Subjective Return Expectations, Information and Stock Market Participation: Evidence from France

Recent research has separately uncovered that stock ownership strongly correlates with both expectations and realizations of stock market returns, as well as with measures of …financial literacy, ability or trust. This paper reconciles all, and reports new findings from a unique survey containing individual level data on both expectations and (knowledge of) realizations for a representative sample by age and wealth. Stock market participation monotonically increases with the conditional expectation of a positive stock market return, even among the affluent and the young. Information is very heterogeneous, increases with age and own past experience, and identifies a causal effect of expectations on stock ownership.


Introduction
Prior to the 2008 …nancial crisis, nonparticipation in risky asset markets was awarded the status of '…nancial mistake', with potentially large consequences for equilibrium asset prices and the equity premium. 1 The 'nonparticipation' puzzle uncovers the fact that a signi…cant fraction of households hold no risky assets despite of their historical excess average returns over riskless assets, or 'equity premium' (Haliassos and Bertaut, 1995), against elementary theory predictions from standard expected utility maximization models .
To date, and since the educated and the wealthier are more likely to participate, information and transaction costs remain the most important quantitatively (Vissing-Jorgensen, 2002;Haliassos and Michaelides, 2003). But several questions remain, like (i) the substantial heterogeneity in portfolio allocations (Curcuru, Heaton, Lucas and Moore, 2010), (ii) the nonparticipation of the wealthiest , or (iii) the precise nature of information costs.
Recently uncovered factors such as cognitive ability (Christelis, Jappelli and Padula, 2010;, trust , …nancial literacy (van Rooij, Lusardi, Michaud and Mitchell, 2012), '…nancial awareness' , (time spent in acquiring) …nancial information (Guiso and Jappelli, 2007) or social interactions  are shaping our understanding of the nature and importance of …nancial information costs. However the precise mechanism whereby di¤erences in (ability to process, access to or in the actual stock of) …nancial information translate into di¤erences in stock market participation remains elusive . 2 This paper contributes to all the aforementioned open questions, by showing that di¤erences in information 3 a¤ect participation behaviour through their impact on stock market return expectations, and thereby reconciles investor behaviour with traditional models in …nancial economics. 4 But the crisis, that has so far lead to the "Great Recession", is also shaking the foundations of macro-economics (Hall, 2010). At the heart of the debate, is the role of expectations in state-ofthe-art macro-economic models (Woodford, 2013), and in particular, in their …nancial counterparts (Stiglitz, 2011). The standard practice has been to adopt the rational expectations (RE) paradigm, whereby households hold a (common) statistically correct unbiased view of the future. RE have a crucial advantage: rather than attempting the di¢ cult task of measuring expectations, they can be inferred from (past equilibrium) realizations. Because the stock market is a public non-manipulable event, under RE di¤erences in household …nancial choices cannot be explained by di¤erences in what they expect, only by di¤erences in either what they want (preferences) or, in what they have (endowments) when participation is costly. Against this received wisdom, the importance of (heterogeneous) subjective expectations in …nancial markets 5 has been ascertained from evidence gathered (i) in laboratory experiments (Hommes, 2011), (ii) from agent-based computational algorithms (Arthur, 2006), or (iii) from survey data (Pesaran and Weale, 2006;Greenwood and Schleifer, 2013), among others. To measure households'stock market return expectations, here we report novel survey based evidence collected in March 2007, before the …nancial crisis.
An incipient strand of research in survey expectations, reviewed in Hurd (2009), uncovers that households'expectations regarding the future evolution of the stock market are: (i) for the majority, no better than a 50-50 chance that the stock market index will go up in the year ahead, albeit (ii) extremely heterogeneous Kézdi and Willis, 2011);(iii) able to explain di¤erences in …nancial choices both at a point in time, and through the life-cycle Hurd, van Rooij and Winter, 2011;Miniaci and Pastorello, 2010), and (iv) able to identify households'implicit risk preferences, when combined with data on …nancial choices ). These novel contributions rest on the methodological corner stone put by Dominitz and Manski (1997) and on Manski (2004), who advocate for treating expectations as primitives of the model, and undertake probabilistic elicitation to obtain quantitative measures of individual expectations in surveys. 6 So far, survey data has been exploited for (i) stock market investors only (Vissing-Jorgensen, 2004), for (ii) a speci…c population subgroup which includes non-stockholders (by age, Manski, 2007, 2011;) and for (iii) a representative (internet) sample of the population by age and wealth ((Hurd et al., 2011);Miniaci and Pastorello, 2010). Here, we exploit data from a new wave of the Taylor-Nelson Sofres French survey (TNS 2007), which contains information on attitudes, preferences, subjective expectations, (a novel proxy for) individual information and socio-economic and demographic characteristics for a representative sample of 3,826 households, by age and wealth.
We contribute to this literature methodologically, since we elicit belief probability densities both prospectively (expectations) and retrospectively (information sets) for the …rst time, and over a longer forecasting horizon (Pesaran and Weale, 2006) for a representative sample by asset classes, age and wealth (Campbell, 2006). Extending probabilistic elicitation techniques to obtain a quantitative measure of individual information sets is crucial, because "...little is known about what kind of information rational-expectations investors should learn. Since information learned determines which assets are invested in [...]" (Van Nieuwerburgh and Veldkamp, 2010). We …nd (i) less 50-50 percent responses to probability questions, possibly conveying absolute uncertainty, at the expense of more answers conveying absolute certainty, i.e. 0 ('no chance') and 100 ('for sure') type of answers; that (ii) average …ve-year ahead probabilistic stock market forecasts appear hump-shaped in age, are higher for males and increase with total wealth, and (iii) monotonically increase with the probability of holding stocks but not with educational attainment. (iv) Our measure of information, when averaged across individuals, is also hump-shaped in age (King and Leape, 1987), is higher for males, and (unconditionally) increases with total wealth. Finally, (v) the conditional cross-sectional average of …ve-year ahead probabilistic stock market forecasts also appears hump-shaped in age.
From the perspective of life-cycle (heterogeneous) portfolio choice models, these novel empirical facts appear consistent with (i) observed age-portfolio pro…les at the extensive margin, uncovering (ii) heterogeneity in information sets as a novel source of heterogeneity in portfolio allocations (Curcuru, Heaton, Lucas and Moore, 2010;Malmendier and Nagel, 2011).
Conditioning on risk preferences, endowments, constraints, inertial/delegation factors and information, we …nd that subjective expectations determine stock market participation (i) amongst the elderly, con…rming the robustness of  …ndings, but (ii) not amongst the young, for whom information appears instead crucial (King and Leape, 1987;Hurd, 2009).
Our measure of information is consistent with information being costly acquired (Peress, 2004;Van Nieuwerburgh and Veldkamp, 2010), gathered from social interactions  and specialised (Cabrales and Gottardi, 2011) media (Carroll, 2003), and increases with own's past experience ('frequence of recent trades'or household trade intensity, Linnainmaa 2011;Malmendier and Nagel, 2011;Seru, Shumway and Sto¤man, 2009) and age. Optimists and income constrained respondents appear worse informed, consistent with rational inattention (Sims, 2003;Huang and Liu, 2007). However, information does not (conditionally) increase with the respondents' own or parents' educational attainment, family background, total wealth or respondents' preferences for either risk (Cabrales, Gossner and Serrano, 2013) or time. Most importantly, (iii) when we interpret our novel information measure as an instrumental variable, we …nd evidence in support of a causal e¤ect of expectations on participation decisions, in line with elementary portfolio choice theory predictions and under incomplete information, Genotte, 1986). 7 Hence, and although households do have limited information, they appear to act rationally upon it.
The rest of the paper is organized as follows: in section 2 we describe the methodology used to elicit expectations and individual information sets. Given the aforementioned di¤erences, we construct measures of expectations similar to  to assess the quality of our data against the 2004 wave of the Health and Retirement Study (HRS 2004), which contains a much larger sample of households. In section 3 we describe the TNS 2007 data set and provide descriptive statistics. Section 4 reports the main empirical results on stock market participation, while section 5 inspects the mechanism. Finally, section 6 concludes.

Survey Design
In surveys, respondents are asked to state their perception of a future event in order to understand if it determines their current behaviour. The recent literature on measuring expectations privileges the use of probability questions rather than eliciting point expectations or the traditional qualitative approach of attitudinal research (Manski, 2004). Answers to such questions are used to understand if expectations and outcomes are related, and to evaluate if individual behaviour changes in response to changes in expectations.   To validate our dataset, we build upon their work and extend it along di¤erent dimensions.
First, by extending the forecasting horizon to …ve years, we intend to untie expectational answers from the bussiness-cycle conditions prevailing at the time of the survey (March 2007) to better capture (i) the historic average upward trend of the stock market index, and (ii) inertia in portfolio management (Bilias et al., 2010). The latter is important since it remains an open question with which horizon households invest in the stock market. Second, and to comply with limitations of survey administration (…ll-in questionnaires as opposed to telephone interviews in the HRS), we extend the methodology of the Survey on Household Income and Wealth (SHIW) conducted by the Bank of Italy (Guiso et al., 1996) to the stock market. Probability densities are elicited on seven points of the outcome space, instead of just two points of the cumulative distribution functions (cdfs.), to obtain more precise individual estimates of the relevant moments. Third, we exploit data from a representative sample by age, wealth and asset classes to examine the relationship between age-portfolio pro…les and subjective expectations at the extensive margin. Finally and most importantly, probabilistic elicitation of recent past stock market performance (past Positive Nominal Return, pPNR) provides a quantitative measure of households'degree of awareness regarding their investment opportunity set, to capture: (i) di¤erences in information across households , and (ii) the relationship between information and expectations (Van Nieuwerburgh and Veldkamp, 2010). Without it, households who do not invest because they expect the stock market to burst over the given forecasting horizon are indistinguishable from those who do not invest because they are (pessimistic and) unaware of the investment opportunities available in the stock market.  -40. 9 Conditional on (continuously compounded) returns (on a buy-and-hold portfolio tracking/mimicking the index) being normally distributed, those sample moments would characterize the subjective beliefs of those respondents who base them on the history of observed stock market index monthly closing values. 10

Expectations
To measure expectations, we elicited households'subjective beliefs regarding the likely evolution of the stock market index …ve years ahead in time, I t+5 ; relative to March 2007, I t ; from the following questions (translated wording): C6. 'Five years from now, do you think that the stock market... -For each category write down the likelihood of occurrence assigning a value between 0 and 100. The sum of all your answers must be equal to 100-: ... will have increased by more than 25% ... will have increased by 10 to 25% ... will have increased by less than 10% ... will be the same ... will have decreased by less than 10% ... will have decreased by 10 to 25% ... will have decreased by more than 25% C7b. 'In your opinion, if you expect the stock market to increase within the next 5 years, which would be the highest possible increase (as a percentage)?' C8b. 'In your opinion, if you expect the stock market to decrease within the next 5 years, which would be the lowest possible decrease (as a percentage)?' Question C6 inquires household i about the subjective relative likelihood of occurrence, p i t+1;k , of each of the seven alternative scenarios, k = 1; :::; 7. Each scenario represents a possible outcome range for the percentage change in the index between t and t + 5, R t+1 (5) I t+5 It 1. 11 Questions 9 The density of nominal yearly (and 5-year rolling) log returns on the CAC-40 computed from monthly data between July 1987 and July 2011 is depicted in Figure 4, panel (a) (panel (b)) in the not for publication appendix B. The distribution has sample moments = 0:034 ( (5) = 0:109) and = 0:093 ( (5) = 0:188).
1 0 Those respondents are also more likely to form a rational expectation, at least from the perspective of the adaptive learning literature. See for example Evans and Honkapohja (2001), where they characterize the general conditions under which, even if individuals are initially uncertain about the underlying structure of the economy, they can end up learning it in the limit from equilibrium realizations. 1 1 We follow the standard convention in …nance for long-horizon returns, and let 1+Rt+1(s) denote the stock market index gross return over s periods ahead (hence the subindex t + 1), which is equal to the product of the s single-period (or yearly) returns: Similarly, we let 1 + Rt(s) denote the stock market index gross return over the most recent s periods from date t s to date t (hence the subindex t): See Campbell et al. (1997) (2000). 15 For all ages, 31% (21%) gave answers consistent with absolute certainty that the index would go down (up) over the coming 5 years.
Evidence from the empirical …nance literature on long horizon returns suggests that the longer time horizon given to evaluate stock market performance might explain the di¤erences, because of mean-reversion (Campbell et al., 1997). In the next subsection we further examine this question. Consistent with the …ndings reported in   We are interested in how well you think the economy will do in the next year. By next year at this time, what is the percent chance that mutual fund shares invested in blue chip stocks like those in the Dow Jones Industrial Average will be worth more than they are today? Kleinjans and Van Soest (2013) explicitly model (six) anomalies in the HRS 'reporting behaviour'and …nd that incorporating them has small e¤ects on the estimated distribution of the genuine subjective probabilities.
1 6 Table 2 in the not for publication appendix C reports the distribution of responses and the response rate conditioning on age, gender, and marital and stockholding status.
(noisily) increase with the respondent's education and households'total wealth. The most a-uent households (with wealth above the 90th percentile, e413,476) appear more optimistic regarding the future evolution of the stock market. However, respondents with some college education or more are only slightly more optimistic than those having at most completed high school, while both become similarly more optimistic as they age. 17 Finally, expectations of a positive nominal return appear roughly hump-shaped in age, as does the response rate to the probabilistic question. In Figure 4, the mean response increases until the late 40s, when expectations reach its peak, only to decline from the mid 60s, although the pattern is very noisy with potential time/cohort e¤ects present. 18 The mean percentage chance of a positive nominal return is estimated to increase (fall) by about 8 to 12 (5 to 6) percentage points as age increases (decreases) from 20 to 50 (late 60s onwards). Standard life-cycle portfolio choice models predict that, conditional on being aware of the existence of a historical equity premium, the young should invest heavily in the stock market to take advantage and quickly accumulate wealth (Guiso et al., 2002;Ameriks and Zeldes, 2004;Gomes and Michaelides, 2005). 19 The descriptive evidence reported here suggests that expectations vary systematically with age, and that both the young and the elderly appear particularly pessimistic.
Although the evidence is consistent with existing …ndings for the elderly in the US, in France the 1 7 Figures 6 and 7 in the not for publication appendix C display kernel-smoothed estimates of the mean percentage chance of a positive nominal return conditional on total wealth and educational attainement, respectively. 1 8 In line with the …ndings reported by Linnainmaa (2011) or Malmendier and Nagel (2011), comparison of Figure 4 (expectations) with Figure 9 (information) in the next subsection suggests that the time e¤ects possibly correspond to respondents overweighting a particular event in the past to which they were exposed, like the burst of the technology bubble in 2002.
1 9 Except if labour income and dividends were cointegrated (Benzoni et al., 2007), in which case even if the young were aware of the historical equity premium, they would be willing to short stocks. Intuitively, the young would be implicitly over-exposed to stock market risk through their human capital investments (the returns of) which are non-diversi…able and highly correlated with dividends in the long run, i.e. the longer the available (life-cycle) investment horizon. young appear pessimistic rather than optimistic (Dominitz and Manski, 2011;Vissing-Jorgensen, 2003

Measuring Information
Another possibility is that the young are particularly unaware of the investment opportunities offered by the stock market (King and Leape, 1987;Hurd, 2009). Recent studies stress the importance of (i) coginitive ability (Christelis et al., 2010;, of (ii) the stock of speci…c knowledge, like …nancial literacy 20 , or of (iii) measures of sources of (ex. social interactions, ; time spent in acquiring …nancial information, Guiso and Jappelli (2006); frequency of and gains/losses in recent stock market operations, Linnainmaa, 2011) or lack of access to (ex. lack of trust,  that speci…c knowledge, when accounting for stock market participation decisions. Here, we are more speci…c and inquire respondents about the most recent stock market return realization over the relevant forecasting horizon, in line with the …nance literature (e.g. Biais, Bossaerts and Spatt, 2010;Campbell et al., 1996;Malmendier and Nagel, 2011;Zhang, 2006).
To that purpose, we inquired respondents about the likely evolution of the stock market index ... has increased by more than 25% ... has increased by 10 to 25% ... has increased by less than 10% ... has remained the same ... has decreased by less than 10% ... has decreased by 10 to 25% ... has decreased by more than 25% Question C9 inquires household i about the subjective relative likelihood of occurrence, p i t;k , of each of the seven alternative scenarios, k = 1; :::; 7. Each scenario represents a possible outcome range for the percentage change in the index between t 5 and t, R t (5) 1. Since ranges k = 1 and k = 7 are unbounded, we set (R max ; R min ) to match observed values.The outcome ranges for R t are therefore identical to those of question C6 described above. Accordingly, households' subjective likelihoods are given by:  To capture (i) heterogeneity in accessing/processing public information and (ii) the relationship with answers to forward-looking probability questions (Dominitz and Manski, 2011), information regarding past stock market performance is elicited as a probability density function. While the mean response conveys what most likely happened according to the respondent, the dispersion of the probability mass convenes the respondent's subjective degree of reliability in the respondent's mean response. According to Figure 5, a perfectly informed individual should allocate all probability mass (100 points) to the outcome range "...has increased by 10 to 25%" (k = 2). 21 Out of the 3,826 sample respondents, around 59% (2,253) provided a meaningful answer to the information question. 22 Figure 6 below depicts histogram of the average of the individual probability density functions.
Surprinsingly, the modal response coincides with the truth (outcome range k = 2) indicating that respondents are on average well informed.
A striking …nding is that households tend to be also pessimistic regarding how well has the stock market performed over the last …ve years. Although this might be due to imperfect recall given the unusually long horizon, it might also be related to the 'dot-com'bust being overweighted on respondents'memory (Hurd et al., 2011), even if only half the bust is inside the time window spanned by the question. Table 2 reports summary sample statistics for respondents'answers regarding past and future stock market returns, imposing a uniform distribution within the di¤erent outcome ranges. Although the big spread around the sample mean realized return came as no surprise (possibly indicating ambiguity), it is remarquable that it remains smaller than the spread around the sample mean expected stock market return. Notice also that the cross-sectional dispersion of both expected and realized stock market perfomance measures is about twice the size of the respective spreads, indicating that 'disagreement' is very important, in line with the behavioural …nance literature (e.g. Hong and Stein, 2007).
In Figure 7, we depict the frequency distribution of responses to pPNR for all ages. As previously, there is hipping of responses around round numeric probability answers indicating that rounding is not speci…c to forward looking questions but rather, to respondents rounding when confronted with the probabilistic elicitation format. For all ages, the mean response is 68%, while the true answer is a 100% chance of a positive nominal return over the last 5 years. Around 44% of sample respondents (990 individuals) gave an answer consistent with the truth.  In Figure 8 we examine what type of information had those respondents who were absolutely certain regarding the future evolution of the stock market (see panel (b), Figure 3). Panel (a) shows that amongst those who were absolutely certain that the stock market would go down (24%, 567 answered PNR=0%), around 35% were absolutely certain that it had not increased over the last 5 years, while 43% were absolutely certain that it had gone up. Around 5% gave a 50 percent chance of either going up or down. This contrasts with panel (b), for respondents who were absolutely certain that the stock market would go up (21%, 446 answered PNR=100%): 83% were absolutely certain that the stock market had gone up, while only 6% gave answers consistent with absolute certainty about the stock market having gone down. Only 2% gave a 50 percent response. Hence, individual information regarding the past contributes to (i) signi…cantly unbundle the 'hipping' on responses conveying absolute certainty regarding the future, i.e. P N R = f0; 100g, thereby (ii) capturing a novel source of heterogeneity amogst respondents (Curcuru et al., 2010). Table 4 in the not for publication appendix D reports the distribution of responses and the response rate conditioning on age, gender and stockholding status 23 . In accordance with the …ndings reported in  on the …nancial literacy of US adults, male respondents who are older, single and stockholders report higher mean (and a lower standard deviation of) percentage chances of a past positive nominal return. Although information broadly increases with age irrespective of gender, males are better informed than females on average. 24 In addition, information broadly 2 3 Stockholders report a higher mean by about 10 percentage points, and are around 6 percentage points more likely to give a response.
2 4 See Figure 8 in the not for publication appendix D. increases until the 50th percentile of wealth (e118,792), remains constant until the 90th percentile (e413,476), only to increase again albeit very heterogeneously. 25 The richest households (with wealth above the 90th percentile), may thus be more optimistic (and disagree more) regarding the future investment opportunities because they are better (albeit more heterogeneously) informed.  increases with age until the mid 40s, mildly increases until the mid 70s, and then decreases, although the point estimates are much noisier. 26 In line with King and Leape's (1987) conjecture and Lusardi 2 5 However, the increased heterogeneity in information in the top decile of the wealth distribution might just be a small sample problem, since only 272 respondents within that decile answered to the information question. See Figure 9 for total household wealth by age in the not for publication appendix D for additional evidence. Surprisingly, information about past stock market performance does not increase with own's educational attainement, although it broadly increases with age within educational groups. 28 This …nding is con…rmed in Table 2 below, which reports marginal e¤ects of estimating a two-way censored Tobit speci…cation for answers to question C9 (censored below by '0' and above by '100'). The likelihood of being informed is speci…ed to be a function of age, gender, sources of advice (friends, family, professional, broad media, specialised media) and of information (TV, economics/…nance emissions), own and parents'educational attainment, family background (middle/lower/other class), endowments (income and wealth), …nancial decision taking (no/partial/complete delegation of …nancial decisions), own past experience (proxied by the 'frequency of recent trades'), preferences (risk aversion and impatience), constraints in either accessing information ('online banking') or related to inertia in informational sources (parents' stockownership status, 'parents own stocks'), and of the tightness of households'budget constraint ('importance of money in life').
Categorical answers to frequency, variety and access specialised media, advice from professionals, as well as age or the number of stock market transactions carried over the last year, increase the likelihood of being informed. 29 Interestingly, parents' stockownership status and educational attainment or family background (omitted from the table) do not increase the odds of being informed, and actually signi…cantly decreases them for those who follow 'family advice'. Since those who follow 'friends'advice'are more likely to be informed, we interpret it as being consistent with social interactions being instrumental in gathering information : while friends are a product of respondents'choices, the family in which they are born is not. Alternatively, advice from the family could be capturing trust, and thereby rationalize Guiso, Sapienza and Zingales' (2008) …nding regarding the negative impact of lack of trust on stock holdings. On the other hand, a measure of optimism ('being lucky in life') has a negative impact on being informed, indicating that an 'overcon…dence bias'is not present once gender is conditioned upon: although males appear (10 to 12) percentage points as age increases until (decreases after) 75. better informed, supporting more optimistic forward looking expectations, optimists appear consistently worse informed. 30 We do not …nd evidence of either temporal or risk preferences determining information sets, in line with Van Nieuwerburgh and Veldkamp's (2010) theoretical prediction that risk aversion does not determine the demand for information. 31 Although total wealth does not increase the odds of being informed, income does (even if we condition on the number of stock market operations carried over the last year), in line with a costly information acquisition interpretation (Peress, 2004). 32 Overall, these …ndings are consistent with …nancial information being slowly acquired through the life-cycle (King and Leape, 1987;Lusardi et. al., 2012) from own past experience (Linnainmaa, 2011;Malmendier and Nagel, 2011), from others  and from specialised media (Carroll, 2003). On the other hand, the negative e¤ect of the 'importance of money in life', which scores higher the poorer and the more …nancially constrained the respondent is, reveals a novel aspect in information acquisition: disenfranchisement. Notice that the negative impact of both disenfranchisement and optimism is consistent with rational inattention theory (Sims, 2003), since both decrease the expected returns of costly gathering/processing publicly available relevant information.

Expectations, Information and Stock Market Participation
An important puzzle in the literature is why so few households hold stocks (Haliassos and Bertaut, 1995). Table 3 reports the frequency of non-stock holders by motive for not holding stocks, as well as their relative incidence by age groups. 33 Quantitatively, the percentages reported suggest borrowing/liquidity constraints (Guiso et al., 1996), being 'too risky'and 'having other priorities' as the most important, closely followed by not trusting the stock market , being uninformed and entry/management costs being too high (Vissing-Jorgensen, 2002) in accounting for overall non-participation amongst non-participants. 34 Although in an expected utility framework, the standard two-asset model predicts that decision takers invest in the risky asset if and only if its expected return exceeds the return of the riskless asset , only recently have researchers started to collect data on subjective expectations of stock market returns Hurd et al., 2011). 35 Here we go one step further and examine the extent to which conditional subjective expectations determine households' stock ownership decision, conditioning on what they know (Merton, 1987;O'Hara, 2003;Biais et al., 2010).
To obtain a measure of stock ownership, question C19 in the TNS 2007 inquires respondents about the di¤erent types of …nancial instruments and accounts they hold, and in particular whether they invest in the stock market either directly or indirectly. We de…ne direct stockholdings as the sum of stocks of privatised public companies, listed stocks of private companies and stocks of foreign …rms held. Indirect stockholdings are those held through mutual funds and managed investment accounts. 36 The proportion of households who hold stocks directly is 22%, and 37% either directly or indirectly. Although low, the participation rates are slightly higher than those obtained from previous past surveys 37 and similar to the …gures reported by Haliassos (2008) for other countries at that time. In Figure 10, stock market participation amongst respondents displays a clear humpshaped pattern by age.
The literature on household …nance has found that those who are better educated, older and wealthier, are more likely to hold stocks.  report that the probability of holding stocks monotonically increases with the perceived chance of a positive return of investing in the stock market amongst the elderly. 38 Table 4 reproduces their  Since subjective expectations have been found to systematically vary with risk preferences, information, and demographic and socio-economic characteristics (Hurd, 2009), here we estimate the conditional e¤ ect of the percentage chance of a positive nominal return on stockholdings. Conditioning on individual information is important for both theoretical and empirical reasons. Theoretically, households form their expectations conditioning upon their individual information sets, i .
Although in the rational expectations tradition i would contain "all relevant information", here we proxy it by the individually elicited degree of knowledge of the most recent stock market return realization over the relevant horizon, i = fR t (5)g. 40 Although admittedly simplistic, minimal information survey elicitation provides results beyond individuals overweighting more recent stock market return realizations because of learning from experience (Linnainmaa, 2011;Nagel, 2011, 2013), while uncovering a novel age-dependent imperfect knowledge fact, broadly consistent with recent …ndings from the …nancial literacy literature (Lusardi et al., , 2012. Empirically, Dominitz and Manski (2011) or Hurd and Rohwedder (2012) conjecture that di¤erences in the way people discount publicly available information may explain much of the observed heterogeneity in subjective expectations. Our information measure, pP N R i ; precisely measures (probabilistically) the extent to which respondents know about the most recent realized stock market realization. 41 Most importantly, the availability of observable measures of both expectations and information sets allows us to examine whether households' behaviour is consistent with the theoretical prediction of elementary (static/dynamic) portfolio choice models without having to worry about the rationality of their stock market return forecasts.
Accordingly, we estimate households'probability of holding stocks Pr( s i t = 1 p i t+1 ; p i t ; x i ) as a function of the percentage chance of a positive nominal return (p i t+1 P N R i ), 42 conditioning on information (p i t pP N R i ), and a vector of observables x i , containing measures of (rate of) time and risk (aversion) preference, endowments (income and total wealth), household constraints (being 4 0 In the empirical …nance literature, it is typically assumed to be i = fRt(5); Rt 1(5); :::; R0(5)g = ; 8i: In the rational expectations tradition, i includes also knowledge of the data generating process of stock market return realizations, as well as of the true economic model compatible with such data generating process. However, Guesnerie (1992) shows that common knowledge of rationality, of the model and of the data generating process are not su¢ cient to form a rational expectations within a game-theoretic epistemic formulation encompassing Muth's original model. 4 1 Instead of attributing di¤erences in information sets to di¤erences in private information (e.g. amongst professional forecasters, as in Keane and Runkle, 1990), the previous section points towards rational inattention as being instrumental (e.g. Sims, 2003). 4 2 To obtain subjective expectations from answers to the probability question (PNR i ),  show that if (i) stock market returns are normally distributed, with cdf. (:) : and if (ii) a common variance is assumed, i = (for example, equal to the value obtained from historical records), then: meaning that respondents reporting a higher percentage chance that the stock market will increase over the next …ve years (P N R i ), have a higher subjective mean return expectation ( i ), and should then be more likely to invest in the stock market. Since we inquire about a longer investment horizon, we exploited monthly data on the CAC 40 stock market index between July 1987 and March 2007 (228 observations) to compute the standard deviation of …ve-year log returns to be 0:188. When inserted into the above expression, the sample average percentage chance of a positive nominal return of 46 percent (reported in the appendix, Table 11) corresponds to a sample mean expected return of 0:019; about …ve times smaller than the historical sample mean of 0:109. A respondent reporting a value of P N R i = 70 percent, would match the historical sample mean of 0:109. liquidity constrained, access to online banking), demographics (age, gender and marital status) or inertial factors (who takes …nancial decisions, stocks in pay, parents own stocks or trust 43 ) previously found in the literature to matter at the extensive margin: where (:) denotes the standard normal cumulative distribution function, since we assume that there is a normally distributed unobserved error term e i t . Table 11 in the appendix reports descriptive statistics for the main variables, for the whole and selected samples. Table 5 reports the marginal e¤ects of the probit estimation, for all ages. The variables have the expected signs with minor di¤erences across columns 44 , con…rming the robust e¤ect of subjective expectations on the probability of holding stocks, conditional on heterogeneity in individual information. Column (5) reports that an increase of 1 percentage point (pp.) in the percent chance of a positive nominal return increases the probability of holding stocks by around 9 percent, corresponding to an increase of 28:3% in the unconditional probability (from 32:1% to 41:2%). 45 The e¤ect of information is also sizable: comparing those who were certain that the stock market had (indeed) increased between March 2002 and March 2007 (pP N R = 100) with those who were certain that it had not (pP N R = 0), raises the probability of holding stocks by 7:5% (relative to the unconditional probability of 31:4%). Notice that the positive e¤ect of information remains statistically signi…cant once heterogeneity in either preferences, expectations, decision taking or constraints is taken into account, but that when omitted (column 6), it biases upwards the estimated e¤ect of expectations on stockownership.
In the presence of transaction costs in capital markets, households' endowments (proxied by income and total wealth) in ‡uence portfolio choice. 46 The empirical analysis reveals that their e¤ect is best captured by a second order polynomial, which facilitates the comparison with existing results in the literature (Calvet and Sodini, 2013;Guiso et al., 2003;King and Leape, 1998). 47 Both have a positive e¤ect on participation and are statistically signi…cant at the 1 percent level. An increase of 100,000 euros in mean total wealth (233,757 euros) increases the probability of participation by 9 pps., corresponding to an increase of 26% in the unconditional probability, while an increase of 10,000 euros in mean income (19,634 euros) increases the probability of stockownership by 5 pps. 4 3 Our measure of trust di¤ers from Guiso et al.'s (2008) in that TNS survey question I25 inquires the respondent about 'the extent to which s/he trusts online payment systems'. Hence, and although our results are not directly comparable, our measure of trust captures still the extent to which respondents 'trust others'. 4 4 Results in Table 5 refer to both direct and indirect stockownership. But the sign and magnitude of the reported estimates are robust to changes in the de…nition of stockownership (only direct stockholders, Table 9 below), and to a semi-log speci…cation in income and total wealth (unreported, but available upon request).  -6 .7 6 0 * * -5 .5 3 1 * -5 .4 4 3 * -1 2 .8 9 (2 .9 8 9 ) (3 .1 5 4 ) (3 .1 5 6 ) (7 .9 2 8 ) To ta l w e a lth (1 0 E -7 ) 1 2 .9 4 * * * 9 .2 1 1 * * * 9 .2 7 1 * * * 2 4 .3 7 * * * (corresponding to an increase of 12:5 percent in the unconditional probability). Given that we condition on our measure of information, and that wealth does not increase the conditional odds of being better informed, the identi…ed positive and statistically signi…cant e¤ects are consistent with the presence of …xed/transaction costs of accessing the stock market.
Although previous empirical studies also …nd that education increases the probability of participation, most of them interpret its e¤ect as a proxy variable for information. The results in Table 5, column (5) reveal that, conditioning on our individual measure of the most recent past stock market performance, holding a college degree (or further) does not increase the probability of participation at a statistically signi…cant level, relative to those who hold only a high school diploma or less. (Not even when we exclude it: column (6), Table 5).
Management variables also appear important: although those who take …nancial decisions by themselves are less likely to participate relative to those who totally or partially delegate in a …nancial advisor, the e¤ect is not statistically signi…cant. 48 On the other hand, those who manage their accounts online ('online banking') are around 11 percent more likely to be stock owners, and if respondents'parents are stock owners themselves ('parents own stocks'), they are 16 percent more likely to own stocks themselves. Since Table 2 reports that neither signi…cantly increases the odds of being informed, we interpret these e¤ects as inertial factors in stockownership.
Also, measures of preference heterogeneity are important and consistent with recent theoretical contributions. Individuals who have a long planning horizon (temporal preference) are 1:4 pps. more likely to participate than those who are impatient, in line with the empirical results obtained by Donkers and van Soest (1999) for The Netherlands. More risk averse individuals also have a lower probability of participation, although the e¤ect is not statistically signi…cant 49 . 50 Overall, these e¤ects are consistent with Van Nieuwerburgh and Veldkamp (2010), who model optimal information acquisition within the standard two-asset two-period portfolio choice model. They …nd that at the extensive margin, preference for an early resolution of uncertainty matters since it determines the optimal amount of information, while risk aversion does not. Intuitively, within an expected utility framework, risk aversion has a second order e¤ect, a¤ecting only the intensive margin, and subjective stock market return expectations are formed conditional on respondents' individual information sets.
Constraints are very signi…cant, in line with existing empirical results in the literature. Households who have been liquidity constrained or who think that they will be so in the future are less likely to participate (around 14 percent less likely). Deaton (1992) explains how the expectation of being liquidity constrained in the future leads prudent households to save more ('bu¤er stock'), which results in an overall reduction in stock ownership for those households whose preferences display both decreasing risk aversion (DARA) and prudence (DAP) - Elmendorf and Kimball (2000). 51 Although income risk has a negative e¤ect on stock ownership, in line with theoretical predictions (and simulations) that treat it as exogenous, the e¤ect is not statistically signi…cant. 52 Finally, the age variables indicate that the probability of owning risky assets is lower for younger households, although it has a hump-shaped e¤ect reaching its maximum at the age of 50. In Tables 6 and 7 below, we decompose the e¤ect of expectations on stock market participation by age groups.

Inspecting the Mechanism
In Table 6 we report the maginal e¤ects of the estimation for respondents in the same age bracket However, information regarding past stock market performance does not because, as Figure   9 illustrates, they are overall (similarly) well informed.
In Table 7, we complete the life-cycle picture and report the estimated marginal e¤ects of the probit speci…cation only for the young (18-49 age bracket). The main message conveyed is that although subjective expectations determine the decision to enter the stock market by the young unconditionally, once we condition on individual information sets, the e¤ect of expectations becomes statistically insigni…cant.
The two-step econometric speci…cation (2) is more e¢ ciently estimated jointly by maximum likelihood. It e¤ectively assumes that "agents solve the investment decision problem in two stages: derivation of the vector of conditional expected returns, and choice of an optimal portfolio of assets using estimated expected returns" (Separation Theorem in Gennotte, 1986). 53 The advantage of the two-step estimation strategy is that it allows us to consider individual information as an instrumental variable for subjective expectations and test its statistical validity, in the sense that the exclusion restriction requires that information has no direct e¤ect on stockownership other than through expectations. Table 7, column (7)  Similarly, below column (7) in Tables 5 and 6, we report the maximum likelihood coe¢ cient estimates of speci…cation (2) for all ages and the elderly, respectively. For all, the reported quantitative e¤ect corresponds to a 115:1 percent increase in the probability of holding stocks, when comparing the conditional probability of detention amongst those who are certain that the stock market will not increase (23.9%) with the probability of those who are sure that it will increase over the next 5 years (51,4%). The Chi-square statistic of 4:72 reported at the bottom of Table 5 column (7), has an associated P-value of 0:0298, con…rming that there is weaker statistical evidence in support of the null hypothesis of exogeneity for all ages than there is amongst the young. The Amemiya-Lee-Newey Chi-squared statistic for overidentifying restrictions with 1 degree of freedom (when optimism is interpreted as a valid additional instrument; Kézdi and Willis, 2008) reports a value of 1:014; with an associated P-value of 0:3140; con…rming the validity of information as an instrument, conditional on optmism being also a valid instrument. However, and in contrast to the young, we are unable to reject the null of exogeneity of subjective expectations on the stockownership decisions amongst the elderly, and hence the results under speci…cation (1) remain valid (and causal) for them.
To further inquire into the causal e¤ect of conditional sujective expectations on stockownership, we conduct a counter-factual test, reported in Table 8  determine their stockownership decisions. In unreported regressions, we further inquired into the robustness of our …ndings to unobserved state dependence, measured by the number of stock market 5 3 The crucial assumption for the separation between the estimation of future stock market returns and the selection of the optimal portfolio to hold is that the distribution of realized returns does not depend on the level of investment.
Otherwise, the quality of information depends on how much was invested in the past, and hence on past return realizations. See Genotte (1986), pp. 742-3, for further details.  operations carried over the previous year. Amongst respondents that have not recently traded in the stockmarket (inertial non-/stockholders), we …nd that their conditional expectations do not (consistently) determine their stock ownership decisions. 54 Figure 11 reports kernel-smoothed estimates of the mean reported realized nominal return conditional on age and stockownership status: stockholders appear better informed than nonstockholders between the late 20s and the early 50s, being statistically indistinguishable at earlier and later stages. The displayed patterns are not completely consistent with "learning from experience" (Linnainmaa, 2011;Nagel, 2011, 2013), whereby young stockholders should be much better informed about the most recent stockmarket return realization than old stockholders, while the opposite holds in Figure 11. As well, they are di¢ cult to reconcile with a pure life-cycle "…nancial literacy" argument (Lusardi et al., 2012), since even non-stockholders seem to accumulate relevant …nancial information over their life-cycles (although they start at a later stage than stockholders).  These results, together with Figure 9, lend support to King and Leape (1987) and Hurd's (2009) conjectures: what determines stock market participation amongst the young is their degree of awareness regarding the investment opportunities the stock market o¤ers, and we add 'through their impact on subjective stock market return expectations'. 55 Table 9 reports estimated marginal e¤ects for the same speci…cation as in Table 5, but on a narrower de…nition of stockholdings (direct stockholders only), by age groups (18-49, 50-80 and all ages). Since mutual funds are professionally managed, narrowing the de…nition to exclude them should lead to respondents' decisions being more responsive to their expectations. For each age group, we examine the within e¤ect that conditioning on information (even numbered columns) has on the unconditional e¤ect (odd numbered columns) of expected stock market performance on the decision to invest in shares of national and foreign …rms. For all age groups, the main message remains although quantitatively the estimated coe¢ cients are roughly similar. Importantly, comparison of the last two columns of the table lends support to Dominitz and Manski's (2011) conjecture about the importance of heterogeneity in the amount of public information when accounting for heterogeneity in subjective expectations: the upwards bias in the unconditional marginal e¤ect of expectations on decisions (all ages, column (5)) due to the e¤ect of information on expectations (all ages, column (5)) is larger with a narrower de…nition of stock ownership. 56 Finally, Table 10 reports the estimated marginal e¤ects by respondents'(top) quartile of total wealth (under columns (3) and (4)), and by respondents' information (last two columns). For each subgroup, we examine the e¤ect of conditioning on information (even numbered columns) on the unconditional e¤ect (odd-numbered columns) of expectations on the decision to own stocks (directly and indirectly). Amongst those who are in the top quartile of the total wealth distribution (stock of total wealth above e236,000), the conditional marginal e¤ect of expectations on stockownership roughly doubles in size relative to those in the lower quartiles. Hence, the e¤ect of conditional subjective expectations is strenghtened amongst the rich, contrary to the e¤ect of participation/transaction costs. Also, and although our measure of trust is not comparable to , its positive e¤ect on stockownership becomes statistically insigni…cant for the wealthier. Therefore, when accounting for non-participation amongst the most a-uent, heterogeneity in conditional return expectations appears as a di¤erent alternative to better private investment opportunities  or taxation , while encompassing the ability to process it , its sources (social interactions, trust, Guiso et al., 2008) or more broadly, …nancial literacy (van Rooij et al., 2011) through our novel information measure.
Comparing columns (5) and (6) of Table 10, notice that even amongst the uninformed, the e¤ect of expectations on stock market participation is quantitatively very important and statistically very signi…cant (column 2, pP N R < 100), in line with elementary portfolio choice predictions  and with extensions to incorporate incomplete information (Merton, 1987;O'Hara, 2003;Biais et al., 2010). Compared to the informed (column 1, pP N R = 100), expectations matter even more. 57 We rationalize this last …nding as follows: if information a¤ects decisions 5 6 Qualitatively similar conclusions follow when we examine the conditional e¤ect of expectations on decisions by …nancial decision taker: conditioning on information, the e¤ect of expectations on decisions is quantitatively more important for those who delegate than for those who do not. In addition, and consistent with Table 4 results, we …nd that (i) amongst those who do not delegate …nancial decisions partially or totally, males are about 9% more likely to be stock owners than females, and about 11% less likely amongst those who delegate. Similarly, (ii) having access to online banking increases the probability of owning stocks by 12% amongst those who do not delegate, while it has no e¤ect amongst those who delegate. These results are unreported to save on space, but are available upon request. 5 7 This e¤ect appears very robust to relaxing the de…nition of "informed". For example, when classifying respondents as informed if "pPNR>50" (those who gave more than a 50-50 percent chance of the stock market index going up  only through expectations, in accordance with speci…cation (2), within the most homogeneous information group one would expect expectations to di¤er less, and hence to be less important empirically in accounting for di¤erences in investment decisions. In the limit, perfectly informed individuals would all form rational expectations, and cross-sectional di¤erences in decisions could not be explained by di¤erences in expectations, as implicitly assumed in the literature until recently. Dominitz and Manski (2011) report evidence consistent with persistence in the modal type of revision of expectations with new public information. Hence, if the informed process information similarly, they will revise their expectations similarly, and there will be less cross-sectional variation in their expectations than there will be amongst the uninformed.

Conclusion
Elementary static  and dynamic ) models of portfolio choice put emphasis on the importance of individuals' expectations to explain stock market participation. However, it has been pervasive in the empirical literature on household portfolios to adopt the rational expectations assumption, thus neglecting a potential source of heterogeneity that, in addition to heterogeneity in preferences, endowments and constraints, could help reconcile economic theory predictions with empirically observed low participation rates.
In line with some recent e¤orts in the literature Hurd et al., 2011;Miniaci and Pastorello, 2010), here we have collected novel data on households' expectations and, for the …rst time, on households' information sets (TNS 2007).
To validate our novel data set, and for comparison purposes, we have adopted   But, taking advantage of our novel information measure, we are able to empirically (i) con…rm Leape (1987) -Hurd's (2009) conjecture for the …rst time, on the importance of being aware of the investment opportunities o¤ered by the stock market (the 'investor recognition hypothesis'of Merton, 1987), specially to account for low participation rates of the young; (ii) con…rm the basic principle of elementary portfolio choice models, since even amongst the uninformed and the a-uent, subjective stock market expectations determine their decision to participate , and when individually elicited information is exploited as an instrumental variable, we identify a causal e¤ect of expectations on stock market participation over the last 5 years), and uninformed otherwise, the marginal e¤ect of expectations on decisions for the informed was 0:0021; whereas for the uninformed was 0:0057: conditional on wealth, income, and measures of attitudes, preferences and socio-economic and demographic characteristics; (iii) con…rm the e¤ect of social interactions, professional advice, past own experience and specialised media access, as relevant sources of information at the individual level, thereby contributing to the literature on …nancial literacy, trust and adaptive expectations.
However, (iv) although males appear better informed and are also more likely to take …nancial decisions by themselves instead of delegating; and conditioning on gender, optimists appear less well informed, at odds with a behavioural overcon…dence bias interpretation (Guiso and Jappelli, 2006), but in line with inertia amongst the general population (Bilias et al., 2010). Finally, (v) poor or constrained households, for whom stock market information is useless, appear less well informed in line with rational inattention theory (Sims, 2003).
Our results suggest novel and important policy implications, that deepen and complement those already identi…ed: (i) in the …nancial literacy literature (e.g. Christelis et al., 2010;, i.e. absence of …nancial speci…c knowledge is pervasive amongst the young, irrespective of their level of educational attainement, with potentially dramatic consequences for wealth accumulation over the life-cycle and hence, for wealth inequality (Lusardi et al., 2012); (ii) in macroeconomics, i.e. publicly available information appears costly to acquire in terms of money, e¤ort or time, explaining information stickiness and hence stickiness in expectations (e.g. Carroll, 2003); (iii) in …nance, i.e. recent contributions examining the asset pricing consequences of heterogeneous return expectations, since expectational heterogeneity apears to be fuelled by heterogeneity in public information gathering/processing (e.g. Allen, Morris and Shin, 2006).
However, many questions remain that would require further data collection and analysis. 58 Perhaps the most important one is that much observed heterogeneity remains unexplained at the extensive margin. In light of our results and the recent crisis, attempts to understand Dominitz and Manski's (2011) conjecture about heterogeneity in processing public information feeding heterogeneity in subjective expectations, is likely to be the most promising and challenging one (Frydman and Phelps, 2013). In that respect, we welcome the recent launch of the Survey of Consumer Expectations by the Federal Reserve Bank of New York 59 , and hope that the results reported convey the complementary usefulness of including also retrospective probabilistic assessments of public information events.  T h is a llow s u s to o b ta in a ra n g e m e a su re o f re la tive risk ave rsio n u n d e r th e a ssu m p tio n th a t p re fe re n c e s a re stric tly risk ave rse a n d u tility is o f th e C R R A ty p e . T h e d e g re e o f re la tive risk ave rsio n is le ss th a n 1 if th e in d iv id u a l su c c e ssive ly a c c e p ts c o ntra c ts A a n d B ; b e tw e e n 1 a n d 2 if h e a c c e p ts A b u t re fu se s B ; b e tw e e n 2 a n d 3 .7 6 if h e re fu se s A b u t a c c e p ts C ; a n d …n a lly m o re th a n 3 .7 6 if h e re fu se s b o th A a n d C .  In this work we are only interested in the participation condition. For an estimation of the demand for risky assets at both the intensive and extensive margins, see .

The conditional subjective expectation
We extract the information component from subjective expectations, by regressing expectations (PNR i ) on information (pPNR i ), and recover the predicted residuals, b i ; which are plotted by age in Figure 1.

Histograms of CAC 40 index historical log returns
The density of nominal yearly (and 5-year rolling) log returns on the CAC-40 computed from monthly data between July 1987 and July 2011 is depicted in Figure 4, panel (a) (panel (b)). The distribution has sample moments = 0:023 ( (5) = 0:108) and = 0:10 ( (5) = 0:19). The densities depicted in Figure   4 can be thought as representing the subjective beliefs of those respondents who base them on the history of observed stock market index monthly closing values.

Missing/Erroneous answers to the expectations question
In      Figure 5 shows that also in France, males are more optimistic than females. Even when conditioning on marital and stockholding status and for all age brackets, men give more optimistic reports than do women, and are 6-7 percentage points more likely to give a response.   The solid curve depicts point estimates and the grey area around it represents (bootstrap) 95% con…dence intervals. The median of total wealth is e118,792, and the 90th percentile e413,476. We excluded 42 households with wealth above e800,000. The richest households (with wealth above the 90th percentile), appear more optimistic regarding the future evolution of the stock market. An increase in wealth from the 10th to the 90th percentile, is estimated to increase the mean percentage chance of a positive nominal return by about 2 to 3 percentage points. Figure 7 compares by age, the mean percentage chance of a positive nominal return of respondents with some college education or more relative to those having at most completed high school. Broadly, the former seem to be slightly more optimistic than the latter, although both tend to similarly become more optimistic as they age.   and our replication using instead data from the TNS 2007 survey, for respondents in the same age bracket (50-80 years old). Figure shows that among the 50-80 year-olds, the probability of holding stocks is increasing in the percent chance of a positive Stock Market return, albeit in a more volatile way than in the US, since we have less observations.    Table 4 reports the distribution of responses and the response rate conditioning on age, gender and stockholding status. In accordance with the …ndings reported in  on the …nancial literacy of US adults, male respondents who are older, single and stockholders report higher mean (and a lower standard deviation of) percentage chances of a past positive nominal return. The di¤erential is 11.4 percentage points higher for men than for women. Although information broadly increases with age, irrespective of gender, the uncertainty of the reports decrease with age for males, while for females, it remains broadly constant.

C. Additional Data Validation Results
Stockholders report a higher mean by about 10 percentage points, and are around 6 percentage points more likely to give a response. Figure 8 shows that males are broadly better informed than females.  Figure 9 shows that information broadly increases until the 50th percentile of wealth (e118,792), remains constant until the 90th percentile (e413,476), only to increase again albeit very heterogeneously. The richest households (with wealth above the 90th percentile), may thus be more optimistic (and disagree more)  Note: Sample restricted to those with own or spouse/partner report of whether or not household holds 'stocks or stock mutual funds'.
regarding the future investment opportunities because they are better (and more heterogeneously) informed.
Relative to non-participation amongst the most a-uent, and in line with  …ndings, heterogeneity in stock market information appears as a di¤erent alternative to better private investment opportunities  or taxation , while encompassing the ability to process it , its sources (social interactions, trust, Guiso et al., 2008) or more broadly, …nancial literacy . Figure 10 shows that information about past stock market performance does not increase with own's educational attainement, although it broadly increases with age within educational groups.