Biased Financial Advisers, Regulation, andTransparency∗
Juan José Ganuza† , Fernando Gomez‡, and Jose Penalva§
April, 2022.

Abstract
We study the effects of transparency and investor sophistication over the incentives of a financial
adviser to provide honest and suitable financial advice to partially informed consumers. The
novel aspect of our analysis is the inclusion of courts as a costly mechanism to provide incentives
to reduce incorrect advice, where the cost arises from judicial errors due to imperfect evidence.
We show that the cost of using courts to provide appropriate incentives is decreasing in investor
sophistication and transparency. However, the judicial system may not be able to implement thefirst best without appropriate regulation when advisers can choose their level of transparency.
In such a case, advisers with strong incentives to provide incorrect advice may be tempted toreduce transparency if it increases the prevalence of judicial error. The analysis sheds lights on
the structure of legal duties of investment services firms, such as those under the recent European
MiFID II scheme.
Keywords: Transparency, Retail Investors, Financial Advice and Liability.
JEL classification numbers: L51, H57, H24, D44, K13, K23, L51.

∗

We wish to thank the comments from audiences at AEDE (University of Lleida), EALE
(University Milano-Bicocca), University of Bologna, European University Institute and University of Copenhagen. Juan-Jose Ganuza gratefully acknowledges the support of the Barcelona
GSE Research, the government of Catalonia, and the Spanish Ministry of Science and Innovation through the project PID2020-115044GB-I00. Fernando Gomez acknowledges the financial
support of the Spanish Ministry of Science and Innovation under projects DER 2017-82673R. José Penalva’s research has benefited from the Agencia Estatal de Investigación (PID2019104649RB-I00/AEI/10.13039/501100011033) and the Comunidad de Madrid (Programa Excelencia para el Profesorado Universitario, convenio con Universidad Carlos III de Madrid, V Plan
Regional de Investigación Cientı́fica e Innovación Tecnológica, EPUC3M12). Corresponding author:jpenalva@emp.uc3m.es.
†

Department of Economics. University Pompeu Fabra.
Department of Law. University Pompeu Fabra.
§
Department of Business Administration, Universidad Carlos III de Madrid.
‡

i

1

Introduction

Financial decisions are hard to make. Most individuals, even those with some knowledge offinancial matters, are subject to mistaken beliefs, biases and inadequate information. All of theselead them to make poor choices in the financial sphere. The behavioral economics literature has
unearthed some of the shortcomings resulting in far from desirable decisions, as in Benartzi andThaler (2007) and Gomes et al. (2021).
Given the above, it comes as no surprise that financial advice from experts plays a large rolein ”helping” people to make better choices.1 Advisers, however, sometimes fail to do a properjob. Investment decisions that turn out badly for investors are found in abundance.2 Among thedifferent reasons for poor advice, the literature has primarily focused on conflicts on interest, and,more recently, on a lack of personalization of advice to clients’ needs.
Another important factor is investor sophistication and financial literacy, and whether andhow the their absence leaves investors exposed to bad advice and manipulation.3
Correspondingly, the provision of financial advice is heavily regulated, and financial advisers
are subject to a strict set of duties and liabilities.4 Courts play an important role in providing
incentives for honest financial advice, one that has been often overlooked in the finance literature.
Courts intervene when there is an infringement of the adviser’s duties that gives rise to liabilities
1

Although as shown in Bhattacharya et al. (2012) , the mere presence of unbiased financial advice is necessary
but not sufficient to lead to better decisions.
2
Hackethal et al. (2012) find that advised accounts exhibit lower net returns and inferior Sharpe ratios, and higher
portfolio turnover. In Chalmers and Reuter (2020) clients of brokers earn significantly lower alphas and Sharpe
ratios than matched target-date-fund (TDF) portfolios that provide similar risk and avoid brokerage fees; Hoechle
et al. (2018) , in turn, document that advisers employed by a large bank advice clients to choose the investmentsthat are more profitable for the bank and that these investments perform poorly vis-á-vis independently chosen
ones.
3
Lusardi and Mitchell (2014) provide an extensive overview of the literature on financial literacy that addresses
the role of financial advice. Calcagno and Monticone (2015) also show that financial literacy increases the probabilityof consulting a financial adviser, and reduces the probability of making independent investments; Egan et al.
(2019) find that adviser misconduct is more present in locations with low education, and with older and wealthier
populations; Guiso et al. (2022)’s model of banks selling mortgages estimates the cost of the distortion from bank’s
recommendations to unsophisticated borrowers to be equivalent to an increase in the annual mortgage payment by
11%.
4
For example, in the EU context, the MIFID II Directive, the main regulatory instrument in this area, imposes
upon firms offering investment services to customers a broad legal duty to act honestly, fairly, and in the bestinterests of the client (art. 24 (1)), while in the US Regulation Best Interest plays a similar role.

1and can review fines and other sanctions imposed by regulatory agencies.
In this paper we analyze the role of Courts in disciplining financial advisers. We mainly
focus on the problem of conflict of interest but later in the paper, we also analyze the lack ofpersonalization of the advise. Conflict of interest arises when financial advisers receive different
commissions from the sale of different instruments.5 The advice may cover instruments from both
inside and outside the investment firm which again distorts the incentives of the adviser.6 The
importance of this problem was specially visible both before and after the financial crisis, wheninvestors suffered substantial losses giving rise to serious concerns about the mis-selling of certain
financial investments to customers. In many cases, this has led to important numbers of lawsuits
filed against firms providing the investment services. Battiston et al. use data from a Spanish
investment firm to estimate the losses to investors from distortions in advice, and find that theselosses amount to between 6 and 9%.
Spain and Italy provide clear illustrations of the problem.7 In Spain, banks and speciallysavings banks sold large amounts of “preferentes” to their clients. Preferentes are equivalent toperpetual junior debt, repayable only at the discretion of the issuer and without voting rights
to the holder. Savings banks found in the preferentes a valuable tool to recapitalize, because
preferentes qualify as regulatory capital, so they started marketing them to their own depositors.
Many of those recapitalization efforts failed in the end, and the savings banks had to be rescued by
the taxpayer. Investors in preferentes saw their investments wiped out or subject to a substantial
haircut. According to the regulator the face value of preferentes issued only by two of the rescued
savings banks (Bankia and Caixa Catalunya) approached €8 bn, affecting 400,000 investors.
Over 78% of them brought legal claims against the savings banks who sold them the preferentes.8
5The literature provides numerous evidence on conflicts of interest in financial advice: Anagol et al. (2017) ,Christoffersen S. E. and K. (2013) , Hackethal et al. (2012) , Hoechle et al. (2018) . Chalmers and Reuter (2020)
find that brokers are more likely to recommend products with higher commissions; Egan et al. (2019) find thatbrokers are incentivized to sell the dominated bonds, typically earning two times greater fees for selling them.
6
Pool et al. (2016) find that mutual fund families acting as service providers in 401(k) plans display favoritism
toward their own affiliated funds; Foà et al. (2019) find that banks bias households choosing a mortgage towards
those more beneficial to the bank.
7
See on the details of the schemes both in Italy and Spain, Della Negra (2014).
8
For further details see Santos (2017) and Comisión de Seguimiento de Instrumentos Hı́bridos de Capi-

2

Similarly, in Italy many depositors were seriously exposed to the banks’ risk through subordinateddebt sold by banks to their customers, and a similar wave of investor losses and lawsuits took
place (Enriques and Gargantini (2017).
The goal of the paper is to analyze the role of transparency in the behavior of financial advisers
subject to liabilities for the provision of incorrect advice to partially informed clients. In doing
so we also explore the potential contribution of regulation to improve the provision of investment
advice, as well as the limits to what legal regulation may add. For this, we build a simple agency
model of financial advice under the shadow of potential legal liabilities, where these liabilities arise
from the penalties imposed by the court based on imperfect observation of the financial advice
provided by the firm. Our basic model is presented in a setting where there is only one type ofadviser, while the main results are established in a setting of heterogeneous advisers.
There is also evidence pointing at advisers not tailoring their advice to the various profiles,
preferences and relevant characteristics of clients. Advisers, instead, appear to give investment
recommendations that reflect both their own (or their companies’) self-interest, or their misguided
beliefs about investment strategies.9
The main finding is that the level of stringency of court-imposed liability on financial advisers
for the lack of fairness and honesty in the advice decreases optimally with the experience andsophistication of the investor, and with the level of transparency of the overall informational
instruments that the firm uses to communicate with customers. The court’s role is limited incases where the court’s observation of the adviser’s behavior is too noisy, or when the adviser canchoose between advising methods that differ in terms of transparency. In such cases, regulation
has a role to play by limiting advisers both in terms of the products on which they may advice,
tal y Deuda Subordinada (2015).
9
Foerster et al. (2017) find that advisers do relatively little to tailor their advice on risk-taking to clients’ risk
tolerance or other characteristics associated with varying risk preferences, but rather project their own beliefs andpredispositions; Mullainathan et al. (2012) find that financial advice fails to de-bias behaviorally impaired investors,
and even amplifies some of the prevailing biases among financial customers that are in the financial advantage ofthe adviser; Linnainmaa et al. (2021), find that advisers do not display personalized recommendations but rather
recommend a similar investment profile to their various client categories, one, in fact, that is strikingly close to
their own personal choices as investors.

3

as well as in terms of the transparency choices available to them, to ensure an adequate policing
by the courts.
Our paper contributes to several strands of the literature. Bolton et al. (2007) provide an early
analysis of the conflicts of interest that arise in the provision of financial advice, while Campbell(2016) discusses the challenges for regulators in the context of a stylized model. A number of
papers explore specific aspects of conflicts of interest in financial advice, how alert and naı̈ve
consumers would react differently to the advice, and the welfare consequences of various policy
interventions: Inderst and Ottaviani (2009, 2012a,b,c); Inderst et al. (2010), Stoughton et al.
(2011), Guiso et al. (2022). Other contributions explore similar issues in a long-term setting,where cancelling the contract ex post is a relevant feature (Inderst and Ottaviani (2012c)). Others
have analyzed experimentally how the disclosure of conflicts of interest affects both sides of theinteraction, that is, the reactions by investors and advisers to the disclosure: Cain et al. (2005,2011), Loewenstein et al. (2011), and Sah et al. (2013). A different perspective is provided by
Gennaioli et al. (2015) where the adviser acts as a source of information but also as ‘money doctor’by providing a trusted channel for investors to invest in risky assets with less anxiety about theoutcome.
Other than Carlin and Gervais (2012), the previous literature does not consider the role ofliability in the provision of incentives to give honest financial advice, nor the contribution andlimits of an ex post regulatory scheme in the functioning of investment services firms. In contrast,
the current paper explicitly incorporates the social welfare costs from the court’s involvement(or by regulators more generally) via imperfect observation of the underlying adviser’s behavior,something that is absent in the literature, and focuses on the importance of transparency.
In terms of the modelling approach our paper builds on previous literature that has analyzed
how courts set liability standards in order to minimize judicial errors: Demougin and Fluet (2005,
2006), Artigot et al. (2018) and Ganuza et al. (2022), among others.
The paper is organized as follows. Section 2 presents the basic model of financial advice and4potential firm misbehavior, as well as how standards of liability are set in the presence of evidentiary uncertainty as to the kind of financial advice actually provided. Section 3 defines the optimal
policy by the court in fixing the standards for liability. Section 4 explores how standards should
depend on the transparency of the overall marketing and advisory policies displayed by firms,
and on the sophistication of the client receiving the advice. Section 5 deals with an important
extension of our basic setting, namely that of heterogeneous advisers. Section 6 considers threeextensions, namely when transparency enhances the quality of the evidence that courts may use,
the endogeneity of transparency and the characteristics of the client base of the investment firm,with the presence of forward-looking investors. Section 7 derives implications for understanding
legal and regulatory policy in this area. Section 8 briefly concludes.

2
2.1

The model

Financial advice, transparency and revenue

We device a very simple agency model of financial advice. Consider an adviser (a financial
institution, or, more generally, a firm) who sells assets and provides recommendations to an
investor and potential client.
The investor has access to three possible assets: a riskless asset S, that generates zero returnand zero rents to the financial institution (the supply of such an asset is perfectly competitive)
and two risky assets, S1 and S2 , that generate rents r1 < r2 for the financial institution.
The return of the risky asset to the investor depends on the matching between the assets
payoffs and the preferences of the investor. If the match is bad (state B), the net return of theasset to the investor (discounting the price) is negative and generates a loss of L with probability 1.
If the match is good (state G), then with probability p the return is negative and generates aloss of L but with probability 1 − p the project generates a net return of 1. We focus on the casewhere the expected return of the risky asset when the match is good is higher than that of the5

1.
riskless asset, i.e, 1 − p − pL > 0 ⇒ p < 1+L

Assets are perfectly negatively correlated in the sense that if asset 1 is a good match (state G)then asset 2 is a bad match and viceversa.10 The probability that asset S1 (S2 ) is a good matchis α (1 − α). The financial adviser knows how the asset matches with the investor, and decides torecommend either S1 or S2 . The investor decides between the riskless asset and the recommended
risky asset. To make this decision, the investor uses the effective information available to her.
The effective information available to the investor is captured by the accuracy parameter
γ. A higher value of γ, represents better, more effective information. The effectiveness of theinvestor’s information, γ(θ, δ), positively depends on two factors: the level of sophistication of theinvestor, θ, and the amount, quality, and clarity of the information provided by the adviser, δ,that we label as transparency for short. More effective information should lead to better decisions
by the investor. To capture this we introduce the outcome of the investor’s decision process in
reduced form: Let pG (γ) be the probability that the investor buys the asset when it is a good
match, and pB (γ) the probability that the investor buys the asset when it is a bad match. With
complementary probability the investor decides to buy the riskless asset S.
We assume that pG (γ) > pB (γ) for all positive levels of accuracy, since it seems intuitive toimagine that it is always more likely that a product that is a good match will be sold and bought
rather than a financial product that is a bad match.11 Furthermore, the higher the accuracy
parameter γ, the higher (the lower) the probability that the client buys a good product (a bad
10
We are implicitly assuming, as Inderst and Ottaviani (2009), a Hotelling environment in which investors arelocated either close to asset 1 or close to asset 2.
11This assumption is intuitive, but it is not necessary for our results.

6

product), pG (γ)0 > 0 and pB (γ)0 < 0.12,13 As an example we will use the following parametrization:pG (γ) =1+γ
2

and pB (γ) =

1
− γ.
2

An additional issue is how aligned the interests of adviser and investor are. With probability
1 − α the incentives of the financial adviser and the investor are aligned, since S2 , which is themost profitable recommendation for the financial institution, is in fact also the best product for
the investor. However, with probability α, there is a conflict of interest and the financial adviser
may follow one of two policies, P ∈ {H, D}, where H stands for honesty, that is, advising theinvestor to buy S1 , and D for dishonesty, that is, advising the investor to buy S2 . In the latter
case, we assume that the financial adviser incurs a moral or reputational cost β.14
Then, the expected revenues for the financial adviser from honest and dishonest policies are
R(H, γ) = (1 − α)pG (γ)r2 + αpG (γ)r1 ,R(D, γ) = (1 − α)pG (γ)r2 + α(pB (γ)r2 − β),respectively.
Depending on the value of the parameters, the difference may be positive or negative and withit the incentives of the financial adviser to provide honest advice:
R(H, γ) − R(D, γ) = α(pG (γ)r1 − pB (γ)r2 + β)
It is important to analyze how this difference between both revenue functions depends on theaccuracy parameter γ and indirectly on the level of the buyer sophistication θ and the level of
12This assumption allows us to incorporate in reduced form a number of approaches in the literature. For example,
it incorporates the case where agents receive the advice and review it or receive additional information, which they
later incorporate into whether or not to make the investment. Alternatively, as in Campbell (2015), it allows fora fraction of the population, who is less sophisticated, to overstate the value of the recommended option. Our
assumption then reflects the reduction in revenue difference from providing honest advice that would result for an
increase in the proportion of rational/sophisticated investors in the population.
13
Collins (2012) and Finke (2013) argue that financial literacy and financial advice are complements. Our setting
is flexible enough to allow them to be complements or substitutes. For the investor, the expected utility difference
between good (honest) and bad (dishonest) advise is pG (γ)(1−p−pL)+pB (γ)L > 0. This expression may increase or
decrease with γ (and hence with the sophistication and literacy of the investor) because pG (γ)0 > 0 and pB (γ)0 < 0.
Later in the paper, we discuss several specific models of investor behavior consistent with the characterization ofpG (γ)0 > 0 and pB (γ)0 < 0.
14This moral or reputational cost is a common assumption in the literature on corruption, see Burguet et al(2018) for a recent review of this literature.

7

transparency δ. As the benefits from selling a good product increase with γ and the benefits fromselling a bad product decrease with γ, the difference of revenues between honest and dishonest
policies is increasing with γ or, in other terms, the revenue function is supermodular in honesty
and accuracy (and sophistication and transparency). This supermodularity means that more
effective information makes it more likely that following a policy of honesty is optimal for theadviser.
Given the importance of this property of the revenue function for the subsequent analysis westate it as a proposition.
Proposition 1 The revenue function, R(x, γ), is supermodular in the honesty decision and accuracy.
An immediate corollary of this result is that the adviser’s incentives depend on the level of γ.
If the adviser’s decision is not trivial, and absent other factors such as liability and litigation, hewill choose to be dishonest for lower values of γ and honest for higher values of γ.

2.2

The litigation phase: the evidence available to the court

Regardless of the adviser’s behavior, we assume the investor will bring a case before thecourt whenever she suffers a loss. In order to simplify the analysis we disregard litigation costs,
the possibility that the victim does not bring the case before the court, and the possibility ofsettlement. These are non-trivial assumptions, but ones that allow us to abstract from otherdimensions of the problem.
The court’s role is to determine whether the adviser has been dishonest or not. If the court
finds the adviser to have been dishonest the court will rule for the adviser to pay an amount L to
the investor, and nothing otherwise. The court makes this ruling with knowledge of both the levelof sophistication of the investor, θ, and the level of transparency in the information provided by
the adviser, δ, (we believe this is plausible since the characteristics of the investor can be ex post8

assessed by the court, and the information materials used by the firm are likely to have produced
hard evidence as to their content and properties) but without direct observation of the honestyof the advice.
In order to establish the nature of the adviser’s behavior, the court has to rely on the evidence
brought before it by the parties in any admissible form: examination and cross-examination ofexperts and witnesses, looking into the exchanges and communications between investor/client
and adviser, etc. Let the total evidence available to the court be represented by a generic signal π ∈[0, 1], which summarizes an index of the amount of evidence indicating honesty. Formally, a signal
π is a realization of a random variable Π with distribution function f (π|P ). This distribution
depends on the type of advice, P = H or D, but not on γ, θ or δ. It is quite natural for thefinancial literacy of the investor not to influence the court’s ability to rule on the quality of
the advice. However, prior information and the transparency of the advice may do so, and we
consider this possibility after the main results are established. For convenience, we assume that f
is differentiable and non-zero on [0, 1].15 Let F (π|P ) denote the cumulative distribution function
corresponding to the court’s signal.
A higher value of π represents greater evidence that in the particular case before the court
the advice was honest. To ensure that honesty translates into more evidence of good behavior,
we assume that signals are monotone, that is, f (π|P ) satisfies the Monotone Likelihood Ratio
Property (MLRP):f (π|H)f (π|D)is increasing in π.

This condition ensures that more evidence is “good news” about honesty (Milgrom (1981)),that is, Pr(H|π) is increasing in π.
15

One of the implications of having full support on [0, 1] is that the evidence before the court is insufficient to
identify the honesty of the advice with certainty.

9

2.3

The court’s decision problem

We focus on the interesting case where it is not in the financial adviser’s self-interest to follow a
policy of honesty in the absence of potential liability, that is when R(H, γ) ≤ R(D, γ). Under thisassumption, the incentives provided by the court are needed for financial advisers to act honestly.
We also assume that the court is concerned about social welfare, which in this setting is affectedby judicial errors when honest advisers are sanctioned.
The court can commit to a decision rule that is based on the evidence presented when theinvestors suffer losses. We assume that the court uses a threshold decision rule which is defined asfollows: if the evidence brought before the court π is above a given threshold level (the evidentiarystandard) , π̄, then the court finds that there is sufficient evidence that the advice was honest,
and rules that there is no liability. On the other hand, if π < π̄, then the court finds the financial
adviser liable.16
For any level of accuracy in the client’s signal and court’s threshold rule characterized by theevidentiary standard, π̄, the adviser will choose the honest policy if the profits from doing so are
greater than those of being dishonest. This is summarized by the following incentive compatibility
condition:
R(H, γ) − pF (π̄|H)L ≥ R(D, γ) − F (π̄|D)L.

(IC)

The court has to set an evidentiary standard, π̄ that satisfies (IC) and induces honest behavior.
Among all evidentiary standards that satisfy (IC), the Court prefers the one generating fewer
judicial errors. Given that (IC) is satisfied, there is no dishonest behavior in equilibrium, andminimizing judicial errors is equivalent to minimizing the liabilities imposed on honest advisers17 .
16

The assumption that the court uses a threshold rule is harmless, as Ganuza et al. (2022) show in a more general
setting that the court’s optimal decision rule in this informational setup (monotone signals) is a threshold rule.
Additionally, threshold rules such as negligence, or the infringement of a legal duty, seem to be pervasive in mostlegal systems, though obviously the specific threshold and the factors underlying it vary greatly across legal systems
and settings.
17
With a single type of adviser, finding an innocent adviser liable (Type I error) is the only type of judicial errorthat can arise in equilibrium. In a subsequent section we will consider the general case, with heterogeneous advisers,
in which both Type I and Type II (acquitting a dishonest adviser) errors may arise in equilibrium.

10Then, the court’s problem can be written as:

min p F (π̄|H)
π̄2.4

subject to

(IC).

(1)

Timing when γ is given

The timing of the model is as follows: 1) Given γ, the court sets the evidentiary standard,π̄. 2) The financial adviser chooses the nature of the advice, x ∈ {H, D}, and the investor makes
her decision. 3) Nature determines returns (and, eventually losses) from the asset, as well as thecourt’s signal π according to the probabilities and information structures described above. 4)
Finally, if the client incurs a loss she files a lawsuit and the adviser will pay L to the investor if
the realized evidence, π, is below the court’s evidentiary standard, π̄.

3The equilibrium: Minimizing errors and maximizing incentives

We can rewrite the court’s problem in terms of judicial errors. Judicial errors can take twoforms: Type I, and Type II error. Type I error is the probability that the court mistakenly holds
an honest adviser liable and Type II error is the probability that the court mistakenly acquitsa dishonest adviser. We use the notation TI (π̄) = F (π̄|H) to denote the probability of Type I
errors committed by a court that imperfectly observes the adviser’s actions and uses an evidentiarystandard π̄. Similarly, Type II errors occur with probability TII (π̄) = 1 − F (π̄|D). We depict
these errors in Figure 1.
The court’s problem, on Equation (1), is equivalent to the following, more convenient, error

11Figure 1: Decision errors and the evidentiary standard.
minimization problem18 :min TI (π̄)π

s.t.

pTI (π̄) + TII (π̄) ≤ 1 +R(H, γ) − R(D, γ)
.
L

(2)

On the left hand side of equation (2) we find the errors generated by the court’s choice of evidentiary standard, π̄, which can be described more compactly using the weighted error functionΦ(π̄) = pTI (π̄) + TII (π̄). The next result characterizes the function Φ(π̄).
Lemma 1 The weighted error function is positive, continuous, and convex, and has a uniqueminimum on the interval [0, 1] at πmin . The function takes values Φ (0) = 1 and Φ (1) = p.19
Let ΦD be the error function defined on the set D = [0, πmin ], so that ΦD is a decreasing
function (and a higher standard increases the incentives to invest in product quality).
18

This method was proposed by Ganuza et al. (2022). In the Appendix we provide further details about thetransformation of the court’s problem.
19
Although for completeness we provide a formal proof in the appendix, this result is known. This characterization
was stated in Ganuza et al. (2022) and can be also derived from Demougin and Fluet (2005, 2006).

12

Figure 2 illustrates the shape of the Φ function (for p = 0.75) as well as πmin , the interval D,
and the function ΦD .20

Figure 2: The weighted error function.

On the right hand side of the equation 2 we find a key parameter of the model which we will
denote by ∆ (γ) = R(H, γ) − R(D, γ). We can interpret ∆ (γ) as the financial adviser’s expected
revenue difference when switching from dishonesty to honesty (without taking into account legal
liabilities). Recall that we have assumed that ∆ (γ) is negative for all values of γ and by thesupermodularity of the revenue function it is increasing in γ, so that when γ increases ∆(γ)
decreases in absolute value. The next proposition characterizes the solution to the court’s problem:
20

This figure is generated using signals with the following linear information structure which satisfies MLRP:
γ
+ γπ,
2
γ
f (π|D) = 1 + − γπ,2f (π|H) = 1 −

1
γπ (1 − π) ,21
F (π|D) = π + γπ (1 − π) ,2
F (π|H) = π −where γ = 1.75).

13

Proposition 2 For all γ, there exists a cut-off level, ∆min = (Φ (πmin ) − 1)L, such that ifwhich is decreasing in ∆. If∆ ≥ ∆min then the optimal standard is π̄ ∗ (∆) = Φ−1
1+ ∆DL∆ < ∆min the court cannot induce honesty from advisers.
The intuition of this proposition is as follows: for a given ∆ (γ), there is a set of evidentiarystandards for imposing liability on an adviser that generates enough incentives for honest behavior.
As Type I error is monotonically increasing in the evidentiary standard, the court chooses theminimum of these standards. When ∆ (γ) increases (honesty is less costly in terms of lost revenue),
it becomes easier to induce good behavior. The right hand side of the incentive compatibility
constraint is greater, more evidentiary standards satisfy the constraint, and the court’s optimal
standard (the minimum of the incentive compatible standards) decreases. However, if the lost
revenue from being honest is too large or the minimal amount of the weighted error function is high,then courts cannot generate sufficient incentives for honest advice. This leaves direct regulation
as the alternative: for example, prohibiting the sale of certain complex financial products to
unsophisticated retail investors.
Figure 3 illustrates Proposition 2 by characterizing the optimal evidentiary standard when0

p = 0, 75, and ∆L = −0.23.
In Figure 3 we can observe the set of standards inducing honesty, H(∆0 ), and the optimal
standard, π ∗ –the lowest in this set. A higher ∆ (corresponding to the higher green horizontal lineat ∆L = −0.2 ), larger market incentives to be honest imply a more lenient optimal evidentiarystandard, π ∗∗ < π ∗ .

4Investor information and sophistication: optimal court policy

The court’s optimal evidentiary standard as characterized in Proposition 2 depends on thelosses of the investors but also on the amount and quality of information available to clients andon their level of financial sophistication. An increase in transparency (the amount and quality of

14

Figure 3: Changing transparency (∆).
available information parameterized by δ) helps investors to better distinguish between suitableand unsuitable investments. This, in turn, given the supermodularity of the revenue function,
increases revenues for an honest adviser, and reduces revenue for a dishonest one, and thereby
reduces the losses from being honest (∆ increases). This translates into an increase in the adviser’s
incentives for honesty–even in the absence of liability–and reduces the need for court intervention.
Then, rulings can become more lenient and courts optimally impose a lower evidentiary standard.
A similar analysis applies if θ, the level of sophistication of the investor, increases.
Proposition 3 With a single type of financial adviser, the court’s optimal evidentiary standard
depends on the quality of information available to investors and their sophistication. Higher levelsof adviser’s transparency and investor sophistication result in lower court optimal evidentiarystandards.

15

The fundamental idea behind Proposition 3 applies generally and is key in the regulation of
consumer finance. Courts should be more lenient under market conditions that provide more
incentives for appropriate behaviour. In a context with asymmetric information, any enforcement
mechanism will generate costly implementation errors. When market conditions enhance incentives for appropriate behavior, part of this burden can be saved since the need for more stringent
enforcement measures is lower. Applying this principle, Proposition 3 states that if the information over financial assets held by investors and their capacity for interpreting such information
increases, the expected payoffs for dishonest advice decrease, thereby decreasing financial advisers’ incentives for misbehaving, and allowing the courts to implement honest behavior with morelenient standards.
Proposition 3 has been obtained under the assumption that there is a single type of adviser.
Consequently, the court’s objective is to provide enough incentives to be honest and minimize
the possibility of Type I error as much as possible. In the next section we extend our model toa heterogenous population of advisers, where for a given standard typically some advisers will
be honest while other advisers will not.21 Nevertheless, in this more complex setting the main
insights of Proposition 3 are still valid.

5Adviser Heterogeneity

We introduce heterogeneity in the form of a population of advisers with different reputationalcost, β (or a single adviser with private information on his/her type).22 These costs are distributed
uniformly in an interval [β, β]. In such a case, typically, for a given standard, some advisers with
21

The basic model considers a single type of adviser. This generates the classic paradox found in similar principalagent models with imperfect information, where the court (principal) will penalize the adviser (agent) with someprobability despite knowing that the adviser’s optimal policy is to “do the right thing” (which in this case is to givehonest advice), and hence, is always innocent. If the court does not penalize the adviser, then the adviser would nolonger have incentives to do the right thing and then the court would have to reinstate sanctions. By introducing
a heterogeneous population of advisers we allow for a richer set of possible judicial errors where this paradox need
not arise.
22
Advisers may also differ in other dimensions such as their degree of conflict of interest or the rents from thesale of each of the risky assets. A similar analysis would apply.

16

a high reputational cost β would be honest while other advisers, facing a lower reputational cost,
would be dishonest.
Suppose that the court sets a standard π̄ for a given level of effective information, γ. Then,
there will be a marginal type, β ∗ , characterized by the incentive compatibility constraint, whowill be indifferent between being honest and dishonest. This marginal type is characterized by
the solution to the following equation:pTI (π̄) + TII (π̄) = 1 +R(H, γ) − R(D, γ, β ∗ ).
LUsing the resulting solution we obtain that advisers with reputational cost higher than β ∗ whereβ ∗ (π̄, γ) =(Φ(π̄) − 1)L− (pG (γ)r1 − pB (γ)r2 ),αwill be honest, while the rest will be dishonest. Notice that β ∗ (π̄, γ) is decreasing in π̄ and γ.
Then, the proportion of advisers who are honest, which we label as the compliance level η, isgiven byη(π̄, γ) =β − β ∗ (π̄, γ),
β−βwhich is increasing in γ. If the level of accuracy increases, the marginal type decreases and thenthere is more compliance–a higher proportion of advisers are willing to follow a policy of honesty.
The problem for the court becomes more complex as its actions will have consequences along
a number of different dimensions. The court, when choosing a standard, is concerned both withthe level of Type I and Type II errors as well as with the general compliance level. We capture
the court’s objective when balancing the consequences of its legal standards using a social welfare
function, W (η, TI , TII ). Then, the court will set its optimal standard, π̄ ∗ , as the solution to thefollowing problem:π̄ ∗ ∈ arg max W (η, TI , TII ).
To address this problem, rather than using a specific functional form, we think that studying
a class of welfare functions with a set of plausible characteristics is preferable. Assume that W is17

twice differentiable in its arguments. Let Wi denote the derivative of W with respect to its i-th
argument, and Wij as the second derivative of W with respect to its i-th and j-th argument. We
assume the following two types of conditions:(i) Welfare is increasing in compliance (W1 > 0), concave (W11 < 0), and decreasing in TI and
TII , (W2 < 0 and W3 < 0),(ii) More compliance makes TI [TII ] more [less] socially costly (W12 < 0 [W13 > 0]).
An example of a social welfare function that satisfies these conditions is the following:
W (η, TI , TII ) = η − α1 (η)TI − α2 (η)TII ,where α1 (η) is increasing and α2 (η) is decreasing in compliance η. Such a welfare function
will satisfy our properties: it is increasing and concave in compliance, decreasing in court errors,
and more (less) sensitive to Type I (Type II) error as compliance increases.
In addition, we assume that the relative social importance from a change in TI is everywhere
greater than from a change in TII . This additional condition is formalized as:(iii) A change in TI is uniformly greater than a change in TII :
p

∂W
∂W
≥
.
∂TI
∂TII

(3)

This assumption reflects the general fairness concern with the problem of convicting the innocent in legal discourse and practice (“it is better to let a guilty person go unpunished than tocondemn an innocent”). In our previous example of a social welfare function this condition would
require that α1 (η) is sufficiently larger than α2 (η). This should be easily satisfied if we interpret
α1 (η) and α2 (η) as being related to the population weight of honest and dishonest agents, respectively, and we are in a situation where being dishonest is the exception and not the rule in the
population.

18

With this assumption we can concentrate on the decreasing section of the Φ(π̄) weighted error
function, as for two standards, π̄ and π̄ 0 , that generate the same error, Φ(π̄) = Φ(π̄ 0 ), the lower
standard is preferred: π̄ < π̄ 0 ⇒ W (π̄) > W (π̄ 0 ).
From this, we can prove that amongst the relevant evidentiary standards (those that domi∗(π̄,γ)
isnate other standards that generate the same errors), the compliance level η(π̄, γ) = β−ββ−βincreasing in π̄.
Rewriting the social welfare function as a function of (π, γ):f (π̄, γ) = W (η(π, γ), TI (π), TII (π)),
We can now prove that the social welfare function has a key property, namely, that f (π, γ) is
submodular in (π, γ):∂ 2 f (π, γ)= ηy (π, γ)[ηπ (π, γ)W11 + T0I (π)W12 + T0II (π)W13 ] < 0∂π∂γFrom this we obtain the same result as in the baseline model (Proposition 3), namely that the
optimal standard π̄ ∗ ∈ arg max W (η, TI , TII ) is decreasing in γ.
Proposition 4 With heterogeneous types of financial adviser, a court with a social welfare function that satisfies conditions (i)-(iii) above, will set an optimal evidentiary standard that depends
on the quality of information available to investors and their sophistication. Higher levels of adviser’s transparency and investor’s sophistication result in lower court optimal evidentiary standards.
The intuition behind Proposition 4 is as follows: more effective information implies that themarginal type will have lower reputational costs, and hence there will be more compliance. Thismeans that a higher proportion of advisers are willing to be honest. A higher compliance levelmakes less stringent standards more appealing for two reasons: i) as more advisers are giving
honest advice, the weight of Type I error in the objective function increases, and ii) given the
concavity in compliance of the objective function, the court is less willing to increase the standard(and type I error) in order to increase compliance further.
19

6
6.1

Applications and extensions

Transparency and the quality of evidenceFirst, we have assumed that the evidence available to the court, the informativeness of Π,is constant, and does not depend on the accuracy of the investor’s signal or, indirectly, on thetransparency level provided by the firm. Ganuza et al. (2022) shows that optimal standards arelower when the quality of evidence (informativeness of the signal held by the court) is higher.
In our setting, this effect may lead to even further reductions in the optimal evidentiary standards when investors receive more accurate signals about the assets, which in turn happens whenclients are more sophisticated and when the information that advisers provide to investors is moretransparent.
We come back to our dichotomous setting in which the court’s decision problem is written
in terms of minimizing decision errors. If higher transparency or more sophistication increase
the quality of evidence before the court, this implies less errors in imposing liability for any
given standard, i.e if γ 0 > γ then Φ(π̄, γ 0 ) ≤ Φ(π̄, γ) . Then, the set of standards that satisfy
the incentive compatibility constraint is larger and, consequently, the minimum of such set, theoptimal one that minimizes type one error, is lower.
To illustrate this, Figure 3 reproduces Figure 2 and includes what would happen to the error
function if the increase from ∆0 /L = −0.23 to ∆/L = −0.2 (the revenue loss from being honestis reduced due to an increase in transparency) is accompanied by an increase in the quality ofevidence before the court.23 The increase in the quality of evidence is represented by a new error
function (the dashed line) which is below the previous error function for all values of π. Thisimplies that the previous optimal standard, π ∗∗ , is in the interior of the set of feasible standards,
and consequently, the new optimal standard, πb∗∗ , will be smaller than (to the left of) π ∗∗ , and23

In our parameterized example, the parameter γ captures the informativeness of the signal, and the figure 3
captures an increase in γ from a value of 1.75 to one of 2.10.

20

Figure 4: Changing transparency and the quality of the court’s information.
even more so than π ∗ . The court policy is to apply a standard that is even more lenient.
If we consider the case of heterogeneous advisers, in which we expect both types of errors
in equilibrium, the shift in the weighted error function means that we cannot guarantee thatthe new standard will be more lenient without additional assumptions on how the accuracy level
determines the shape of Φ(π̄, γ). However, we can provide a local argument to prove that if
accuracy improves, a lower standard may increase welfare.
In particular, consider the case where a change in transparency only changes the accuracy ofthe evidence (shifts the error function down), keeping the revenue loss from being honest unaltered.
Let π̄ ∗ be the original optimal standard (before, under γ, i.e π̄ ∗ ∈ arg max Wγ (η, TI , TII ). Now
consider standards with the new, more accurate evidence, γ 0 . In particular we consider two
standards π̂I and π̂c . Because γ 0 generates more accurate information to the court, there arefewer errors. This allows the court to achieve the same level of Type I error with lower Type II21

error and greater compliance, or achieve the same level of compliance with less errors. Let π̂I be
the first of these, the standard that achieves the same level of Type I error, and π̂c the second,the one that generates the same level of compliance.
With evidence γ 0 and standard π̂I welfare is greater than with be the original optimal standardπ̄ ∗ under γ, as Type I error is the same, Type II error is lower and compliance greater. We canmake the standard more lenient than π̂I , which will gradually lower Type I error and decrease
compliance, until the point where we reach π̂c . At π̂c we know that welfare is also greater thanwith π̄ ∗ under γ, as compliance is the same and Type I error is lower. Although Type II error
is greater than under π̄ ∗ , given that we are assuming that Type I error is socially more costly
than Type II error, the overall welfare is necessarily greater. So, at both extremes of the interval[π̂c , π̂I ] welfare is greater. Then, for all other standards in the interval, Type I error is lower andcompliance is greater than with π̄ ∗ under γ.Hence, welfare is also larger.
We have characterized a set of standards under γ 0 that are more lenient and generate more
welfare for all welfare functions satisfying our original set of assumptions. Outside of this set,
whether the standard under γ 0 generates more or less welfare than π̄ ∗ under γ depends on theparticular welfare function being considered, and in particular how it evaluates the trade-off
between compliance and judicial errors.
We can now incorporate into the analysis the effect of transparency on the incentives for being
honest. As we found in Figure 4, more transparency reduces the revenue loss from being honest
and increases the incentives of the advisers to provide honest advice for any standard. This willfurther reduce the need to use a harsher standard even when compliance is socially very valuable.

6.2

Endogenous transparency

Thus far, we have not considered that the investor’s level of sophistication and the transparency
level of the financial adviser may be choice variables. In reality, subject to certain constraints andcosts, both are within the ability of the adviser to choose or, at least, to influence.
22Regarding transparency, it appears to be the case that the financial adviser may take many
steps to enhance the amount, quality and transparency of the investment information she provides
to her current or prospective clients. For instance, the firm providing investment services may
prepare information and marketing materials in ways that are reasonably clear and accessible,
and that also address some of the relevant issues pertaining to a (larger or smaller) number ofthe investment products that are offered to various groups of investors. The information can also
attempt to correct some of the biases and shortcomings that investors may frequently incur. With
the size, clarity, and quality of that information, the ability of investors to assess the suitability offinancial products would increase, given the level of experience and sophistication of the investor,
even in the absence of investment advice explicitly or implicitly addressed to them. Obviously,
these measures are costly, since they involve training of personnel, research, and time and effort
in producing and presenting the information.
Customers’ degree of sophistication is also a variable that may be influenced by the financial
adviser. First, because the target population of potential customers depends on the marketing strategies used by the firm, and these may cater to different groups that vary in terms of
their investment experience and sophistication. Second, because investment firms may engage insome educational efforts to expand the financial acumen in their client base. Third, and more
importantly, a financial adviser may devote resources to try to “know its customers”. In fact,
legal regulation of investment advice emphasizes firms’ duties in this area. Art. 25.2 MiFIDII Directive, determines that, “[when providing investment advice or portfolio management theinvestment firm shall obtain the necessary information regarding the client’s or potential client’s
knowledge and experience in the investment field relevant to the specific type of product or service,that person’s financial situation including her ability to bear losses, and her investment objectives
including her risk tolerance [...].” By engaging in these efforts, the financial adviser would havebetter knowledge of the level of sophistication of a given client before providing advice. With thehelp of such knowledge, the firm may design the general investment information in a way that is23

better tailored to the profile of its clients, so that the perceptions that investors will derive fromsuch information become more accurate, since they have a better fit with the investors’ level ofsophistication.
Thus, in the world of our model, when firms may take costly measures to increase investors’
sophistication and informational transparency, they will trade off the cost of these measuresagainst the benefits that will accrue to them in terms of lower liability standards to be appliedin ex post litigation when investors incur losses. More lenient liability standards applied toinvestment advisers with more sophisticated clients and who produce more transparent generalinvestment information will not only reduce the “penalty” on “good”financial advisers, but will
also provide incentives for firms to channel resources into increasing the level of sophisticationof investors in their client base, and to produce information for their clients that allows them tobetter assess the suitability of alternative investment instruments, even without the help of thefirms’ financial advice.

6.3

Forward-looking investors

We were assuming that investors are myopic regarding the liability system, and revenue functions R(H, γ) and R(D, γ), are independent of the standard chosen by courts. In other words,
that the payments imposed on advisers do not translate directly into compensation to investors.
In general, under tort or contract (but not under regulatory sanctions and fines, that accrue
to the agency or the Government) it is likely that investors get some amount of compensation.
Thus, their willingness to pay for financial assets may be affected by the liability system in place.
Revenue functions may depend on the optimal liability standard R(H, γ, π̄) and R(D, γ, π̄). This
complicates the analysis as liability payments will reduce the expected costs for investors when
they receive poor advice, leading them to be less selective in terms of avoiding a bad match withan investment product. This, in turn, is likely to make R(H, γ, π̄)−R(D, γ, π̄) even more negative,
and to decrease the incentives of advisers to follow a policy of honesty. Therefore, introducing
24

tort or contract compensation to clients generates an efficiency loss relative to the benchmark
case consisting on pure sanctions imposed on advisers.
Nevertheless, although the incentives for good behaviour could be lower with forward looking
investors, it would still be true that the incentives to give honest advice are higher when theeffective information in the hands of investors is higher. In our setup, this implies that R(H, γ, π̄)−R(D, γ, π̄) continues to be increasing in the effectiveness of the information, γ, which is the key
property driving our results.

6.4

Know your customer and money doctors

Our analysis is also relevant in a context where the adviser acts as a money doctor (Gennaioli
et al. (2015)) or a source of trust in the stock market (Guiso et al. (2008)). In such a setting
the source of poor advice does not arise from an explicit misalignment of incentives but from a
simple moral hazard problem, where the adviser, whose mere presence is a source of value to theinvestor, needs to exert effort in order to learn the customer’s type to provide suitable advice.
Adapting the model to the moral hazard problem involves the following changes: First let
r1 = r2 . This will eliminate the misalignment of incentives via commissions or differential rents
accruing to advisers. Second, introduce moral hazard by giving the agent no initial information on
the customer’s type, and allow him to learn the customer’s type perfectly by investing an amountof effort equal to e. In addition, assume for simplicity that the agent’s default recommendation
prior to learning the investor’s type is S2 . With these changes, the expected revenues for thefinancial adviser from informed (H) and uninformed (D) policies are the following:
R(H, γ) = (1 − α)pG (γ)r2 + αpG (γ)r2 − e,R(D, γ) = (1 − α)pG (γ)r2 + α(pB (γ)r2 ), c ,respectively. Then, if the advisor invests in learning the asset that best matches customers’
preferences, the probability of selling is always pG (γ). If the advisor does not exert the effort,
25

then he always recommends asset 2. This is good advice only with probability (1 − α). The key
dimension for our results is the difference in revenues between both strategies, ∆E :∆E (γ) = R(H, γ) − R(D, γ) = α([pG (γ) − pB (γ)]r2 ) − e.
As in this version of the model we are assuming that pG (γ) − pB (γ) is increasing with γ, we
can conclude that the incentives for honest/informed behaviour are increasing in the accuracy
parameter γ. As in our benchmark model the revenue function is supermodular in the decision
about being honest and in accuracy, so that all our results continue to hold. The intuition isthat when the investor is better informed or is more sophisticated, the adviser needs to invest lessto provide accurate advice in order to increase the probability of a sale probability and revenue
from it. This is the driving force behind our results, as the courts, not being able to observe
the adviser’s effort directly, anticipates that greater accuracy generates greater incentives to theadviser to behave well.

7

Implications for regulatory policy

Financial advice is heavily regulated in most countries. An extensive set of duties of behavior
and regulatory constraints are imposed. These mandates have liabilities -monetary and otherattached to their infringement. Analyzing how these affect the behavior of investment services
firms appears to be helpful in improving our understanding of financial advice.
The legal and regulatory scheme and its implementation are not in the hands of omniscientlawmakers and adjudicators. The legal and regulatory apparatus typically possesses only incomplete information about the behavior of the regulated investment advisers. Thus, issues of
information are of great importance to design and implement desirable laws and regulations inthis area. In our simple model, we highlight a number of dimensions that we believe fit closelywith plausible accounts of the interaction between advisers and clients.
For instance, what amounts to “advice” as an action that should trigger liabilities vis-à-vis
26

investors is trickier than it seems. Sometimes the financial advice will be ”hard”, in the senseof falling squarely under the legal term of ”financial advice”, i.e. a specific recommendation by
the firm to make a given choice and addressed to a particular client. In other circumstances,it may be a ”softer” or more subtle form of advice, through which the firm conveys an implicit
recommendation, or presents the choices to the client in a way that hints to what constitutes
the preferred alternative. Obviously, such financial advice, either in a ”hard” or a ”soft” version,
may be more or less ”honest”, in the sense that it may or may not correspond with what the firm
observes as the best interest of the client in terms of the match between the long-term profitability
and riskiness of the investment and the needs of the client.
Part of that investment information may become available to the client through various sources,
but a substantial fraction of it would be provided -or not- by the financial adviser, in the formof, among others, easily readable reports on past returns and volatility from a range of products
or a set of issuers of financial instruments, accessible information provided by the firm on certain
general features of investment decisions and alternatives (diversification, hedging, risk profile, adjustment of characteristics to different age- and income-profiles, etc.), and other similar pieces
of information. These may contribute to making the information investors possess on alternative investment products more accurate. The information elaborated and communicated by theinvestment firm, moreover, may be drafted and presented with varying degrees of clarity and comprehensibility, and may be more or less complete in terms of coverage. In the model we labeled as”transparency” the overall quality of that general information affecting the accuracy with whichinvestors perceive the match of a product with her own preferences or characteristics.
It should be noticed that we do not include within the notion of transparency used in themodel other pieces of information that would allow investors to directly assess the honesty of
the advice and the existence and severity of a conflict of interest afflicting the financial adviser.
Think of the presence of third-party inducements or commissions, the dependent or independent
nature of the financial advice, the incentive scheme of employees or agents performing the advisory27

services. These are factors that surely have an important and immediate bearing on the perception
by clients of the presence and magnitude of conflicts of interest and how they will influence
the honesty and fairness of the financial advice to the investor. Obviously, we do not consider
these issues in the paper, not because we think they are uninteresting or unimportant (quite theopposite), but they have already been extensively analyzed in the literature.24 Moreover, thelegal and regulatory regime governing financial advice has grown in size and importance in viewof the concerns with problems in the marketing and sale of financial products to retail investors,
comprising the financial advice linked to the distribution of financial instruments.
In the EU and in other places, unsurprisingly, the increased public distrust of the functioningof financial markets in the aftermath of the financial crisis reached the area of financial advice.
Some of the important modifications in the legal and regulatory framework governing financial
institutions and financial activities have touched this area, in addition to others (such as regulationand supervision of financial institutions, and increased regulation of some ”sensitive” markets, suchas the mortgage market).
Prior to the financial crisis, the EU had adopted a comprehensive framework for investment
services trying to ensure that high standards be observed by investment firms in their dealings
with their clients,25 and especially, with retail investors. The uneasiness about the ability of theserules to deter misconduct in the area of marketing and financial advice to retail investors led to
new and ambitious legislative scheme in this area, the MiFID II framework.26
The new regulatory architecture for investment services comprises Directive 2014/65/EU (MiFID II) and Regulation 600/2014/EU (MiFIR), together with a very large number of detailed
measures implemented through the European Securities and Markets Authority (ESMA). A crucial portion of these new regulatory tools tries to subject the firms involved in providing investment
services of various kinds (transmission and execution of orders, management of investment port24
Inderst and Ottaviani (2009, 2012a,b,c); Inderst et al. (2010), although without an ex-post imperfect liability
system in place.
25
This is the so-called MiFID I, resulting from Directive 2004/39/EC (MiFID I), Directive 2006/73/EC (MiFID
I Implementing Directive), and Regulation 1287/2006/EC (MiFID I Implementing Regulation).
26
See generally on MiFID II, Busch and Ferrarini (2017).

28

folios, commercialization of financial products, investment advice) to certain duties and rules ofconduct that would (or at least have such aims) improve investor protection and secure stablefinancial markets. The goal of consumer protection and market stability are explicit in the recitalsof MiFID II.
The overarching legal duty presiding over the behavior of a firm that provides investment services is that of acting ”honestly, fairly and professionally in accordance with the best interests of
its clients”. Other more specific duties, with requirements that depend on various circumstances-type of service, type of client, type of financial instrument, etc.- arise in connection with information disclosure, knowledge and assessment of the client -Know Your Customer Rules, leading
eventually to tests of appropriateness and suitability of the product to the investor-, managementof conflicts of interest, execution of instructions, recording and communication, and so forth.
Even beyond the boundaries of this extensive set of duties under MiFID II, the implications ofour model are relevant, for how the law deals with the provision of financial advice to investors by
experts, be they explicitly framed as advice, personally addressed to a customer, or as a vaguer
and less explicit ”nudge” towards a given investment product. These more ”subtle” or ”covered”
forms of implicit recommendation actually complicate the ex post observation by courts of theunderlying adviser’s behavior, and thus neatly match the setting we explore.
Our model focuses precisely into such a setting, where investors’ perceptions as to the suitability of financial instruments, the advice provided by the expert financial advisers, and thedecisions by courts who impose liability ex post with only informative signals about the firms’
actual compliance with their legal duties, intersect.

8

Conclusions

Financial advice, both explicit and implicit, is a pervasive phenomenon in the area of household
finance, which includes key financial decisions such as borrowing, stock market participation,
investment products, insurance, and pensions. Moreover, it is an activity subject to extensive
29

regulation in terms of the legal duties imposed on firms that engage in it. Our model focuses on theinteraction between the legal system and the incentives of financial advisers. More specifically, we
address an scenario where investors’ observations about financial instruments, the honesty of theadvice provided by the expert financial advisers, and legal sanctions administered by imperfectly
informed courts, interact.
In this setting we have provided a theoretical analysis of how clients’ sophistication, and thetransparency of general investment information from the firm should affect the stringency of thecourt-imposed liability regime that applies to financial advisers . We find that transparency andinvestor sophistication generally improve the incentives of advisers to provide honest and suitableadvice. As such an advice may be too costly to provide, courts and supervisory entities can playa role by introducing penalties to align private incentives with social incentives to induce honest
advice. Given the unavoidable costs arising from judicial errors linked to the imperfect observationof advisers’ behavior, we find that it is optimal to apply more lenient standards in settings withgreater transparency and/or investor sophistication. However, with insufficient transparency or
low investor sophistication, or if judicial errors are too frequent, the justice system may not beable to induce adequate financial advice. At this point, direct regulation of the activity, in theform, among others, of the selective prohibition of recommendations for certain assets to certain
types of investors, may become necessary.
We also find that private incentives for increasing transparency are aligned with social ones as
greater transparency not only reduces court penalties but also increases the private revenue fromproviding honest advice. However, advisers with reputational costs that are too low or with highcosts of learning about her client’s specific financial needs may prefer a less transparent regime. In
this case, additional measures will be required. For example, courts could impose a much higher
standard on less transparent advisers–even strict liability for investors’ losses–or regulation could
impose minimum transparency standards, or a combination of both.
We believe our analysis is relevant for an improved economic understanding of how the im-30

plementation of the regulatory solutions (the new EU new MiFID II regime or some others) may
prove economically desirable to improve incentives for fair financial advice.
Naturally, we are fully aware that the current analysis is just a first step in the effort to clarify
how various parameters involved in the interaction between investors and financial advisers should
impact the implementation of the regulatory regimes intending to improve market outcomes in
the area of investment services.

A

Appendix

Transformation of the court’s decision problem:
The court’s problem can be written as:
min pF (π|H)π

s.t.

R(H, γ) − pF (π̄|H)L ≥ R(D, γ) − F (π̄|D)L.

Then, the objective function is directly pTI (π̄). The incentive compatibility constraint (IC)can be rewritten using the definitions of decision errors:
R(H, γ) − pF (π̄|H)L ≥ R(D, γ) − F (π̄|D)L.
−F (π̄|D)L + pF (π̄|H)L ≤ R(H, γ) − R(D, γ).
L − F (π̄|D)L + pF (π̄|H)L ≤ L + R(H, γ) − R(D, γ)
pTI (π̄) + TII (π̄) ≤ 1 +R(H, γ) − R(D, γ).
L

Proof of Lemma 1: We include this proof for completeness since it can be also found in
Ganuza et al. (2022). The values of Φ are obtained by direct computation while the existence anduniqueness of the minimum is obtained by looking at the derivative of Φ:Φ0 (π) = f (π|qL )[pf (π|qH )− 1].
f (π|qL )As the likelihood ratio integrates to one (with respect to f (π|qL )) and is monotone, Φ has at
most one sign change (from negative to positive). As the likelihood ratio is increasing it starts
31off negative so that the minimum of Φ is either in the interior of [0, 1] or at π = 1. Uniquenesscomes from the differentiability of f .
minProof of Proposition 2: The level ∆min is determined as the solution to Φ(πmin ) = 1 + ∆D.

∆
In case of ∆ < ∆min , for all π ∈ [0, 1], Φ (π) > 1 + D
so that it is not possible to induce highquality. For ∆ > ∆min , let H (∆) be the set of π that satisfy the incentive compatibility constraint∆
for a given ∆. The set H (∆) is a closed interval such that for all π ∈ H (∆), Φ (π) < 1 + D
, and

∆
∆
. As ΦD is decreasing and 1 + D
the minimum of H (∆) is Φ−1
1+ D
is increasing in ∆ , Φ−1DD isdecreasing in ∆.
Proof of Proposition 3: From Proposition 2 we know that the optimal standard π̄ ∗ isdecreasing in ∆, and ∆ (δ, c) = R(qH , δ) − c − R(qL , δ) is increasing in δ, which implies that π̄ ∗ isdecreasing in δ.

32

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37

B
B.1

NOT FOR DISTRIBUTION

Microfoundations: restricted investments, fixed types with full financial adviser (FA)information

Consider the situation where the population is made up of sophisticated and unsophisticatedinvestors. Let θ be the proportion of sophisticated investors and 1 − θ that of unsophisticatedinvestors. Also, suppose that initially the investor is only aware of the existence of the risklessasset, and will only become aware of the risky asset that the adviser recommends (and neverknow of the existence of the other risky asset). The investors’ optimal action will depend on theirtype, defined by their level of sophistication. Assume the unsophisticated investors will follow therecommendation of the adviser. On the other hand, sophisticated investors will follow the given
advice if it coincides with the signal they receive when they request advice. Then, the expected
revenues from honest and dishonest policies are
R(H, γ) = α(θγ + (1 − θ))r1 + (1 − α)(θγ + (1 − θ))r2
R(D, γ) = α(θ(1 − γ) + (1 − θ))r2 + (1 − α)(θγ + (1 − θ))r2 ) − αβ.
Then, the revenue difference between the two honesty policies is:R(H, γ) − R(D, γ) = α(θγ + (1 − θ))r1 − α(θ(1 − γ) + (1 − θ))r2 + αβ.
LetpG (γ) = θγ + (1 − θ),pB (γ) = θ(1 − γ) + (1 − θ),so that the difference can be rewritten as follows:
R(H, γ) − R(D, γ) = α(pG (γ, θ)r1 − pB (γ, θ)r2 + β),where pG is increasing in γ and pB is decreasing in γ. However, both are decreasing in θ and the38overall effect of an increase in θ may be negative:∂
R(H, γ) − R(D, γ) = α((γ − 1)r1 − ((1 − γ) − 1)r2 )∂θ= α(r2 − (1 − γ)(r1 + r2 ))B.2

Microfoundations: restricted investments, Nash equilibrium with full FA information

Consider the situation where the population is made up of sophisticated and unsophisticatedinvestors. Let θ be the proportion of sophisticated investors and 1 − θ that of unsophisticatedinvestors. Also, suppose that initially the investor is only aware of the existence of the risklessasset, and will only become aware of the risky asset that the adviser recommends (and never knowof the existence of the other risky asset). The investors’ optimal action will depend on their levelof sophistication. Assume the unsophisticated investors will follow the recommendation of theadviser. On the other hand, in equilibrium the sophisticated investor will condition the interpretation on the FA’s optimal action and hence, will believe (and follow) the recommendation if in
equilibrium the FA is honest, and will ignore the recommendation of the adviser if in equilibrium
the FA is dishonest. Note, however, that the sophisticated investor obtains information just fromvisiting the adviser, namely, the investor learns of the existence of the risky asset and obtains thesignal, s, with precision γ regarding the expected return of the risky asset. With this information,
if the adviser is being dishonest, the investor will compare the expected return from the recommended risky asset (after observing the signal) with the riskless asset. Let qi , i ∈ {1, 2}, denotethe posterior probability that the match with the recommended asset is good. This implies thatthe investor will invest in the risky asset only if:0≤

qi (1 − p − pL) + (1 − qi ) (−L)

⇐⇒

qi
L
≥
:= L.
1 − qi1 − p (1 + L)

39

The ratio of posterior expectations depends on both the informativeness of the signal, γ, as wellas the prior, α, namely:
αγ
q1
=
,
1 − q1(1 − α)(1 − γ)

(1 − α)γq2=.
1 − q2α(1 − γ)To simplify the analysis, consider that γ is sufficiently high such that the sophisticated investor
will choose the recommended asset if the signal received suggests it is a good match. Then, theexpected revenues from honest and dishonest policies are
R(H, γ) = α(ξ(qγ + (1 − q))r1 + (1 − ξ)(1 − qγ))r2+(1 − α)(ξ(qγ + (1 − q))r2 + (1 − ξ)(1 − γq))r1 ,R(D, γ) = α(q(1 − γ) + (1 − q))r2 + (1 − α)(qγ + (1 − q))r2 )−(1 − α)(1 − ξ)β − αξβR(H, γ) = αr1 + (1 − α)r2
R(D, γ) = α(θ(1 − γ) + (1 − θ))r2 + (1 − α)(θγ + (1 − θ))r2 ) − αβ.
If ξ = 1, this simplifies as γ̂ξ = γ̂1 = q + (1 − q)γ, so that: Consider the deviations: R(H, γ, d),
the revenue from deviating from a policy of honesty, and R(D, γ, h), the revenue from deviatingfrom a policy of dishonesty (where after observing s1 out-of-equilibrium, the sophisticated investor
believes the FA is being honest):
R(H, γ, d) = αr2 + (1 − α)r2 − αβ.
R(D, γ, h) = αr1 + (1 − α)(θγ + (1 − θ))r2 ).

R(H, γ) = α(ξ(qγ + (1 − q))r1 + (1 − ξ)(1 − qγ))r2+(1 − α)(ξ(qγ + (1 − q))r2 + (1 − ξ)(1 − γq))r1 ,R(D, γ) = α(q(1 − γ) + (1 − q))r2 + (1 − α)(qγ + (1 − q))r2 )−(1 − α)(1 − ξ)β − αξβ40Then, for honesty to be an equilibrium outcome we require
R(H, γ) − R(H, γ, d) = α(r1 − r2 ) + αβ ≥ 0⇐⇒ β ≥ r2 − r1 .
R(D, γ) − R(D, γ, h) = α(θ(1 − γ) + (1 − θ))r2 − αr1 − αβ ≥ 0.
⇐⇒ β ≤ (1 − γθ)r2 − r1 .

B.3

Microfoundations: unrestricted investments, partial FA information

Suppose the investor receives a private signal of the state, s, with precision γ. The adviser also
receives a signal with precision ξ. The adviser sends a message to the investor, m. Suppose that
this message is equal to her signal with probability h and equal to the adviser’s preferred asset
with probability 1−h. Notation: let Gi, i ∈ {1, 2}, denote the state where asset i is a good match.
Similarly, let mi and si represent the events “the message sent by the FA is that asset i is a good
match” and “the signal received by the investor is that asset i is a good match”. Unknown bias
Suppose the investor does not know which asset is preferred by the FA and assumes the FA prefers
each asset with equal probability. Then the investor believes a dishonest message recommends
assets 1 and 2 with equal probability. The posterior after observing m1 isPr{m1|G1}α
Pr{m1}
1
Pr{m1|G1} = hξ + (1 − h)2
Pr{G1|m1} =1
Pr{m1} = h(αξ + (1 − α)(1 − ξ)) + (1 − h)2hξ + (1 − h) 12 αPr{G1|m1} =h(αξ + (1 − α)(1 − ξ)) + (1 − h) 12
Pr{G1|m1}
1 − Pr{G1|m1}=α(hξ + (1 − h) 12 )(1 − α)(h(1 − ξ) + (1 − h) 12 )With unknown bias, the “precision” of the message is hξ + (1 − h) 21 which is directly comparablewith the precision of the signal γ. Then, the investor would always follow the signal rather than41

the message if
1γi > hξ + (1 − h) ,2
and follow the message over the signal if the inequality is reversed. With ξ = 1, the inequality is
γi >

1+h
.
2

Known bias Suppose that the investor knows that the FA prefers to sell asset 2. Then, the honest
FA will communicate the message truthfully but the dishonest one will always recommend asset
2. If the investor observes m1, then it comes from the truthful type for sure, and the precision of
the signal is ξ. If the investor observes m2, then the posterior is obtained as follows:
Pr{m2|G2} = hξ + (1 − h)Pr{m2} = h((1 − α)ξ + α(1 − ξ)) + (1 − h)Pr{G2|m2} =Pr{G2|m2}
1 − Pr{G2|m2}==(hξ + (1 − h)) (1 − α)h(α(1 − ξ) + (1 − α)ξ) + (1 − h)
(1 − α)(hξ + (1 − h))α(h(1 − ξ) + (1 − h))(1 − α) hξ+(1−h)
2−hα(1 − hξ+(1−h))
2−hWith known bias, the “precision” of the message depends on the bias. If the FA-preferred option
is 2 then upon observing m1 the investor would follow the signal if
γi > ξ,that is, always if ξ = 1. While, upon observing m2 the investor would follow the signal if
γi >hξ + (1 − h).
2−hThe FA’s optimal action To obtain a strategy where the FA mixes between being honest
and dishonest we can appeal to two possibilities: (i) the FA is following a mixed strategy in a
Nash Equilibrium [see above section on Nash equilibrium with full FA information]; (ii) anotherpossibility is that the FA is mixing in response to a random signal on the investor’s type (γi ). A
42

particular version of case (ii) is as follows: the FA receives a signal σ that is informative about theinvestor’s level of sophistication, with values {H, L} where H refers to the case where the investor
has a higher γi and will ignore the FA’s advice, and L refers to the case where the investor has
a lower γi and will follow the FA’s advice. The following argument points at the hypothesized
supermodularity of the revenue function without reference to the exact informational content
of the signal or whether we assume the FA’s bias is known or unknown. Let q(σ) be the FA’sposterior that the investor is unsophisticated (and will follow the FA’s advice) and 1 − q(σ) thatthe investor is sophisticated (and will ignore the message and follow si)–we obviate the σ when
it is inferable from the context. Let γ̂ξ = qξ + (1 − q)γ, where γ is the average precision on theparameter of sophisticated investors, so that γ̂1 = q +(1−q)γ. The expected revenues from honest
and dishonest policies are

R(H, γ, σ) = α(γ̂ξ r1 + (1 − γ̂ξ )r2 ) + (1 − α)((γ̂ξ r2 + (1 − γ̂ξ )r1 )),R(D, γ, σ) = α((γ̂1 − q)r1 + (1 − γ̂1 + q)r2 )+(1 − α)(γ̂1 r2 + (1 − γ̂1 )r1 )−(1 − α)(1 − ξ)β − αξβIf ξ = 1, this simplifies to γ̂ξ = γ̂1 = q + (1 − q)γ, so that:
R(H, γ, σ) = α(γ̂1 r1 + (1 − γ̂1 )r2 ) + (1 − α)(γ̂1 r2 + (1 − γ̂1 )r1 ),R(D, γ, σ) = α((γ̂1 − q)r1 + (1 − γ̂1 + q)r2 )+(1 − α)(γ̂1 r2 + (1 − γ̂1 )r1 ) − αβ.
Let ∆ = r2 − r1 . Depending on the value of the parameters, the difference may be positive or
negative, and so will be the incentives of the financial adviser:

43

R(H, γ) − R(D, γ) = (1 − α)((γ̂ξ − γ̂1 )r2 − (γ̂ξ − γ̂1 )r1 ))+α((γ̂ξ − γ̂1 + q)r1 − (γ̂ξ − γ̂1 + q)r2 )+(1 − α)(1 − ξ)β − αξβR(H, γ) − R(D, γ)= (1 − α)(γ̂ξ − γ̂1 )(r2 − r1 )−α(γ̂ξ − γ̂1 + q)(r2 − r1 )+(1 − α)(1 − ξ)β + αξβR(H, γ, σ) − R(D, γ, σ)= ∆ ((1 − 2α)(γ̂ξ − γ̂1 ) − αq)+(1 − α)(1 − ξ)β + αξβ.
Which, for ξ = 1, simplifies to:R(H, γ, σ) − R(D, γ, σ) = α(β − q∆).
So that (with ξ = 1) we can generically write
R(H, γ, σ) − R(D, γ, σ) = α(β + pG (γ)r1 − pB (γ)r2 ),where pG = pB . It is natural to assume that the posterior probability q(σ) is decreasing in the
distribution of γ, and hence the revenue of the FA is supermodular in γ and honesty. The signal
σ parametrizes the FA’s types. As long as σ is good news (in the sense of Milgrom) about theprobability of meeting a sophisticated investor, then the FA’s incentives to be honest will also be
increasing in σ. This will occur if higher types are more likely to ignore the message, and for thisto be true one needs that the incentives for honesty of the adviser increase more rapidly than theinvestor’s level of sophistication.

44