Robo Advisers and Mutual Fund Stickiness ∗

Michael Reher†and Celine Sun‡

November 2016

Abstract

We document a puzzling finding that robo advisers, firms which pursue automated,

passive investment strategies for their clients, outperform both self-managed and mutual

fund portfolios on a risk adjusted basis, but mutual fund holders are significantly less

likely to respond to underperformance by setting up a robo account. We provide evidence

consistent with a theory where more risk averse investors hold mutual funds, and where

trust in one’s fund manager plus costly liquidation subsequently discourage delegating

management to robo advisers. However, using a regression discontinuity design, we find

that portfolio-specific financial advice about diversification and fees can mitigate this

effect.

Keywords: Portfolio Choice, Financial Advice, Houeshold Saving, Financial Innova-

tion

JEL Classification: G11, G23, D14, D18

∗We thank John Campbell, Ben Friedman, Pedro Gete, Andrei Shleifer, Stas Sokolinski, Jeremy

Stein, Boris Vallee and seminar participants at Harvard for comments.†Harvard University. Email: mreher@g.harvard.edu‡Wealthfront. Email: celine@wealthfront.com

1

1 Introduction

One of the most studied and important questions in household finance is why retail investors

underperform relative to passive benchmarks (Campbell 2006). This question is especially

puzzling given the availability, low costs, and broad exposure of many exchange traded funds

(ETFs). It is further complicated by the fact that households rely heavily on outsiders for

portfolio management and advice, with 89% of mutual fund assets held by retail investors

(ICI, 2015) and a majority of households seeking expert opinion before conducting a financial

transation (Hung et al., 2008). We address this question by sutdying how a novel class of fund

managers might affect household diversification, and how this effect depends on households’

relationship with their existing fund manager.

Our focus is on robo advisers: firms which practice automated, algorithm-based portfo-

lio management via an online platform based on a passive investment strategy. These firms

emerged in 2008, and their subsequent growth was facilitated by a strong U.S. stock market,

tighter regulation of financial custodians, and the introduction of the smartphone (Sironi 2016).

As of December 2015, the five largest robo advisers had $44 billion under management, rep-

resenting a small, yet rapidly growing subset of the asset management industry. What makes

these firms distinct is not only their low costs, but their emphasis on attaining diversification

rather than abnormal return (Malkiel 2015). This last point is much in line with the stan-

dard recommendations of financial economists, making robo advisers an attractive instrument

through which to understand several key questions about household portfolio management.1

To the authors’ knowledge, ours is the first paper to study robo advisers from this perspective.

Using a company specific shock, we are able to match security-level data on individuals’

non-taxable brokerage accounts to that of a counterfactual robo portfolio. Our first core finding

is that robo portfolios are substantially more diversified than their matched brokerage portfo-

lios, which is robust across relative portfolio sizes and mutual fund exposure. This result is

itself somewhat surprising given that the individuals in our sample are relatively wealthy and

financially sophisticated. However, our second core finding is more novel and more puzzling:

1Guiso and Sodini (2013) provide an excellent, recent survey of the household finance literature.

2

while individuals with self-managed portfolios respond to this underdiversification by delegating

management to a robo adviser, mutual fund holders are almost unresponsive.2

The puzzle is not so much that robo advisers attain more diversified portfolios than

self-managing households or mutual fund managers. There is an ample literature on the is-

sue of houeshold portfolio inefficiency, which relates to both asset allocation and rebalancing

(e.g. Odean (1998), Ameriks and Zeldes (2004), Calvet, Campbell, and Sodini (2007, 2009a),

DeMiguel, Garlappi, and Uppal (2009), or Badarinza, Campbell, and Ramadorai (2016)). Sep-

arately, there is a literature on the risk-taking and underperformance of mutual fund managers,

which often focuses on their incentives (e.g. French (2008), Bergstresser, Chalmers, and Tufano

(2009), Christoffersen, Evans, and Musto (2013), or Balduzzi and Reuter (2015)). Our second

contribution, after documenting the findings above, is to address why mutual fund holders

respond differently to this underperformance than individuals with few or no mutual funds.

We propose a model to explain this apparent mutual fund stickiness which features costly

liquidation and trust in one’s fund manager, in the Gennaioli, Shleifer, and Vishny (2016) sense

of reducing the perceived riskiness of financial markets. In brief, more risk averse individuals

invest with mutual funds because they place greater value on a trustworthy manager. This

imbues the relationship between households and fund managers with a stickiness that discour-

ages re-delegation to another fund manager, even if it is known that the existing manager has

provided a less efficient portfolio. We provide empirical support for the key mechanisms of

this theory. Specifically, as predicted by the model, more risk averse and less sophisticated

households are more likely to rely on mutual funds, where we measure risk aversion using the

individual’s response to a specific behavioral question. We find an important role for liquidation

costs, in the form of rear loads, in discouraging mutual fund holders from re-delegating to other

managers. Finally, using the choice of mutual fund sponsor to gauge an individual’s preference

for the “human” versus “robotic” aspects of financial management, we find that individuals

more comfortable with robo advisers are more likely to set up accounts with them. We inter-

pret this last result as consistent with a role for trust when deciding whether to delegate one’s

portfolio.

2By “self-managed”, we mean portfolios with a relatively low share of their value invested in mutual funds.

3

While the model presupposes that less sophisticated investors are aware of their limits, it is

quite plausible to think that some individuals do not have this awareness and thus might respond

to financial advice. To consider this possibility, we use a sharp regression discontinuity design

to assess the role of advice in the portfolio delegation decision. Specifically, we exploit arbitrary

thresholds in a robo adviser’s advice-generating algorithm. Individuals whose stock portfolios

featured a Herfindahl-Hirschman concentration above a certain level received a warning that

their portfolios were underdiversified. Similarly, portfolios with a rear load whose expense

ratio exceeded a given value triggered a warning of excessive fees. Around the cutoff, we find

a significant role for advice in encouraging participation with the robo adviser. Surprisingly,

when we move away from the cutoff, the very factors which trigger advice actually discourage

portfolio delegation. This is because, in our data, concentrated portfolios are actually more

efficient, which matches evidence from Ivkovic and Weisbenner (2005). Moreover, portfolios

which receive the excessive fee warning we study also have rear load mutual funds, which entail

a first order cost of liquidation. This last point suggests that advice can mitigate but not

necessarily overcome mutual fund stickiness.

Our result on financial advice is novel in that much of the related literature has studied how

such advice can encourage return chasing (Mullainathan, Noth, and Schoar 2012) or expensive,

complex products (Celerier and Vallee 2016). The advice studied in this paper is unique in that

it instead emphasizes portfolio risk and fees. More generally, an additional contribution of our

paper is to explicitly study a style of portfolio management which advertises low fees, efficient

risk-taking, and automation, that is, the “robotic” rather than the “human” aspect of portfolio

management.

In the remainder of the paper, we begin with a description of our data and its generating

event in Section 2. In Section 3 we document our key empirical findings related to robo diversi-

fication and mutual fund stickiness. Section 4 presents a model which attempts to explain these

findings, and it provides empirical evidence consistent with the model. In Section 5 we study

the role of financial advice using a regression discontinuity framework. Section 6 concludes.

Appendix A contains details about robo advisers’ business model and Section B describes our

methodology for estimating the mean and variance of portfolio returns. All figures and tables

4

may be found at the end of the document.

2 Data Source

Our data provider is Wealthfront Inc., a robo adviser.3 Appendix A describes Wealthfront’s

business model in greater detail, but, in brief, its benchmark product is a portfolio of 10 ETFs.

The weights are determined by a questionnaire which asks the client several questions about

her financial situation and risk tolerance. In this paper, we exploit a specific product offered by

our data provider called the Portfolio Review tool, which was introduced on January 13, 2016.

This tool enables individuals with or without a Wealthfront account to obtain portfolio-specific

advice about their brokerage account free of charge. Specifically, an individual provides their

log-in credientials for their brokerage account. Then, our data provider will take a snapshot

of the account holdings and will run an advice-generating algorithm on it. As we describe in

greater detail in Section 5, this algorithm will produce a critique of the observed portfolio based

on its fees, cash holdings, and diversification. The upper panel of Figure 1 displays an example

report generated by Portfolio Review.

While the advice algorithm is running, our data provider asks the individual to answer

its standard questionnaire. At the conclusion of the Portfolio Review report, the robo adviser

shows the individual the portfolio it would receive as a Wealthfront client. The lower panel of

Figure 1 shows an example of such a recommended portfolio. From the research perspective,

this program offers a rare opportunity to study the motivations for portfolio delegation. In

particular, we can address the question of whether the delegation decision differs for individuals

who manage their own portfolios versus those who rely on mutual funds. The following section

describes the information we use to answer this question.

3We will use the terms “data provider”, “Wealthfront”, and “the robo adviser” synonymously.

5

2.1 Data summary

For individuals who have used the Portfolio Review tool and set up an account with our data

provider, we observe: (i) a security-level snapshot of their revealed brokerage accounts; (ii) their

self-reported age, annual income, and financial wealth; and (iii) their response to the following

question meant to gauge risk aversion: “When deciding how to invest your money, which do

you care about more: (a) maximizing gains, (b) minimizing losses, or (c) both equally?”. With

the exception of the demographic information on age, income, and wealth, we observe the same

data for individuals who used Portfolio Review but never set up an account with our provider.

For simplicity of language, we will call the first group “robo participants” and the second group

“robo non-participants.”4 The sample includes portfolios reviewed by our data provider between

January 13, 2016 and November 9, 2016.

Since we are interested in diversification, we focus on estimating the expected excess return

and volatility of the portfolios in our sample. Given the difficulties in measuring expected

return, we follow Calvet, Campbell, and Sodini (2007) and use a global version of the capital

asset pricing model (CAPM) to estimate the mean and variance of return for the securities in

our sample. Specifically, for each security i, we estimate

Rit −Rft = βi

[Rm

t −Rft

]+ εit, (1)

where Rmt denotes the monthly market return, based on the global Morgan Stanley Capital

International Index (MSCII), Rft denotes the 1-month Treasury yield, and Rit denotes the

monthly return on security i, net of expense ratio. As standard, εit is an indiosyncratic, zero-

mean shock to security i with variance σ2i . Our data on monthly returns come from the Center

for Research in Security Prices (CRSP) and Kenneth French’s website. We also check our

results across several asset pricing models described in Appendix B.

4Although we cannot observe whether the robo non-participants in our sample have an account with an-other robo adviser, this is unlikely to occur in any systematic way. In Figure 9, we plot the realized returnsfor Wealthfront and its closest competitor, Betterment, and note that they are quite similar. Moreover, thesimilarity of robo advisers’ business models suggests that the issue of unobserved robo portfolios would mostlikely represent classical measurement error and not introduce bias in our results.

6

There are two important data cleaning steps we take.5 First, we only retain non-taxable

portfolios, which are almost always individual retirement accounts (IRAs), Roth IRAs, or 401k

plans that have been transferred to the robo adviser. Focusing on non-taxable accounts mini-

mizes the impact of capital gains taxes on the decision to re-delegate one’s portfolio to another

manager. In addition, we hold fixed any effect related to the desirability of our data provider’s

tax-loss harvesting algorithms. These algorithms are a secondary, yet important part of many

robo advisers’ business models, but studying them is outside the scope of this paper. Second,

we focus on the sub-portfolio comprised of stocks, mutual funds, and ETFs, which Calvet,

Campbell, and Sodini (2007) the “risky portfolio”. This is because bonds and options are held

by few portfolios in our sample, and pricing them is less straightforward. Moreover, cash plays

a minor role in most of our portfolios, as indicated by the summary statistics in Table 1 which

we will discuss below.

Given the estimates {βi, σi} from (1), we compute the estimated moments of excess return

on portfolio p with weights {wi} as

E[Rp

t −Rft

]=

(∑i

wiβi

)E[Rm

t −Rft

]Var

[Rp

t −Rft

]=∑i

w2i σ

2i +

(∑i

wiβi

)2

Var[Rm

t −Rft

].

Appendix B has our calibrated moments of the market’s excess return. In Figure 2, we plot the

expected return and standard deviation of return, or volatility, for the portfolios in our sample.

By construction, no portfolio can lie above the mean-variance efficient frontier. However, there is

substantial heterogeneity, with some portfolios far-removed from the frontier, primarily because

of greater volatility. This is especially so among robo participants who, as we discuss below,

tend to own more directly-held stocks and fewer mutual funds than non-participants.

In Table 1, we display summary statistics for the primary variables in our analysis. The

upper and lower panels of the table display these statistics for robo participants and non-

participants, respectively. First, notice the substantial variation in mutual fund exposure for

5More details on our data cleaning may be found in Appendix B.

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both participants and non-participants, with roughly a quarter of portfolios concetrating at

least 90% of their value in mutual funds and another quarter with mutual fund exposure less

than 10%. In fact, 32% of portfolios hold over 70% of their value in mutual funds. Moreover,

the median non-participant’s portfolio has 52% of its value in mutual funds compared to 43%

for participants, with the difference primarily accounted for by direct stock ownership. As a

result of this difference in mutual fund exposure, the median non-participant also has a higher

average expense ratio, defined as the value-weighted expense ratio among stocks, mutual funds,

and ETFs. However, when considering the fund expense ratio, defined as the value-weighted

expense ratio among mutual funds and ETFs, the median robo participant and non-participant

are more similar. This last point suggests that robo non-participants own more mutual funds,

but the funds they choose are not necessarily more expensive.6

It is also important to recognize that the individuals in our sample are not representative

of most U.S. households. For example, Bilias, Georgarakos, and Haliassos (2010) estimate that

under a fifth of U.S. households have a brokerage account. Moreover, the median brokerage

account size exceeds $400,000 for both participants and non-participants, which is well above

most Americans’ financial wealth. That said, based on the age data we observe for robo partic-

ipants, these individuals are fairly young, with a median age of 34. They are thus an important

group to study, given that the early thirties is when most individuals begin participating in

risky asset markets (Fagereng, Gottlieb, and Guiso 2013).

3 Diversification and Robo Advisers

In this section we study the difference between individuals’ brokerage portfolio and their

matched robo portfolio. As mentioned in Section 2, we restrict our attention to individu-

als’ non-taxable, retirement portfolios. Importantly, the matched robo portfolio is revealed to

the individual at the conclusion of the Portfolio Review session described above. It thus repre-

sents the portfolio the individual would receive if she were to liquidate her brokerage portfolio

and invest the proceeds with the robo adviser. Our focus on non-taxable accounts ensures that

6The t-statistic for the test of a difference in means between robo participants and non-participants is 2.42for the fund expense ratio compared to 4.77 for the average expense ratio.

8

such a liquidation would not incur a capital gains tax, although, as studied in detail in Section

4, it may entail other costs like a rear load.

For a given variable Xpi describing portfolio p for robo participant i, we define

∆Xi ≡ XRoboi −XBrokerage

i , (2)

which is the difference in X between the individual’s matched robo and brokerage portfolios.

This is the key statistic we study in the following analysis. This statistic has two interpreta-

tions. The first, which we prefer, is the change in X that could be realized if portfolio p were

liquidated and replaced by a robo portfolio. Under this interpretation, ∆X is informative about

the difference between sub-portfolios within the part of financial wealth meant for retirement.

To account for the possibility that the observed brokerage portfolio may hedge unobserved re-

tirement portfolios, we conduct a robustness check in Section 3.2.3 in which we only consider

portfolios which represent between 80% and 100% of the individual’s reported financial wealth,

and we obtain similar results.7

The second interpretation, which requires that we restrict our attention to robo partici-

pants, is the change in X realized by portfolio p upon replacement by a robo portfolio. Under

this interpretation ∆X represents the difference between a brokerage portfolio and its real-

ized counterfactual robo portfolio. This interpretation is not necessarily more meaningful than

the first, and it comes with the additional complication that the robo portfolio may have

been funded using unobserved resources. For example, suppose an individual’s initial wealth is

equally divided into cash and a non-robo IRA account. If this individual were to become a robo

participant after our data provider’s Portfolio Review session, we could not observe whether

the new robo account came from the cash portfolio or the IRA. To address this issue, in Section

3.2.3 we consider only portfolios which underwent an Automated Customer Account Transfer

Service (ACATS) transfer.8 While the sample is substantially smaller, we obtain similar results

7Additionally, since the observed portfolio constitutes a dominant fraction of the individual’s financial wealthfor this sub-sample, it is unlikely meant to serve as a hedge against other financial assets held by the individual.

8An ACATS transfer is a security-by-security transfer of a portfolio from one financial custodian to another.If a mutual fund is transferred to our data provider, it immediately liquidates the fund. Otherwise, it maytemporarily use the transferred stocks or ETFs in the client’s portfolio before gradually liquidating them.

9

to our baseline. Therefore, we use the full sample in our core analysis below, and defer our

analysis of various sub-samples to Section 3.2.3.

3.1 Robo difference

In Table 2, we show summary statistics of ∆X for the following X variables: log Sharpe ratio,

expected excess return, volatility, average expense ratio, and fund expense ratio, which, as

in Section 2 is the value-weighted expense ratio among mutual funds and ETFs.9 The first

takeaway is that most portfolios have a lower Sharpe ratio than their matched robo portfolio,

that is, ∆log(Sharpe) > 0. Based on the standard log approximation, the median value suggests

a 17.1% higher the Sharpe ratio. As indicated in the second and third rows of Table 2, this

increase primarily comes from a reduction in volatility as opposed to a higher expected excess

return, with median values of -3.27 percentage points (pps) and 0.12 pps for ∆Volatility and

∆Expected Excess Return, respectively. The second takeaway is that over half of brokerage

portfolios feature higher average and fund expense ratios than their matched robo portfolio,

a point we will return to in Section 3.2.1 below. The average expense ratio for most robo

portfolios is around 12 basis points (bps).

Since our emphasis is on diversification, and for the sake consistency with the model in

Section 4 below, we focus most of our attention on the Sharpe ratio. In Figure 3, we plot

the distribution of ∆log(Sharpe). The upper panel plots the unconditional distribution, as a

histogram. Notice that, while most of the support is positive, there appear to be two critical

masses, the first between 0 and 25, and the second between 50 and 100. To explore this potential

bimodality further, in the lower panel of Figure 3 we plot the distribution of ∆log(Sharpe), in

the form of a kernel density, for portfolios with and without a mutual fund tilt, defined as

having over 70% of its value in mutual funds.10 We choose 70% as the cutoff because roughly

one third of portfolios satisfy this condition, although our results are robust to alternative cutoffs

above 50%. Perhaps as expected, portfolios with a mutual fund tilt appear better diversified

relative to the robo adviser than those without, with a smaller right tail of ∆log(Sharpe). More

9The Sharpe ratio is the ratio of expected excess return to the standard deviation of return, or volatility.10The density function is estimated using a Epanechnikov kernel function, as are all kernel densities in the

paper.

10

interestingly, there appear to be two critical masses among portfolios without a mutual fund

tilt, one which is substantially less diversified than the other. The model in Section 4 will

attempt to explain this heterogeneity in diversification.

We have so far studied ∆X without considering whether the portfolio holder actually set

up an account with our data provider and became a robo participant. In Figure 4, we produce

a distribution which conditions both on mutual fund tilt and robo participation status. Among

portfolios with a mutual fund tilt, there appears to be little difference in relative Sharpe ratio

between participants and non-participants. Table 3 confirms this intuition by performing a

Kolmogorov-Smirnov test for the equality of the distribution of ∆log(Sharpe) based on robo

participation status. Among portfolios with a mutual fund tilt, we do not find evidence that

the the distribution of ∆log(Sharpe) differs for robo participants. However, among portfolios

without a mutual fund tilt, there is more convincing evidence that non-participants perform

better relative to the robo adviser than participants, with median Sharpe ratio gaps of 29.2%

and 47.8%, respectively.

One would imagine that individuals with a high relative Sharpe ratio (low ∆log(Sharpe))

would be less willing to become robo participants, all else equal. To consider this possibility,

Figure 5 plots the probability of robo participation based on an individual’s relative Sharpe

ratio. Motivated by the heterogeneity from Figures 3 and 4, we produce this plot for port-

folios with and without a mutual fund tilt. Among portfolios without a mutual fund tilt, we

find a positive and significant relationship between ∆log(Sharpe) and the probability of robo

participation.11 Somewhat surprisingly, yet consistent with Figure 4, we find no evidence of

a relationship between relative Sharpe ratio and robo participation among portfolios with a

mutual fund tilt.12 Section 4 explores this last finding.

To summarize, brokerage portfolios appear relatively underdiversified compared to their

matched robo portfolios. This result is not novel given the extensive literatures on household

and mutual fund performance relative to passive benchmarks. What is more striking is that

11Based on the slope of the best fit line, a 10 percentage point increase in relative Sharpe ratio loss raises theprobability of robo participation by 1 percentage point.

12These portfolios have less to gain in terms of diversification than those with less mutual fund exposure, but,even so, according to Table 3 over half have at least a 4% lower Sharpe ratio than their matched robo portfolio.

11

mutual fund holders appear unresponsive to this relative underdiversification, whereas individ-

uals with less mutual fund exposure are more likely to participate with the robo adviser the

lower their relative Sharpe ratio. In Section 4, we explain this puzzle using a model of mutual

fund stickiness, and we provide evidence consistent with the model. Before proceeding to the

model, though, the next subsection performs several extensions and robustness checks.

3.2 Extensions and robustness

In this subsection, we perform three additional exercises: (i) we consider the importance of

expense ratios and other fees; (ii) we check our results across alternative asset pricing models

and consider the role of alpha; and (iii) we check our results on two sub-samples: portfolios

which represent over 80% of the holder’s financial wealth, and portfolios which underwent an

ACATS transfer.

3.2.1 Expense ratios and other fees

Since robo advisers typically advertise their low costs of management, our study would be

incomplete if we did not consider the difference in fees between brokerage portfolios and their

matched robo portfolios. As indicated by Table 2, the majority of brokerage portfolios feature

higher expense ratios than their matched robo portfolio, both when including stocks in the

average (Avg Exp Ratio) and when restricting attention to mutual funds and ETFs (Fund

Exp Ratio). Figure 6 confirms this observation by plotting the distribution of the difference in

average expense ratio, ∆Avg Exp Ratio. In the lower panel of Figure 6, we plot the conditional

distribution based on mutual fund tilt. As expected, the distribution for portfolios with a

mutual fund tilt has a thicker left tail.13 A quarter of such portfolios have an average expense

ratio gap of over 37 bps.14

However, there are two points worth making. First, as evident in Table 1, the portfolios

13Apparently, there are some portfolios without a mutual fund tilt which still average an expense ratio 200bps greater than the robo portfolio’s, which is typically around 12 bps.

14Put differently, these portfolios have an average expense ratio greater than 49 bps given most robo portfolios’average of 12 bps.

12

in our sample feature relatively low expense ratios compared to the U.S. average of 64 bps

(Rawson 2015). Moreover, because these individuals chose to use the Portfolio Review tool in

the first place, they may be naturally fee-conscious. Second, there are likely other fees besides

the expense ratio incurred by the portfolios in our sample, especially those with a mutual

fund tilt.15 Most importantly, advisory services offered by brokerage firms often average fees

in excess of 100 bps, according to a 2015 study by Personal Capital.16 The corresponding

advisory fee charged by our data provider is 25 bps. Therefore, although we do not observe

these additional advisory fees, one can obtain a very conservative estimate of the total fee

difference by subtracting 25 bps from the difference in average expense ratios. That said,

quantifying the total fee gap is not the focus of this paper.

3.2.2 Other asset pricing models

For simplicity, we have used the CAPM to estimate expected returns for the assets in our

sample. However, it is well known that the CAPM is subject to mispricing (e.g. Gruber and

Ross 1978). We therefore re-estimate expected returns for several other tractable asset pricing

models: a simple market model, a Fama-French three-factor model, and a Vanguard two-factor

model. Full details are provided in Appendix B. The upper panel of Figure 7 plots the difference

in expected excess return, ∆Expected Excess Ret, for these various models. Table 4 presents

the corresponding summary statistics. While there is heterogeneity, especially in the tails, the

distributions are fairly similar around the mode. Notably, our baseline CAPM stands out as

the most moderate distribution.

In the lower panel of Figure 7, we consider a portfolio’s value-weighted alpha, as estimated

by the market model. Specifically, we plot the distribution of ∆Alpha conditional on fund tilt.

For ETF and mutual fund tilted portfolios, most of the distribution has small, yet negative

support. This is not surprising given that robo advisers explicitly promote passive investment

15For example, Edelen, Evans, and Kadlec (2013) highlight the importance of unlisted trading costs for mutualfund performance.

16Unlike the expense ratio, which pertains to a single product, advisory fees are charged to recommend whichproducts a client should purchase. As of the third quarter in 2014, the following firms had average advisory feesabove 100 bps: E-Trade (114 bps), Fidelity (113), Merrill Lynch (130), Morgan Stanley (126), TD Ameritrade(153), UBS (121), and USAA (82).

13

strategies. However, there are some portfolios with a direct stock tilt that substantially outper-

form the robo adviser in terms of abnormal return. We return to this finding in Sections 4 and

5 where we consider heterogeneity in investor sophistication and response to financial advice.

3.2.3 Robustness to sub-samples

Since we do not observe all components of an individual’s financial wealth, and since we only

observe the reported level of this wealth for robo participants, it is difficult to make a statement

about the efficiency of an individual’s total portfolio. For example, Van Nieuwerburgh and

Veldkamp (2009) present a model in which agents rationally hold a diversified portfolio and a

learning portfolio in which they acquire information about new assets. Yet given our focus on

retirement accounts, it is unlikely that investors are engaging in this type of behavior in our

sample. Another possibility is that the observed portfolio is meant to hedge returns on the

individual’s nonfinancial assets, such as real estate or labor income. However, using Swedish

data, Massa and Simonov (2006) find that most households do not use financial wealth as an

income hedge, with the exception of the richest households.

We argue that it is meaningful to study diversification within our observed sample of

retirement portfolios, but to make a stronger statement about total wealth we turn to two sub-

samples: individuals whose brokerage portfolios represent over 80% of their financial wealth, and

individuals whose brokerage portfolios underwent an ACATS transfer.17 For the former group,

the observed brokerage account offers a more complete picture of the individual’s financial

wealth. For the latter group, we can interpret the matched robo portfolio as the realized

counterfactual of the observed robo portfolio.

Table 5 contains summary statistics of these two sub-samples. Compared to the full sample

in Table 1, these portfolios tend to be smaller, although they have similar expected returns

and volatilities to other robo participants. Most portfolio sizes in the upper panel are fairly

plausible given that they are reportedly at least 80% of the holder’s financial wealth, although

17By construction, members of both groups are robo participants. This is because we only observe reportedfinancial wealth for robo participants and because an ACATS transfer involves a security-by-security transferto the robo adviser.

14

we acknowledge that there is likely measurement error due to misreporting, as the tails of

the distribution seem unrealistically extreme. In terms of composition, ACATS transferred

portfolios feature fewer mutual funds, which makes sense given that the robo adviser cannot

hold such securities in the client’s portfolio.

In Table 6, we replicate Table 2 by displaying summary statistics of ∆X for the log Sharpe

ratio, expected excess return, volatility, and the average and fund expense ratios. As with the

baseline, over 75% of portfolios in both groups feature lower Sharpe ratios than their matched

robo portfolio. Although it is difficult to draw strong conclusions from a small sample size, we

fail to reject the null hypothesis that each sub-sample has the same distribution of ∆log(Sharpe)

as the whole sample. That is, our result that individuals’ brokerage portfolios are less diversified

than their matched robo portfolio is consistent across these sub-samples.

4 Mutual Fund Stickiness

We now present a framework to understand one of our most puzzling findings from the previous

section: why are mutual fund holders less sensitive to performance in deciding whether to par-

ticipate with a robo adviser? Briefly, our model generates the prediction that less-sophisticated,

more risk averse individuals prefer to invest with mutual funds than manage their own portfo-

lios because they place greater value on the trustworthiness of fund managers. Consequently,

they are less willing to delegate portfolio decisions to a new outsider, even if it outperforms

their current fund manager. Moreover, the model features costly mutual fund liquidiation, in

the form of, say, rear load fees, which further discourages delegation to a robo adviser. These

mechanisms are corroborated by the data, as we discuss below.

4.1 Model environment

The model features two periods t ∈ {0, 1}, a individual investor I and a mutual fund M .

There is a riskless asset with net return Rf = 0 and a set of risky assets A which, according

to Tobin’s mutual fund theorem (1958), may be combined to generate a composite net return

15

R. However, the investor and the mutual fund differ in their ability to attain a mean-variance

efficient portfolio, with Sharpe ratios SI and SM respectively. For example, on the individual

side, investors may have limited information about the assets in A (Merton 1987) or they may

prefer to hold certain stocks inelastically despite the resulting loss in efficiency (Fama and

French 2007). On the fund manager side, pursuit of excess return and the resulting fees may

result in a underperformance relative to a passive benchmark (Berk and Green 2004).18 This

assumption matches the substantial heterogeneity in Sharpe ratios we documented in Section

3 among portfolios with or without a mutual fund tilt.

At t = 0, individuals decide whether to manage their own portfolio or to delegate portfolio

management to a mutual fund. We assume they cannot do both, which is consistent with our

finding that most portfolios are dominated by either mutual funds or a combination of ETFs

and directly-held stocks. For simplicity, we also assume individuals have constant absolute

risk aversion γ and that R is normally distributed. Together, these assumptions imply they

have mean-variance preferences. However, following Gennaioli, Shleifer and Vishny (2015), we

suppose that individuals’ coefficient of absolute risk aversion is shrunk by a factor 1/θM(γ) if

their portfolio has been delegated to a mutual fund manager, with θM(γ) > 1 and θ′M(γ) > 0. As

GSV (2015) put it succinctly, this trust is best thought of as the knowledge that one’s portfolio

is “in good hands”.19 The assumption θ′M(γ) > 0 says that more risk averse individuals attach

greater value to such peace of mind.

Thus, having decided that agent j ∈ {I,M} will manage their portfolio, individuals choose

a risky share w to maximize the following objective function

Uj(w) = wE[Rj]−γ

2θj(γ)w2Var[Rj]. (3)

where θi = 1 if i = I, that is, if the individual manages its own portfolio. This gives rise to the

18Since our focus is on the individual’s choice of portfolio delegation, we abstract from the determination offund fees and subsume these fees into the mutual fund’s expected return.

19They further elaborate: “Trust describes confidence in the manager that is based on personal relationships,familiarity, persuasive advertising, connections to friends and colleagues, communication, and schmoozing”.

16

value function

Vj =1

2γSjθj(γ), (4)

where, again Sj denotes the Sharpe ratio attained by agent j ∈ {I,M}. In the next subsection,

we characterize the choice between self-management (j = I) and delegation to a mutual fund

(j = M), and we evaluate this characterization in our data. Then, in the subsection after, we

introduce a robo adviser, characterizing the decision to participate with the robo adviser based

on whether one initially chose self-management or a mutual fund, and we again evaluate this

characterization empirically.

4.2 Delegation to a mutual fund

Based on the value function 4, individuals will delegate their portfolio to a mutual fund if

VM ≥ VI and manage their own portfolio otherwise. Put differently,

j∗ = M ⇐⇒ 1 ≤ θM(γ)

(SM

SI

)2

≡ ∆M,I , (5)

where ∆M,I is the value of mutual fund delegation relative to self-management. From 5, it is

straightforward that

∂∆M,I

∂SI

< 0,∂∆M,I

∂γ> 0. (6)

In words, individuals are more likely to delegate portfolio management to a mutual fund when

they are relatively unsophisticated (SI low) or risk averse (γ high). In the former case, indi-

viduals benefit from mutual funds’ efficiency, and in the latter they benefit from trust in their

fund manager.20

To evaluate this characterization, we construct measures of risk aversion γ and sophistica-

20An interesting question is whether individuals know whether SI < SM , that is, if they know their own limitsto achieving diversification. We take up this issue in the context of financial advice in Section 5.

17

tion s and estimate the following regression,

Mutual Tilti = δ0 + δ1γi + δ2si + ui, (7)

where Mutual Tilti indicates whether individual i’s portfolio has a mutual fund tilt, which,

as in Section 3, we define as over 70% of its value in mutual funds.21 Our sample includes

both robo participants and non-participants. To measure risk aversion, we use the individual’s

response to the question: “When deciding how to invest your money, which do you care about

more: (a) maximizing gains, (b) minimizing losses, or (c) both equally?”. In our data, 50%

of respondents care more about maximizing gains, none care more about minimizing losses,

and 50% care about both equally. We therefore set γ = 0 if the individual cares more about

maximizing gains, and γ = 1 otherwise. To measure sophistication, we use the log of the

brokerage portfolio’s size and, where observable, the log of the account holder’s annual income.

Both measures are consistent with the Calvet, Campbell, and Sodini (2009b) index of financial

sophistication. We also use an indicator of whether the individual’s brokerage account has

any ETFs. Even among portfolios with a mutual fund tilt, only 58% have 100% mutual fund

exposure. It is therefore still instructive to consider whether such individuals hold any ETFs in

the remaining 30% of their portfolio, as one might imagine a more sophisticated investor would

do.

Table 7 contains the estimates of (7). Consistent with the theory, more sophisticated

individuals, as measured by the variables in the second through fourth rows, are less likely

to have a mutual fund tilt, as are more risk tolerant individuals. According to the theory,

these individuals would choose to manage their own portfolios. It is worth mentioning that we

cannot observe pure self-management in our data, since individuals whose portfolios have only

directly-held stocks or ETFs may act only on advice from their broker. However, even in this

case the individual ultimately makes the decision about which securities to hold, in contrast to

mutual fund holders who have delegated this decision to their fund manager. We take up the

question of financial advice more explicitly in Section 5.

21The results are similar for alternative cutoffs above 50%. We choose 70% because it implies a mutual fundtilt for one third of our sample.

18

4.3 Introducing robo advisers

We now suppose that at time t = 0+, after individuals have chosen who will manage their

portfolios, a robo adviser R appears.22 Participation with the robo adviser gives rise to a value

function analogous to (4) with j = R. For individuals who initially chose self-management,

participating with the robo adviser requires VR ≥ VI , or

j∗ = R ⇐⇒ 1 ≤ θR(γ)

(SR

SI

)2

≡ ∆R,I , (8)

where, like before, ∆R,I is the relative value of delegating one’s portfolio to a robo adviser.

On the other hand, individuals who initially chose mutual fund delegation must pay a

fraction τ of their initial mutual fund exposure w0 in transaction costs, such as rear load fees.

Robo participation thus requires VR − τw0 ≥ VM , or

j∗ = R ⇐⇒ 1 ≤ S2RθR(γ)− 2τw0γ

S2MθM(γ)

≡ ∆R,M . (9)

We can see from (9) that

∂∆R,M

∂θR> 0,

∂∆R,M

∂τ< 0. (10)

That is, doubt in the robo adviser (θR low) and costly liquidation (τ high) discourage robo

participation among mutual fund holders.

We can also use (9) to understand why, as suggested by Figure 5, underperforming mutual

fund holders may be less likely to participate with a new adviser than underperforming self-

managers. Let us compare a mutual fund holder and self-manager with the same Sharpe ratio

(SI = SM = S), and differentiate their relative robo values, ∆R,I and ∆R,M , with respect to

22We could have also supposed that this adviser existed from the beginning, but introducing it at a slightlylater date improves the model’s exposition, since it is better captures the data generating process from Section3.

19

the exsting Sharpe ratio S, holding w0 fixed.23 Taking the ratio of these derivatives gives

|∂∆R,M/∂S||∂∆R,I/∂S|

=1

θM(γ)

[1− 2τw0γ

VR

]< 1, (11)

provided the relative robo value is not too small (VR ≥ 2τw0γ). In words, mutual fund holders

are less responsive to low Sharpe ratios than individuals managing their own portfolios. This

is both because they trust their existing adviser (θM(γ) > 1) and because re-delegating their

portfolio requires costly liquidation (τ > 0).

Returning to the data, we evaluate the characterization in this subsection by estimating

Robo Participanti = δ0 + δ1τi + δ2θRi + β3 log(SM)i + ui, (12)

where τ is a measure of liquidation costs for individual i, θR is a measure of i’s relative trust

in the robo adviser, and Robo Participanti indicates whether i is a robo participant. Our focus

is on individuals who have delegated their portfolios to mutual fund managers, so we estimate

(12) on the subsample of portfolios with a mutual fund tilt, that is, with over 70% of their value

in mutual funds. To measure liquidation costs, we use an indicator of whether the portfolio has

any mutual funds with a rear load. Note that rear loads are the more appropriate interpretation

of τ than capital gains taxes, since taxes apply to self-managed portfolios as well.24

Our measure of confidence in the robo adviser θR is based on mutual fund sponsor. The

most common mutual fund sponsors in our data are Vanguard, Charles Schwab, and Fidelity.

However, it is plausible that these firms’ clientele differ in their comfort with robo advisers. For

example, Vanguard and Charles Schwab both launched robo adviser services in the spring of

2015, whereas Fidelity did not publicly launch an analogous service until summer 2016. More-

over, one might argue that some mutual fund sponsors, like Fidelity, have a marketing culture

which emphasizes the personal contribution of their services.25 We thus measure robo confi-

23Technically, w0 is a function SM , but accounting for this reduces tractability while not changing the keyproperty of the result in (11).

24Neither are potential capital gains taxes an omitted variable, since we estimate (12) on non-taxable portfo-lios.

25For example, at the 2016 Investment Company Institute General Membership Meeting, Fidelity presidentof clearing and custody remarked: “I don’t believe that robo-advisors will be a substitute for human advisors ...There’s so much that [human advisors] do that adds value to investors which goes well beyond asset allocation”

20

dence using indicators of whether the portfolio contains mutual funds sponsored by Vanguard,

Charles Schwab, or Fidelity. While admittedly an imperfect measure, any proxy for “trust”

or “confidence” would be based on some form of soft information whose meaning is subject to

debate. However, as described below, we obtain consistent results for all three measures of robo

confidence.

We present our estimates of (12) in Table 8. Based on the consistently significant coefficient

on the rear load indicator, it appears that liquidation costs are an important factor in the

decision to participate with a new adviser. We also find evidence that exposure to mutual funds

sponsored by Vanguard or Charles Schwab, which we argue is a proxy for comfort with robo

advisers, makes robo participation more likely. Consistent with this interpretation, exposure

to mutual funds sponsored by Fidelity, which arguably emphasizes the human aspect of fund

management, makes robo participation less likely, although with a p-value of 0.21 the statistical

significance of this result is in question. Finally, the point estimate on the log Sharpe ratio is

negative, but highly insignificant.26 This result is consistent with the characterization in (11) in

that, among mutual fund holders, underperformance has a relatively weak effect on the decision

to participate with a robo adviser.27

In summary, the model characterized in this section and the supporting empirical evidence

suggest two key frictions that discourage mutual fund holders from re-delegating their portfolios:

liquidation costs and relative trust in one’s existing manager compared to the robo adviser.

Moreover, mutual funds can attract less sophisticated and more risk averse investors, for whom

such trust may matter more saliently.

5 The Role of Advice

To this point, robo advisers have played a passive role in our analysis. However, it is important

to recall from Section 2 that the individuals in our sample voluntarily sought advice from a robo

(as quoted in CityWire, May 26, 2016).26The p-values are greater than 0.46 across specifications.27By contrast, Figure 5 and estimates of specifications analogous to (12) indicate that, among individuals

whose portfolios do not have a mutual fund tilt, Sharpe ratio underperformance does have a significant effecton whether they participate with the robo adviser.

21

adviser, and thus it is appropriate to ask whether the advice provided had any effect on the

decision to participate with it. In the context of the model from Section 4, one might interpret

Sj as the individual’s perceived Sharpe ratio, which may differ from the true Sharpe ratio Sj.

Advice is then information which, if accepted as valid, alters the perceived Sharpe ratio.

To measure the impact of advice, we exploit arbitrary cutoffs in our data provider’s ad-

vice generating algorithm. As described in Section 2, individuals who used our data provider’s

portfolio review tool revealed their brokerage account to the robo adviser, who in turn provided

portfolio-specific advice to the individual based on several observable statistics. The type of ad-

vice received can fall into one of three categories: excessive cash holdings, underdiversification,

and excessive fees. Since, as indicated by Table 1, cash plays a relatively minor role in most

of our sample, we focus on advice related to diversification and fees. Importantly, the advice

provided relied on several hard cutoffs and was not subject to discretion by the robo adviser.

First, portfolios with a Herfindahl-Hirschman Index (HHI) among directly held stocks greater

than 0.20 generated a warning of underdiversification. Secondly, among portfolios with rear

load mutual funds whose load exceeds 50 basis points, those with a fund expense ratio greater

than 25 bps triggerd a warning of excessive fees.28 As in Section 3, the fund expense ratio is

defined as the value-weighted expense ratio among mutual funds and ETFs.

This setting lends itself to a sharp regression discontinuity deisgn. If the assignment

variable z ∈ {Single Stock HHI,Fund Exp Ratio} exceeds a threshold z∗, then the reviewed

portfolio will receive diversification or fee advice, respectively. For z = Single Stock HHI, the

cutoff is z∗ = 0.20, and for z = Fund Exp Ratio, the cutoff is z∗ = 25, provided the portfolio

has a rear load mutual fund with a load greater than 50 bps.29 Our outcome is an indicator of

whether portfolio holder i is a robo participant, Robo Participanti, and the estimator for the

effect of advice on this outcome is

ρ = limzi↓z∗

E [Robo Participanti|zi]− limzi↑z∗

E [Robo Participanti|zi] . (13)

Following Imbens and Kalyanaraman (2012), we estimate (13) using local linear regressions

28The full algorithm for fee-based advice is fairly complicated and proprietary, so we focus instead on thesimple subcase described in the text.

29In our sample, all rear load mutual funds satisfy this requirement.

22

based on a triangle kernel and with their recommended bandwidth selection procedure. We

restrict our sample to portfolios with a single stock HHI between 0.1 and 0.3 or to portfolios

with a fund expense ratio between 15 and 35 basis points and a rear load mutual fund, based

on the corresponding assignment variable.

Figure 8 shows the estimated regressions from (13) and Table 9 contains the estimates ρ for

various bandwidths. The baseline estimates indicate an important role for advice, with the un-

derdiversification warning raising the probability of robo participation by 0.32 percentage points

and the excessive fees warning raising it by 0.26 percentage points. Interestingly, the estimated

impact and statistical significance of fee-based advice is smaller than the diversification-based

advice. This is consistent with the theory and evidence of mutual fund stickiness discussed in

Section 4, since, by construction, only mutual fund holders receive the excessive fee warning.

Moreover, given that the advice cutoffs are essentially arbitrary, it is unlikely that our estimates

are due to either self-selection or other discontinuities around the cutoff.

It is worth emphasizing that the estimates in Table 9 capture a local effect around the

advice threshold. Indeed, there are reasons why, for example, portfolios with a rear load mutual

fund might be less willing to set up a robo account, even though they were warned about their

excessive fees. To explore effect of advice away from the threshold, we estimate the specification

Robo Participanti = δ0 + δ1Div Advicei + δ2Fee Advicei + ui, (14)

where Div Advicei and Fee Advicei indicate whether portfolio i received the diversification-

based and fee-based warnings described above. Interestingly, the results in the first column

of Table 10 indicate that receiving advice based on either diversification or fees significantly

reduces the probability of robo participation. To explore this result further, in the second

column we replace the fee advice indicator with its two components: indicators of whether the

fund expense ratio exceeds 25 bps and whether the portfolio has a mutual fund with rear load

over 50 bps. The results suggest that rear loads are the dominant reason why fee-based advice

correlates with lower participation, on average. In line with the model from Section 4, costly

mutual fund liquidation discourages participation with another adviser.

23

In the third and fourth columns of Table 10, we consider why the underdiversification warn-

ing actually discourages robo participation away from the advice cutoff. Specifically, we check

the correlation between the portfolio’s log Sharpe ratio and whether the portfolio received the

underdiversification warning, which is triggered by a single stock HHI above the 0.20 threshold.

Contrary to standard investment advice, and the intent of advice generating algorithm, having

a relatively high single stock HHI actually corresponds to a higher Sharpe ratio in our data. In

the fourth column, we check that this result is not drived by portfolios with a mutual fund tilt

and thus potentially an artificially high single stock HHI. That more-concentrated portfolios

outperform less-concentrated portfolios on a risk adjusted basis is surprising but not inconceiv-

able, and it is consistent with evidence from Ivkovic and Weisbenner (2005) and Ivkovic, Sialm,

and Weisbenner (2008). Moreover, Figure 7 shows that portfolios with a direct stock tilt actu-

ally feature higher alphas than either ETF or mutual fund tilted portfolios, although it should

be noted that our baseline Sharpe ratio is based on the CAPM and therefore does not include

alpha. It therefore appears that advice based on portfolio concentration only has an impact

where concentration does not affect portfolio efficiency, such as around the HHI threshold.30

Otherwise, individuals with concentrated, yet efficient portfolios are less likely to accept the

advice by becoming a robo participant.

Before concluding, it is worth mentioning that the advice under consideration is non-

standard in that it is fully automated. Many studies on financial advice have emphasized its

more “human” aspects, noting that advisers may pursue their own interests by recommending

complex yet deceptively costly products to their clients (Celerier and Vallee 2016) or encour-

aging investment biases such as return-chasing (Mullainathan, Noth, and Schoar 2012). By

contrast, the style of advice considered here actually pushes for diversification and a reduction

in fees. Moreover, this advice appears to have a significant effect, at least among portfolios

which are otherwise-equivalent in terms of concentration or expense ratios.

However, robo participation is less likely among individuals whose portfolios are efficient

despite the underdiversification warning or who would incur costly rear loads despite the exces-

sive fee warning. This last result suggests that, at least among our sample of relatively wealthy

30We test for a discontinuity in the log Sharpe ratio around the HHI threshold, and obtain a positive, yetstatistically insignificant estimate of 0.144 with a p-value of 0.13

24

individuals, investors do not blindly follow robo advice, which is consistent with Bhattacharya

et al (2012). In addition, that rear loads reversed the effect of the fee warning away from the

advice threshold suggests that costly liquidiation is an important component of the mutual

fund stickiness studied in Sections 3 and 4.

6 Conclusion

In this paper we uncovered the novel finding that portfolios managed by robo advisers out-

perform their matched brokerage portfolios on a risk adjusted basis. This result is surprising

given our sample of relatively wealthy, sophisticated individuals and our focus on non-taxable

retirement accounts. More perplexing, while individuals with self-managed accounts respond

to underperformance by delegating management to a robo adviser, mutual fund holders are

robustly non-responsive.

We propose a model to explain this phenomenon with two forms of mutual fund stickiness:

trust in one’s fund manager and costly liquidation. The self-selection of more risk averse, less

sophisticated households into mutual funds can amplify the importance of stickiness based on

trust. In our data, the effect of costly liquidation is quite strong, although we do find evidence

consistent with a role for relative trust in robo versus human advisers.

Portfolio-specific advice also plays a key role in our setting, but differential advice received

by mutual fund holders alone cannot explain the observed stickiness. This is partly because

the very rear loads which trigger advice imply a first order cost of liquidation. However,

advice that one’s portfolio is excessively risky has a significant effect on the decision to delegate

management to robo advisers. This is in contrast to the more commonly studied form of advice

which emphasizes expected return rather than risk.

Our results have implications for the study of household diversification and the relationship

between retail investors and fund managers. Whether these findings also pertain to a sample

of less-wealthy households is an open question. Relatedly, if the relationship between fund

managers and retail investors is strong enough, households may not participate in financial

25

markets at all without outside management. This possibility, coupled with the importance

of fixed costs for financial market participation (Vissing-Jørgensen 2002), suggest that robo

advisers, with their low minimum account sizes, may have a non-trivial effect on a household’s

decision to participate in financial markets. We leave this as an avenue for future research.

26

References

Ameriks, J. and Zeldes, S.: 2004, How do Household Portfolio Shares Vary with Age?

Badarinza, C., Campbell, J. Y. and Ramadorai, T.: 2016, International Comparative Household

Finance, Annual Review of Economics (forthcoming) .

Balduzzi, P. and Reuter, J.: 2015, Hetergeneity in Target-Date Funds: Optimal Risk-Taking

or Risk Matching?

Bergstresser, D., Chalmers, J. M. R. and Tufano, P.: 2009, Assessing the Costs and Benefits of

Brokers in the Mutual Fund Industry, Review of Financial Studies 22(10), 4129–4156.

Berk, J. B. and Green, R. C.: 2004, Mutual Fund Flows and Performance in Rational Markets,

Journal of Political Economy 112(6).

Bhattacharya, U., Hackethal, A., Kaesler, S., Loos, B. and Meyer, S.: 2012, Is Unbiased

Financial Advice to Retail Investors Sufficient? Answers from a Large Field Study, Review

of Financial Studies 25(4), 975–1032.

Bilias, Y., Georgarakos, D. and Haliassos, M.: 2010, Portfolio inertia and stock market fluctu-

ations, Journal of Money, Credit, and Banking 42.

Calvet, L. E., Campbell, J. and Sodini, P.: 2007, Down or Out: Assessing the Welfare Costs of

Household Investment Mistakes., Journal of Political Economy .

Calvet, L. E., Campbell, J. Y. and Sodini, P.: 2009a, Fight or Flight? Portfolio Rebalancing

by Individual Investors, Quarterly Journal of Economics 124(1), 301–348.

Calvet, L. E., Campbell, J. Y. and Sodini, P.: 2009b, Measuring the Financial Sophistication

of Households, American Economic Review 99(2), 393–398.

Campbell, J.: 2006, Household Finance, Journal of Finance 61, 1553–1604.

Celerier, C. and Vallee, B.: 2016, Catering to investors through security design: Headline rate

and complexity, Quarterly Journal of Economics (Forthcoming) .

27

Christoffersen, S. E., Evans, R. and Musto, D. K.: 2013, What do consumers fund flows

maximize? Evidence from their brokers incentives, The Journal of Finance 68(1), 201–

235.

DeMiguel, V., Garlappi, L. and Uppal, R.: 2009, Optimal Versus Naive Diversification: How

Inefficient is the 1/ N Portfolio Strategy?, Review of Financial Studies 22(5), 1915–1953.

Edelen, R., Evans, R. and Kadlec, G.: 2013, Shedding light on “invisible” costs: Trading costs

and mutual fund performance, Financial Analysts Journal 69(1).

Fagereng, A., Gottlieb, C. and Guiso, L.: 2013, Asset Market Participation and Portfolio Choice

over the Life Cycle.

Fama, E. F. and French, K. R.: 2007, Disagreement, tastes, and asset pricing, Journal of

Finance 83.

French, K. R.: 2008, Presidential address: The cost of active investing, The Journal of Finance

63(4), 1537–1573.

Gennaioli, N., Shleifer, A. and Vishny, R.: 2015, Money Doctors, Journal of Finance 70(1).

Gruber, M. J. and Ross, S. A.: 1978, The current status of the capital asset pricing model,

Journal of Finance .

Guiso, L. and Sodini, P.: 2013, Household Finance: An Emerging Field, Handbook of the

Economics of Finance, Vol. 2, Elsevier, pp. 1397–1532.

Hung, A. A., Clancy, N., Dominitz, J., Talley, E., Berrebi, C. and Suvankulov, F.: 2008,

Investor and industry perspectives on investment advisors and broker-dealers., Technical

report, Rand Corporation.

ICI: 2015, Investment Company Fact Book: A Review of Trends and Activities in the U.S.

Investment Company Industry, Technical report, Investment Company Institute.

Imbens, G. and Kalyanaraman, K.: 2012, Optimal bandwidth choice for the regression discon-

tinuity estimator, Review of Economic Studies .

28

Ivkovic, Z., Sialm, C. and Weisbenner, S.: 2008, Portfolio concentration and the performance

of individual investors, Journal of Financial and Quantitative Analysis 43(03), 613–655.

Ivkovic, Z. and Weisbenner, S.: 2005, Local does as local is: Information content of the geogra-

phy of individual investors’ common stock investments, The Journal of Finance 60(1), 267–

306.

Malkiel, B.: 2015, A Random Walk Down Wall Street: the Time-Tested Strategy for Successful

Investing, W.W. Norton and Company, Inc.

Massa, M. and Simonov, A.: 2006, Hedging, familiarity and portfolio choice, Review of Finan-

cial Studies 19(2).

Merton, R. C.: 1987, A simple model of capital market equilibrium with incomplete information,

Journal of Finance 42.

Mullainathan, S., Noth, M. and Schoar, A.: 2012, The market for financial advice: an audit

study, NBER Working Paper .

Odean, T.: 1998, Are Investors Reluctant to Realize Their Losses?, The Journal of Finance

53(5).

Rawson, M. and Johnson, B.: 2015, 2015 fee study: Investors are driving expense ratios down,

Morningstar Technical Report .

Sironi, P.: 2016, FinTech Innovation: From Robo-Advisors to Goal Based Investing and Gami-

fication, John Wiley & Sons.

Tobin, J.: 1958, Liquidity Preference as Behavior Towards Risk, Review of Economic Studies

25.

Van Nieuwerburgh, S. and Veldkamp, L. L.: 2009, Information acquisition and under-

diversification, Review of Economic Studies 77.

Vissing-Jørgensen, A.: 2002, Towards an explanation of household portfolio choice heterogene-

ity: Nonfinancial income and participation cost structure, NBER Working Paper .

29

A Robo Advisers’ Business Model

In this section, we discuss the business strategy of our data provider, Wealthfront, and how it

compares to its competitors. Wealthfront’s benchmark product is a portfolio of 10 ETFs. These

ETFs are meant to span 10 asset classes.31 When portfolio weights among the 10 asset classes

drift far enough from their target, Wealthfront will rebalance. Each asset class is represented by

several ETFs, so that, when rebalancing, Wealthfront may choose to switch to an asset class’

backup ETF to harvest a capital loss if the client has subscribed to the company’s tax-loss

harvesting service.

To determine the appropriate portfolio weights, Wealthfront solves a mean-variance prob-

lem

maxw

R′w − 1

λw′Σw s.t. w ∈ R10

+ ,∑i

wi = 1,

where the risk tolerance parameter λ is determined by the client’s response to the questionnaire

described below. Wealthfront’s primary competitor, Betterment, features a similar business

model with 13 core ETFs. The next two subsections describe the questionnaires for each

company. Each company allows the client to make ex post changes to its recommended risk

tolerance. In practice, there is substantial clustering of both recommended and selected risk

tolerance around a moderate level.32

Wealthfront’s questionnaire

Wealthfront’s questionnaire consists of the following questions: (i) What is your age?; (ii) What

is your retirement status: retired or not retired?; (iii) What is your annual income?; (iv) What

are you looking for in a financial adviser? Please check all that apply: (a) I’d like to create a

diversified investment portfolio, (b) I’d like to save money on my taxes, (c) I’d like someone

31The primary ETFs for each asset class are: Vanguard U.S. Total Stock Market (VTI), Vanguard FTSEDeveloped Market (VEA), Vanguard FTSE Emerging Markets (VWO), Vanguard Dividend Appreciation (VIG),Schwab U.S. TIPS (SCHP), iShares National AMT-Free Muni Bond (MUB), iShares Corporate Bond (LQD),iShares JPMorgan Emerging Markets Bond (EMB), Vanguard REIT (VNQ), and Energy Select Sector SPDR(XLE).

32For example, the interquartile range for both the recommended and selected Wealthfront risk tolerance forrobo participants in our sample is [7.5, 9], on a scale of 1 to 10 in increments of 0.5.

30

to completely manage my investments, so that I don’t have to, (d) I’d like to match or beat

the performance of the markets; (v) What is your annual pre-tax income? (vi) Which of the

following best describes your household? Please select one: (a) Single income, no dependents,

(b) Single income, at least one dependent, (c) Dual income, no dependents, (d) Dual income,

at least one dependent, (e) Retired or financially independent; (vii) What is the total value

of your cash and liquid investments (e.g. savings, CDs, mutual funds, IRAs, 401(k)s, public

stocks)?; (viii) When deciding how to invest your money, which do you care about more: (a)

maximizing gains, (b) minimizing losses, or (c) both equally?; (ix) The global stock market is

often volatile. If your entire investment portfolio lost 10% of its value in a month during a

market decline, would you: (a) sell all your investments, (b) sell some, (c) keep all, or (d) buy

more?

Betterment’s questionnaire

Betterment’s questionnaire consists of the following questions: (i) What is your age? ; (ii)

What is your retirement status: retired or not retired?; (iii) What is your annual income? ;

(iv) Please select an investment goal:

1. Safety Net: A Safety Net is a conservative portfolio. We recommend a target of about

$Y1 to cover 3-6 months of unplanned expenses.

2. Retirement: Based on your age and income we recommend you invest long-term with a

target of $Y2 for an annual retirement income of $Y3. This can be a regular investment

account, or an IRA account.

3. General Investing: Grow and preserve capital over time. This is an excellent goal type

for unknown future needs or money you plan to pass to future generations. There is no

target amount for this goal.

31

B Estimating Moments of Returns

For the reasons discussed in Section 2 of the text, we focus on estimating the expected value

and variance of the portfolio’s excess return. Our baseline methodology for estimating these

moments involves first estimating the capital asset pricing model (CAPM) for each security i,

Rit −Rft = βi

[Rm

t −Rft

]+ εit, (15)

where Rmt denotes the monthly market return, based on the global Morgan Stanley Capital

International Index (MSCII), Rft denotes the 1-month Treasury yield, and Rit denotes the

monthly return on security i, net of expense ratio. The idiosyncratic shock εit has variance σ2i .

We can then compute the estimated moments of excess return on portfolio p with weights {wi}

as

E[Rp

t −Rft

]=

(∑i

wiβi

)E[Rm

t −Rft

](16)

Var[Rp

t −Rft

]=∑i

w2i σ

2i +

(∑i

wiβi

)2

Var[Rm

t −Rft

], (17)

Our weights {wi} are based on the sub-portfolio consisting of stocks, mutual funds, and ETFs.

For reasons described in Section 2, we only retain non-taxable accounts. For individuals who

used Portfolio Review on both a taxable and non-taxable account, we only retain the non-

taxable account.

We consider three alternatives to the CAPM. The first is a global Fama-French three-factor

model, specified as

Rit −Rft = βM

i

[Rm

t −Rft

]+ βH

i RHMLt + βS

i RSMBt + εit, (18)

where RHMLt denotes the spread in monthly return between high book-to-market stocks and

low book-to-market stocks, RSMBt denotes the spread in monthly return between stocks with a

small market capitalization and a big market capitalization, and all other notation is the same

32

as in (15). The second model is a Vanguard two-factor model, we we specify as

Rit −Rft = βV

i

[RV T

t −Rft

]+ βB

i

[RBND

t −Rft

]+ εit, (19)

where RV Tt denotes the monthly return Vanguard’s total stock market ETF (VT) and RBND

t

denotes the return on Vanguard’s total bond market ETF (BND). Third, we consider a market

model,

Rit −Rft = αi + βi

[Rm

t −Rft

]+ εit. (20)

The difference relative to the CAPM in (15) is that we allow stocks to have an abnormal return,

or alpha.

In all models (18)-(20), we assume that εit are independently and identically distributed.

This allows us to compute the expected value and variance of portfolio return using expressions

analogous to (16)-(17). We use the sample mean and covariance matrices to arrive at the

following calibration for the moments of the factors:

E[Rm

t −Rft

]= 0.068

E[RHML

t

]= 0.0360

E[RSMB

t

]= 0.0036

E[RV T

t −Rft

]= 0.0480

E[RBND

t −Rft

]= 0.0504

Cov[(Rm

t −Rft ), RHML

t , RSMBt

]=

0.0288 −0.0019 −0.0003

−0.0019 0.0060 −0.0077

−0.0003 −0.0077 0.0048

Cov

[(RV T

t −Rft ), (RBND

t −Rft )]

=

0.0360 −0.00001

−0.00001 0.0007

.

Finally, we winsorize the sample based on value-weighted estimated CAPM beta (∑

iwiβi),

33

estimated CAPM idiosyncratic variance (∑

iw2i σ

2i ), and expense ratio by 1% on both sides. We

also drop brokerage portfolios under $100 in value. To obtain annualized estimates, we multiply

the estimated mean and variance from (16)-(17) by 12. Our data on monthly returns, expense

ratios, and load fees comes from the Center for Research in Security Prices (CRSP). Our data

on the market return and factors in (15), (18) and (20) come from Kenneth French’s website.

34

Figures

***

Figure 1: Example use of Portfolio Review tool. This figure shows sample screenshots

from a session with our data provider’s Portfolio Review tool. The upper screenshot shows the robo

adviser’s assessment of the revealed portfolio, which in this example features a recognition of the

portfolio’s low fees and a critique of its concentration and excessive cash holdings. The lower screenshot

shows the robo adviser’s recommended portfolio. The Portfolio Review tool may be accessed at

https://www.wealthfront.com/portfolio-review.

35

05

1015

20Ex

pect

ed R

etur

n (%

)

0 10 20 30 40Volatility (%)

No WF Account Security Market Line

Robo Non-Participants

05

1015

20Ex

pect

ed R

etur

n (%

)

0 10 20 30 40Volatility (%)

Has WF Account Security Market Line

Robo Participants

Figure 2: Mean-variance efficient frontiers by robo participation. This figure plots

the expected return and volatility for the brokerage accounts of our data provider’s clients, whom we

call robo participants, and non-clients, whom we call robo non-participants. The solid line marks the

mean-variance efficient frontier. Section 2 contains details on how expected return and volatility are

computed.

36

05

1015

2025

Perc

ent

0 50 100 150 200 250Robo Log Sharpe Ratio - Brokerage Log Sharpe Ratio (scaled by 100)

Distribution of Log Sharpe Ratio Difference

0.0

1.0

2.0

3.0

4.0

5D

ensi

ty

0 50 100 150 200 250Robo Log Sharpe Ratio - Brokerage Log Sharpe Ratio (scaled by 100)

% Mutual < 70 % Mutual > 70

Log Sharpe Ratio Difference by Fund Tilt

Figure 3: Distribution of Sharpe ratio difference. This figure plots a histogram of the

difference in log Sharpe ratio between matched robo portfolios and brokerage portfolios. The sample

includes both robo participants and robo non-participants. In the lower panel, we plot the distribution

for portfolios with and without a mutual fund tilt, defined as having over 70% of its value in mutual

funds, based on a Epanechnikov kernel density.

37

0.0

2.0

4.0

6D

ensi

ty

0 50 100 150 200 250Robo Log Sharpe Ratio - Brokerage Log Sharpe Ratio (scaled by 100)

Participants, % MF < 70 Non-prtcpnts, % MF < 70Participants, % MF > 70 Non-prtcpnts, % MF > 70

Log Sharpe Ratio Difference by Robo Participation Status

Figure 4: Distribution of Sharpe ratio difference by mutual fund tilt. This

figure plots the distribution in the difference in log Sharpe ratio between matched robo and brokerage

portfolios. The distribution is plotted by robo participation and mutual fund tilt, which is defined as

having over 70% its value in mutual funds, based on a Epanechnikov kernel density.

38

.5.6

.7.8

.91

Prob

abilit

y of

Rob

o Pa

rtici

patio

n

0 .5 1 1.5Robo Log Sharpe Ratio - Brokerage Log Sharpe Ratio

% MF < 70 % MF > 70

Robo Participation by Relative Sharpe Ratio

Figure 5: Robo participation, Sharpe ratio, and mutual fund tilt. This figure

plots the probability of robo participation based on the difference in log Sharpe ratio between an

individual’s matched robo and brokerage portfolios. The plot is produced for portfolios with and

without a mutual fund tilt, defined as having over 70% of its value in mutual funds. The x-axis is

divided into 20 equal-sized bins, and the mean within each bin is plotted. The slopes of the best fit

lines are -0.03 (p-value 0.73) and 0.1 (p-value 0.00) for the tilted and non-tilted portfolios, repsectively.

39

05

1015

20Pe

rcen

t

-250 -200 -150 -100 -50 0Robo Avg Expense Ratio - Brokerage Avg Expense Ratio (bps)

Distribution of Expense Ratio Difference

0.0

1.0

2.0

3.0

4D

ensi

ty

-250 -200 -150 -100 -50 0Robo Avg Expense Ratio - Brokerage Avg Expense Ratio (bps)

% Mutual < 70 % Mutual > 70

Expense Ratio Difference by Fund Tilt

Figure 6: Distribution of expense ratio difference. This figure plots a histogram of

the difference in average expense ratio between matched robo and brokerage portfolios. The average

expense ratio is the value-weighted expense ratio among stocks, ETFs, and mutual funds. The sample

includes both robo participants and robo non-participants. In the lower panel, we plot the distribution

for portfolios with and without a mutual fund tilt, defined as having over 70% of its value in mutual

funds, based on a Epanechnikov kernel density.

40

0.1

.2.3

.4D

ensi

ty

-30 -20 -10 0 10Robo Expected Excess Return - Brokerage Expected Excess Return (pps)

CAPM FF 3 FactorVanguard 2 Factor Market Model

Expected Return Difference for Various Pricing Models

01

23

Den

sity

-5 -4 -3 -2 -1 0Robo Alpha - Brokerage Alpha (pps)

% Direct Stock > 70 % ETF > 70% Mutual > 70

Alpha Difference by Fund Tilt

Figure 7: Distribution of return and alpha difference by asset pricing model.

This figure plots the distribution of the difference in expected excess return between matched robo

and brokerage portfolios for various asset pricing models, based on a Epanechnikov kernel density.

Appendix B describes the models in detail. In the lower panel, we plot the distribution of the difference

in alpha, which comes from the market model. We plot this difference for portfolios with a direct stock

tilt, mutual fund tilt, and ETF tilt, where a tilt is defined as having over 70% of the portfolio’s value

in the given security type.

41

0.2

.4.6

.81

Prob

abilit

y of

Rob

o Pa

rtici

patio

n

-.1 -.05 0 .05 .1Single Stock HHI (Difference from Advice Cutoff)

Robo Participation and Diversification Advice

0.2

.4.6

.81

Prob

abilit

y of

Rob

o Pa

rtici

patio

n

-10 -5 0 5 10Fund Expense Ratio (in bps, difference from advice cutoff)

Robo Participation and Fee Advice

Figure 8: Advice and robo participation based on regression discontinuity. This

figure plots the estimated regressions from the regression discontinuity specification (13) for each

assignment variable. In the upper panel, the assignment variable is the Herfindahl-Hirschman index

(HHI) among directly held stocks, and in the lower panel it is the value-weighted expense ratio among

mutual funds and ETFs, which we call the fund expense ratio. Section 5 of the text contains details

on estimation, and Table 9 contains the estimates. In each panel, we also include a scatterplot based

on 20 equal-sized bins of the assignment variable.

42

-4-2

02

4

2013m7 2014m1 2014m7 2015m1 2015m7 2016m1date

Wealthfront Betterment

Wealthfront and Betterment Realized Returns

Figure 9: Realized returns for a Wealthfront and Betterment portfolio. This

figure plots the realized return on Wealthfront’s and Betterment’s portfolio for a 35 year old non-

retired, single individual without dependents, with annual income of $105,000 and financial wealth of

$176,500, and with moderate risk aversion.

43

Tables

Table 1: Summary Statistics by Robo Participation

Min 25th Pctl 50th Pctl 75th Pctl Max

Robo Participants:% ETF 0.00 0.00 2.23 37.86 100.00% Mutual Fund 0.00 3.22 43.02 89.74 100.00% Direct Stocks 0.00 0.00 15.01 49.71 100.00% Cash 0.00 0.00 0.55 7.17 96.81Avg Exp Ratio (bps) 0.00 7.86 16.11 32.63 201.37Fund Exp Ratio (bps) 0.00 13.33 23.77 51.76 246.00Expected Excess Ret (pps) 1.86 4.73 5.43 6.29 23.04Volatility (pps) 7.36 14.97 19.19 35.03 124.79Portfolio Size ($’000) 0.22 113.34 466.99 2120.81 2.5×106

Age 18 29 34 41 78Observations 3419

Robo Non-participants:% ETF 0.00 0.00 3.94 39.83 100.00% Mutual Fund 0.00 10.84 52.38 98.21 100.00% Direct Stocks 0.00 0.00 5.25 38.64 100.00% Cash 0.00 0.00 0.06 4.63 77.43Avg Exp Ratio (bps) 0.00 10.17 18.00 37.28 237.31Fund Exp Ratio (bps) 0.00 13.82 23.67 52.84 311.00Expected Excess Ret (pps) 1.86 4.52 5.23 5.89 22.86Volatility (pps) 6.62 14.40 16.80 26.17 127.53Portfolio Size ($’000) 0.22 74.24 414.06 2326.80 1.9×107

Observations 1213

Note: This table displays summary statistics of brokerage accounts for individuals who are Wealthfront

clients (robo participants) and who are not. Avg Exp Ratio denotes the portfolio’s value-weighted

expense ratio, in basis points, and Fund Exp Ratio denotes this statistic among mutual funds and

ETFs. Excess Return and Volatility denote the expected value and standard deviation, respectively,

of the portfolio’s excess return over the 1-Month Treasury yield. The variables % ETF, % Mutual

Fund, and % Direct Stock denote the value-weighted fractions of the portfolio allocated to ETFs,

mutual funds, and directly-held stocks, respectively. Portfolio Size denotes the value of the observed

brokerage portfolio. Age data are not observed for robo non-participants.

44

Table 2: Difference between Matched Robo and Brokerage Portfolios (∆X ≡ XRobo−XBrokerage)

Min 25th Pctl 50th Pctl 75th Pctl Max∆log(Sharpe) × 100 -13.59 3.91 17.14 65.99 265.13∆Expected Excess Ret -18.22 -0.78 0.12 0.82 4.23∆Volatility -112.40 -17.30 -3.27 0.48 9.32∆Avg Exp Ratio (bps) -225.00 -20.78 -3.81 4.49 16.26∆Fund Exp Ratio (bps) -298.24 -39.34 -10.93 -0.50 13.71Observations 4632

Note: Expected Excess Ret and Volatility denote the expected value and standard deviation, respec-

tively, of the portfolio’s excess return over the 1-Month Treasury yield. Sharpe denotes the ratio

of expected excess return to volatility. Unless otherwise indicated, the units are percentage points.

Avg Exp Ratio denotes the portfolio’s value-weighted expense ratio, in basis points. Fund Exp Ratio

denotes the portfolio’s value-weighted expense ratio, in basis points, among mutual funds and ETFs.

The sample includes individuals with and without an account with our data provider.

45

Table 3: Sharpe Ratio Difference by Participation Status and Mutual Fund Tilt

Min 25th Pctl 50th Pctl 75th Pctl Max

% Mutual Fund < 70:Robo Participants -13.51 9.98 47.75 85.07 265.13Robo Non-participants -8.78 6.96 29.18 71.32 223.89D-statistic (p-value): 0.00

% Mutual Fund > 70:Robo Participants -13.59 -0.12 4.80 11.93 116.34Robo Non-participants -6.69 0.01 4.01 12.31 129.87D-statistic (p-value): 0.31

Note: The variable under consideration is the difference in log Sharpe ratio between the individual’s

matched robo and brokerage portfolios: ∆ log(Sharpe) ≡ log(SharpeRobo) − log(SharpeBrokerage). We

scale this difference by 100. The upper and lower panels do this for portfolios without and with a

mutual fund tilt, defined as over 70% of its value in mutual funds. Expected Excess Ret and Volatility

denote the expected value and standard deviation, respectively, of the portfolio’s excess return over

the 1-Month Treasury yield. Sharpe denotes the ratio of expected excess return to volatility. Unless

otherwise indicated, the units are percentage points. Avg Exp Ratio denotes the portfolio’s value-

weighted expense ratio, in basis points. Fund Exp Ratio denotes the portfolio’s value-weighted expense

ratio, in basis points, among mutual funds and ETFs. Robo participants and non-participants are those

with and without a Wealthfront account, respectively. The D-statistic corresponds to the combined

Kolmogorov-Smirnov test for the equality of distributions for robo participants and non-participants.

46

Table 4: Difference between Robo and Brokerage Portfolios by Asset Pricing Model

Min 25th Pctl 50th Pctl 75th Pctl Max

CAPM:∆Expected Excess Ret -18.22 -0.78 0.12 0.82 4.23

Fama-French 3 Factor:∆Expected Excess Ret -21.44 -2.37 -0.67 0.15 2.89

Vanguard 2 Factor:∆Expected Excess Ret -27.61 -2.07 0.24 1.40 4.82

Market Model:∆Expected Excess Ret -20.24 -1.33 -0.13 0.63 4.06∆Alpha -5.00 -0.65 -0.21 -0.02 0.21

Observations 3953

Note: As in Table 2, ∆X denotes the difference in X between the the individual’s matched robo and

brokerage portfolios: ∆X ≡ XRobo − XBrokerage. The remaining notation is the same as in Table 2,

except that Alpha denotes the estimated alpha from the market model, in percentage points. Appendix

B contains details about the estimation procedure for each model. The sample includes individuals

with and without an account with our data provider.

47

Table 5: Summary of Statistics by Relative Portfolio Size and Transfer Status

Min 25th Pctl 50th Pctl 75th Pctl Max

Portfolios > 80% Financial Wealth:% ETF 0.00 0.00 0.00 35.07 100.00% Mutual Fund 0.00 0.00 33.99 91.27 100.00% Single Stocks 0.00 0.00 17.86 52.00 100.00% Cash 0.00 0.00 0.36 9.02 70.46Avg Exp Ratio (bps) 0.00 6.35 14.20 23.55 104.25Fund Exp Ratio (bps) 4.14 12.28 20.31 35.11 115.82Excess Return 2.70 4.68 5.53 6.52 19.28Volatility 8.21 14.72 18.81 33.51 122.18Portfolio Size ($’000) 0.94 44.47 131.30 306.06 14605.75Age 22 29 34 40 65Observations 121

ACATS Transferred Portfolios:% ETF 0.00 0.00 24.78 65.82 98.71% Mutual Fund 0.00 0.00 17.84 66.48 100.00% Single Stocks 0.00 0.00 19.12 40.22 98.47% Cash 0.00 0.68 2.20 9.49 46.80Avg Exp Ratio (bps) 0.00 9.45 19.46 43.19 88.28Fund Exp Ratio (bps) 5.00 11.77 28.60 55.15 104.02Excess Return 3.08 4.47 5.36 5.80 13.97Volatility 9.32 14.60 18.09 25.70 82.00Portfolio Size ($’000) 0.94 9.91 38.67 203.53 669866.63Age 22 30 35.5 41.5 58Observations 41

Note: This table presents summary statistics for portfolios which represent between 80% and 100% of

the holder’s reported financial wealth and which underwent an ACATS transfer to Wealthfront. The

notation is the same as in Table 1.

48

Table 6: Robo Difference by Relative Portfolio Size and Transfer Status

Min 25th Pctl 50th Pctl 75th Pctl Max

Portfolios > 80% Financial Wealth:∆log(Sharpe) × 100 -7.66 5.08 20.49 67.12 162.65∆Expected Excess Ret -13.05 -0.73 0.13 0.75 3.03∆Volatility -105.21 -17.70 -2.42 0.47 7.60Sharpe Ratio D-statistic (p-value): 0.80

ACATS Transferred Portfolios:∆log(Sharpe) × 100 -4.22 4.53 12.41 49.07 128.86∆Expected Excess Ret -8.46 -0.59 0.23 1.03 2.43∆Volatility -69.04 -10.24 -2.74 0.65 6.13Sharpe Ratio D-statistic (p-value): 0.71

Note: As in Table 2, ∆X denotes the difference in X between the the individual’s matched robo

portfolio and their brokerage portfolio: ∆X ≡ XRobo − XBrokerage. The upper panel shows the

distribution of ∆X for portfolios which represent between 80% and 100% of the holder’s financial

wealth. The lower panel shows the distribution of ∆X for portfolios which underwent an ACATS

transfer to Wealthfront. The remaining notation is the same as in Table 2. The D-statistic corresponds

to the combined Kolmogorov-Smirnov test that the ∆log(Sharpe) has the same distribution for the

given sub-sample as for the whole sample.

49

Table 7: Mutual Fund Tilt, Risk Aversion, and Sophistication

Outcome: Mutual Tilt Mutual Tilt Mutual TiltRisk Averse 0.037∗∗ 0.052∗∗∗ 0.053∗∗

(0.015) (0.018) (0.024)Has ETF -0.482∗∗∗

(0.016)log(Value) -0.022∗∗∗

(0.004)log(Income) -0.035∗∗

(0.015)R-squared 0.260 0.013 0.007Number of Observations 2748 2748 1510

Note: This table contains the estimates of specification (7). Has ETF indicates whether the individ-

ual’s brokerage portfolio has an ETF. Value denotes the value of the individual’s brokerage portfolio.

Income denotes the individual’s reported annual income, which we only observe for robo participants.

Risk Averse equals 0 if the individual answered “maximizing gains” in response to the question “When

deciding how to invest your money, which do you care about more: (a) maximizing gains, (b) min-

imizing losses, or (c) both equally?”. If the individual answered “both equally”, then Risk Averse

equals 1. No individual answered “minimizing losses”. Heteroskedasticity robust standard errors are

in parentheses (*p-value < 0.10; *p-value < 0.05; ***p-value < 0.01).

50

Table 8: Robo Participation, Liquidation Costs, Diversification, and Comfort with Robo

Outcome: Robo Participant Robo Participant Robo ParticipantHas Load -0.103∗∗∗ -0.122∗∗∗ -0.109∗∗∗

(0.028) (0.027) (0.029)log(Sharpe) -0.056 -0.023 -0.041

(0.076) (0.074) (0.075)Has Vanguard 0.070∗∗∗

(0.026)Has Schwab 0.184∗∗∗

(0.060)Has Fidelity -0.035

(0.028)R-squared 0.018 0.018 0.014Number of Observations 1640 1640 1640

Note: This table contains the estimates of specification (12). The outcome, Robo Participant, is an

indicator of whether the individual has an account with our data provider. Has Load indicates whether

the individual’s brokerage portfolio has a mutual fund with rear load greater than 50 basis points.

Has Vanguard, Has Schwab, and Has Fidelity indicate whether the individual’s brokerage portfolio

has a mutual fund sponsored by Vanguard, Schwab, or Fidelity, respectively. Sharpe denotes the

Sharpe ratio for the individual’s brokerage portfolio. Heteroskedasticity robust standard errors are in

parentheses (*p-value < 0.10; *p-value < 0.05; ***p-value < 0.01).

51

Table 9: Advice and Robo Participation based on Regression Discontinuity

Outcome: Robo ParticipantAssignment Variable: Single Stock HHI Fund Expense RatioIK bandwidth 0.316∗∗ 0.261∗

(0.102) (0.152)IK bandwidth×0.9 0.336∗∗ 0.273∗

(0.111) (0.162)IK bandwidth×1.1 0.297∗∗ 0.248∗

(0.095) (0.147)Observations 608 495

Note: This table contains the estimates of the regression discontinuity specification (13). Robo Par-

ticipant is an indicator of whether the individual has an account with our data provider. Single Stock

HHI is the Herfindahl-Hirschman index among directly held stocks. Fund Expense Ratio is the value-

weighted expense ratio among mutual funds and ETFs. In Column 1, the sample is all brokerage

portfolios with a single stock HHI between 0.1 and 0.3. In Column 2, the sample is all brokerage

portfolios with a fund expense ratio between 15 and 35 basis points, and which have a mutual fund

with rear load greater than 50 basis points. Each row is based on a different bandwidth. The IK

bandwidth is the value recommended by the Imbens and Kalyanaraman (2012) bandwidth selection

procedure. The recommended bandwidths are 0.08 and 3.29 when the assignment variables are sin-

gle stock HHI or fund expense ratio, respectively. Heteroskedasticity robust standard errors are in

parentheses (*p-value < 0.10; *p-value < 0.05; ***p-value < 0.01).

52

Table 10: Advice and Robo Participation away from the Advice Cutoff

Outcome Robo Participant Robo Participant log(Sharpe) log(Sharpe)Div Advice -0.091∗∗∗ -0.093∗∗∗ 0.441∗∗∗ 0.429∗∗∗

(0.013) (0.013) (0.010) (0.013)Fee Advice -0.047∗∗

(0.015)Exp Ratio Cutoff -0.022

(0.014)Has Load -0.035∗

(0.014)Sample Full Full Full % Mutual < 70Number of Observations 5114 4758 5114 3474

Note: This table contains the estimates of the specification (14). Robo Participant is an indicator

of whether the individual has an account with our data provider. Div Advice and Fee Advice are

indicators of whether the portfolio received the underdiversification or excessive fee warnings described

in Section 5. Sharpe denotes the Sharpe ratio. Exp Ratio Cutoff indicates whether the portfolio has

a fund expense ratio greater than 25 basis points. Has Load indicates whether the portfolio has a

rear load mutual fund with a load greater than 50 bps. Columns 1-3 contain estimates based on the

full sample, and Column 4 only uses portfolios with less than 70% of their value in mutual funds.

Heteroskedasticity robust standard errors are in parentheses (*p-value < 0.10; *p-value < 0.05; ***p-

value < 0.01).

53