of distribu-

tions. The plot excludes households with liquid assets above $500,000. The density is based on a Gaussian

kernel.

28

Figure 2: Distribution of Robo Investors Across U.S. Wealth Quintiles

0

.1

.2

.3

.4

.5

Shar

e of

Rob

o In

vest

ors

Q1(<$1k)

Q2($1k-6k)

Q3($6k-42k)

Q4($42k-211k)

Q5(>$211k)

Robo Investors by U.S. Wealth Quintile

Pre-Reduction Post-Reduction

-.1

-.05

0

.05

.1

Cha

nge

in S

hare

of R

obo

Inve

stor

s

Q1(<$1k)

Q2($1k-6k)

Q3($6k-42k)

Q4($42k-211k)

Q5(>$211k)

SCF Quintile

Change in Wealth Distribution of Robo Investors

Note: Panel (a) plots the distribution robo investors across U.S. wealth quintiles during the pre-reductionand post-reduction periods. Panel (b) plots the change in the share of robo investors from each quintile fromthe pre-reduction period to the post-reduction period. Explicitly, panel (b) plots the estimated coefficientsfrom a regression of the form

Quintileq,i = α+ βPostt + ui,t,

where i and t index investor and period; periods are defined as the 7 months preceding or following the

reduction; Quintileq,i indicates whether i belongs to quintile q; and Postt indicates whether t is the post-

reduction period. The sample consists of robo investors as of period t. Wealth quintiles are constructed

using the 2016 SCF. Brackets correspond to a 95% confidence interval.

29

Figure 3: Pre-Trend in Robo Investment by U.S. Wealth Quintile

.5

1

1.5

2

2.5

3

3.5N

umbe

r of I

nves

tors

(rel

ativ

e to

Jun

e '1

5)

2015

m1

2015

m2

2015

m3

2015

m4

2015

m5

2015

m6

2015

m7

2015

m8

2015

m9

2015

m10

2015

m11

2015

m12

2016

m1

2016

m2

Bottom 3 Quintiles Top 2 Quintiles

Robo Investors by U.S. Wealth Quintile

(a) Number of Investors

0

.5

1

1.5

2

2.5

3

3.5

Dol

lar I

nflo

w (r

elat

ive

to J

une

'15)

2015

m1

2015

m2

2015

m3

2015

m4

2015

m5

2015

m6

2015

m7

2015

m8

2015

m9

2015

m10

2015

m11

2015

m12

2016

m1

2016

m2

Bottom 3 Quintiles Top 2 Quintiles

Robo Investment by U.S. Wealth Quintile

(b) Dollar Inflow

Note: Panel (a) plots the number of robo investors from the bottom 3 and top 2 quintiles of the U.S. wealth

distribution each month, normalized by the number of investors the month before the reduction. Panel (b)

contains an analogous plot in terms of dollar inflow from the bottom 3 and top 2 quintiles. Wealth quintiles

are constructed using the 2016 SCF. The shaded region corresponds to the period after the reduction.

30

Figure 4: Baseline Effect on Risky Share and Total Portfolio Return

0

.05

.1

.15

.2

Coe

ffici

ent:

Mid

dle

x Po

st

Pre-Reduction Post-Reduction

Effect of Reduction on Risky Share

(a) Risky Share

0

.2

.4

.6

.8

1

1.2

Coe

ffici

ent:

Mid

dle

x Po

st

Pre-Reduction Post-Reduction

Effect of Reduction on Total Portfolio Return

(b) Total Portfolio Return

Note: This figure plots the baseline estimated effect of the reduction on new robo investors’ risky share andtotal return, and it is a companion to Tables 2 and 3. Explicitly, panels (a) and (b) plot the estimatedcoefficients β from the regressions in column 1 of Table 2 and column 1 of Table 3, respectively. Thesecoefficients are obtained by estimating the first-difference of the following equation,

Yi,t = µi + αPostt + β (Middlei × Postt) + ui,t,

where i indexes household; and t indexes period, where the set of periods are the 7 months before or after the

reduction. The outcome Yi,t is either the household’s risky share or total portfolio return. The remaining

notes are the same as in Tables 2 and 3.

31

Figure 5: Heterogeneous Effects within the Middle Wealth Quintiles

0

.1

.2

.3

Coe

ffici

ent:

Wea

lth Q

uint

ile

Q1(<$1k)

Q2($1k-6k)

Q3($6k-42k)

Q4 & Q5(>$42k)

Effect on Risky Share by U.S. Wealth Quintile

(a) Risky Share

0

.5

1

1.5

2

2.5

Coe

ffici

ent:

Wea

lth Q

uint

ile

Q1(<$1k)

Q2($1k-6k)

Q3($6k-42k)

Q4 & Q5(>$42k)

Effect on Total Portfolio Return by U.S. Wealth Quintile

(b) Total Portfolio Return

Note: This figure plots the estimated effect of the reduction on risky share and total return after partitioningthe middle wealth bin into its constituent quintiles (i.e. Q2 and Q3), and it is a companion to Table 4.Explicitly, panels (a) and (b) plot the estimated coefficients β from the regressions in columns 1 and 3 ofTable 4, respectively. These coefficients are obtained by estimating the following equation,

∆Yi = α+ β0Lower Middlei + β1Upper Middlei + δXi + ui,

where i indexes household. The outcome ∆Yi is the change in either the household’s risky share or total

portfolio return. The remaining notes are the same as in Table 4.

32

Figure 6: Robustness of Effect on Total Portfolio Return

0

.5

1

1.5

2

2.5

Effe

ct o

n To

tal P

ortfo

lio R

etur

n (%

)

Q1(<$1k)

Q2($1k-6k)

Q3($6k-42k)

Q4 & Q5(>$42k)

CAPM Fama French Fama French + Bond 3-Year Realized

Effect on Total Portfolio Return by U.S. Wealth Quintile

Note: This figure plots the estimated effect of the reduction on new robo investors’ total portfolio returnfor different measures of expected return, and it is a companion to Table 3. Explicitly, the figure plots theaverage estimated increase in total portfolio return within each set of wealth quintiles, where the estimatedincrease in total portfolio return is defined as

∆Total Returni = ∆Risky Sharei∗ × Risky Returni,

where i indexes household; ∆Risky Sharei∗ is the effect of the reduction on risky share as estimated in

column 1 of Table 2; and Risky Returni is a measure of the return on the robo portfolio. The baseline

measure is the expected return implied by the CAPM. The remaining measures are: the expected return

implied by the Fama-French 3 Factor Model (Fama French); the expected return implied by the Fama-French

3 Factor Model augmented with U.S. and global bond returns (Fama French + Bond); and the investor’s

realized return over the 3-year period after her initial investment. All returns are net of fees. The remaining

notes are the same as in Table 3.

33

Figure 7: New Stock Market Participants from Middle Wealth Quintiles

0

.2

.4

.6

.8

1

Shar

e of

New

Rob

o In

vest

ors

Random Forest Boost Lasso Ridge

New Stock Market Participants by Classification Method

Note: This figure plots the share of new robo investors from the second and third quintiles of the U.S.

wealth distribution who were imputed non-participants in the stock market before the reduction, and it is a

companion to Table 8. Participation status is imputed, and each bar corresponds to a separate imputation

methodology. Random Forest corresponds to a random forest classification algorithm applied to the 2016

SCF, where the set of features are age, income, and liquid assets. Boost corresponds to a similar gradient

boosting algorithm. Lasso and Ridge correspond to logistic Lasso and logistic ridge regressions, respectively.

Section 5.1 contains further methodological details. Participation is defined as ownership of stocks, mutual

funds, a trust, or an IRA.

34

Figure 8: Financial Development in the Home States of New Robo Investors

40

50

60

70

80Pr

obab

ility

of B

eing

a N

ew R

obo

Inve

stor

(%)

15 20 25State Stock Market Participation Rate (%)

Slope: -1.43 (p = 0.03)

New Robo Investors by State Stock Market Participation

(a) New Investors and State Stock Market Participation

0.38 − 0.790.23 − 0.380.11 − 0.230.03 − 0.110.00 − 0.03-8.63 − 0.00

Change in Share of Robo Participants From Each State (%)

(b) Change in Geographic Distribution of Robo Investors

Note: This figure summarizes the geography of new robo investment, which assesses whether the baselineresults are driven by changes in stock market participation. Panel (a) plots a binned scatterplot associatedwith equation (14), and it is a companion to Table 9. Explicitly, the regression is of the form

∆Robo Investori = α+ βParticipations(i) + ui,

where i and s index investor and state; ∆Robo Investori indicates whether i becomes a robo investor after

the reduction; Participations(i) is the share of IRS tax returns reporting dividend income, a proxy for the

stock market participation rate in state s. Panel (b) plots the change in the share of robo investors from

each U.S. state from the pre-reduction period to the post-reduction period. The remaining notes are the

same as in Table 9.

35

Tables

Table 1: Household Summary Statistics

MeanStandard Percentiles

Deviation 5th 10th 25th 50th 75th 90th 95th

(a) Pre-Reduction:

Agei 35.79 8.72 25 27 30 34 40 47 53

Incomei ($000) 157.36 110.67 42.29 60 87 130 200 300 400

Liquid Assetsi ($000) 436.44 660.82 16.89 30 75 200 500 1000 1700

High Risk Tolerancei .15 .35

Californiani .45 .5

Observations: 4,366

(b) Post-Reduction:

Agei 35.57 9.43 24 26 29 33.5 40 48 55

Incomei ($000) 134.71 104.83 32 45 70 102.5 165 250 337.5

Liquid Assetsi ($000) 342.27 574.96 10 16 50 130 400 900 1400

High Risk Tolerancei .14 .35

Californiani .37 .48

Observations: 9,702

(c) New Investors:

Agei 35.4 9.97 24 25 28 33 40 49 56

Incomei ($000) 116.17 95.9 28 39.07 60 90 140 220 300

Liquid Assetsi ($000) 265.21 480.25 8 11.62 32.5 100 275 700 1025

High Risk Tolerancei .14 .34

Californiani .3 .46

Observations: 5,336

(d) Post-Minus-Pre:

Agei -0.213 0.168

Incomei ($1,000) -22.651 1.944

Liquid Assetsi ($1,000) -94.170 10.988

High Risk Tolerancei -0.006 0.006

Californiani -0.086 0.009

Note: This table presents household-level summary statistics of the main dataset. Subscript i denoteshousehold. Panels (a) and (b) summarize robo investors before and after the reduction, respectively. Panel(c) summarizes household who become robo investors after the reduction. Panel (d) summarizes the differencein means between panels (a) and (b), and the standard error for this difference is shown in the second column.High Risk Tolerance indicates whether i voluntarily chooses a riskier robo portfolio than that recommendedby the advisor. Each observation is a household. The sample period spans December 2014 through February2016. The reduction occurs on July 5, 2015.

36

Table 2: Baseline Effect of Reduction on Robo Investors’ Risky Share

Outcome ∆Risky Sharei

Middlei 0.143 0.132 0.134(0.000) (0.000) (0.000)

ControlsAgei -0.000 -0.000

(0.320) (0.707)log (Incomei) -0.012 -0.014

(0.013) (0.004)High Risk Tolerancei 0.003 0.002

(0.736) (0.820)

State FE No No YesR-squared 0.074 0.075 0.087Number of Observations 5088 5087 5087

Note: P-values are in parentheses. This table contains the results of equation (9), which estimates the effectof the reduction on new robo investors’ risky share. Explicitly, the regression is of the form

∆Risky Sharei = α+ βMiddlei + δXi + ui,

where i indexes household; Middlei indicates whether i belongs to the second or third U.S. wealth quintile($1k-$42k); and ∆Risky Sharei is the ratio of robo investment over the post-reduction period to the investor’sliquid assets. The sample consists of households who become robo investors after the reduction. The referencegroup is households from the fourth or fifth U.S. wealth quintiles, since there are no robo investors from thefirst quintile. Controls are defined in Table 1. Wealth quintiles are constructed using the 2016 SCF. StateFE denotes a vector of fixed effects for the investor’s home state.

37

Table 3: Baseline Effect of Reduction on Robo Investors’ Total Portfolio Return

Outcome ∆Total Returni

Middlei 1.134 0.994 1.007(0.000) (0.000) (0.000)

ControlsAgei -0.013 -0.011

(0.000) (0.000)log (Incomei) -0.061 -0.074

(0.091) (0.041)High Risk Tolerancei 0.077 0.071

(0.295) (0.335)

State FE No No YesR-squared 0.084 0.090 0.101Number of Observations 4772 4772 4772

Note: P-values are in parentheses. This table contains the results of equation (12), which estimates theeffect of the reduction on new robo investors’ total portfolio return, defined as the expected return on liquidassets. Explicitly, the regression is of the form

∆Total Returni = α+ βMiddlei + δXi + ui,

where i indexes household; and ∆Total Returni is the change in total portfolio return. Total portfolio returnis defined as in equation (10) as

∆Total Returni ≡ ∆Risky Sharei × Risky Returni,

where ∆Risky Sharei is the change in risky share as defined in Table 2; and Risky Returni is a measure ofthe return on the robo portfolio. The baseline measure, used in this table, is the expected return implied bythe CAPM. All returns are net of fees. The remaining notes are the same as in Table 2.

38

Table 4: Heterogeneity within the Middle Wealth Quintiles

Outcome ∆Risky Sharei ∆Total Returni

Lower Middlei 0.282 0.269 2.176 2.049(0.000) (0.000) (0.000) (0.000)

Upper Middlei 0.127 0.119 1.009 0.906(0.000) (0.000) (0.000) (0.000)

ControlsAgei -0.000 -0.001

(0.285) (0.006)log (Incomei) -0.008 -0.044

(0.118) (0.225)High Risk Tolerancei 0.002 0.074

(0.827) (0.315)

State FE No Yes No YesR-squared 0.074 0.075 0.096 0.112Number of Observations 5088 5087 4772 4772

Note: P-values are in parentheses. This table contains the results of a variant of equation (9), which testsfor heterogeneous effects within the middle wealth quintiles. Explicitly, the regression is of the form

∆Risky Sharei = α+ β0Lower Middlei + β1Upper Middlei + δXi + ui,

where i indexes household; Lower Middlei indicates whether i belongs to the second U.S. wealth quintile($1k-6k); and Upper Middlei indicates whether i belongs to the third quintile ($6k-42k). The remainingnotes are the same as in Table 2.

39

Table 5: Consistency with Models of Portfolio Choice

Outcome ∆Risky Sharei ∆Total Returni

Middlei 0.132 0.137 1.089 1.077(0.000) (0.000) (0.000) (0.000)

Middlei × Highi 0.044 0.045 0.421 0.367(0.008) (0.035) (0.001) (0.026)

Highi -0.039 -0.010 -0.307 -0.087(0.000) (0.348) (0.000) (0.298)

High Variable Income Risk Tolerance Income Risk Tolerance

R-squared 0.076 0.074 0.088 0.085Number of Observations 5088 5088 4772 4772

Note: P-values are in parentheses. This table contains the results of a variant of equation (9), which assesseswhether the baseline results in Tables 2 and 3 are consistent with benchmark models of portfolio choice.Explicitly, the regression is of the form

∆Risky Sharei = α+ β0Middlei + β1 (Middlei ×Highi) + δXi + ui,

where i indexes household; and Highi indicates whether i belongs to one of the following groups: is above the75th percentile in income (Income); or voluntarily chooses a riskier robo portfolio than that recommendedby the advisor (High Risk Tolerance). The remaining notes are the same as in Table 2.

40

Table 6: Evaluating whether New Robo Investment is Temporary

Outcome Probability of Withdrawali,t

Rmt -0.012 -0.013 -0.025

(0.034) (0.024) (0.003)Rmt × Newi 0.019

(0.098)Household FE No Yes YesR-squared 0.000 0.047 0.047Number of Observations 336552 336552 336552

Note: P-values are in parentheses. This table contains the results of equation (13), which assesses whetherthe baseline results dissipate after market downturns. Explicitly, the regression is of the form

Probability of Withdrawali,τ = β1Rmτ + β2 (Rmτ ×Newi) + αi + ui,τ ,

where i indexes household and τ indexes week; Probability of Withdrawali,τ indicates whether i withdrawsfunds from her robo account in τ ; Newi indicates whether she joins after the reduction; and Rmτ is the weeklyreturn on the CRSP value-weighted return index in excess of the risk free rate, measured as the one monthTreasury yield. The sample is restricted to robo investors as of week τ . Standard errors are clustered byinvestor.

41

Table 7: Robustness of Effect on Risky Share to Costly-to-Liquidate Portfolios

Outcome ∆Risky Sharei

Middlei 0.127 0.111 0.134(0.000) (0.000) (0.000)

ControlsAgei -0.000 -0.000

(0.880) (0.686)log (Incomei) -0.027 -0.025

(0.066) (0.098)High Risk Tolerancei -0.003 -0.006

(0.934) (0.848)

State FE No No YesR-squared 0.037 0.042 0.131Number of Observations 653 653 653

Note: P-values are in parentheses. This table contains the results of equation (9) after restricting the sampleto IRA portfolios, which assesses whether the baseline results are driven by liquidation of unobserved riskypositions. The remaining notes are the same as in Table 2.

42

Table 8: New Stock Market Participants from Middle Wealth Quintiles

Methodology: Random Forest Boost Lasso Ridge

New Participants79% 78% 98% 98%

(% new robo investors)

Accuracy (%) 99% 99% 75% 74%

Note: This table shows the share of new robo investors from the second and third quintiles of the U.S.wealth distribution who were imputed non-participants in the stock market before the reduction, whichassesses whether the baseline results are driven by changes in stock market participation. Participationstatus is imputed, and each column corresponds to a separate imputation methodology. Random Forestcorresponds to a random forest classification algorithm applied to the 2016 SCF, where the set of featuresare age, income, and liquid assets. Boost corresponds to a similar gradient boosting algorithm. Lasso andRidge correspond to logistic Lasso and logistic ridge regressions, respectively. The second row in the tableshows the share of households in the SCF whose participation status is correctly classified by the indicatedmethodology. Section 5.1 contains further methodological details. Participation is defined as ownership ofstocks, mutual funds, a trust, or an IRA.

43

Table 9: New Robo Investors by State Stock Market Participation Rate

Outcome ∆Robo Investori

Participations(i) -1.427 -1.406(0.028) (0.028)

ControlsMiddlei 0.136

(0.000)Agei 0.002

(0.103)log (Incomei) -0.109

(0.000)High Risk Tolerancei -0.011

(0.677)

R-squared 0.005 0.062Number of Observations 9634 9634

Note: P-values are in parentheses. This table contains the results of equation (14), which assesses whethernew robo investors disproportionately live in states with lower stock market participation rates. Explicitly,the regression is of the form

∆Robo Investori = α+ βParticipations(i) + δXi + ui,

where i and s index investor and state; ∆Robo Investori indicates whether i becomes a robo investor afterthe reduction; Participations(i) is the share of IRS tax returns reporting dividend income, a proxy for thestock market participation rate in state s. Data on tax returns come from the IRS’ 2015 zip code level data,and we calculate the average participation rate across zip codes with average investor income above $50,000.Observations are weighted by the population of the state relative to the number of robo investors from thestate. Standard errors are clustered by state. The remaining notes are the same as in Table 2.

44

For Online Publication:

Online Appendix to

“Does FinTech Democratize Investing?”

A Calibration of Optimal Risky Investment

We argue in Section 3 that the absence of an effect on low-wealth households reflects

the existence of additional frictions that constrain household investment, such as acquiring

education or financial literacy, as postulated in Hypothesis 3 from Section 3. However, it

is also possible that account minimums dominate these other frictions, but reducing the

minimum to $500, as opposed to $0, was too modest of a reduction to induce low-wealth

households to invest with the robo advisor, which is consistent with the logic of Hypothesis 2

and the presence of borrowing constraints. For example, if households have an optimal risky

share less than 0.5 and cannot borrow to overcome the minimum, then the non-response by

households with less than $1,000 in liquid assets may be optimal.

To distinguish between these two explanations, we perform a basic calibration of the

benchmark Merton (1969) model. Specifically, we consider an investor who: is less wealthy

than the least wealthy robo participant (i.e. $3,000); has at least $500 in liquid assets; and

chooses to invest with the robo advisor at the new account minimum, $500. Then, we ask

what coefficient of relative risk aversion makes that investment optimal through the lens of

Merton (1969). Recall that the corresponding formula for household i’s optimal risky share

is

w∗ =1

γi

E[RRi,t

]Var

[RRi,t

] (A1)

where γi is the coefficient of relative risk aversion; and RRi,t is the return on the household’s

robo portfolio in excess of the return to cash and net of all fees. Under the frictionless

benchmark in equation (A1), household i with liquid assets Wi would find it optimal to

45

invest at least $500 with the robo advisor as long as

γi ≤Wi

500

E[RRi,t

]Var

[RRi,t

] . (A2)

We calibrate the bound in (A2) for households with liquid assets between $500 and

$3,000 using the moments of the robo portfolio associated with a risk score of 8.5, the

median risk score among households in the second quintile of the U.S. wealth distribution.

The standard deviation of this portfolio’s return is 11.78%, and, from Appendix Table B2,

the CAPM-implied expected return is 7.94%.

Appendix Table B3 summarizes the implied upper bound on γi by household wealth.

For example, a household with $3,000 in liquid assets would choose to invest at least $500

provided her coefficient of relative risk aversion is no greater than 34.3, while a household

with only $1,000 would still invest at least $500 provided her risk aversion is 11.4 or smaller.

These values are large relative to the values found in experimental papers, which typically

range from 3 to 10 as noted by Giglio et al. (2019). Moreover, a nontrivial 9% of the U.S.

population have liquid assets between $1,000 and $3,000, and an additional 6% have liquid

assets between $500 and $1,000.

Together, the large coefficients of risk aversion required to rationalize non-investment

by households with liquid assets less than $3,000 combined with the large share of the

population within this segment of the wealth distribution imply that we should observe

at least some increase in robo participation among such households. The absence of a

response is inconsistent with the notion that account minimums are the dominant constraint

on household investment (i.e. Hypothesis 2). Instead, it is consistent with the argument that

both account minimums and other frictions (e.g. acquiring education or financial literacy)

constrain household investment in the stock market (i.e. Hypothesis 3).

46

B Additional Figures and Tables

Figure B1: Robustness of the Change in Wealth Distribution of Robo Investors

-.05

0

.05

Cha

nge

in S

hare

of R

obo

Inve

stor

s

Q1(<$1k)

Q2($1k-6k)

Q3($6k-42k)

Q4($42k-211k)

Q5(>$211k)

SCF Quintile

Residualized Change in Robo Wealth Distribution

-.1

-.05

0

.05

.1

Cha

nge

in S

hare

of R

obo

Inve

stor

s

Q1(<$1k)

Q2($1k-6k)

Q3($6k-42k)

Q4($42k-211k)

Q5(>$211k)

SCF Quintile

Value-Weighted Change in Robo Wealth Distribution

This figure evaluates the robustness of Figure 2, which plots the change in the share of robo investors from

each bin. Panel (a) is analogous to Figure 2 after controlling for the investor’s age and log income. Panel

(b) is analogous to Figure 2 after weighting observations by robo dollar investment. The remaining notes

are the same as in Figure 2.

47

Table B1: Robustness of Effect on Risky Share to Changes in Savings Rate

Outcome ∆Risky Sharei

Middlei 0.090 0.081 0.083(0.000) (0.000) (0.000)

ControlsAgei -0.001 -0.000

(0.013) (0.069)log (Incomei) -0.007 -0.008

(0.015) (0.005)High Risk Tolerancei 0.003 0.002

(0.639) (0.727)

State FE No No YesR-squared 0.089 0.092 0.104Number of Observations 5088 5087 5088

Note: P-values are in parentheses. This table contains the results of equation (9) after redefining∆Risky Sharei according to equation (8), which assesses whether the baseline results are robust to assumingrobo investment comes from an increase in savings versus an investment of existing savings. The remainingnotation is the same as in Table 2.

48

Table B2: Summary of Robo Portfolios

Risk Tolerance Beta Expected Return Stocks Bonds Other(0.5 to 10) (%) (%) (%) (%)

0.50 0.32 4.25 33.00 60.00 7.002.00 0.45 5.24 47.00 48.00 5.002.50 0.49 5.46 50.00 44.00 6.003.00 0.52 5.66 53.00 41.00 6.003.50 0.57 6.06 59.00 35.00 6.004.00 0.58 6.12 59.00 35.00 6.004.50 0.61 6.38 62.00 33.00 5.005.00 0.64 6.62 66.00 29.00 5.005.50 0.67 6.84 69.00 26.00 5.006.00 0.70 7.05 72.00 23.00 5.006.50 0.72 7.20 74.00 21.00 5.007.00 0.75 7.36 77.00 18.00 5.007.50 0.77 7.54 80.00 15.00 5.008.00 0.79 7.69 82.00 13.00 5.008.50 0.82 7.94 86.00 9.00 5.009.00 0.85 8.12 89.00 6.00 5.009.50 0.88 8.35 90.00 5.00 5.0010.00 0.91 8.54 90.00 5.00 5.00

Note: This table summarizes the robo portfolios assigned to households in our sample. Portfolios are indexedby risk tolerance, which ranges from 0.5 to 10 in increments of 0.5. Each portfolio has a unique vector ofweights assigned to 10 possible ETFs, which are chosen to represent exposure to different asset classes.Stocks, Bonds, and Other respectively denote the sum of weights for ETFs that track stock market indices(VIG, VTI, VEA, VW), bond market indices (LQD, EMB, MUB, SCHP), and other asset classes, namelyreal estate (VNQ) and commodities (XLE). Expected Return and Beta are based on the CAPM, as describedin Section 4. The table is restricted to taxable portfolios.

49

Table B3: Minimal Risk Aversion to Rationalize a Robo Investment Less Than $500

Liquid AssetsCoefficient of Relative

Risk Aversion

$500 5.7$1,000 11.4$2,000 22.8$3,000 34.3

Note: This table summarizes the minimal coefficient of relative risk aversion to rationalize a robo investmentless than $500 by household wealth. The minimal risk aversion is obtained using the Merton (1969) formula,and the calibration is described in Appendix A.

50