2.1 Survey structure

The experiment was conducted via the internet over 2 weeks in May 2010. We sampled 1,220 adults from the PureProfile online web panel of over 600,000 Australians and randomly assigned them to four treatments. PureProfile filtered the sample to ensure that all respondents currently held retirement savings (superannuation) accounts, that genders were equally represented and that the age distribution did not deviate far from population proportions. Of the 1,220 respondents, 1,199 (about 300 respondents per treatment) fully completed the survey over the internet, and were paid a flat rate of $3AUD ($3USD). The demographic characteristics of the survey sample is consistent with the general Australian population on most measures, with some oversampling of the employed and more educated, partly a consequence of selecting superannuation account holders (Table 1).

Table 1. Demographics ¹

Notes: Table shows responses to survey questions compared with Australian census population data where possible. The survey sample of 1,220 is taken from the PureProfile web panel of 600,000 Australians and filtered to ensure that respondents were over 18 and current holders of a superannuation account. The entire survey is available at http://survey.confirmit.com/wix/p1250911674.aspx.

¹ Source for population statistics: Australian Bureau of Statistics Census of Population and Housing and Household Wealth and Wealth Distribution, Australia, 2005–2006 .

Respondents completed a four-part questionnaire:

• • Introductory questions about subjects' retirement savings, including the name of their superannuation fund (pension plan provider) and the aggregate amount in their accounts;

• • 14 questions to measure financial competence as well as questions to elicit self-assessed knowledge of finance, access to financial education, use of financial advice and expectations of repeated stock market crises;

• • A hypothetical asset allocation task for retirement savings; and

• • Demographics.Footnote ⁷

2.2 Financial literacy, education and advice

The survey assessed three dimensions of financial competence: numeracy, basic financial literacy and sophisticated financial literacy (Table 2). Higher financial capability is linked to retirement preparedness (Lusardi and Mitchell, Reference Lusardi and Mitchell2009; van Rooij et al. Reference van Rooij, Lusardi and Alessie2009) increased stock market participation (van Rooij et al. Reference van Rooij, Clemens and Prast2007; Yoong, Reference Yoong2010), higher private retirement saving (Bucher-Koenen, Reference Bucher-Koenen2010) and greater portfolio diversification (Guiso and Jappelli, Reference Guiso and Jappelli2008).

Table 2. Numeracy and financial literacy responses

Note: Table shows proportion of correct responses in aggregate to numeracy and basic and sophisticated financial literacy questions. a. ‘Incorrect’ includes ‘don't know’ and ‘refuse to answer’. See notes to Table 1 for survey sample characteristics. Note that the factor analysis reassigns Q9 on money illusion to numeracy rather than basic financial literacy skills.

Numeracy is associated with general cognition, and poor numeracy has been shown to predict aspects of financial inefficiency such as low savings, mortgage defaults and mistakes using credit cards (Banks and Oldfield, Reference Banks and Oldfield2007; Gerardi et al. Reference Gerardi, Goette and Meier2010; Agarwal and Mazumder, Reference Agarwal and Mazumder2011). Numeracy questions test concepts such as fractions, percentages, division, multiplication and simple probability.

For other components of financial literacy, we follow the American Life Panel (ALP), the Health and Retirement Survey (HRS) and the Dutch Household Survey (DHS), dividing questions into ‘basic financial literacy’ covering compound interest, inflation, time value of money and money illusion, and ‘sophisticated financial literacy’ relating more closely to the asset allocation decisions frequently required for retirement saving, and covering knowledge of the differences between bonds and stocks and the impact of risk and diversification. For some questions we adapted the wording to Australian terminology and practices.

Respondents also gave a self-assessment of their understanding of finance on a scale of 1 (very low) to 7 (very high), reported current (and prior) access to financial education at school and in the workplace, and indicated if they had recently paid for financial advice. Further questions assessed respondents’ expectations of the prospect of another stock market crash within five years of the survey.Footnote ⁸

Self-assessed financial competence was high, (particularly for males) with more than 80% of respondents reporting at least an average understanding of finance. Views on the likelihood of another stock market crash in the near future were diffuse, and about 20% of respondents could not assign a probability to the prospect. The distribution of self-reported retirement savings account balances closely matched Australian Bureau of Statistics survey data (ABS, 2008), showing fairly modest accumulations, with 70% at $80,000 or less. Table 1 reports responses to key introductory survey questions.

Most respondents answered numeracy questions correctly, although 17% scored at least one incorrect response (Table 2). Results for the financial literacy questions were more variable, with only 36.5% of respondents correctly answering all basic financial literacy questions. Similarly, subjects had trouble with the sophisticated financial literacy questions, although disaggregated data not reported here showed higher scores for older respondents with large superannuation accounts. Only 35.5% of respondents correctly answered all sophisticated financial literacy questions.

To simplify econometric modeling of account choices, we constructed numeracy and financial literacy indices, along the lines of Lusardi and Mitchell (Reference Lusardi and Mitchell2009) and van Rooij et al. (Reference van Rooij, Lusardi and Alessie2009). We began by assigning a value of one to correct answers and zero to incorrect (which included ‘incorrect’, ‘do not know’ and ‘refuse to answer’) and then conducted an exploratory principal components analysis of the correlation matrix of the 14 recoded responses. Next, we retained the (three) factors with eigenvalues larger than one and applied a varimax rotation to obtain factor loadings that closely aligned with the original classification of the questions as numeracy, basic and sophisticated financial literacy. With the exception of question nine, the factor analysis preserved the original groupings. We then split the 14 instruments, into six numeracy questions, four basic literacy questions and four sophisticated literacy questions and conducted another principal component analysis. The result was three indices which could be used to describe the numeracy and financial literacy of each respondent in the modeling discussed below.

2.3 Allocation task

The discrete choice task reflects the fact that retirement portfolio decisions involve a substantial fraction of lifetime wealth, where risk preferences shape choices. We asked subjects to choose an investment option for their entire current mandatory retirement accumulation and all future contributions under a (hypothetical) simplification of retirement savings arrangements by the Government. Such regulatory simplifications have been enacted in the recent past and made a plausible context for the survey (Super System Review, 2010).

The instructions for the experiment are reproduced in Appendix 1 and present a simplified retirement savings scheme in which the only investment options are a 100% bank account (‘bank’) with a guaranteed real rate of return, 50% bank account and 50% growth assets (‘50:50’) and 100% growth assets (‘growth’) comprised of risky financial assets such as ‘shares and property’. The experiment instructions did not specify the exact composition of the growth account for two reasons: first, growth options in Australian superannuation investment menus often include a wide range of conventional and alternative asset classes and respondents may be distracted by descriptions of relatively unfamiliar alternative assets such as private equity and infrastructure. Secondly, as far as possible, we wanted to deflect attention away from current conditions in a particular financial market and encourage respondents to focus on the information given in the choice sets. Although we anchored the experimental settings of risk and returns in historical data, we did not say that they were past rates of return or risk levels to avoid, as far as possible, confounding the experimental information with personal views on the predictability of returns or parameter uncertainty.

We asked respondents to select which option he or she would be most likely to choose, and which option he or she would be least likely to choose, in a series of settings in which average real returns remain the same but levels of risk and presentation of risk vary. There are 36 settings in total in the experiment, of which each respondent sees 12. Each setting presents the annual returns net of inflation (2% for the bank account, 3.25% for the 50:50 account, and 4.5% for the growth account) together with a presentation of risk for the 50:50 and growth accounts. (Figure 1 shows an example choice set.) The 12 settings are the product of four risk levels (common to all respondents) and three of the nine risk presentations, which we now describe.

Figure 1. Example investment choice task. Note: Figure shows example investment choice task using presentation 3 (P3 as defined in Table 3) at risk level 1. There are 36 such settings in total. Each of 1,199 survey respondents answered 12 such tasks where rates of returns stayed constant and risk level (×4) and risk presentation (×3) varied.

2.4 Risk presentations

Presentations: We utilized modified versions of standard risk formats, drawn from retail financial documents in Australia and the United States, as well as from related studies (Vlaev et al. Reference Vlaev, Chater and Stewart2009). Table 3 sets out the nine formats. Presentations 1, 2 and 9 give returns ranges expressed as annual percentages with the probability of falling outside or within the range expressed as a frequency (‘1 in 10’, ‘9 in 10’) via text (P1 and P2) and as a graph (P9). Graphical presentation of returns ranges were proposed as a preferred risk disclosure format in the recent public review of the Australian retirement system (Super System Review, 2010, Chapter 4, p. 118) and ranges of returns for investment asset classes appear in typical retirement fund prospectuses, such as AustralianSuper, one of the largest general membership retirement funds in Australia.Footnote ⁹ Similarly, The Vanguard Group (US) use a risk description in mutual fund disclosures where the minimum and maximum quarterly returns over a 10-year period are reported via text, the implicit frequency of these events being around 1 in 20.Footnote ¹⁰ Following Vlaev et al. (Reference Vlaev, Chater and Stewart2009), to test sensitivity to range information, we break it down into right and left tail quantiles in presentations 3 and 4. The left tail quantile corresponds to Value at Risk measures more commonly used in institutional risk management and banking regulation (Jorion, Reference Jorion2007) and but which appears in some pension fund documentation.Footnote ¹¹

Table 3. Alternative presentations for investment risk

Notes: Table shows nine alternative formats for investment risk information as inserted into retirement savings choice sets (see Figure 1). Each respondent answered 12 choice sets (3 out of the 9 presentations×4 risk levels). The nine investment risk presentations were arranged into four presentation groups then randomly assigned to one quarter of the sample of respondents: group A, 1, 2 and 9; group B, 3, 4 and 9; group C, 5, 6 and 9; and group D, 7, 8 and 9. Values of x and y depend on quantities derived from four log normal growth account returns densities with mean equal to 1.045 and standard deviation taking four values from the 0.12 to 0.28. Table 3 reports all x and y values that entered the risk presentations.

Presentations 5 and 6 convey risk as the average number of years in 20 that returns will be positive or negative. The negative frame of this presentation was recommended as good practice for investment risk descriptions by the Australian prudential regulator and is now mandatory in short form product disclosure statements.Footnote ¹² The positive frame of this format has also been used by retirement funds.Footnote ¹³ We also introduce presentations 7 and 8, which benchmark against the bank account, the risk-free rate. For P7 and P8, the average number of years below benchmark sometimes includes a half-year (e.g., 9.5 years in 20) because of different underlying risk levels implied the same number of whole years with rounding in several cases.

Framing effects occur where changing the statement of an objectively equivalent scenario tilts preferences in different directions (Tversky and Kahneman, Reference Tversky and Kahneman1981). Numerous studies have demonstrated the sensitivity of preferences to lottery outcomes framed as gains or losses but investigation of framing effects have widened to include many additional modes of presentation and different contexts, including retirement savings choices returns. (Levin et al. (Reference Levin, Schneider and Gaeth1998) gives a survey and typology of framing studies. See Maule and Villejoubert (Reference Maule and Villejoubert2007) for a more recent review.) The presentations utilized here are not always objectively equivalent scenarios: presentations 1 through 4 and presentation 9 convey risk through the cumulative distribution function of annual returns whereas presentations 5 through 8 convey risk through the frequency of returns exceeding or falling below simple reference points or benchmarks. Presentations 3 and 4 inform respondents about either the left or right tail of the returns distribution, whereas presentations 1, 2 and 9 give information about both tails. We include these information differences in the experiment because financial service providers and regulators do not confine themselves to presentations that are strict reframings of equivalent content when comparing disclosure formats.

Some subsets of the nine presentations do convey equivalent information and allow conventional framing tests. Presentation 1 emphasizes the likelihood of returns within the range, presentation 2 emphasizes the complementary likelihood of returns outside the range, and presentation 9 shows the range in a graph. These three create a test of sensitivity to wording that emphasize the center or the tails of the returns distribution (P1 versus P2) and also of changing from text to graphs (P1 and P2 versus P9). Similarly, presentations 5 and 6 (7 and 8) convey equivalent information on gains or losses around a benchmark.

We arranged the nine investment risk presentations into four groups (denoted ‘presentation groups’), each made up of three risk presentations with the visual range graph (P9) common to each group. For one group of respondents, A, the presentations are 1, 2 and 9; for group B, 3, 4 and 9; C, 5, 6 and 9; and for group D, 7, 8 and 9.

Investment risk levels: The standard deviation of returns to the growth asset enters the choice sets at four levels ranging from 12% to 28% p.a. Every subject made choices across all four risk levels in each of three of the nine presentations. Table 4 reports the simulated values that entered the risk presentations. By holding the expected return constant and allowing the risk of the 50:50 and growth accounts to vary, we created mean-preserving spreads of the returns distributions. Bateman et al. (Reference Bateman, Ebling, Geweke, Louviere, Satchell and Thorp2010) gives a description of the theoretical model and underlying returns densities used to calibrate the choice sets.

Table 4. Investment risk levels and presentation parameters

Notes: Top panel shows net rates of return entered into retirement account choice sets (see Figure 1 for example choice set), and four volatility levels of the distributions of mixed and growth account returns. Lower panel shows numerical values entered into choice sets for presentations 1–8 at four risk levels (Table 2).

The experimental design provided nearly 14,400 rankings of the three accounts: around 1,200 per format for P1–P8, and nearly 4,800 for P9. In the econometric analysis below, we concentrate on explaining ‘most preferred’ choices using investment risk, risk presentation, financial competence and demographics. This allows us to estimate presentation effects on stated preferences for retirement investments in a general framework.Footnote ¹⁴

4.1 Investment risk

The benchmark (median) respondent is 35–44 years of age and has a retirement savings account balance of $20,000–39,900, considers the prospect of another large stock market crash within the next 5 years to be as likely as not (a ‘toss-up’) and has numeracy and basic and sophisticated financial literacy scores above the (zero) mean at 0.466, 0.227 and 0.272, respectively. Along with all other respondents, this individual evaluated the graphical risk presentation (P9). If the underlying risk level of the growth account is set at 20% p.a., a respondent with this median profile chooses the bank account with a 1.9% probability, the 50:50 account with a 76.9% probability and the growth account with a probability of 21.2% (Table 6, last row, third column) showing a preference for the middle choice among three of increasing risk, consistent with Benartzi and Thaler (Reference Benartzi and Thaler2002).

Table 6. Predicted account choice probabilities for median respondent

Notes: Table shows estimated choice probabilities for retirement savings account choices for median respondent by risk level and risk presentation. The median respondent is 35–44 years of age and has a retirement savings account balance of $20,000–$39,900, considers the prospect of another large stock market crash within the next five years to be as likely as not (a ‘toss-up’) and has numeracy and basic and sophisticated financial literacy scores of 0.466, 0.227 and 0.272, respectively. Approximate standard errors, computed using the delta method, are in brackets.

Moving along the last row of Table 6, holding risk presentation fixed but allowing the risk level to increase, we see that the probability of choosing the growth account declines by 9 percentage points (standard error of 3%) as volatility rises by 16 percentage points, while the bank account gains 1 percentage point and the 50:50 account, 8 percentage points. This pattern of risk aversion holds for all presentations. The largest change in choice probability due to increasing volatility is estimated for P4, when only the chance of left tail returns are reported. (Note that P4 does not give information about possibly high returns, just as P3 does not give information about possible low returns, so we anticipate more extreme responses.) In this case, the probability of the median respondent choosing the bank account increases from 48% to 65% for a 16 percentage point increase in risk. Overall, however, the effect of increasing returns volatility on stated preferences is modest.

4.2 Presentation effects

To give some context to presentation and framing effects described here, we can compare account choices using a certainty equivalent wealth measure. Differences in preferences, work history and background wealth make measuring individual welfare losses due to misperception of risk very difficult. As a rough guide to the potential impact of choosing the ‘wrong’ account, Table 7 shows certainty equivalent wealth reductions at retirement for a representative plan member with CRRA preferences who chooses the wrong account. Take a worker who earns a constant real wage close to the current median (around $50,000 p.a.) for a 30 year working life and who contributes a fixed $4500 p.a. (9%) to a retirement savings account that is invested in either the growth, 50:50 or bank accounts. (When investing in the growth account, this strategy results in accumulations of around $290,000, in the 50:50 account of close to $230,000 and over $190,000 in the bank account). Assuming that returns are net of fees and taxes and allowing growth account risk to take one of four values from 12% to 28% p.a., we simulate the expected utility of 10,000 retirement wealth values for relative risk aversion levels from 0 to 8 then compare the certainty equivalent wealth levels at retirement.

Table 7. Variations in certainty equivalent retirement wealth (percent reduction in optimal wealth)

Notes: Table reports percentage reduction in certainty equivalent wealth at retirement due to suboptimal allocation of retirement savings to growth, 50:50 or bank account for CRRA investor. Optimal choices are indicated by 0%. Certainty equivalent wealth is computed as the inverse of expected utility of 10,000 simulated values of retirement wealth for a worker contributing $4,500 p.a. into an account over a 30 year working life. Agents annuitize wealth at retirement. Growth account returns are computed as 30 draws from a lognormal distribution with mean 1.045 and standard deviation of 0.12, 0.16, 0.20 or 0.28. Bank account returns accumulate at a constant gross return of 1.02 p.a.; 50:50 account returns are the sum of half the growth account return and half of the bank account return.

Welfare comparisons for retirement depend on mortality, future investment and spending patterns, so to simplify here, we assume that members purchase a lifetime annuity with their accumulation.Footnote ¹⁵ On this basis, the cost of mistakes range from as little as 3% to as much as 74%. At the lowest risk level, a plan member with risk aversion at or below unity would be 30% worse off if they chose the bank account instead of the risky account. The opposite extreme is a very risk averse member who mistakenly chooses the risky account at the highest risk level and is 74% worse off in utility terms. For members with relative risk aversion in the more conventional range of 0.5–3, losses range from 3% to 44%. So if presentation and framing distort choices, mild to moderate losses for plan members are likely.

Compared with the effect of higher risk, the changes in account choices due to switching risk presentation are dramatic: we see much greater variation down the columns than along the rows of the Table 6. Switching from text to graphs for example, has a large impact. Visual displays of risk are popular in documentation and may help understanding of numerical risks by effective depiction of proportions, by evoking automatic mathematical operations and facilitating better comparisons (Lipkus, Reference Lipkus2007). Here, the range graph (P9) is associated with the least probability of choosing the bank account and highest probability of 50:50 and growth account choice probabilities. Under P1, for instance, the growth account choice probability declines by 6 percentage points as risk rises from 12% to 28%, but keeping risk constant and reframing from text to graph (switching from P1 to P9) causes an increase in growth account probability of nearly twice that amount, 11 percentage points.

The largest switch in choice probabilities within the same treatment group is for Group B, when respondents see the upper (P3) and then the lower (P4) tail values at risk. It appears that this group does not infer that a high probability of losses also implies a high probability of gains when evaluating accounts, and exhibit more caution than recklessness. Their flight-to-safety when presented with the lower tail risk is much larger (57% probability of choosing the bank account and 3% of choosing the growth account) than the switch to growth when seeing the upper tail risk (23% probability of choosing the growth account). For investors with relative risk aversion of one or less, if hearing only about lower tail risk leads to a mistaken choice of the bank account rather than the risky account, welfare losses as high as 30% may follow (Table 7).

The least variation in probabilities is for changes in the range presentations (Group A) where choices are largely constant despite P1 emphasizing the center of the returns distribution and P2 emphasizing the tails. The stability of choices under range presentations confirms results of Vlaev et al. (Reference Vlaev, Chater and Stewart2009) .

Benchmark presentations (P5–P8) induce generally more conservative choices and show more variation than range presentations (P1, P2 and P9). Just changing the benchmark from a zero return to the bank account return creates a 30 percentage point variation in the probabilities of choosing the 50:50 account and close to 20 percentage point variation in probabilities of choosing the bank account. These mistakes are also potentially costly: wrongly choosing 50:50 over bank or vice versa can penalize utility of wealth at retirement by between 5% and 35% (Table 7). Within-group variations for Group A, and for the first two presentations in Groups C and D, are strict framing effects and we consider these next.

4.3 Framing effects

Beginning with Tversky and Kahneman's (Reference Tversky and Kahneman1981, Reference Tversky and Kahneman1986) Asian Disease problem, most framing experiments find that people accept more risk under loss frames and less risk under gain frames (Levin et al. Reference Levin, Schneider and Gaeth1998). However, when we give subjects a choice among three accounts of increasing risk, the impact of loss and gain framing on risk aversion is not monotonic. Here we find that loss versus gain framing causes people to choose the 50:50 account more, and both the bank and growth accounts, less. The effects of loss and gain framing contrast in group C and D choices, where respondents see the average frequency in a 20-year period of experiencing returns above or below a benchmark. For example, when shown the gain frame P5 (average number years out of 20 when returns will be positive at 20% risk, Table 6), the median respondent chooses the bank account with 28% probability, and when shown the same information reframed as a loss (P6), this probability falls to 12%, consistent with the standard result. However, the growth account probability is higher (14%) for the gain frame than for the loss frame (9%) indicating that the gain frame leads to more risk tolerant behavior. Clearly, if the probability of bank and growth both go up, the probability of choosing the 50:50 account must be much lower under the gain frame (58%) than under the loss frame (79%). (All these effects are large relative to the estimated standard errors.) In other words, rather than uniformly inducing risk aversion, information about frequencies of positive returns shifts choices away from the 50:50 account toward both the safe and risky extremes, whereas emphasizing negative returns does the reverse.

Moreover, when respondents are told the average number of years out of 20 when returns will be above (P7) or below (P8) the bank account, we find the same pattern of choices shifting away from the extremes, but now reversed for gains and losses. Here, the median respondent chooses the bank account and the growth account with a significantly higher probability, and the 50:50 account with significantly lower probability, when the frame emphasizes losses (P8). So in one reframing (P5 and P6) ‘gains’ induce extreme account choices and in the other reframing (P7 and P8), ‘losses’ do.

At this point we need to distinguish between using ‘framing’ as the label for internal representation of a choice by the decision maker and ‘framing’ as the way the problem is formulated by the experimenter (Maule and Villejoubert, Reference Maule and Villejoubert2007). It seems likely that either our classification of P5 as a ‘gain’, or P8 as a ‘loss’, does not fit the internal representations of the survey respondents but we cannot infer which classification might be wrong. What is clear is that reframing losses as gains does not change risk preferences monotonically, as often concluded in past studies, but shows up as a movement toward the middle from the extremes. Further, these reframings may be important: the 50:50 account is optimal at several risk levels for investors with CRRA parameters of 1–3, and shifting to the extremes can result in losses of 4%–20% of certainty equivalent wealth.

Finally, presentations 1 and 2 are textual reframings of the range graph and this reframing is associated with a substantial change in choice probabilities. Switching to the graphs from P1 or P2 raises the probability of the median respondent choosing the growth account by around 10 percentage points (standard errors about 2%), whereas switching emphasis from the center of the distribution (‘9 in 10 chance of a return between’) in P1 to same information emphasizing the tails (‘1 in 10 chance of a return outside’) has no significant effect. By constrast, some psychological studies show that graphical representations of risk reduction induce a greater willingness to pay to avoid risk than numerical information (see, for example, Schirillo and Stone, Reference Schirillo and Stone2005).

4.4 Variations in numeracy

Figures 2–4 show an array of graphs that capture the effects of risk level and risk presentation on choice probabilities at varying levels of financial competence, and we turn to those results now. Each graph shows the probabilities of choosing the bank, 50:50 and growth accounts as either numeracy (Figure 2), basic (Figure 3) or sophisticated (Figure 4) financial literacy index scores move from the 1st to the 99th percentile. Standard errors for each choice probability computed using the delta method are summarized in the figure notes. Each row of the figures corresponds to one of the nine risk presentations (P1–P9) and the four panels along each row correspond to the risk level for the growth account indicated near the head of the figure (12% to 28%).

Figure 2. Probabilities of account choice as a function of numeracy. Notes: Each panel indicates the predicted probability that a respondent chooses the bank account (black), 50:50 account (pale gray) and the growth account (dark gray) as a function of the quantile of the respondent's numeracy score (horizontal axis). The panels in each row correspond to a given risk presentation, indicated at the left end of the row and defined in Table 3. In each row, each of the four panels corresponds to the risk level indicated near the head of the table. All other respondent characteristics are set to median values. 90% of the standard errors fell between 0.0032 and 0.0502.

Figure 3. Probabilities of account choice as a function of basic financial literary. Notes: Each panel indicates the predicted probability that a respondent chooses the bank account (black), 50:50 account (pale gray) and the growth account (dark gray) as a function of the quantile of the respondent's basic financial literacy score (horizontal axis). The panels in each row correspond to a given risk presentation, indicated at the left end of the row and defined in Table 3. In each row, each of the four panels corresponds to the risk level indicated near the head of the table. All other respondent characteristics are set to median values. 90% of the standard errors fell between 0.0028 and 0.0570.

Figure 4. Probabilities of account choice as a function of sophisticated financial literacy. Notes: Each panel indicates the predicted probability that a respondent chooses the bank account (black), 50:50 account (pale gray) and the growth account (dark gray) as a function of the quantile of the respondent's sophisticated financial literacy score (horizontal axis). The panels in each row correspond to a given risk presentation, indicated at the left end of the row and defined in Table 3. In each row, each of the four panels corresponds to the risk level indicated near the head of the table. All other respondent characteristics are set to median values. 90% of the standard errors fell between 0.0034 and 0.0509.

Numeracy scores depend on correct answers to questions testing general arithmetic skills with no stronger link to retirement savings decisions than to other financial decisions, but changes in numeracy have some surprising effects on account choices. At very low levels of numeracy, the model predicts high probabilities of choosing the growth or bank accounts that decline in favor of the 50:50 account as numeracy improves. For example, the bottom right panel shows the least numerate have choice probabilities for bank, 50:50 and growth of 7%, 57% and 36%, whereas the most numerate have probabilities of 2%, 81% and 17% (standard errors below 2%). This pattern can be seen for all risk presentations except P3 and P4, suggesting that very innumerate respondents may tend to choose concentrated portfolios in preference to mixtures.

Further, changes in choice probabilities due to presentation switches are larger as numeracy declines. For example, moving from P2 to P9 (reframing range information from text to graph) at the highest risk level, changes the choice probabilities for bank, 50:50 and growth by an average of 20 percentage points for the least numerate but by an average of 5 percentage points for the most numerate.

Our results confirm Peters and Levin's (Reference Peters and Levin2008) finding that numeracy moderates framing effects. They attribute this to a tendency of innumerate subjects to integrate fewer items of information and to respond more to non-numeric information sources. In addition, several existing studies show that higher cognitive scores are correlated with lower risk aversion and lower error rates in complex decisions (see, among others, Burks et al. Reference Burks, Carpenter, Goette and Rustichini2009), although Dave et al. (Reference Dave, Eckel, Johnson and Rojas2010) demonstrate that risk aversion measures from innumerate subjects are sensitive to elicitation method. Our results do not necessarily connect low numeracy with low risk aversion rather a tendency to choose at the extremes. This can be costly to moderately risk averse investors, as we observe in Table 7.

4.5 Variations in basic financial literacy

Unlike innumerate subjects, respondents with poor basic financial literacy prefer the bank and 50:50 accounts over the growth account but as basic financial literacy improves, subjects begin to accept more risk (Figure 3) overall. In terms of the estimated model, the main source of this increasing preference for riskier accounts is shifting intercepts. The positive estimates of alternative-specific constants for basic financial literacy scores, α_{j, 12}, cause the odds of the risky account choices to rise as the basic scores rise. However, the coefficient on the interaction between basic literacy and the underlying risk level of the growth account, β _{j, 3}, is negative and works to reduce the demand for risky accounts as risk and basic literacy rises. In other words, respondents who score well in the key components of basic financial literacy (time value of money, compounding and inflation) have a mean tendency to accept riskier investments, but at the same time are more sensitive to changes in risk than respondents who score poorly on the basic literacy score.

A close examination along the rows of Figure 3 shows that choice probabilities change more at the right-hand side than at the left-hand side of each graph. For example, shifting from the first panel to the fourth panel in the bottom row (P9) covers an increase in growth account volatility of 16 percentage points. This large rise in risk causes no significant change in choice probabilities by subjects with low basic literacy, whereas for subjects with high basic literacy, the same increase in volatility means a significant decrease in choices of growth (from 25% to 15% with standard errors below 2%). In other words, respondents with basic literacy scores two or more standard deviations below the mean become insensitive to rising risk, whereas at the same time choosing more conservative accounts overall than their more literate peers. Consequently, individuals with poor basic financial literacy are unlikely to switch to higher yielding growth portfolios even if investment risk declines sharply. If the tendency of those with poor financial literacy to choose safe accounts is due to misunderstanding the risk-return trade offs, rather than because of risk aversion per se, they can end up much worse off. Growth and 50:50 account choices are likely to be optimal for moderately risk averse investors at historically average volatilities, and certainty equivalent wealth penalties of 4%–30% could apply for failing to make the risk-return trade off (Table 7).

Presentation effects are reduced by better basic literacy but not removed. For example, moving from P2 to P9 at 28% risk changes the choice probabilities for bank, 50:50 and growth by an average of 17 percentage points for the lowest basic literacy percentile, but by 5 percentage points for the highest percentile. The changes exceed two standard errors at both the lowest and highest percentiles of basic literacy.

4.6 Variations in sophisticated financial literacy

Figure 4 shows the same analysis holding numeracy and basic financial literacy constant at median scores and allowing sophisticated financial literacy to vary. Improvements in sophisticated financial literacy – knowledge of diversification and the risk and return features of financial assets – is associated with a greater probability of choosing growth and 50:50 accounts. However, unlike the previous two measures of financial competence, risk sensitivity and preference for mixed accounts is relatively constant across different sophisticated financial literacy levels.

We continue to observe many large presentation effects even at high levels of sophisticated financial knowledge although some effects are reduced. In particular, reframing from text to graph creates a significant change in choices at the lowest sophisticated literacy quantile, but not for the highest. Moving from P2 to P9 (reframing range information from text to graph) at 28% risk changes the choice probabilities for bank, 50:50 and growth by an average of 12 percentage points for the lowest sophisticated literacy percentile but only by 4 percentage points for the highest percentile. Changes at the highest sophisticated literacy percentile are smaller than two standard errors.

4.7 Profiles of respondents by investment account choice

Finally, we profile the respondent most likely to select the growth or bank accounts. Setting aside the effects of risk presentation, the probability of choosing the growth account is maximized at 94.4% for a respondent of any age but of maximum wealth, who considers the prospect of another stock market crash within the next 5 years as ‘very unlikely’, who has relatively poor numeracy, but high sophisticated and basic financial literacy and who is making choices at the lowest volatility level for the risky asset. (We count 87 respondents who score below the median for numeracy but above the median for other financial literacy measures, and 150 respondents who score above median for numeracy and below median for the other financial literacy scores.) This respondent has a 5.5% chance of selecting the 50:50 account and his or her probability of choosing the bank account approaches zero. The respondent most likely to choose the bank account is among the 18–24 years age group, the lowest wealth level, is uncertain about the probability of a future stock market crash, and has relatively high numeracy skills but low basic and sophisticated financial literacy. For this profile, the probability of choosing the bank account is 93.2%, with a 6% probability of choosing the 50:50 account and a 0.9% probability of choosing the growth account.