Accepted Manuscript

Financial Literacy and the Demand for Financial Advice

Riccardo Calcagno, Chiara Monticone

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DOI: http://dx.doi.org/10.1016/j.jbankfin.2014.03.013

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To appear in: Journal of Banking & Finance

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Please cite this article as: Calcagno, R., Monticone, C., Financial Literacy and the Demand for Financial Advice,

Journal of Banking & Finance (2014), doi: http://dx.doi.org/10.1016/j.jbankfin.2014.03.013

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Financial Literacy and the Demand for Financial

Advice

Riccardo Calcagno∗ Chiara Monticone†

April 20, 2014

Abstract

The low level of financial literacy across households suggests thatthey are at risk of making suboptimal financial decisions. In this paper,we analyze the effect of investors’ financial literacy on their decisionto demand professional, non-independent advice. We find that non-independent advisors are not sufficient to alleviate the problem of lowfinancial literacy. The investors with a low level of financial literacyare less likely to consult an advisor, but they delegate their portfoliochoice more often or do not invest in risky assets at all. We explain thisevidence with a highly stylized model of strategic interaction betweeninvestors and better informed advisors with conflicts of interests. Theadvisors provide more information to knowledgeable investors, whoanticipating this are more likely to consult them.Keywords: financial literacy, financial advice.JEL classification: G11, G24, D80

∗EMLYON Business School, 23 Avenue Guy de Collongue, 69130 Ecully, France;CeRP/Collegio Carlo Alberto, Moncalieri, Italy. E-mail: calcagno@em-lyon.com

†Organisation for Economic Co-operation and Development, 2 rue Andre Pascal, 75775Paris Cedex 16, France; CeRP/Collegio Carlo Alberto, Moncalieri, Italy; Netspar, Tilburg,the Netherlands. E-mail: chiara.monticone@oecd.org

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“For unto every one that hath shall be given, and he shall have abundance:but from him that hath not shall be taken away even that which he hath”.

Mattheus, 13:12

1 Introduction

The growing literature on financial literacy suggests that the consumers’knowledge of basic financial principles and products is minimal (see Lusardiand Mitchell, 2011b; Atkinson and Messy, 2012) and might not be sufficientto guarantee that households make sound financial decisions. For instance,the empirical evidence shows that more financially illiterate households aremore prone to inefficiently low participation in the stock market, to portfo-lio under-diversification, to inertia in their portfolio management, to over-indebtedness, and to the use of informal sources of borrowing (Guiso andJappelli, 2008; Kimball and Shumway, 2010; Klapper et al., 2013; Lusardiand Mitchell, 2007; Lusardi and Tufano, 2009).

A low level of financial literacy does not necessarily imply that house-holds are bound to make poor financial decisions. At least in principle, theycan seek advice and guidance from qualified sources. As long as householdscan resort to the advice of experts for their financial decisions, this advicecan act as a substitute for their own learning, thus avoiding the effort ofacquiring financial expertise. However, two problems might undermine thisargument. First, advice might be biased when financial advisors act as sell-ers of financial products (Bolton et al., 2007; Inderst and Ottaviani, 2009;Stoughton et al., 2011), and biased advice might not improve customers’portfolio allocations or might even be to their detriment (Bergstresser et al.,2009; Mullainathan et al., 2012; Shapira and Venezia, 2001). Second, con-sumers might not demand advice. For instance, Bhattacharya et al. (2012)observe that even unbiased and free advice is not demanded, and concludethat the supply of fair advice is not sufficient to improve on the investors’portfolio allocations. Their findings suggest that the problem might lie inthe demand for advice by investors, and not only in its supply.

In this paper, we analyze the effect of the degree of financial literacy onthe investors’ willingness to delegate their portfolio decision and on theirdemand for financial advice. We consider a stylized model of portfolio allo-cation in which an investor decides whether to delegate the choice betweena riskless and a risky security to a better informed financial intermediary, toask him or her for advice, or to choose the portfolio allocation autonomously.We derive empirical implications regarding the effect of financial literacy onthe participation in the risky market and on the demand for advice versusdelegation. Then we test our results using the 2007 Unicredit CustomersSurvey, a representative sample of customers of the largest Italian bank.

Our model shows that advisors disclose their superior information only

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to the most knowledgeable investors, while they do not provide additionalinformation to the less informed ones. This phenomenon is similar to the“Matthew effect” used in sociology (Merton, 1968) to describe situations inwhich “the poor get poorer and the rich get richer.” Experimental evidencefrom an audit study in Mexico shows that less informed customers indeedreceive less information from financial institutions about saving and creditproducts than more experienced customers (Gine et al., 2013), thereforesupporting the mechanism described in our model. Hence, rational investorswho are aware of the advisor’s selling incentives will demand professionaladvice only if they are sufficiently knowledgeable, but the less informed in-vestors will either delegate the portfolio choice to the advisor or choose theirown portfolio autonomously. However, the poorly informed investors withlow initial wealth do not buy risky assets at all. From our analysis it thenfollows that financial knowledge and the quality of advice are complements,not substitutes.

Our empirical findings confirm these predictions. A high degree of finan-cial literacy increases the probability of consulting an advisor, and it reducesthe probability of delegating the portfolio choice. This finding holds evenafter controlling for a number of factors such as the investor’s wealth, age,experience with financial products, opportunity cost of time, trust in the ad-visor, years of education, self-confidence in his or her financial ability, andthe quality of advice. Our results are also robust to potential endogeneity.

Overall, our paper shows that the presence of non-independent advisors,who at the same time provide advice and sell financial assets, does littleto alleviate the problem of low financial literacy for financially illiterateinvestors. These investors, who need advice the most, rarely rely on advi-sors. Our results add to the literature on the propensity to consult financialadvisors (Hackethal et al., 2012; Collins, 2012; Marsden et al., 2011) by pro-viding a more refined theoretical and empirical investigation that involvesthree options (portfolio allocation based on investor’s own judgment, on en-hanced information provided by the advisors, or on delegation). Further,we perform various robustness checks to account for potential endogeneity.

Based on our results, we conclude that there is scope for various types ofinterventions, such as financial education initiatives targeted at the popula-tion groups with the highest private costs for accessing financial knowledge,for rules that reduce the conflicts of interests between clients and interme-diaries, as well as for the subsidization of independent advisors.

The rest of the paper is organized as follows. The next subsection reviewsthe relevant literature. Section 2 informally describes the stylized model andits main empirical implications. Section 3 introduces the empirical analysis,describes the data set, discusses the empirical strategy and presents theresults from the baseline analysis and from the robustness checks. Section4 concludes. The Appendices collect the full analysis of our model as wellas the proofs.

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1.1 Literature review

The research literature that explores the relation between the consumers’financial literacy and their demand for professional advice is recent andrelatively limited.

As long as financially literate investors have a better understanding offinancial products and concepts, they should have easier access to financialmarkets and a lower need for financial advisors. Hung and Yoong (2010)show experimental evidence that advice is chosen by the least financiallyliterate, hence the authors support the concept of substitutability betweenfinancial literacy and the demand for advice.

However, several other studies provide descriptive evidence that pointsto complementarity. Lusardi and Mitchell (2011a) show that individualswho correctly answer three financial literacy questions tend to use formaltools for retirement planning (attending a retirement seminar, using a cal-culator/worksheet, and consulting a financial planner) rather than informalones (talking to family, friends, and coworkers). van Rooij et al. (2011)find similar evidence in the Netherlands. They show that those who dis-play high levels of financial literacy are more likely to rely on formal sourcessuch as newspapers, financial advisors, and the internet.1 Hackethal et al.(2012) show that advisors are matched with wealthier and older investors,playing a role similar to the one of “babysitters” in the sense that they per-form a task that investors are better suited to perform themselves. Collins(2012) examines the issue of substitutability more explicitly using the 2009FINRA Financial Capability Survey and finds that individuals with higherlevels of financial literacy are more likely to seek financial advice than lessknowledgeable investors.

Few papers have tried to give a formalized theoretical explanation of thecomplementarity between financial literacy and advice.

Following the classic cheap-talk communication game of Crawford andSobel (1982), Dessein (2002) studies the choice of an uninformed principal(e.g., a customer) between delegating the investment decision to an informedagent (e.g., an advisor) with biased preferences and communicating with theagent while keeping authority. He shows that messages that suggest an ac-tion that goes in the direction of the agent’s bias contain more noise at equi-librium and are hence less informative. If the principal does not have prior

1Arguably, these “formal” sources might act misleadingly and resorting to them isnot necessarily a guarantee of sound financial decisions. In addition to the conflict ofinterest issue, investors might follow unscrupulous financial gurus or use unreliable internetadvisory websites and the financial press. However, these sources are still more likely toprovide valuable information than non-professional sources, such as friends, neighbors, andrelatives. This can be the case especially if individuals pair with similar people in termsof education and financial literacy (i.e, if low financial literacy investors have low financialliteracy friends), and if investment knowledge is shared through the social interaction withpeers (Hong et al., 2004; Duflo and Saez, 2002).

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information, Dessein (2002) proves that the principal is better off delegatingbecause the communication is extremely noisy compared to the agent’s bias.A key difference between our stylized model and Dessein (2002) is that inour case the bias of the advisor is not systematic; further, we are able toprovide a closed-form solution of the choice of delegation versus communi-cation when the principal’s initial information precision changes. Ottavianiand Sorensen (2006) study a communication game between an informed ex-pert who is concerned about his or her reputation and an uninformed client,who evaluates the expert’s advice comparing it ex post with the actual stateof realization. They find that an expert whose payoff depends solely on hisor her reputation never reports his or her information truthfully, but typ-ically biases the advice towards the evaluator’s prior belief. In contrast, inour model, advisors are concerned not only with their reputation but alsowith the fees they can earn selling the risky security. This concern in turn in-duces them to truthfully reveal their information when the benefit (in termsof expected fees) of hiding it is low.

Other papers focus on the investors’ characteristics, especially their so-phistication, and on how these affect the information transmission betweenthe informed advisor and the uninformed investors. Ottaviani (2000) allowsinvestors to differ with respect to their degree of strategic sophisticationand shows that the nature of the communication in equilibrium changesdrastically according to the investor’s naivety. Inderst and Ottaviani (2012)and Stoughton et al. (2011) assess how the investors’ sophistication affectsthe advisors’ optimal compensation structure. Inderst and Ottaviani (2012)show that in the presence of wary customers, product providers commit notto pay commissions (“kickbacks”) that bias advice, and the advisors chargea high fixed fee for the advice. In our stylized model, we do not analyze therelation between providers of the financial asset and advisors and implicitlyassume that providers cannot commit to not pay a rebate to the advisors inthe case of a product sale. Stoughton et al. (2011) study the effects of differ-ent pay schemes for financial advisors in a model where portfolio managerspay kickbacks to the advisors to push the sale of their funds. As in Inderstand Ottaviani (2012), Stoughton et al. (2011) distinguish between sophis-ticated investors and unsophisticated ones who can be persuaded to investin suboptimal assets by the advisor. They prove that kickbacks subsidizethe cost of advice to small, sophisticated investors and support aggressivemarketing by the advisor to unsophisticated ones. In their paper, there isno communication game between advisors and investors; because the latter,if they choose to invest through advisors, simply delegate their investmentchoice fully.

A number of studies consider other investors’ characteristics. Geor-garakos and Inderst (2011) show that the investors’ decision to rely on theadvisor’s recommendations also depends on their perception of their ownfinancial capability. Investors participate in the stock market and rely on

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professional advice only when their own perceived financial capability issufficiently low and their trust in the advisor is sufficiently high. On thecontrary, investors who believe they are well informed enter the stock mar-ket but disregard the advice. Hackethal et al. (2010) introduce the investors’knowledge of financial matters and their perception of the advisor’s conflictof interest in a cheap-talk game. In contrast with us, they do not focus on theinvestors’ decision to consult an advisor, but rather study the investor’s deci-sion to follow the advisors’ recommendation. They show that both financialknowledge and the perception of conflicts of interest reduce the likelihoodthat the investor follows the advisor’s recommendation. Bucher-Koenen andKoenen (2010) provide a theoretical model of the demand for advice show-ing complementarity between the investor’s degree of sophistication and theadvisor’s quality of advice. In their model it is assumed that investors withbetter financial knowledge understand advice more frequently. This in turnprovides the advisor with more incentives to exert high, costly effort and tofind better investment alternatives for the more knowledgeable investors. Onthe contrary, in our framework the complementarity between the investors’information and the quality of advice arises at the equilibrium of the model,and it holds even if investors are able to fully understand the advice.

However, the idea that more knowledgeable investors demand advice isalso the conclusion of the psychological research. This literature points tothe fact that individuals who do not know much about a subject tend not torecognize their ignorance and so fail to seek better information. Relativelyless knowledgeable people are more likely to overestimate their abilities andas a consequence of their incompetence, they also lack the metacognitiveability to realize it (Kruger and Dunning, 1999). This effect appears to bepresent also in the financial domain (Forbes and Kara, 2010).

2 A stylized model

In this section, we describe a stylized model that provides empirical impli-cations regarding the relation between the degree of financial literacy andthe investors’ choice to delegate or to consult a financial advisor. We referto Appendix A for a full analysis and to Appendix B for the proofs.

The model has two agents: a financial intermediary (A, he) who simul-taneously sells a risky financial product and provides advice to clients, andan investor-customer (B, she). Our financial intermediary represents a pro-fessional advisor working for a bank or a mutual fund company who sellsmanaged accounts to individual investors. The latter in turn plays the roleof a potentially uninformed customer. The investor, who has mean-variancepreferences, chooses the optimal allocation of her initial wealth between twofinancial securities, a risky and a riskless asset. Advisor A knows the futurerealization of the risky asset’s return r perfectly, while the investor only

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knows its initial probability distribution. Investor B is fully aware of theinformational advantage of the advisor and rationally anticipates that thelatter might have an incentive not to truthfully communicate information inorder to sell the risky security. In other words, B understands the conflictof interest with A, as do wary investors in Inderst and Ottaviani (2012).

Advisor A’s payoff depends on B’s investment decision and consists ofa commission fee f > 0 proportional to the quantity of the risky asset soldto B, as in rebate-based compensation schemes dominant in the mutualfund industry. We also assume that A pays a penalty for misselling (as inBolton et al. 2007; Inderst and Ottaviani 2009; Carlin and Gervais 2009)when his investment decision imposes a loss to the investor if A is delegatedand when he does not provide the correct advice. This penalty representsthe reputational cost, the expected legal costs for litigation procedures, orthe monetary costs of forgone customers.

The timing of the model is the following (see also a graphical repre-sentation in Figure 1). First, B chooses the optimal precision of a privateinformative signal about the risky asset’s return. Because the cost of ac-quiring such precision decreases with the degree of financial literacy of theinvestor, a more financially literate one collects more information about therisky security than a poorly literate one.2

Investor B then decides whether to delegate her portfolio choice to Aor not. If B delegates, then A chooses the share of the investor’s initialwealth to invest in the risky asset on her behalf. If B does not delegate,then she observes the realization of a private signal and updates her beliefdistribution over the risky return r accordingly. Then, B chooses whetherto autonomously select the fraction of wealth to invest in the risky asset(we call this “she invests by herself”) or to ask A for further informationabout the realization of r (we call this “she asks for advice”). If B asks foradvice, then A and B engage in a communication game in which the beliefs,hence the investment decision, of B might change due to the communicationstrategy of A.

At the last stage, the return r is realized, and the payoffs are distributed.

We solve the model backward, starting from the communication gamebetween the advisor and the investor. Our main result (see Proposition 1 inAppendix A) shows that the advisor does not reveal additional informationto the investor with relatively coarse information of her own. On the con-

2According to some definitions (see for example Mason and Wilson, 2000), financialliteracy is defined as “the ability of an individual to obtain, understand and evaluate therelevant information necessary to make decisions,” and various empirical works show apositive relation between the level of financial literacy of individuals and their ability tocorrectly process financial information. For example, Hastings and Tejeda-Ashton (2008)show that financially illiterate individuals face higher costs of interpreting information inan experiment concerning the choice among social security funds in Mexico.

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trary, investors who enter the communication game with a relatively precisesignal over the risky asset’s return receive extra information when they con-sult a professional advisor. Financial advisors then have a regressive effecton the distribution of information among investors. They increase the infor-mation of the relatively more informed ones but do not provide additionalinformation to the less informed. In an audit study of the market for advice,Mullainathan et al. (2012) find that advisors, if anything, do not correct thesuboptimal investment decisions of their customers.

Because investors are able to anticipate the informativeness of advice,professional advisors are consulted only by sufficiently informed investors(Corollary 2). This in turn suggests that the lack of use of financial advice(reported for example by Bhattacharya et al., 2012) is not only related to abiased or costly supply, but also to the demand side. Empirically, we predictthen that investors with higher financial literacy are more likely to consultfinancial advisors, in line with the evidence described above (Lusardi andMitchell, 2011a; van Rooij et al., 2011).3

These results also imply that only well-informed investors are able to im-plement the first-best investment decision by consulting a financial advisor.Instead, less informed investors might suffer ex post losses – whether theydecide autonomously or ask for advice – precisely because they are not suffi-ciently informed to obtain meaningful advice from professionals. Hence, thestrategic communication between the advisor and the investor has a strongregressive effect not only on the distribution of the information but also onthe welfare of investors.

Given that the investor payoff both from asking for advice and frominvesting autonomously increases with more precise prior information, onlypoorly informed investors delegate their portfolio decision to advisors, asshown in Proposition 3. On the contrary, well-informed investors neverchoose to delegate. This latter finding is analogous to Dessein (2002) inwhich a relatively well-informed principal is better off communicating ratherthan delegating its choice to the agent.4 This last result implies that poorly

3This framework does not analyze the optimal reaction of advisors who anticipate thatthey will be consulted only by more knowledgeable investors. However, taking this intoaccount does not modify the complementarity between the financial literacy/informationand the quality of advice. If advisors anticipate that only more knowledgeable investorswill ask for their advice, then they will commit to provide these clients with additionalinformation in order to satisfy such a demand. Facing better informed investors, advisorswill then earn higher fees in equilibrium.

4However, the strategic rationale behind this result is different in Dessein (2002). Awell-informed principal prefers communication rather than delegation because even if thecommunication is not informative, the portfolio allocation he chooses by himself dominatesthe delegation. In our model, he prefers to communicate because this provides him withmore information.

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informed investors end up again being worse off than more informed onesbecause they obtain a portfolio allocation that does not necessarily corre-spond to the optimal portfolio from their point of view.

Our model also shows (in Proposition 4) the effect of financial literacyand wealth on the acquisition of private information. The investors witha higher degree of financial literacy acquire a relatively more precise signalso that they can then obtain informative advice, while investors with alower degree of financial literacy acquire no private information becausebeing aware of and understanding financial concepts is too costly for them.They then end up investing based on their own judgment or delegating.Ceteris paribus, richer investors collect more precise private information(as in Peress, 2004) because thanks to this information they obtain betteradvice.

The reasoning behind the predictions on the effect of wealth are some-what less clear. Only low-wealth investors choose to delegate because anypotential loss induced by delegation is proportional to their wealth. Moreinterestingly, as her initial wealth increases, an investor is more willing toacquire private information and to demand advice. The result that higherwealth associates with a higher propensity to seek financial advice or to in-vest through advisors/brokers has been documented extensively in the em-pirical research, see Hackethal et al. (2012) and Bhattacharya et al. (2012)about Germany, as well as Lee and Cho (2005) and Marsden et al. (2011)about the United States.

Finally, the model examines how the degree of financial literacy and thelevel of initial wealth affect the decision to hold the risky asset. In Corol-lary 5, we prove that rational investors with a very low degree of financialliteracy and low initial wealth do not participate in the market for riskyfinancial securities. Non-participation derives from the fact that for theseinvestors the cost of obtaining private information is too high and participa-tion exposes them to a high risk of portfolio losses. The empirical literatureprovides evidence that investors with low financial literacy and high costsfor gathering and processing information are less likely to participate in thestock market (van Rooij et al., 2011; Christelis et al., 2010). Similarly, theempirical literature supports the idea that wealthier investors are more likelyto hold risky assets (Haliassos and Bertaut, 1995; Guiso et al., 2001).

To summarize, our stylized model provides a number of empirical impli-cations. The empirical analysis that follows is based on these implications:

1. investors with the lowest degree of financial literacy and low initialwealth are less likely to invest in risky assets, even if (i) the transactioncosts for trading the risky assets are relatively low, and (ii) if financial

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advisors might provide them with additional information about therisky asset

2. investors with lower financial literacy are more likely to delegate theirportfolio choice or to choose their portfolio autonomously (conditionalon investing in risky assets) than investors with high financial literacy

3. investors with higher financial literacy are more likely to consult fi-nancial advisors than investors with a low degree of financial literacybecause they anticipate that they will receive valuable informationfrom advisors

4. wealthier investors are more likely to consult advisors than less wealthyones, because the former collect more precise private information andas a result they obtain better advice

3 Empirical analysis

3.1 Data and descriptive statistics

The Unicredit Customers’ Survey (UCS) is a representative sample of thecustomers of the largest Italian bank (Unicredit group). Eligible intervieweesare account holders with at least 10,000 euro in the bank at the end of 2006.The survey provides detailed information on the demographic characteristicsof account holders and of their household members, including their labormarket position, income, and household wealth (financial wealth, real assets,insurance policies, and pensions).5 Additionally, account holders are askedabout their relation with the bank, their attitudes towards investments, andtheir level of financial literacy.

The sample selected for the analysis includes only the account holderswho report that Unicredit is their main or only bank. From the original sam-ple of 1,686 observations, 1,581 are retained, while observations for whichUnicredit is not their main bank are dropped. Appendix C contains a de-scription of the main variables used in the analysis and Table 1 reports thesummary statistics. Respondents to the sample are on average 55 years oldand about 33% are females, 32% are employees, 28% are self-employed, and33% are retired; they earn an average (total) individual income of about50,000 euro per year, and almost half of the sample has been a customer ofUnicredit for at least 20 years.

5Analyzing respondents who are customers of the same bank has advantages and dis-advantages. One drawback is that the choice of the bank is certainly not random, andit might be driven by the same factors that affect the extent of reliance on the bank asa source of advice. This selection cannot be controlled for. Moreover, cross-bank hetero-geneity cannot be used to explore, for instance, cost effects. On the positive side, analyzingcustomers of the same bank reduces unobserved heterogeneity (for instance in terms ofthe cost and type of advice provided).

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The rationale for concentrating on financial intermediaries as providersof advice has to do with the fact that they represent an important source offinancial information not only in Italy but also in other European countriesand in the United States. A survey representative of Italian adults holdingan account at a financial institution shows that in the period of 2001 to2007 about half of the respondents mentioned banks as their most importantsource of financial information and advice (see Beltratti, 2007). Data fromthe Survey of Consumer Finances show that in the United States, financialintermediaries were also important sources of financial information (afterfamily and friends): during 1998 to 2007, more than 30% of the respondentsmentioned bankers and brokers as sources of information for investmentdecisions.

Table 2 reports the respondents’ demand for financial advice (see Ap-pendix C for a full description of the dependent variable). About 11% ofthe respondents that hold risky assets report that they decide completelyby themselves about their investments, 69% ask for their advisors’ recom-mendations before forming their own decisions, while almost 20% delegatemost or all of their decisions to their advisors. These three groups are de-fined respectively as Self, Advice, and Delegation in the rest of the empiricalanalysis.

Our financial literacy measure is constructed as in Guiso and Jappelli(2008) and equals the number of correct answers to eight questions on inter-est, inflation, understanding of risk diversification, and the understandingof the riskiness of various financial products. The wording of the tests isreported in Appendix C and Table 3 displays the answers. The averageindex corresponds to 4.7 correct questions out of 8, and less than 1% ofthe sample can answer all of them correctly. The overall distribution of thecorrect answers is hump-shaped and is displayed in Figure 2.

3.2 Empirical strategy

We concentrate on the relation between investors and professional advi-sors. Table 2 shows that investors choosing to consult advisors (Advice)have higher financial literacy than those who invest by themselves (Self),or delegate. More precisely, the financial literacy index of bank customerswho consult advisors is 1% higher than that of customers who decide au-tonomously, and 10% higher than those who delegate. This difference isrelatively sizeable: as a matter of comparison, the financial literacy of re-spondents with at least a university degree is 9% higher than the financialliteracy of respondents without a degree. In what follows, we investigatewhether this finding is confirmed in a multivariate analysis.

We first examine jointly the choices of relying on advisors and of holdingrisky assets, to reflect the structure of the theoretical model. Given thatthe UCS asks about the demand for advice only to respondents who hold

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risky assets, we estimate the following generalized ordered probit model withsample selection:6

P (Pi = 0) = Φ(−Zγ)

P (Pi = 1;Ai = 1) = Φ2(Zγ, κ1 −Xβ1,−ρ)

P (Pi = 1;Ai = 2) = Φ2(Zγ, κ2 −Xβ2,−ρ)− Φ2(Zγ, κ1 −Xβ1,−ρ) (1)

P (Pi = 1;Ai = 3) = Φ(Zγ)− Φ2(Zγ, κ2 −Xβ2,−ρ)

where Pi represents participation (i.e., Pi = 1 if the respondent holds riskyassets and zero otherwise) and Ai represents the demand for advice (i.e.,Ai = 1 for Self, Ai = 2 for Advice, and Ai = 3 for Delegation). TheΦ2(·) is the joint cumulative distribution of the bivariate normal. Differentlyfrom standard ordered probit models, the generalized ordered probit allowsthe parameters βj (j = 1, 2) to vary across alternatives by generalizing thethreshold parameters κj (j = 1, 2) by making them dependent on covariates:

κj = κj +Xγj j = 1, 2

Hence, the parameters βj in (1) are defined as βj = β − γj .The X is a vector of explanatory variables that includes financial lit-

eracy, self-confidence (self-assessed financial literacy), trust in the advisor,time preference (patience), experience in trading financial products, lengthof the bank relationship, whether the respondent works in the financial sec-tor; as well as socio-demographic controls (gender, age, years of education,occupational status, log individual income, financial wealth categories, andmacro regions of residence). The Z is a vector of explanatory variables thatcomprises the same variables as in X with an additional variable used toidentify the model. The exclusion restriction (i.e., the additional variable invector Z) is the investor’s risk preference, based on the idea that it affectsthe propensity to hold risky assets, but it is not obviously related to thedemand for advice.

3.3 Baseline results

The first column of Table 4 reports the marginal effects of the covariates onthe probability of participation. Financial literacy increases the probabilityof holding risky assets, as predicted by our stylized theoretical model and asfound by van Rooij et al. (2011). Also higher wealth increases the probabilityof holding risky assets, as predicted by our model. The effect of the othercovariates is in line with the expectations from the literature. The investorswho trust their advisors are more likely to participate, which is in line with

6See Greene and Hensher (2010); Boes and Winkelmann (2006); Terza (1985) for adescription and discussion of the generalized ordered probit model.

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the evidence that the lack of trust in the financial system and financialintermediaries reduces the probability of holding risky assets and pensionplans (Guiso et al., 2008; Georgarakos and Pasini, 2011; Agnew et al., 2012).A higher participation probability exists among respondents with higher self-assessed financial knowledge, higher patience, longer experience, a longerrelationship with the bank, higher education, and a higher risk tolerance.

The second to fourth columns of Table 4 report the (conditional) proba-bility of choosing one of the three options related to the demand for advice,as in model (1). The most interesting result is the effect of financial literacyon the investors’ choice across Self, Advice and Delegation, as shown in Table2 and consistent with the theoretical predictions derived from our stylizedmodel (Section 2). Higher financial literacy increases the probability of con-sulting the advisor (an additional correct answer increases the probability ofasking for advice by about 3 percentage points) and reduces the probabilityof delegating (an additional correct answer reduces the probability of dele-gation by 2 percentage points). Financial literacy does not statistically andsignificantly affect the probability of investing autonomously, even thoughthe marginal effect has a negative sign.7

Other interesting results emerge from Table 4. Self-assessed financialknowledge is sometimes used as a measure of the actual financial knowl-edge (Hung et al., 2009, review various studies that analyzed self-reportedfinancial literacy in addition to a test-based measure), and indeed it is of-ten correlated with objective measures of financial knowledge (Guiso andJappelli, 2008; van Rooij et al., 2011). However, Guiso and Jappelli (2008)cross-tabulate the distributions of self-assessed and objective financial liter-acy, showing sizeable proportions of over confident respondents (e.g., theiractual knowledge is lower than what they think) or under confident ones(e.g., their actual knowledge is higher than what they think). Our resultsshow that the two measures have different and independent impacts on thedemand for financial advice. Differently from the effect of objective financialliteracy, investors with higher self-perceived financial knowledge are morelikely to invest their assets while relying on their own judgment, and lesslikely to delegate to an advisor. This finding confirms the idea that self-assessed and objective financial literacy have a different effect on financialbehavior. Moreover, our result supports the theoretical predictions of Geor-garakos and Inderst (2011) who find that households rely on professionaladvice when their perceived financial capability is sufficiently low.

Trust is also an important explanatory factor, because the market forfinancial advice is affected by conflicts of interests, and misselling practicesmight occur. In our results, the investors’ trust towards their advisors in-creases the likelihood of delegation and reduces that of autonomous invest-

7Quantitatively similar findings result from estimating a non-ordinal model, such as amultinomial logistic regression (not reported, but available from the authors on request).

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ment.The time preferences have been added to the analysis with the control

variables as a way to mitigate the potential endogeneity problems, becausethey are likely to be correlated both with financial literacy (as shown inMeier and Sprenger, 2013) and with the demand for advice (as long as morepatient individuals are more willing to spend time to decide about theirfinancial investments). The effect of patience on the demand for adviceturns out to be not statistically significant.

Both the experience in dealing with risky assets and the years of ed-ucation are positively correlated with self-assessed financial literacy: thecorrelation coefficients of both variables with self-assessed financial literacyare about ρ = 0.3, significant at the 1% level. We expect both variablesto increase the probability of investing autonomously. Indeed, more yearsof education increase the probability of investing autonomously and reducethat of delegation. In contrast, experience does not have a statistically sig-nificant impact on the choice across Self/Advice/Delegation. This result isnot at odds with the literature, which does not give clear results on the effectof experience on the demand for advice (possibly because previous studies donot disentangle the effect of experience from that of age, see Collins, 2012;Elmerick et al., 2002; Finke et al., 2011; Hackethal et al., 2012; Marsdenet al., 2011).

The investors that work in the financial sector are less likely to dele-gate and are more likely to invest autonomously. Investors who have beenUnicredit customers for more than ten years are more likely to invest bythemselves than more recent customers. The investors who have been cus-tomers for more than 20 years are less likely to ask for advice than recentcustomers. The length of the relationship with the bank does not have astatistically significant effect on delegation.

The fact that women are more likely to delegate is not easy to inter-pret. Their higher propensity to delegate might be an indirect effect ofself-confidence: because women are typically less overconfident than men(Barber and Odean, 2001), they might be less prone to invest autonomously.

Some of the remaining controls might be considered as proxies for theinvestors’ opportunity cost of time, such as their occupational status or theirindividual income. Hackethal et al. (2012) show that advisors tend to bematched with wealthier and older investors, who presumably delegate theirinvestment decisions (also) because of the high opportunity cost of time.Lee and Cho (2005) find that the high opportunity cost of time increases thelikelihood of using information intermediaries. However, in our estimationhaving higher income, being self-employed, or being retired does not affectthe probability of investing autonomously, asking for advice, or delegating.

Higher financial wealth (above 50,000 euro) appears to be related toa lower probability of investing autonomously (even though not all wealthcategories are significant). The prediction that wealthier investor should

14

be more likely to ask for advice is not supported by our results becausefinancial literacy does not affect the probability of consulting an advisor.Higher wealth (weakly) increases the probability of delegating.

3.4 Robustness checks

Model 1 estimates jointly a participation equation and an equation relatedto the demand for advice. The results presented in Table 4 indicate thatthe correlation coefficient between these two equations is not statisticallydifferent from zero. For this reason, the rest of the paper focuses only onthe results that concern the demand for advice obtained from estimatingthe following (independent) generalized ordered probit:8

P (Ai = 1) = Φ(κ1 −Xβ1)

P (Ai = 2) = Φ(κ2 −Xβ2)− Φ(κ1 −Xβ1) (2)

P (Ai = 3) = 1− Φ(κ2 −Xβ2)

where Ai represents the demand for advice (i.e., Ai = 1 indicates that therespondent invests by herself, Ai = 2 that she asks for advice, and Ai = 3that she delegates), and Φ(·) is the cumulative normal distribution. Table 5reports the marginal effects from model (2) and shows that the main resultsare quantitatively very similar to those of Table 4.

The rest of this section presents a number of additional analyses to verifythe robustness of the main results of Tables 4 and 5. The robustness checksinvolve: i) the potential endogeneity of financial literacy; ii) the potentialendogeneity of trust towards the advisor; and iii) the selection of the sam-ple, the definition of the dependent variable (demand for advice), and theconstruction of the main explanatory variable (financial literacy).

3.4.1 Potential endogeneity of financial literacy

The fact that financial literacy is empirically associated with the tendencyto consult rather than to delegate to professional advisors does not necessar-ily provide indications on the direction of the causality. Financial literacymight be positively correlated with a preference for advisors because individ-uals learn from advisors, rather than because financially literate individualschoose them. In other words, investors who consult professional advisorsmight be more likely to learn from them than those who delegate or investautonomously. Moreover, endogeneity might also arise from unobserved fac-tors (different from the time preferences that have already been taken intoaccount) driving both the willingness to acquire financial literacy and thedemand for financial advice.

8This analysis is carried out on the sample of 1,116 observations that hold risky assets.

15

Model (2) is estimated again by allowing for potential endogeneity viathe control function approach (Rivers and Vuong, 1988).9

The instrumental variable for financial literacy is the previous experiencewith financial products. The measure of the previous experience is based ona question that asks at what age the individual first traded a given financialproduct (either government bonds, stocks, or mutual funds). The previousexperience is strongly related to financial literacy, but it is not related tothe demand for advice (controlling for age and the length of the bank re-lationship, see Table 5). The upper part of Table 6 reports the estimatesfrom a first-stage regression that shows that the experience positively andsignificantly affects financial knowledge.10 The results from the lower partof Table 6 show that the positive relation between financial literacy and thepropensity to consult an advisor is robust to potential endogeneity. Theeffect of financial literacy on delegating turns nonsignificant even thoughit carries the same sign as before. Moreover, estimating the coefficient onthe fitted residuals allows us to test financial literacy’s exogeneity. The factthat the marginal effects of the residuals are not significant supports thenull hypothesis that financial literacy is exogenous.

3.4.2 Potential endogeneity of trust towards the advisor

The trust towards financial advisors might be endogenous with respect to thechoice of consulting/delegating. Endogeneity can arise if investors increasetheir trust because they delegated in the past and were satisfied with theadvice received, or if respondents try to rationalize ex post their delegationbehavior when answering the trust question.

We try to address this issue by resorting to instrumental variables asabove and estimating model (2) by allowing for potential endogeneity via thecontrol function approach (Rivers and Vuong, 1988). The data set containstwo variables that gauge the respondents’ trust towards people in generalwith no reference to their relationship with the bank or the bank’s advisor

9When estimating a probit model with a continuous endogenous variable, the two-stepapproach from Rivers and Vuong (1988) consists of saving the residuals from the first-stageregression and then plugging them into the structural probit equation. This procedure canbe extended to ordered probit response models (Wooldridge, 2007) and can analogouslybe extended to a generalized ordered probit model because the generalization does notaffect the error term of the discrete choice equation.

10As an alternative specification, we use two instrumental variables for financial literacy:experience and the average financial literacy at the regional level (taken from the Bank ofItaly’s SHIW). The regional financial literacy can increase individual knowledge throughsocial interaction (Bonte and Filipiak, 2012). Both experience and regional financial lit-eracy positively and significantly affect the financial knowledge of Unicredit customers.Moreover, the two instruments allow for the computation of the Sargan-Hansen test ofthe over-identifying restrictions with the joint null hypothesis that the instruments arevalid. The Hansen’s J-test does not reject the null hypothesis of the instruments’ validity(p-value 0.132)

16

(the exact wording is reported in Appendix C). As shown in Table 7, thesevariables are strongly correlated with trust for the advisor (upper panel),and the effect of trust on the demand for advice is consistent with previousresults (lower panel). Higher trust towards the advisor increases the proba-bility of delegation, but has no statistically significant impact on investingautonomously. Again, the marginal effects of the fitted residuals are notstatistically significant, which supports the null hypothesis that trust in theadvisor is not endogenous.

3.4.3 Robustness on sample selection and the definition of themain variables

The first robustness check has to do with the sample used for estimation. Aspreviously mentioned, the estimation sample includes only the observationswhere Unicredit is the main or only bank (excluding about 6% of the totalsample). We repeat the estimation of model (2) by using alternative samples(details in Appendix D). The estimates from Table 8 show that the resultswith all of the alternative samples are very similar.

Another robustness check is related to the definition of the dependentvariable. The dependent variable used in the analysis is constructed byusing a variable contained in the data set (we refer again to Appendix D forthe exact wording). If one defines as Di how much the investor i relies onthe advisor, then the dependent variable is defined as a Self/Autonomousdecision if Di = 1, Advice if Di = 2 or Di = 3, or a Delegation if Di = 4or Di = 5. Table 9 reports the results for financial literacy if the dependentvariable is instead defined as a Self/Autonomous decision if Di = 1 or Di =2, Advice if Di = 3, or a Delegation if Di = 4 or Di = 5. The size of themarginal effects is about the same as in Table 5.

A final robustness check has to do with the construction of the finan-cial literacy index. As discussed in subsection 3.1, our financial literacyindex is constructed as in Guiso and Jappelli (2008). This index equals thenumber of correct answers to four questions about interest, inflation, andrisk diversification, plus four questions based on understanding the riskinessof various financial products. The construction of the index involves somedegree of arbitrariness, and the index itself might be overly dependent onsome specific question(s). As a robustness check, we again estimate model(2) with alternative financial literacy indices. Appendix D reports the de-tails of these indices. Table 10 reports the estimation results that showthat the effect of financial literacy is qualitatively the same across three outof the four alternative indices, but in one case the results are nonsignificanton almost all of the values of the dependent variable.

17

3.5 Summary of empirical findings

Our empirical results confirm most of the testable implications derived fromthe theoretical model (as summarized at the end of Section 2):

• concerning stock market participation, investors with higher financialliteracy and higher wealth are more likely to invest in risky assets

• investors with higher financial literacy are more likely to consult fi-nancial advisors than investors with a low degree of financial literacy(conditional on investing in risky assets)

• investors with higher financial literacy are less likely to delegate theirportfolio choice (conditional on investing in risky assets), as predicted.However, the degree of financial literacy does not affect the probabilitythat investors choose their portfolio autonomously

• Wealthier investors are less likely to invest by themselves than lessaffluent ones, and (weakly) more likely to delegate. Wealth does notappear to affect the probability of consulting the advisor

4 Discussion and concluding remarks

In this paper, we analyze the effect of the investors’ financial literacy ontheir decision about whether and how much to rely on financial advisors.The data set we use offers the opportunity to closely examine the relationbetween the consumers’ characteristics, such as their financial knowledgeand their demand for advice. The results do not hinge on any peculiarity ofthe Italian market and can be of relevance to other developed countries inEurope and the United States.

Our empirical findings show that a high degree of financial literacy in-creases the probability of consulting an advisor, and it reduces the probabil-ity of delegating the portfolio choice. This result holds even after controllingfor a number of factors such as the investor’s wealth, age, experience withfinancial products, opportunity cost of time, trust in the advisor, years ofeducation, self-confidence in his or her financial ability, and the quality ofadvice. Our results are also robust to potential endogeneity.

To explain the effect of financial literacy on the investors’ willingness toconsult advisors, we present a highly stylized model of strategic interactionbetween an informed advisor who at the same time sells a risky financialproduct and provides information to the investor, and a less informed in-vestor. Our model shows that advisors are not informative towards thepoorly informed investors, while they provide valuable information only tothe relatively more informed ones. This insight implies that advisors are notuseful to the investors who need them the most because they fail to be a

18

substitute for self-learning. If investors know the advisor’s selling incentives,then the advisors are visited only by sufficiently knowledgeable investors whocorrectly anticipate they will receive meaningful information. On the con-trary, low financial literacy investors either delegate or invest autonomouslyand the ones among them with the lowest initial wealth might not invest inthe risky assets at all.

The analysis carried out in this study is relevant for both scholars andpolicy makers because it addresses timely policy issues and contributes tothe recent literature on the substitutability versus the complementarity of fi-nancial literacy and advice. The concerns about the lack of financial literacymight be less worrying if individual gaps were compensated for by externaladvice coming from reliable and qualified sources. However, our findingssuggest that the presence of qualified sources of advice that suffer agencyconflicts might not be enough to counteract the effects of the low level offinancial literacy. This possible result implies that further policy measuresmight be needed to ensure sound financial decision making. For instance,our results provide a rationale for financial education initiatives, especiallyfor the segments of the population that have the highest cost of acquiringfinancial literacy. The results further suggest that learning about finance isnecessary in order to make the right financial decisions even in the presenceof qualified financial advisors. At the same time, we show that there is scopefor interventions that reduce the conflicts of interests between intermediariesand clients and that subsidize the supply of independent advice.

5 Acknowledgements

We would like to thank Tabea Bucher-Koenen, Andrea Buffa, Paolo Cam-pana, Efrem Castelnuovo, Elsa Fornero, Maela Giofre, David Laibson, SamuelLee, Erwan Morellec, Giovanna Nicodano, Marco Ottaviani, Mario Padula,Yves Stevens, Gilberto Turati and two anonymus referees for their com-ments and suggestions. We also thank the participants at the XVIII andXIX International Tor Vergata Conferences on Money, Banking and Fi-nance (Rome, December 2009, 2010); the Annual International Conferenceon Macroeconomic Analysis and International Finance (Crete, May 2010);the II SAVE Conference (Deidesheim, June 2010); the 51st SIE confer-ence (Catania, October 2010); the Netspar International Pension Workshop(Turin, June 2011); Financial Innovation and Market Dynamics conference(Bocconi University; February 2012) and the EMLYON Business Schoolseminar participants for their comments and suggestions. Moreover, wewish to thank Laura Marzorati at Pioneer Investments for providing accessto the Unicredit Customers Survey. We kindly acknowledge financial sup-port from CeRP/CCA. The views and opinions expressed in this article arethe sole responsibility of the authors and do not necessarily reflect the of-

19

ficial policy or position of the OECD or of the governments of its Membercountries.

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A Full model description and its results

We consider a model with an advisor A (he) and an investor B (she).The investor B allocates her initial wealth W0 across two financial secu-

rities: a risky security (e.g. individual equity or an actively managed mutualfund) that earns a risky return r; and a riskless security (e.g. a Treasurybond or a passive money fund) that pays a risk-free return normalized tozero. The investor has mean-variance preferences over the final wealth allo-cation, and we denote with v the share of initial wealth that she invests inthe risky security. We assume that v ∈ [0, 1], that is, B cannot borrow toinvest in the risky security nor short-sell it.

Advisor A is better informed than B about the return of the risky se-curity. At the initial date, B only knows the probability distribution of thereturn r that for simplicity we assume is equal to:

f(r) =

{rH with prob. 1/2rL with prob. 1/2

where A can perfectly predict the future realization of r. We consider rH >0, rL < 0, and 1

2rH + 12rL > 0 in order to depict a situation where B might

incur real losses in the case of an ill-advised investment decision. And at thesame time, this excludes from our analysis risky securities that are surelydominated by the risk-free one.

A.1 Timing, strategies, and information sets

Our baseline model develops over five stages (as shown in Figure 1).

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At t = 0, the investor chooses the precision π ∈ [1/2, 1) of a privateand informative signal s ∈ {rH , rL}, that is, s is correct with probabilityπ = Pr(s = ri|ri) for i = H,L. Our previous assumptions on rH and rLimply that there is a precision π0 ∈ (1/2, 1) such that π0rL+(1−π0)rH = 0.11

In choosing π, B trades off the benefits of higher precision with the cost toacquire it. We assume that this cost increases and is convex in π and thatit also increases with the degree of financial illiteracy of B, k. For analytictractability, we consider an information collection cost equal to 1

2k(π − 1

2

)2.

At t = 0, the investor also decides whether to pay or not an entry fee ϕ > 0that represents a fixed transaction cost to enter the market for the riskysecurity, such as the fee to open an account or to obtain access to a bank’sbrokerage services.

If B enters the risky security market, then at t = 1 she decides whether todelegate to A her wealth management or not. If B delegates to A, then thelatter invests the share vdel(rH) (resp. vdel(rL)) ofW0 in the risky asset whenhe knows that rH (resp. rL) realizes. Given that rL < 0, if vdel(rL) > 0,then the investor suffers a loss ex post; and in such a case the advisor paysa reputational or a “misselling” cost (see Inderst and Ottaviani (2009)). Inchoosing vdel, the advisor trades off the benefit of selling the risky asset (acommission fee) with the misselling cost. If B does not delegate then att = 1, then she observes the private signal s = {rL, rH} and updates theprior beliefs distribution f(r) according to its realization.12

At t = 2, B chooses whether to autonomously select the fraction ofwealth to invest in the risky asset by using only the information containedin the private signal (in the following: invest by herself ) or to ask for furtherinformation about the realization of r to A. If B asks for information to A,in the following we say that she asks for advice.

If B invests by herself, her information set is IselfB = {π, s}. Due to themean-variance preferences and short-selling constraints, B’s optimal invest-ment in the risky asset is equal to

v∗(s) =

⎧⎪⎨⎪⎩

E[r∣∣∣IselfB ]

γW0V ar[r∣∣∣IselfB ]

if E[r∣∣∣IselfB ] > 0

0 if E[r∣∣∣IselfB ] ≤ 0

(3)

If insteadB asks for advice, then at t = 3 a communication game betweenA and B occurs. This game is similar to the one in Bolton et al. (2007) where

11The threshold π0 can be interpreted as the highest signal precision below which theinvestor buys the risky asset irrespective of the realization of the signal.

12This timing of decisions allows us to study how the delegation choice depends onthe degree of knowledge of the investor, as in Dessein (2002), without considering theeffect played by the signal realization. It also allows us to provide testable empiricalimplications about the choice of delegation: we cannot verify empirically if the delegationchoice depends on the investor’s ex post belief about the return of the risky asset.

25

the advisor aims to maintain a reputation for honest advice. Therefore, theadvisor suffers a reputational loss when lying to the investor.13

The information sets of the two players in this game are as follows.Because A knows the true realization of r, we say there are two types ofA = {A(rH), A(rL)}. Advisor A also knows the precision π of B’s signalbut not its realization14, while B knows both π and the realization of s.

As for the players’ strategies, A decides which message σ to send to B. Amessage from A is a mapping σ : {rH , rL} → � ({rH , rL}). Conditional onobserving A’s message, B updates her information set to IadviceB = {π, s, σ}and chooses her optimal portfolio allocation vadv(σ) given IadviceB .

Finally, at t = 4, r realizes and payoffs are distributed.

A.2 Payoffs

We start by describing the investor’s payoff if she enters the risky market inthe three cases where i) she delegates the portfolio choice, ii) she does notdelegate and invests autonomously, or iii) she does not delegate and asks foradvice.

If the investor delegates the portfolio decision to A, at t = 0 her expectedpayoff is equal to

EUdel = Ef(r)[rW0vdel(r)]− γ

2V arf(r)[rW0v

del(r)]− 1

2k

(π − 1

2

)2

−ϕ (4)

where vdel(r) ={vdel(rH), vdel(rL)

}denotes the share of risky asset that A

acquires on the investor’s behalf when rH (resp. rL) realizes.If the investor does not delegate and decides to invest autonomously,

then her optimal investment decision is given by v∗(s) in (3) and earns anexpected payoff of

EU self = Ef(r)[rW0v∗(s)]− γ

2V arf(r)[rW0v

∗(s)]− 1

2k

(π − 1

2

)2

− ϕ (5)

Thus,(5) is independent of the initial wealth W0 given B’s mean-variancepreferences.

13This game differs from the class of cheap talk games first studied by Crawford andSobel (1982) and used in the context of financial advice by Inderst and Ottaviani (2009),(2012). The crucial difference from cheap talk games is that in our model the preferencesof the advisor (the informed agent) are not systematically biased with respect to the onesof the investor (the uninformed principal). In our model, when r = rH , advisor A’s andinvestor B’s preferred actions coincide.

14We choose to relax the hypothesis that A knows the information contained in thesignal s. We prove that the set of equilibriums of the game in this case looks qualitativelylike the one presented in Proposition 1 (the proof is available from the authors uponrequest).

26

Further, if the investor does not delegate and subsequently asks for ad-vice, then her expected utility depends on the portfolio allocation vadv(σ)she will select given the advisor’s message σ:

EUadv = Ef(r)[rW0vadv(σ)]−γ

2V arf(r)[rW0v

adv(σ)]−1

2k

(π − 1

2

)2

−ϕ (6)

Advisor A’s payoff depends on the buyer’s investment decision. We as-sume that A earns a percentage commission fee (or a “rebate”) f ∈ (0, 1) forany dollar the investor B invests in the risky asset. If B invests the sharev ∈ [0, 1] of her initial wealth in the risky asset, then the total fee earned byA is then equal to fvW0.

We also suppose that A pays a penalty that represents a reputationalcost. If the advisor is consulted for advice, he pays this cost whenever hedoes not reveal his information truthfully since the investor knows he hasan information advantage: the reputational cost in this case is equal to(σA(ri)− ri)

2. If the advisor is delegated, then the penalty depends on theamount of the risky asset he buys on behalf of the investor. For analytictractability, we let this misselling cost be an increasing and convex penalty

function W02

(vdel

)2. If rH realizes, then we assume that A does not suffer

any cost under full delegation. The advisor’s payoff function becomes then:

UadvA (r) = fvadvW0 − (σA(r)− r)21{σA(ri) �=ri, ∀ri={rH ,rL}} in case of advice

UdelA (r) = fvdelW0 − W0

2

(vdel

)21{rL} in case of delegation

(7)where the indicator function 1{ω} equals one if event ω realizes and zerootherwise.

Given the objective (7), A’s optimal behavior under delegation is:

if rH : buy the maximum amount of risky asset, vdelH = 1if rL : buy an amount vdelL = f

(8)

In order to restrict the analysis to the cases where a conflict of interestbetween A and B arises, we impose the following assumption.

Assumption 1: γ(rH−rL)4

2(rH+rL)≤ f ≤ γπ0(rH−rL)

4

π0rH+(1−π0)rL.15

Furthermore, A and B know each other’s payoff functions (4), (5), (6)and (7); that is, B is perfectly aware of the conflict of interest with A.

A.3 The solution of the model

We start by analyzing the communication game taking place at t = 3 in caseB asks for advice.

A Perfect Bayesian equilibrium (PBE) in this game is defined as a set ofstrategies (σ∗, vadv) and beliefs p = Pr(rH), p : {rL, rH} → [0, 1] such that:

15The interval is non-empty if rH > 1−3π0π0

rL, that is, if rH is sufficiently higher than|rL|.

27

(i) for both types A(ri), ri = {rL, rH}, σ∗ maximizes UadvA (ri) as in (7)

given B’s optimal investment decision vadv;

(ii) B’s optimal investment decision vadv corresponds to (3) given the in-formation set IadviceB = {π, s, σ∗};

(iii) the belief distribution (p, 1−p) is rational and consistent with σ∗, thatis, p = Pr(rH |π, s, σ∗ ).16

We show that this equilibrium critically depends on the level of π, thatis A’s communication behavior is different depending on the accuracy of theinformation owned by B.

Proposition 1: If Assumption 1 holds, then the information revelationgame at t = 3 admits

(i) a unique pooling PBE (σ∗(rH) = rH ;σ∗(rL) = rH) if π ∈ [1/2, π0);(ii) a unique fully informative PBE (σ∗(rH) = rH ;σ∗(rL) = rL) if π ∈

[π0, 1).Point (i) of Proposition 1 shows that the advice to buy the risky asset,

which corresponds to message σ∗ = rH , contains less information than theadvice not to buy it, that is, σ∗ = rL. This is because the investor knowsthat A is biased towards recommending the risky asset and anticipates thatsuch a recommendation has less value. The same effect is present in Dessein(2002): the messages that go in the direction of the agent’s bias are morenoisy at equilibrium.

Next, we determine B’s choice to invest by herself or to ask for adviceat t = 2, anticipating the equilibrium in the communication game describedin Proposition 1.

Corollary 2: At t = 2:(i) if π ∈ [1/2, π0), then the investor is indifferent between consulting

the advisor or not. For any arbitrarily small cost of advice, the investor doesnot consult the advisor.

(ii) if π ∈ [π0, 1), then the investor strictly prefers to consult the advisor.Because investors are able to anticipate the informativeness of A’s sig-

nal at equilibrium, professional advisors are consulted only by sufficientlyinformed investors who know they will receive meaningful information fromthem.

Anticipating this behavior, we characterize B’s choice to delegate herinvestment decision to A or not at t = 1. In the following, we considerinvestors whose risk aversion is sufficiently low:

Assumption 2: Let γ < 4(rH−rL)(vH−vL)

W0(r2H−r2L)(v2H−v2L)

.

16We make use of the intuitive criterion of Cho and Kreps (1987) in order to restrictthe out-of-equilibrium beliefs.

28

Proposition 3: If Assumption 1 and 2 hold and f ≥ (1 − π0)rH

(−rL),17

at t = 1:(i) if the information precision is π ∈ [1/2, π0) then

(i.a) investors with initial wealth W0 ≥ W ′ do not delegate.(i.b) investors with initial wealth W0 ∈ [W ′′,W ′] with W ′′ < W ′

delegate only if the precision of their information is π ∈ [12 , π

t), where

πt < π0, otherwise they do not delegate if π ∈ [πt, π0

).

(i.c) investors with initial wealth W0 < W ′′ always delegate theirportfolio choice.18

(ii) if their information precision is π ∈ [π0, 1), then investors alwaysprefer not to delegate.

The interpretation of the above proposition goes as follows. Considerfirst less informed investors with π ∈ [1/2, π0). They are better off suffer-ing the bias in the decision due to delegation rather than asking for advicebecause they anticipate that the advice contains no information. Moreover,because the expected payoff they obtain investing autonomously increaseswith more precise prior information, delegating is relatively less attractivethan investing by themselves when the precision of their information in-creases. Also, ceteris paribus, rich investors with relatively imprecise infor-mation prefer not to delegate because the risk they are exposed to whendelegating is higher, being proportional to the (square of) their wealth level.Well-informed investors (π ∈ [π0, 1)), on the contrary, anticipate informativeadvice (Proposition 1) and hence do not delegate their portfolio choice.

A.4 The effect of financial literacy on the optimal signal pre-cision and on participation

Given the subsequent rational choices described in Proposition 1, Corollary2, and Proposition 3; at t = 0, B decides the optimal signal precision π∗

she wants to acquire as well as whether to pay or not the transaction feeϕ to buy the risky asset. We assume that B first chooses whether to payϕ and afterwards selects π∗ so that at the moment of selecting the optimalprecision ϕ is sunk.

Proposition 4: Suppose that k ≥ max{k, 4πrHW0

2π−1

}, and for an investor

with initial wealth W0 < W ′ (resp. W0 ≥ W ′), define k′ (respectively k′′) asthe threshold level of k that makes her indifferent between delegating (resp.investing autonomously) and asking for advice.19 At t = 0 an investor withW0 < W ′ chooses:

17This condition is consistent with Assumption 1 if (1 − π0)rH

(−rL)< γπ0(rH−rL)4

π0rH+(1−π0)rL⇔

γ < rH(−rL)

π0rH+(1−π0)rL(rH−rL)4

, that is again, as in Assumption 2, for investors whose degree of

risk aversion is not too high.18The exact expressions for W ′ and W ′′ are available in the proof of the proposition.19The exact expressions for k′ and k′′ are available in the proof. See the sup-

plementary material to verify that there is a non-empty set of k that satisfies both

29

i) π∗ = π0 and subsequently asks for advice if k < k′;ii) π∗ = 1/2 if k ≥ k′ and subsequently delegates her portfolio choice.An investor with W0 ≥ W ′ chooses:iii) π∗ = π0 and subsequently asks for advice if k < k′′;iv) π∗ = 1/2 if k ≥ k′′ and subsequently invests autonomously.When k is relatively low, that is, the degree of financial literacy is high,

B acquires private information in order to obtain meaningful advice (thatis π∗ = π0); but when k is higher, B decides to spend no effort on privateinformation acquisition (i.e., π∗ = 1/2) giving up the possibility to obtaininformative advice. Given that k′′ > k′, wealthier investors are more likelyto consult advisors than investing by themselves and delegating, our lastempirical implication.20

Finally, investors with low financial literacy and low wealth do not enterthe market for risky securities, due to the participation cost ϕ and to the factthat they have too little financial literacy to be able to access informativeadvice.

Corollary 5: If the degree of financial literacy of the investor is suffi-ciently low, that is, k ≥ k′, and her initial wealth W0 ≤ W ′, then the investordoes not buy the risky asset for any fixed entry fee ϕ ≥ 1

2W0 (rH + rLf) −γ8W

20 (rH − rLf)

2.

B Proofs

Proof of Proposition 1: Consider the case π ∈ [1/2, π0).

• Existence. Let v∗(rH) > 0 (resp. v∗(rL) > 0) be the quota of the initialwealth B invests in the risky asset when observing signal s = rH (resp.s = rL). From (3), for any π ∈ [1/2, π0), v

∗(rH) > v∗(rL) > 0 sinceE[r |s = rH ] > E[r |s = rL ] > 0 and V ar[r |s = rH ] = V ar[r |s = rH ] =π(1−π)(rH − rL)

2. Our candidate equilibrium is a pooling one whereσ∗(ri) = rH for both ri = {rH , rL}. Given that at equilibrium adviceis not informative, B buys v∗(rH) if s = rH and v∗(rL) if s = rL.Hence A’s equilibrium expected payoffs are

U∗A(rH) = fW0 [πv

∗(rH) + (1− π)v∗(rL)]

U∗A(rL)

= fW0 [(1− π)v∗(rH) + πv∗(rL)]− (rH − rL)2

Consider a deviation σ(rL) = rL. Observing this out-of-equilibriummessage, B assigns a probability q = Pr(rH |σ = rL) to the event thatsuch a message is sent by A(rH). B then buys v = 1 with probability

k ≥ max{k, 4πrHW0

2π−1

}, and k < k′ < k′′.

20A formal proof of this result can be found in the supplementary material to the answerletter.

30

q and v = 0 with probability 1−q. Advisor A(rH) obtains an expectedpayoff Udev

A(rH) = fqW0 − (rH − rL)2 from the deviation. If the beliefs

q ≤ q, with q := πv∗(rH)+(1−π)v∗(rL) > 0, the deviation is certainlynot profitable for A(rH). On the contrary, the deviation might beprofitable for A(rL) if the investor buys a fraction higher than (orequal to) v∗(rL) of risky asset when receiving message σ(rL) = rL.More formally, if Udev

A(rL)= fqW0 ≥ fW0 [(1− π)v∗(rH) + πv∗(rL)] −

(rH −rL)2, i.e., fW0[q− ((1−π)v∗(rH)+πv∗(rL))] > −(rH −rL)

2, thedeviation is profitable for A(rL). Thus, we can conclude that for out-of-equilibrium beliefs q ≤ q, the deviation is not profitable for A(rH),but it might be profitable for A(rL). Using the intuitive criterion (Choand Kreps, 1987), we can then restrict the out-of-equilibrium beliefsto q = 0. With q = 0, the payoff obtained by A(rL) following thedeviation is Udev

A(rL)= 0. Thus, the deviation is not profitable for A(rL)

if

fW0 [(1− π)v∗(rH) + πv∗(rL)]− (rH − rL)2 ≥ 0

f

((1− π)

πrH + (1− π)rLγπ(1− π)(rH − rL)2

+ π(1− π)rH + πrL

γπ(1− π)(rH − rL)2

)≥ (rH − rL)

2

f ≥ γπ(1− π)(rH − rL)4

2π(1− π)(rH − rL) + rL(9)

for all π ∈ [1/2, π0). The RHS of (9) decreases with π, hence the in-

equality is stricter at π = 1/2. This implies that if f ≥14γ(rH−rL)

4

12(rH−rL)+rL

=

γ(rH−rL)4

2(rH+rL), then (9) is always satisfied for all π ∈ [1/2, π0), and the de-

viation is not profitable for A(rL). Finally, consider any deviation inmixed strategies, where, for example, A(rL) sends message σ(rL) = rLwith probability τ > 0. When B observes σ = rL, then she assignsprobability one to the event that such message was sent by A(rL)(indeed, as described above, it would be more profitable to deviateto σ = rL for A(rL) than for A(rH)). But then A(rL) would obtaina lower payoff sending σ(rL) = rL than playing the equilibrium if

f ≥ γ(rH−rL)4

2(rH+rL).

Uniqueness. In the region π ∈ [1/2, π0), the pooling equilibrium (σ(ri)∗ =

rH) is unique.

– Rule out the perfectly revealing strategy profile (σ(rH) = rH ;σ(rL) =rL). A’s payoffs are U∗

A(rH) = fW0 and U∗A(rL)

= 0. In this case

A(rL) is better off sending σ(rL) = rH and obtaining

UdevA(rL)

=fW0 [(1− π)v∗(rH) + πv∗(rL)]− (rH − rL)2 ≥ 0

whenever f ≥ γ(rH−rL)4

2(rH+rL), as shown at the point above.

31

– Rule out the perfectly revealing strategy profile (σ(rH) = rL;σ(rL) =rH). Its payoffs are U∗

A(rH) = fW0 − (rH − rL)2 and U∗

A(rL)=

−(rH − rL)2 < 0. However, A(rL) is better off deviating σ(rL) =

rL (resulting in payoff UdevA(rL)

= 0).

– Rule out partially revealing strategies where σ(rH) = (rH , rL)with probability (m, 1−m) and σ(rL) = (rH , rL) with probability(n, 1−n), where 0 < m < 1 and 0 < n < 1. A necessary conditionfor the existence of such a mixed strategy equilibria is that, forevery A’s type, the payoff obtained by playing either signal is thesame at equilibrium. This is clearly not true. For instance thepayoff for A(rL) sending σ = rL can be either U∗

A(rL)+(rH −rL)

2

or 0, while the payoff for A(rL) sending σ = rH is equal to eitherU∗A(rL)

or −(rH − rL)2.

Now consider the case π ∈ [π0, 1).

• Existence. If B does not receive any additional information from A,she chooses v∗(rH) = E[r|s=rH ]

γW0V ar[r|si ] > 0 if s = rH , and v∗(rL) = 0 ifs = rL. A does not observe the realization of the signal s. Hence,A(rH) expects to sell v∗(rH) ∈ (0, 1) with probability π and v∗ = 0with probability (1−π) in case he does not provide any information toB. A(rL) expects v

∗(rH) > 0 with probability (1−π) and v∗ = 0 withprobability π in case of no information transmission. Our candidateequilibrium is a fully revealing equilibrium where σ∗(ri) = ri for ri ={rH , rL}. A’s equilibrium payoffs are U∗

A(rH) = fπW0 since the investorreceiving σ = rH and s = rH invests her whole initial wealth in therisky asset, and U∗

A(rL)= 0. Consider a unilateral deviation σ(rH) =

rL by A(rH). Observing a recommendation σ = rL, B believes rLrealizes, hence she chooses v∗(rL) = 0: this deviation is not profitablebecause A(rH)’s payoff would be Udev

A(rH) = −(rH − rL)2 < fπW0 =

U∗A(rH). Consider now a unilateral deviation σ(rL) = rH by A(rL).

Observing σ = rH , B buys v = 1 if s = rH , an event with probability1−π if the true state is rL. The deviation then gives A(rL) the payoffUdevA(rL)

= fW0(1−π)v∗(rH)− (rH − rL)2 < 0 = U∗

A(rL)by Assumption

1. Indeed,

fW0(1− π)v∗(rH)− (rH − rL)2 ≤ 0

f(1− π)E[r|s=rH ]γV ar[r|si ] ≤ (rH − rL)

2

f(1− π) πrH+(1−π)rLγπ(1−π)(rH−rL)2

≤ (rH − rL)2

f ≤ γπ(rH−rL)4

πrH+(1−π)rL(10)

with the RHS increasing in π. The inequality (10) is then stricter at

π = π0, which gives f ≤ γπ0(rH−rL)4

π0rH+(1−π0)rL, verified under Assumption 1.

32

Finally, consider a deviation in mixed strategies, where A(rH) sendsmessage σ(rH) = rL with probability τ > 0. This, again, is not aprofitable deviation because it results in a payoff fW0πv

∗(rH)− (rH −rL)

2 < fW0 = U∗A(rH) when the outcome of the mixed strategy is

rH . A similar argument applies for a deviation in mixed strategiesby A(rL) who sends message σ(rL) = rH with probability τ > 0 thatobtains a negative payoff, by Assumption 1.

• Uniqueness. In the region π ∈ [π0, 1), the fully revealing equilibrium(σ(ri)

∗ = ri) is unique. Consider all other possible equilibrium candi-dates:

– Pooling strategy profile (σ(rH) = rH ;σ(rL) = rH). Its payoffsare U∗

A(rH) = fπv∗(rH)W0 and U∗A(rL)

= f(1 − π)v∗(rH)W0 −(rH − rL)

2 < 0 by Assumption 1. These payoffs cannot arise atequilibrium because under this strategy it would be profitable forA(rL) to send message σ(rL) = rL, that gives U

devA(rL)

= 0.

– Pooling strategy profile (σ(rH) = rL;σ(rL) = rL). If this is anequilibrium, the payoffs are U∗

A(rH) = fπv∗(rH)W0 − (rH − rL)2

and U∗A(rL)

= f(1− π)v∗(rH)W0. Again, these payoffs cannot beequilibrium ones because in such a case it would be profitable forA(rH) to send message σ(rH) = rH , that gives Udev

A(rH) = fπW0 >U∗A(rH).

– Partially revealing strategy profile where σ(rH) = (rH , rL) withprobability (m, 1 − m) and σ(rL) = (rH , rL) with probability(n, 1 − n), where 0 < m < 1 and 0 < n < 1. Analogous to theproof for point (i). �

Proof of Corollary 2: Compare the utility that B obtains by consultingA and by investing autonomously. For π ∈ [1/2, π0) (irrespective of s = rLand s = rH), by Proposition 1, B anticipates an uninformative signal fromA; hence, for any arbitrarily small cost of advice ε > 0, B prefers not todemand advice.

For π ∈ [π0, 1), by Proposition 1, B anticipates an informative signalfrom A. We distinguish two cases:

- s = rL: the expected utility that B obtains by consulting A is strictlypositive. This is because when s = rL, if rH occurs, then B knows thatA divulges it, so that B obtains an (ex post) utility equal toW0rH > 0;if rL occurs, then B does not invest in the risky asset, obtaining a zeroex post utility. On the other hand, the utility B obtains investingautonomously is U self

B = 0, because, when π ∈ [π0, 1), E[r |s = rL ] =πrL+(1−π)rH < 0. From this reasoning it follows that when s = rL,B strictly prefers to ask for advice.

33

- s = rH : if the true state is rH , B knows that A reveals it at equilib-rium, and in that case B invests her whole wealth in the risky asset,obtaining an ex post payoff equal to W0rH . This payoff is higher thanthe ex post payoff she obtains investing by herself, v(rH)W0rH sincev(rH) < 1. If instead the true state is rL, A advises B not to buythe risky asset: B’s ex post utility is equal to zero, while investingautonomously B makes a loss v(rL)W0rL < 0 since v(rL) > 0 andrL < 0. Since in both contingencies the ex post utility of asking adviceis higher than the one of investing autonomously, B is better off withadvice. �

Proof of Proposition 3: Consider first investor B with π ∈ [1/2, π0).By Corollary 2, B anticipates that if she does not delegate the portfoliochoice to A, she invests autonomously. From (3), her self-investment choicesare:

if s = rH : buy an amount of risky asset v(s) = vH = E[r|s=rH ;π]γW0V ar[r|s=rH ;π]

if s = rL : buy an amount of risky asset v(s) = vL = E[r|s=rL;π]γW0V ar[r|s=rL;π]

Before receiving the signal s, the two realizations rH and rL have equalprobability 1/2, while for any precision π the events s = rH and s = rL haveprobability (π, 1− π) (resp. (1 − π, π)) if rH realizes (resp. if rL realizes).B’s expected utility from investing by herself is equal to:

EU self =1

2W0 [(πrH + (1− π)rL)vH + ((1− π)rH + πrL)vL] + (11)

−γ

4W 2

0

[(1− π)

(r2Hv2L + r2Lv

2H

)+ π

(r2Hv2H + r2Lv

2L

)]Anticipating A’s behavior described in (8) under delegation, B’s ex-

pected payoff from delegation is equal to:

EUdel = 12W0 (rH + rLf)− γ

2

(12 (rHW0 − (rH + rLf)W0)

2 + 12 (rLfW0 − (rH + rLf)W0)

2)

= 12W0 (rH + rLf)− γ

8W20 (rH − rLf)

2 (12)

There is a trade-off that corresponds to the choice of delegation: the investorknows that in case of delegation, A buys an amount of risky asset larger thanthe one she would buy autonomously both when rH and rL realize. This inturn makes her better off delegating in case rH realizes, while the oppositeis true if rL realizes.

An investor with π ∈ [1/2, π0) prefers to delegate rather than investingby herself if EUdel > EU self . Given that for investors with a sufficientlylow degree of risk-aversion EU self is increasing in the information precision

34

π, 21 while EUdel does not depend on π, then among the investors withπ ∈ [12 , π0), the least informed ones prefer delegation, while the relativelybetter informed ones instead prefer not to delegate.

Let us compute first EU self at π = 12 . From (11) we have:

EU self(π = 1

2

)=

1

2W0

[(1

2rH +

1

2rL)vH + (

1

2rH +

1

2rL)vL

]+

−γ

4W 2

0

[1

2

(r2Hv2L + r2Lv

2H

)+

1

2

(r2Hv2H + r2Lv

2L

)]

=1

2W0(rH + rL) (vH + vL)− γ

4W 2

0

[(r2H + r2L

) (v2H + v2L

)]and compare it with EUdel. We obtain that EU self

(π = 1

2

)< EUdel for

W0 < W ′ = 4γ

rH(1− vH2 )+rL(f− vL

2 )(r2H+r2L)(1−v2H−v2L)−2rHrLf

(13)

and given that EU self is increasing in π, we know that there is a closed andcompact interval Idel =

[12 , π

t]such that all investors with W0 < W ′ and

π ∈ Idel prefer to delegate. Conversely, investors with W0 ≥ W ′ or withW0 < W ′ and π ∈ [

πt, π0]invest autonomously.

Next, let us compute EU self at π = π0 :

EU self (π0) =1

2W0 [(π0rH + (1− π0)rL)vH + ((1− π0)rH + π0rL)vL] +

−γ

4W 2

0

[(1− π0)

(r2Hv2L + r2Lv

2H

)+ π0

(r2Hv2H + r2Lv

2L

)]=

1

2W0 [(π0vH + (1− π0)vL) rH + ((1− π0)vH + π0vL) rL] +

−γ

4W 2

0

[(π0v

2H + (1− π0)v

2L

)r2H +

((1− π0)v

2H + π0v

2L

)r2L

]and compare it with (12). Characterizing the values ofW0 for which EU self (π0) <EUdel, we can conclude that investors with such initial wealth delegate theirportfolio decision for any π ∈ [

12 , π0

). Solving for EU self (π0) = EUdel in W0

we find

W0 =4γ

rH(1−vL−π0(vH−vL))+rL(f−vH+π0(vH−vL))

r2H(1−2v2L−2π0(v2H−v2L))+r2L(f2−2v2H+2π0(v2H−v2L))−2rHrLf= W ′′

and investors with W0 < W ′′ always delegate.21

∂EUself

∂π=

1

2W0 (rH − rL) (vH − vL)− γ

4W 2

0

(r2H − r2L

) (v2H − v2L

)> 0

γ <4 (rH − rL) (vH − vL)

W0 (r2H − r2L) (v2H − v2L)

35

Consider now an investor B with π ∈ [π0, 1). Corollary 2 shows that att = 2 she asks for advice rather than investing autonomously, in case shehad decided not to delegate her portfolio choice. From (6), the investor’sexpected payoff for asking for advice is equal to

EUadv =1

2πrHW0 − γ

8W20 r

2H (2− π0)

2 (14)

Choosing instead to delegate, B obtains an expected payoff equal to (12).For a given W0 EUdel < EUadv if:

rH + rLf ≤ πrH

r2H (2− π)2 ≤ (rH − rLf)2 (15)

Assuming f ≥ rH−rL

(1− π0) guarantees the first inequality, while consideringf = rH

−rL(1 − π0), the second inequality is satisfied for all π ∈ [π0, 1) :(

rH − rLrH−rL

(1− π0))2

= r2H (2− π0)2 ≥ r2H (2− π)2. Because vdelL < 0,

the RHS of (15) is increasing in f and (15) is then always satisfied forf ≥ rH

−rL(1− π0). �

Proof of Proposition 4:Given Proposition 1, Corollary 2, B’s portfoliodecision (3), and Proposition 3, we obtain B’s expected utility at t = 0 asa function of the precision π the investor chooses at that point in time. Weknow that:

(i) for π ∈ [12 , π0), B anticipates she will not ask for advice. We alsoknow that either she invests autonomously, obtaining (11), or she delegatesthe portfolio choice to A, obtaining (12). Notice that (12) is independentof π: when the investor delegates the portfolio choice, she does not payany information collection cost, so that π∗ = 1/2. Also, for k ≥ k =8(rLvH+rHvL+π(rH−rL)(vH−vL))−4(r2Hv2L+r2Lv

2H+π(r2H−r2L)(v

2H−v2L))γW0

2π−1 , the func-tion (11) is decreasing in π, so that an investor anticipating not to delegateand to invest autonomously chooses π∗ = 1/2. We can conclude then thatfor k ≥ k we have π∗ = 1/2, and the investor delegates if W0 < W ′ whileshe invests autonomously if W0 ≥ W ′ (see proof of Proposition 3).

(ii) From Proposition 1 and 3 and Corollary 2, we know that for π ∈[π0, 1), B anticipates she asks for advice because this choice dominates bothinvesting autonomously (Corollary 2) and delegating (Proposition 3).

When asking for advice, B optimally acquires only the minimum infor-mation precision π∗ = π0 necessary to obtain meaningful advice wheneverk > 4πrHW0

(2π−1)2. From (14), the expected utility that B obtains with π∗ = π0

is then

EUadv =1

2π0rHW0 − γ

8W20 r

2H (2− π0)

2 − k

2

(π0 − 1

2

)2

(16)

36

Thus, for k ≥ max{k, 4πrHW0

(2π−1)2

}, when B has the choice of selecting the best

π∗, there are only two possible cases:

W0 < W ′ π∗ = 1/2 and delegate OR π∗ = π0 and ask for adviceW0 ≥ W ′ π∗ = 1/2 and ”self” OR π∗ = π0 and ask for advice

Notice that (16) is decreasing in k while both (12) and (11) are independentof it. We can then conclude that investors with higher k (relatively low levelof financial literacy) choose π∗ = 1/2 and delegate or invest autonomouslyaccording to their level of wealth; while investors with a lower k (relativelyhigh level of financial literacy) choose π∗ = π0 and asks for advice. SolvingEUadv = EUdel in k, we obtain k′:

1

2π0rHW0 − k′

2

(π0 − 1

2

)2

= 12W0 (rH + rLf)− γ

8W20 (rH − rLf)

2

k′ =W0( 1

4γW0(rH−frL)

2+rH(π0−1)−frL)(π0− 1

2)2

so that investors with k > k′ choose π∗ = 1/2 and delegate. Solving EUadv =EU self

(π = 1

2

)in k gives us k′′:

1

2π0rHW0 − k′′

2

(π0 − 1

2

)2

=1

2W0(rH + rL) (vH + vL)− γ

4W 2

0

(r2H + r2L

) (v2H + v2L

)k′′ =

2W0( 12γW0(r2H+r2L)(v

2H+v2L)−(rH+rL)(vH+vL)+π0rH)(π0− 1

2)2

and investors with k > k′′ choose π∗ = 1/2 and invest autonomously. Finally,

k′′ > k′ if γ > 2(vH+vL)(rH+rL)

W0((v2H+v2L− 14)(r

2H+r2L)+

12frLrH)

. �

Proof of Corollary 5: When k ≥ k′ and W0 ≤ W ′, by Proposition3, B delegates her investment choice obtaining (12). If the entry costs arehigher than this amount, B does not enter the risky asset market. Noticethat (12) increases with W0 , hence an investor with sufficiently high k ≥ k′

and sufficiently low W0 does not enter the risky market. �

C Variable Description

Demand for advice: the dependent variable is constructed from a questionasking: “Which of these statements best describes your behavior in decidinghow to invest your savings?”. If we denote withDi how much investor i relieson the advisor, the questionnaire allows for five alternative answers:

Di = 1 investors decide completely by themselves, and the advisor simplyexecutes their decisions

37

Di = 2 investors tell the advisor how they intend to invest and ask theiropinion before deciding

Di = 3 investors consider advisors’ proposals before deciding

Di = 4 investors rely mainly on advisors for their investment decisions

Di = 5 investors let the advisors decide everything.

The dependent variable used in (most of) the analysis is defined as aself/autonomous decision if Di = 1, advice if Di = 2 or Di = 3, and del-egation if Di = 4 or Di = 5. An alternative definition is proposed as arobustness check.

Financial Literacy: The financial literacy measure is constructed as inGuiso and Jappelli (2008). One point is given if the respondent can answercorrectly each of the following questions:

- Inflation: Imagine an account yields 2% yearly (net of costs and taxes).With inflation at 2% per year, how much do you think you will be ableto buy after two years (without moving funds in the account)? Morethan what I could buy today | Less | The same | Do not know;

- Interest : Imagine you know with certainty that in six months theinterest rates will rise. Do you think you should buy fixed rate bondstoday? Yes | No | Do not know

- Diversif1 : What do you think having correctly diversified investmentsmean? Having in one’s own portfolio both bonds and stocks | Do notinvest for too long in the same financial product | Invest in as manyassets as possible | Invest in several assets at the same time in orderto limit exposure to risks linked to single assets | Do not invest in veryrisky products | Do not know

- Diversif2 : Which of these portfolios is better diversified? 70% T-bills,15% European equity funds, 15% in 2-3 Italian stocks | 70% T-bills,30% European equity funds | 70% T-bills, 30% in 2-3 Italian stocks |70% T-bills, 30% in stocks of companies I know well | Do not know

Four other indicators are based on the question: “How risky do youthink these products are? ”The answers can be from 1 (Not risky at all) to5 (Very risky) and ‘Do not know’ is always an option. One point is given ifthe respondent can correctly state that

- Risk1 : Private bonds are at least as risky as deposits

- Risk2 : Stocks are at least as risky as government bonds

- Risk3 : Stocks mutual funds are at least as risky as bonds mutual funds

38

- Risk4 : Housing is at least as risky as deposits

Self-confidence (Self-assessed financial knowledge): Self-confidenceis based on the question: “For each of these ten assets I would like you totell me how much you think you know about it? ”The answer can be inthe range of 1 (I do not know it at all) to 5 (I know it very well). The as-sets are: government bonds, repurchase agreements, private bonds, mutualfunds, derivatives, unit-linked or index-linked life insurance, ETFs, managedportfolios, and structured products. The self-confidence index used in theanalysis is the average of these ten measures and ranges from 1 to 5.

Trust towards own financial advisor: Trust is based on the question“Overall, how much trust do you have in your bank advisor or financialadvisor concerning your financial investments?” The answers range from 1(no trust at all) to 5 (trust a lot).

Time preference (Patience): Patience is based on the question: “Imag-ine you win 100,000 euro in a lottery. This amount of money will be given toyou in a year. However, if you give up part of the money, you can receive therest immediately. To receive the money immediately, would you be willingto receive: 80,000 / 90,000 / 95,000 / 97,000 / 98,000 euro? ”The discountfactor is taken from the point where the respondent prefers the smaller pay-ment X sooner with respect to 100,000 euro in a year, i.e., X/100, 000.

Experience: Three questions are used in measuring experience in trad-ing assets. If the respondent has ever invested in either bonds, stocks, ormutual funds; then the UCS asks at which age the respondent first investedin each. Experience in each asset is computed as the difference between thecurrent age and the age of the first investment. Overall, the experience iscomputed as the maximum of these three numbers. If the respondent hasnever invested in any of the three assets, the experience is set to zero.

Finance sector: A dummy variable taking the value of one if the re-spondent works in the monetary and financial intermediation and insurancesectors.

Financial wealth: Financial wealth dummies are based on the bank’sadministrative records (indicating the amount of financial wealth held bythe customer at the end of June 2006) and on self-reported financial wealth(the self-reported bracket is used whenever it indicates higher wealth thanthe administrative records; this allows for the possibility that respondentshold additional financial assets outside their Unicredit account). Using ad-ministrative data allows us to avoid to some extent item non-response andunder-reporting of the ‘subjective’ financial wealth measure.

Risk tolerance: Risk tolerance is based on the question: “In managingyour financial investments which of these attitudes do you usually have?”When I invest I usually look for: Very high returns, even with a high riskof losing part of my principal | High returns with a fair degree of principalsafety | Fair returns with high safety for my principal | Low returns without

39

risk of losing my principalGeneralized trust (1) is a dummy based on a question borrowed from

the World Values Survey: “Generally speaking, do you think that mostpeople can be trusted or that you have to be very careful in dealing withpeople?” The dummy takes the value of one if the respondent answers: Ithink that most people can be trusted; and zero if the answer is: You can’tbe too careful in dealing with people.

Generalized trust (2) is based on the question: “How important itis for you to build trust relationships with people in everyday life? ”withanswers ranging from 1 (Not at all important) to 5 (Very important).

D Robustness checks

Alternative indices (all of them are re-scaled so as to range between zeroand ten):

- Financial literacy 1. It is the same as the main index (Guiso andJappelli, 2008), rescaled: 10 × (Inflation + Interest + Diversif1 +Diversif2 +Risk1 +Risk2 +Risk3 +Risk4)/8

- Financial literacy 2. Since the quizzes Risk1 − Risk4 are highlycorrelated among themselves, this index gives them a lower weight:10×[Inflation+Interest+Diversif1+Diversif2+(Risk1+Risk2+Risk3 +Risk4)/4]/5

- Financial literacy 3. It is the same as the previous one with the differ-ence that the inflation question is eliminated because it shows a verylow correct response rate (34%) – much lower than a similar question(60%) in the 2006 SHIW (i.e., the nationally representative Surveyof Household Income and Wealth conducted by the Bank of Italy) –which might be related to a misinterpretation of the question ratherthan to financial illiteracy. The index is: 10× [Interest+Diversif1+Diversif2 + (Risk1 +Risk2 +Risk3 +Risk4)/4]/4

- Financial literacy 4: 10× [Interest+Diversif1 +Diversif2]/3

Alternative subsamples (conditional on holding risky assets):

- Unicredit is the main or only bank (i.e., the baseline), with N = 1,116

- Unicredit is the only bank, with N = 802

- Unicredit is the main or only bank and the respondents uses brokersfor advice never, seldom, or sometimes, with N = 847

- Unicredit is the main or only bank and the respondent never or seldomuses brokers for advice, with N = 705

40

E Figures

t = 0B chooses optimal and decides whether

to pay a fixed transaction cost

t = 2B decides whether to

ask for advice or invest by

herself

t = 3If Advice, then A and B interact in a

communication game, where A decides whether to disclose

information or not and B decides her portfolio allocation

t = 4is realized

and payoffs distributed

r

t = 1B decides whether to

delegate to A. If B doesnot delegate she

observes the signal s

Figure 1: Timing

010

2030

Per

cent

0 2 4 6 8Financial literacy (Number correct)

Figure 2: Financial literacy distribution (baseline definition)

41

F Tables

Table 1: Summary statistics

Mean Median Std. Dev. Min Max

Financial literacy 4.658 5 1.476 0 8Self-assessed financial knowledge 2.877 2.9 0.846 1 5Trust towards advisor 3.798 4 0.905 1 5Patience 0.931 0.95 0.067 0.8 1Experience 13.038 11 12.753 0 53Financial sector 0.034 0 0.180 0 1Years at Unicredit : < 1 0.011 0 0.103 0 1Years at Unicredit : 1-5 0.100 0 0.300 0 1Years at Unicredit : 6-10 0.187 0 0.390 0 1Years at Unicredit : 11-20 0.236 0 0.425 0 1Years at Unicredit : 20+ 0.466 0 0.499 0 1Female 0.306 0 0.461 0 1Age 54.827 57 12.313 25 89Years of schooling 12.410 13 4.051 0 20Employee 0.324 0 0.468 0 1Self-employed 0.267 0 0.442 0 1Unemployed 0.005 0 0.071 0 1Retired 0.336 0 0.473 0 1Other out of the labour force 0.067 0 0.250 0 1Total individual income (th. Euro) 49.947 31 67.933 0.2 822Fin wealth: 10-50,000 euro 0.155 0 0.362 0 1Fin wealth: 50-100,000 euro 0.227 0 0.419 0 1Fin wealth: 100-150,000 euro 0.193 0 0.395 0 1Fin wealth: 150-250,000 euro 0.176 0 0.381 0 1Fin wealth: 250-500,000 euro 0.182 0 0.386 0 1Fin wealth: 500,000+ euro 0.066 0 0.249 0 1North 0.509 1 0.500 0 1Center 0.243 0 0.429 0 1South and Isles 0.248 0 0.432 0 1Holds risky assets 0.706 1 0.456 0 1Generalized trust (1) 0.260 0 0.439 0 1Generalized trust (2) 4.187 4 0.853 1 5

Source: UCS 2007. N = 1,581

42

Table 2: Descriptive statistics on the demand for advice and financial liter-acy

Full sample Sample holding risky assets Financial literacyPercent Percent Mean Std. Dev.

Demand for advice:Self 7.84 11.11 4.96 1.30Advice 48.39 68.55 5.01 1.29Delegate 14.36 20.34 4.57 1.41

Does not hold risky assets 29.41

Total 100 100 4.66 1.47N 1,581 1,116 1,116 1,116

Source: UCS 2007.

43

Table 3: Answers to financial literacy tests

Freq. Percent

Inflation:More than today 38 2.40Less than today 812 51.36Same as today (correct) 545 34.47Do not know 186 11.76

Interest :Yes 359 22.71No (correct) 814 51.49Do not know 408 25.81

Diversification 1 :To have both bonds and stocks 263 16.64Do not hold same asset for too long 105 6.64Invest in as many assets as possible 136 8.60Invest in more assets to limit risk exposure of single ones (correct) 616 38.96Do not invest in very risky assets 279 17.65Do not know 182 11.51

Diversification 2 :70% T-bills, 15% European equity fund, 15% in 2-3 Italian stocks 644 40.7370% T-bills, 30% European equity fund (correct) 202 12.7870% T-bills, 30% in 2-3 Italian stocks 111 7.0370% T-bills, 30% in stocks of companies I know well 137 8.67Do not know 305 19.29

Correct on Risk 1 1,321 83.55Correct on Risk 2 1,404 88.80Correct on Risk 3 1,274 80.58Correct on Risk 4 1,188 75.14

Source: UCS 2007. (N =1,581)

44

Table 4: Demand for advice and holding risky assets

Hold risky assets Self Advice Delegation

Financial literacy 0.048*** -0.007 0.027** -0.021**(0.009) (0.006) (0.011) (0.009)

Self-confidence 0.030* 0.022* 0.025 -0.047***(0.017) (0.012) (0.020) (0.017)

Trust advisor 0.047*** -0.088*** -0.028 0.116***(0.013) (0.011) (0.020) (0.017)

Patience 0.296* 0.030 -0.199 0.169(0.172) (0.128) (0.206) (0.176)

Experience 0.008*** -0.001 0.002 -0.001(0.001) (0.001) (0.001) (0.001)

Finance sector 0.041 0.130** -0.048 -0.082(0.072) (0.065) (0.077) (0.051)

Years at UC: 6-10 0.091*** 0.085 -0.123 0.038(0.035) (0.068) (0.084) (0.057)

Years at UC: 11-20 0.210*** 0.107* -0.089 -0.018(0.029) (0.065) (0.076) (0.049)

Years at UC: > 20 0.216*** 0.095** -0.111* 0.015(0.038) (0.046) (0.064) (0.049)

Female 0.002 -0.029 -0.038 0.067**(0.027) (0.018) (0.033) (0.029)

Age 0.004 -0.002 0.010 -0.008(0.008) (0.006) (0.010) (0.009)

Age squared -0.000 0.000 -0.000 0.000(0.000) (0.000) (0.000) (0.000)

Years school 0.009*** 0.005* 0.006 -0.011***(0.003) (0.002) (0.004) (0.003)

Self-employed 0.014 0.023 -0.028 0.005(0.030) (0.022) (0.036) (0.031)

Retired -0.039 0.030 -0.009 -0.020(0.040) (0.028) (0.042) (0.034)

Log tot ind income 0.001 -0.014 0.002 0.012(0.014) (0.011) (0.017) (0.014)

FinW 50-100 th 0.109*** -0.052** -0.041 0.094*(0.030) (0.020) (0.052) (0.050)

FinW 100-150 th 0.139*** -0.031 -0.043 0.074(0.030) (0.022) (0.054) (0.052)

FinW 150-250 th 0.155*** -0.056*** -0.035 0.091*(0.030) (0.019) (0.055) (0.054)

FinW 250-500 th 0.165*** -0.056*** -0.018 0.074(0.031) (0.019) (0.055) (0.053)

FinW 500+ th 0.173*** -0.004 -0.034 0.038(0.041) (0.033) (0.068) (0.064)

North 0.083*** 0.049** -0.049 -0.000(0.029) (0.022) (0.037) (0.031)

Center 0.100*** 0.032 -0.052 0.020(0.029) (0.028) (0.043) (0.035)

Risk tolerance (self) 0.079*** 0.009 0.002 -0.011(0.018) (0.009) (0.002) (0.007)

N obs 1581Log-Lik -1520.473ρ 0.426Wald test ρ = 0 1.478Wald test p-value 0.224

Source: UCS 2007. Model: Generalized Ordered Probit with Sample Selection(marginal effects on conditional probabilities are reported). Subsample of in-vestors for whom Unicredit is the main or only bank. Dependent variable: Self =Prob(Di = 1); Advice = Prob(Di = 2|Di = 3); Delegation = Prob(Di = 4|Di = 5).Standard errors reported in parentheses are robust to heteroskedasticity. Signifi-cance: *** p<0.01, ** p<0.05, *p<0.1.

45

Table 5: Demand for advice (investors who hold risky assets)

Self Advice Delegation

Financial literacy -0.007 0.027*** -0.020**(0.006) (0.010) (0.009)

N obs 1116Log-Lik -786.146

Source: UCS 2007. Model: Generalized Ordered Probit (marginaleffects reported). Subsample of investors holding risky assets andfor whom Unicredit is the main or only bank. Dependent variable:Self = Prob(Di = 1); Advice = Prob(Di = 2|Di = 3); Delegation= Prob(Di = 4|Di = 5). Regressors not reported: same covariatesas in Table 4. Standard errors reported in parentheses are robust toheteroskedasticity. Significance: *** p<0.01, ** p<0.05, * p<0.1.

Table 6: Accounting for the potential endogeneity of financial literacy

First stage – Dep var: Fin Lit

Experience 0.019***(0.004)

Other regressors are not reported

N obs 1116F excl instr 27.929Endog test 0.022Endog test p-val 0.883

Main equation – Dep var: Self Advice Delegation

Financial literacy -0.058 0.136* -0.079(0.044) (0.070) (0.061)

Residuals 0.051 -0.109 0.058(0.045) (0.072) (0.062)

Source: UCS 2007. First stage – Model: linear model estimated byGMM (only the first stage is reported). Regressors not reportedare the same as in Table 4. Standard errors are robust to het-eroskedasticity. Main equation – Model: Generalized Ordered Pro-bit that controls for financial literacy endogeneity via control func-tion approach (marginal effects reported). Dependent variable: Self= Prob(Di = 1); Advice = Prob(Di = 2|Di = 3); Delegation =Prob(Di = 4|Di = 5). Bootstrapped standard errors (200 repe-titions) are robust to heteroskedasticity. Regressors not reported:same covariates as in Table 4. Subsample of investors holding riskyassets and for whom Unicredit is the main or only bank. Standarderrors reported in parentheses are robust to heteroskedasticity. Sig-nificance: *** p<0.01, ** p<0.05, * p<0.1.

46

Table 7: Accounting for the potential endogeneity of trust towards the ad-visor

First stage – Dep var: Trust towards the advisor

Generalised trust (1) 0.173***(0.060)

Generalised trust (2) 0.101***(0.036)

Other regressors are not reported

N obs 1116F excl instr 9.155Hansen J 2.170Hansen J p-val 0.141Endog test 0.634Endog test p-val 0.426

Main equation – Dep var: Self Advice Delegation

Financial literacy -0.008 0.027** -0.019**(0.007) (0.010) (0.009)

Trust advisor -0.112 -0.076 0.188*(0.078) (0.128) (0.110)

Residuals 0.030 0.046 -0.076(0.078) (0.128) (0.112)

Source: UCS 2007. First stage – Model: linear model estimated byGMM (only the first stage is reported). Regressors not reportedare the same as in Table 4. Standard errors are robust to het-eroskedasticity. Main equation – Model: Generalized Ordered Pro-bit that controls for financial literacy endogeneity via control func-tion approach (marginal effects reported). Dependent variable: Self= Prob(Di = 1); Advice = Prob(Di = 2|Di = 3); Delegation =Prob(Di = 4|Di = 5). Bootstrapped standard errors (200 repe-titions) are robust to heteroskedasticity. Regressors not reported:same covariates as in Table 4. Subsample of investors holding riskyassets and for whom Unicredit is the main or only bank. Standarderrors reported in parentheses are robust to heteroskedasticity. Sig-nificance: *** p<0.01, ** p<0.05, * p<0.1.

47

Table 8: Robustness on sample selection

Self Advice Delegation

Sample: Unicredit main or only bank (baseline) (N = 1,116)Financial literacy -0.007 0.027*** -0.020**

(0.006) (0.010) (0.009)

Sample: Unicredit only bank (N = 802)Financial literacy -0.010 0.028** -0.018

(0.006) (0.012) (0.011)

Sample: Unicredit main/only bankand use broker never/seldom/sometimes (N = 847)

Financial literacy -0.010 0.029** -0.020*(0.007) (0.012) (0.011)

Sample: Unicredit main/only bankand use broker never/seldom (N = 705)

Financial literacy -0.009 0.034*** -0.024**(0.007) (0.013) (0.012)

Source: UCS 2007. Model: Generalized Ordered Probit. Regressorsnot reported: same covariates as in Table 4. Dependent variable:Self = Prob(Di = 1); Advice = Prob(Di = 2|Di = 3); Delegation =Prob(Di = 4|Di = 5). Standard errors are robust to heteroskedas-ticity. Significance: *** p<0.01, ** p<0.05, * p<0.1.

Table 9: Alternative definition of the dependent variable

Self Advice Delegation

Financial literacy -0.014 0.034*** -0.020**(0.012) (0.012) (0.009)

Source: UCS 2007. Model: Generalized Ordered Probit(marginal effects reported). Definition of financial literacyindices: see Appendix D. Subsample of investors holdingrisky assets and for whom Unicredit is the main or onlybank. Dependent variable: Self = Prob(Di = 1|Di = 2);Advice = Prob(Di = 3); Delegation = Prob(Di = 4|Di =5). Regressors not reported: same covariates as in Table4. Standard errors reported in parentheses are robust toheteroskedasticity. Significance: *** p<0.01, ** p<0.05, *p<0.1.

48

Table 10: Robustness of financial literacy index

Self Advice Delegation

Financial literacy 1 -0.0057 0.0218*** -0.0161**(0.005) (0.008) (0.007)

Financial literacy 2 -0.0029 0.0124* -0.0095(0.004) (0.007) (0.006)

Financial literacy 3 0.0007 0.0097 -0.0104*(0.004) (0.006) (0.006)

Financial literacy 4 0.0013 0.0045 -0.0059(0.003) (0.005) (0.004)

Source: UCS 2007. Model: Generalized Ordered Probit(marginal effects reported). Definition of financial literacyindices: see Appendix D. Subsample of investors holdingrisky assets and for whom Unicredit is the main or onlybank. Dependent variable: Self = Prob(Di = 1); Advice= Prob(Di = 2|Di = 3); Delegation = Prob(Di = 4|Di =5). Regressors not reported: same covariates as in Table4. Standard errors reported in parentheses are robust toheteroskedasticity. Significance: *** p<0.01, ** p<0.05, *p<0.1.

49