Category Archives: Financial Literacy

Thoughts on Big Three Question #2 used to assess financial literacy: Inflation

Continuing from the savings account interest question, here I will talk about Question #2 of the “Big Three” financial literacy questions created by Annamaria Lusardi and Olivia S. Mitchell.

The prior question asked about the resultant nominal account balance of a savings account after five years earning 2% per year of interest. The second question is similar but introduces the construct of inflation and assesses understanding of erosion of savings via inflation.

2. Imagine that the interest rate on your savings account was 1% per year and inflation was 2% per year. After 1 year, how much would you be able to buy with the money in this account?
More than today
Exactly the same
Less than today
Do not know
Refuse to answer

The prior question was correctly answered by 75% of respondents to the 2015 National Financial Capability Study, but the above question was only correctly answered by 60% of respondents. If we break down respondents by educational attainment, their responses were as follows:

Inflation Question by Educational Attainment

The green (left) bars represent correctly answering the question as “less than today.” The yellow bars represent selecting “Do not know,” and the red bars represent selecting “More than today” or “Exactly the same,” both of which are incorrect. “Refuse to answer” respondents are excluded in the above statistics, and I have used the nationally representative weights provided by the FINRA foundation. The above figure is from my 2017 poster presentation on financial capability and educational attainment.

As we see, more educated respondents get the answer right more often. Although many highly educated respondents select a wrong answer, they are much less likely to select “Do not know” than those with less education.

There are many hidden assumptions in this question which can be confusing for the reader. We must assume inflation refers not to expansion of the money supply but rather to increases in prices of consumer goods. The question deals with generalities rather than specifics; the reader must assume we are talking about goods on average, rather than a particular sector. If we are talking about 16 GB USB flash drives, one would probably be able to buy more of them in a year because technology prices tend to decline, but other goods go up in price. The reader must also assume we are talking about national averages, because prices may fluctuate contrary to overall inflation in certain regions.

Respondents who understand this question are likely able to divine the difference between nominal dollars and real purchasing power. Nominally, the account balance increases from $100.00 to $101.00. This is true whether the 1.00% interest rate is an annual percentage yield (APY) or an annual percentage rate (APR) compounded quarterly or monthly. Even monthly compounding would fail to increase the resultant nominal balance to $101.01 (assuming favorable rounding errors do not occur), as $101.0046 would be rounded down to the nearest cent.

With inflation being 2.00%, this means it takes, on average, 2.00% more dollars to buy the same items a year later. For “Exactly the same” to be the correct answer, the final nominal account balance would have to be $102.00, not $101.00. This means that it took 1.96% less dollars to buy the same goods at Year 0 than Year 1, or 2.00% more dollars to buy the same goods at Year 1 than Year 0. (Incidentally, many people are baffled when I tell them about this quirk of percentages. Examples: If the stock market drops 20%, it has to go up 25% to get back where it was. At Michaels [sic] arts and crafts store, forgetting to use your 50% off coupon means you paid 100% more than you would have had you remembered.)

“How much would you be able to buy” begs a response: “of what?” The question prompt does not provide this, and it couldn’t without being unwieldy. Nonetheless, a respondent could pick “More than today” and be technically correct if they make an undesired assumption about “of what?” If we are talking about quarters, one would be able to go to the bank and get 404 of them after a year, as compared with 400 at the start. A smart aleck could argue the “wrong” answer is actually right, and we must rely on the metaphorical spirit of the law rather than letter of the law to interpret the question appropriately.

In the scenario, real returns, which adjust for inflation, are about –1% in this year, because the nominal return of 1% was overwhelmed by inflation which exceeded the return, at 2%. Specifically, real returns would be ($101.00 / $102.00) – 1, which is .9902 – 1, which is –.0098. Multiplying by 100 to get a percentage, this is –.98%. Therefore, “Less than today” is the correct response with the unlucky individual in the question prompt having lost 0.98% of their real purchasing power. The Internal Revenue Service disregards inflation and would expect income tax to be paid on the $1.00 of increase in your savings account balance, and they actually classify interest income as “unearned” income. These two facts taken together are rather insulting.

In the end, you can buy 4 more quarters, 10 more dimes, 20 more nickels, or 100 more cents. Your account balance increased $1.00 and you owe anywhere from zero to 37¢ to the IRS, and possibly up to 15¢ of state income tax (in California if your income is over $1 million for the year). However, your purchasing power has declined by almost 0.98%.

In truth, the Big Three financial literacy questions are not magical. Although their widespread use has shown us the sorry state of financial literacy both in the United States and abroad, the questions are susceptible to biases such as framing and interpretation, and to an extent they confound financial literacy with linguistic knowledge, mathematical knowledge, and/or knowledge of financial practices and institutions. Regarding framing in particular, Stolper and Walter (2017, p. 596) state:

Another shortcoming of test-based measures of financial literacy is their sensitivity to framing. Specifically, Lusardi and Mitchell (2011a, b) and van Rooij et al. (2011b) document that the answers of survey participants differ significantly based on the wording of the test questions. In fact, the percentage of correct answers doubled in the latter study when the wording for the third question of the Big Three was “buying company stock usually provides a safer return than a stock mutual fund” as compared to phrasing the question reversely, i.e. “buying a stock mutual fund usually provides a safer return than a company stock“. Hence, Lusardi and Mitchell (2014) conclude that some answers classified as “correct” might instead reflect simple guessing of respondents and highlight that measurement error might be an issue when eliciting financial ability based on test questions.

In a future post, I will discuss the final Big Three question on a single stock versus a stock mutual fund, including Stolper and Walter’s criticism of the question’s susceptibility to framing effects.

Decisions and Outcomes

Decisions and outcomes are not necessarily related. One can make a good decision that results in a bad outcome, but this does not mean the decision itself was bad. This can be represented by a simple table:

Good OutcomeBad Outcome
Good Decision
Bad Decision

Here are a few examples that come to mind:

Decision Table

We know that investing a lump sum now is better than dollar-cost averaging your way into stocks or timing the market by attempting to “buy the dip” (e.g., Williams & Bacon, 1993; Panyagometh & Zhu, 2016). Although lump-sum investing is the preferable decision, there is a nontrivial probability of an inferior outcome as compared to investing at a later time. If a bad outcome occurs, it is more salient than had a good outcome of equal magnitude occurred. However, this should basically be chalked up to bad luck. A bad outcome does not mean a bad decision was made.

Separating decisions from outcomes goes against our nature. It is contrary to human psychology. In her 2018 book, Thinking in Bets, poker champion Annie Duke calls the human prediction to judge decisions by the resultant outcomes “resulting.” Resulting is akin to confusing causation for correlation in science.

Making a bet where the odds are in your favor is a good decision, even if you lose. With more and more such bets, a result commensurate with the prudence of the decision approaches inevitability. In the stock market, you can think of each trading day as a bet, with these bets stacking up over time. Below, probabilities from Bloomberg data, compiled by Vanguard, show the probability of positive returns for S&P 500 investment time frames within the selected dates (1/04/1988 to 2/16/2018).

S&P 500 investment during 1/04/1988–2/16/2018Probability of positive return
One day.54
One week.58
One month.64
One year.83
Ten years.91

Although start and end points matter, the pattern has been shown to hold even over the duration of the stock market’s history, including the Great Depression. Above, we see the probabilities of positive returns averaged across all day, week, month, year, and 10-year periods within a 30-year range. A 54% chance of positive returns on any particular day increases to a 91% chance of positive returns during any particular 10-year period within the 30-year period sampled.

Of course, this data nevertheless shows a 9% chance of losing money in a 10-year span. However, if you are unlucky enough to have invested the bulk of your money at an unfortunate time, this does not mean your decision was bad—just that you happened to have a bad outcome. It takes longer than 10 years for the probability of positive returns to approach inevitability—more like 30 years. Time will tell whether the recent market peak on September 20, 2018 will require months, years, or more than a decade to overcome.

The financial industry is built on confounding decisions with outcomes. A hedge fund manager is said to be “hot,” endowed with stock-picking genius, if his speculations pay off in a given year. Even for investors who were lucky enough to pick him, their decision was certainly bad; picking a low-cost index-tracking mutual fund and sticking with it for many years is a better decision. The speculator’s success is based on chance and luck, not skill. The speculator’s decisions are always bad, although their outcomes may be good, for a time. Eventually, good luck will inevitably run out, leading to underperformance of the index-tracking mutual fund, or worse, a spectacular capital wipeout à la Enron or Bernie Madoff.

We must all take a step back to carefully consider whether a good outcome was actually the result of a good decision, and whether a bad outcome resulted from a bad decision, or from a good decision that should be repeated despite a bad outcome occurring this particular time. On the whole, as a series of good decisions lengthens, good outcomes become inevitable, and as a series of bad decisions lengthens, bad outcomes become inevitable. In making such determinations, our psychology and the limited information available may work against us.

This article was also posted on Tippyfi.

Thoughts on Big Three Question #1 used to assess financial literacy: Savings account interest

Regarding assessment of financial literacy, in both the United States and abroad, the “Big Three” multiple-choice questions written by Lusardi and Mitchell are typically used. Findings show that somewhere around 50% or even more people do not answer all three questions correctly, which is evidence of a widespread lack of financial literacy. This varies by sub-groups—for example, those with more education tend to do better. Overall, all groups of people do much worse than we would expect or hope, however.

The Big Three questions balance accuracy of interpretation and conciseness, but nevertheless, and not unexpectedly, there may be issues of understanding related to wording, choices, and arithmetic, rather than substance. Furthermore, as a construct, financial literacy is interrelated with and difficult to disentangle from basic mathematical skills in manipulating numbers and percentages, which might be called arithmetic skills, numeracy, or quantitative literacy. In fact, recent research (e.g., Cole, Paulson, & Shastry, 2016) is showing that taking mathematics courses may improve financial literacy more than taking personal finance courses!

Here, I will discuss the first of the Big Three questions. There are several similar questions that have appeared in the recent S&P Global FinLit Survey and elsewhere that I might also discuss in a future article, after I discuss the Big Three Questions 2 and 3 in other future articles.


Big Three Questions

1. Suppose you had $100 in a savings account and the interest rate was 2% per year. After 5 years, how much do you think you would have in the account if you left the money to grow?
More than $102
Exactly $102
Less than $102
Do not know
Refuse to answer

With this question, we are talking about nominal future dollars rather than real future dollars, although it is not explicitly stated. The major world currencies are fiat money, meaning they are not redeemable with the government or banks for land, precious metals, or other commodities. Central banks that issue currencies, such as the U.S. Federal Reserve and European Central Bank, aim to achieve a gradual devaluation in the purchasing power of the issued currency over time, which is termed “inflation.” The Federal Reserve adjusts monetary policy while presently aiming for about 2% inflation per year, through measures such as adjusting the federal funds rate (“interest rate”) via market actions and paying banks that amount of interest for keeping reserves on deposit with the Fed, and quantitative easing (QE) by which the Fed uses the fiat money and credit it creates to purchase public and private debt. In response to the 2008 financial crisis, the Fed dropped interest rates to 0%, and only began increasing rates about 1.00% in mid-2017.

In considering this question, historical context is relevant. Prior to 2008, there were times when it would be common for U.S. savings accounts to pay much more interest per year than 2%; sometimes even 5% or higher. During 2009–2017, receiving 2% interest on a savings account would have been absurdly high. Given the Fed’s low interest rates, checking and savings accounts that paid 2% during this timeframe likely did so as part of promotional gimmicks with special requirements, such as using a debit card 10 times per month or only receiving the interest rate on balances of up to $5,000. In 2018, the Fed has finally started substantially increasing rates, so as of November 2018 it is now common to find savings accounts offering 2% interest per year.

The United States still uses paper money and coin extensively. One can withdraw cash from their bank account easily, and many banks will allow customers to order $100 boxes of nickels or $500 boxes of quarters with no fee (nickels have the highest metal value of circulating U.S. coinage, besides copper cents from 1982 and prior). Therefore, it is not advisable for the Fed to reduce interest rates below 0%, because it would result in individuals and firms stuffing cash and coin into vaults or mattresses to avoid loss of principal. QE is an additional lever to stimulate the economy when the interest rate lever is already fully depressed (rates at 0%).

Returning to the question at hand, assuming (and this is an important assumption) that the reader knows we are talking about nominal rather than real dollars, the question is absurdly easy. Even if the interest was only compounded once, at the end of the five year period, the nominal account balance would be $110, which is far above $102. The correct answer is “more than $102.”

Given that the question indicates the “interest rate was 2% per year,” this implies that interest is compounded at least once per year (annually). If compounded annually, the balances at the end of each year would be as follows:
Year 0: $100.00
Year 1: $102.00
Year 2: $104.04 (note here that we pick up 4¢ thanks to compounding of the $2.00 of interest earned in the prior year; compounding continues in future years)
Year 3: $106.12
Year 4: $108.24
Year 5: $110.41

As we see above, the effect of compounding five times (once each year) instead of only one time at the end of the five-year period is an additional 41¢ in nominal interest earnings. Therefore, one could change $102 to $110 in the answer choices and “more than $110” would still be correct like “more than $102” is. As it stands, assuming the reader knows we are discussing nominal dollars, the question does not even require an understanding of compounding returns.

When we discuss “interest rate” on a “per year” basis, this infers annual percentage yield (APY) rather than annual percentage rate (APR). Although interest can be compounded once per year, it can also be compounded each quarter (four times per year), each month (12 times per year), each day (365 times per year), or hypothetically it can even be compounded “continuously,” at every instant down to infinitesimal durations (i.e., even more frequently than each nanosecond). As we approach continuous compounding we approach the Pert equation, Pe^(rt) where P is principal (i.e., $100.00), e is the transcendental mathematical constant of approximately 2.718, r is the interest rate (i.e., 2%), and t is time (i.e., 5 years). If we were to continuously compound $100.00 at a rate of 2.00% for 5 years, the result would be $110.52, which is 11¢ higher than annual compounding, as shown below (computation thanks to www.meta-financial.com):

Pert equation

Therefore, depending on frequency of compounding, ranging from one calculation at the end of five years to infinite compounding throughout the duration of five years, at a rate of 2.00%, the account winds up with a minimum of $110.00 after five years and a maximum of $110.52.

Savings accounts typically compound monthly or quarterly and advertise APY, which is slightly higher than APR. Credit cards typically compound daily and advertise APR, which is significantly lower than APY. On my financial education website I have put forth an APR to APY calculator that shows the difference; a credit card that has a 24.99% APR compounded daily actually earns 28.38% APY in interest for the credit card issuer. Naturally, financial institutions advertise APR or APY depending on what looks better to the consumer, unless compelled otherwise, and they compound likewise. Therefore, although credit cards could compound interest once each statement, they compound each day to make more money for the issuer, and although savings accounts could compound each day, banks like to compound monthly or even quarterly to reduce the amount of money they pay out in interest.

It is safe to say that most people do not have a good understanding of the difference between APR and APY, because they do not even understand basic percentage arithmetic involving only two calculations. A majority of people likely do not even understand the difference between “percent more” and “percent off.” For instance, if a coupon takes $5 off a $15 purchase resulting in paying $10 instead of $15, both of these statements are correct:
You saved 33.3% (one-third)
You got 50% more for your money

Moreover, questions frequently appear on standardized tests such as: “If a tree grows 5% per year, how much has it grown after 2 years?” The answer due to compounding is 10.25%, but many erroneously answer 10.00%, showing a lack of understanding of compounding, or potentially a mis-reading of the question.

Regarding the “do not know” and “refuse to answer” choices: Because there are only three legitimate choices, including “do not know” helps prevent guessing, but some respondents may select it when they actually have an inkling of the correct answer—particularly females, who tend to have less confidence in their ability to accurately answer the question. Not many people select “refuse to answer,” and I do not see the rationale to include this choice at all, besides consistency as compared with other questions on a financial questionnaire (such as the National Financial Capability Study) that ask participants personal questions about their finances that they may not want to answer.


I will discuss the other two Big Three questions in future articles:

2. Imagine that the interest rate on your savings account was 1% per year and inflation was 2% per year. After 1 year, how much would you be able to buy with the money in this account?
More than today
Exactly the same
Less than today
Do not know
Refuse to answer

3. Please tell me whether this statement is true or false. “Buying a single company’s stock usually provides a safer return than a stock mutual fund.”
True
False
Do not know
Refuse to answer

Before Adjusting Capital Gains for Inflation, Try Interest on Savings Accounts

Recently, a proposal has been discussed by U.S. Treasury Secretary Mnuchin and President Trump of adjusting capital gains for inflation when it comes to taxation of those gains. This has rightly been criticized as a tax break for the rich, but what has not been widely discussed is the hypocrisy and inequity of not including savings accounts, certificates of deposits (CDs), Treasury bills and bonds, and corporate bonds, which yield “interest” instead of “capital gains,” in the inflation-adjustment proposal.

Although there are no legal restrictions preventing most Americans from investing in stocks (equities), about half do not. Reasons include more pressing financial concerns, fear of loss, and a lack of understanding of how stocks work. Therefore, adjusting capital gains for inflation will mainly be helpful to wealthier Americans.

Capital gains already have numerous tax advantages over earned income, such as:

  • No 15.3% payroll taxes (7.65% employee and 7.65% employer share)
  • If older than one year (long-term), the tax rate is much lower or even 0%
  • Long-term tax rate tops out much lower (20% instead of 37%) for high earners
  • You can choose when to incur capital gains taxes (when to sell)
  • Capital gains tend to be received by high-earners, who gain the most from these advantages because they are in high tax brackets

Presently, interest on savings accounts, CDs, T-bills/bonds, and corporate bonds is taxed at the same rate as earned income and short-term capital gains. Except certain corporate bonds, these types of investments do not yield any capital gains, but rather yield interest only. Thus, none of the above benefits of capitals gains apply. Americans, especially those with lower incomes and net worths, are more likely to put their money in savings accounts, CDs, and Treasury securities rather than stocks. Therefore, they miss out not only on the capital appreciation power of stocks, which is much greater than low-risk assets over the long term; they also miss out on preferential tax treatment that already exists. To add an inflation adjustment on top of this is ridiculous.

Some may quip that stocks do pay something similar to interest, in the form of dividends, which are taxed like earned income and short-term capital gains. This is false; for most “buy and hold” investors in index funds and many individual stocks, the vast majority of dividends are treated as “qualified” dividends which are treated not like interest, but as long-term capital gains. Again, investors in stocks get preferential treatment.

Each year, banks, the U.S. Treasury, and other firms must issue Form 1099-INT to report how much interest income you received in the prior tax year on savings accounts, CDs, T-bills/bonds, et cetera. However, we should not forget that savings accounts typically pay low interest rates—sometimes as little as 0.03% annual percentage yield (APY), with the best accounts paying no more than about 2.0% APY. If we were to adjust savings interest for inflation, which is around 2.4% presently (or 2.9% including food and energy), this would be a loss rather than income! If we adjust capital gains for inflation, shouldn’t we adjust interest too?

Logisitcal challenges aside, if we were to go a step further, offering an above-the-line deduction (like we do with student loan interest) for lost purchasing power on Americans’ savings, capital gains would still be far too advantaged.

Due to the unfairness of how interest is treated, with no consideration of inflation, some have dubbed saving money a suckers’ game. Although a majority of Americans do not understand this, investing, on the other hand, is a winners’ game. The prudent step would be for the government to begin adjusting interest income for inflation but not capital gains. Even then, investors would still be receiving highly preferential treatment as compared with savers.

The Manifesto of the Financial Educator

As a financial researcher and aspiring financial educator, I’ve been thinking at length about the principles behind good financial teaching. These five ideas are by no means new or original. However, they are research-supported and not yet mainstream.

1. Behavior Under Management

Know when the student is not ready.

This is straight from Andy Hart’s podcast and conference, with support from a wealth of research in behavioral psychology, economics, and personal finance. Emotion, perception, knowledge, and experience all play an important role in why people make bad financial decisions.

It is widely accepted that younger people should be fully invested in stocks, because their time horizon is long. As they get older, volatility and profits should both be suppressed by divesting stocks into safer, less profitable assets such as bonds. However, young people commonly freak out when there is a bear market, selling their investments and even losing part of their principal. This is traumatic and may result in them never investing in stocks again, which is a worse outcome than if they had invested later in life with greater knowledge, experience, and resilience.

It is not fair to a student to advise an objectively superior course of action when it will lead to financial ruin because the student is not ready.

2. Educate in Arithmetic and Statistics

When the odds are in your favor, it’s only “gambling” if the consequences are disastrous.

Recent evidence suggests that mathematical education may be more important than financial education. The ability to perform mental computations is important, as well as skill with picturing compound interest and percentages. Understanding risk and reward over time is critical. Anyone with a complete understanding of gambling mathematics should know that as you gamble more, you get closer and closer to a guaranteed loss of money.

Investing in the whole global stock market, on the other hand, is neither speculation nor gambling because the odds are in your favor and the consequences of loss are temporary. Although the market declines in about 25% of given calendar years, over longer spans it almost surely increases from the starting point.

Insurance companies make money because they pay out less money than they take in. On average, the odds are in their favor. For any one individual or family, however, the consequences of losing the bet are disastrous. This is why it is wise to purchase health insurance, term life insurance, auto insurance, et cetera. You are insuring against uncommon yet disastrous events. Nonetheless, these disastrous events are much more likely to occur than winning a large lottery jackpot. On the other hand, purchasing insurance against minor losses, like a SquareTrade warranty or collision insurance on a car, is only necessary if these items are critical to you and you do not have the funds to replace them.

3. Make Choices Simpler

Don’t do business with businesses that put bad choices on the table. (Unless you are beating them at their own game.)

People often ask why one should pick Vanguard over Fidelity, Charles Schwab, or another firm for directing their investments. Although Fidelity and Schwab do offer low-cost index funds and arguably offer superior customer service, they are also determined to sell you on products and services that are very bad for your financial health, such as actively managed investments with high management fees.

It is an unpleasant and cognitively taxing experience to be required to repeatedly decline detrimental options. The extended warranties that are sold at the checkout counter at Best Buy are an awful deal. Likewise for trip “insurance” from your airline and GoDaddy’s upsells of inferior hosting services and over-priced options when all you want to purchase is a simple Internet domain name. It is bad enough when a business puts bad choices on the table; aggressive sales tactics are the coup de grâce.

This is why a hard rule of using cash instead of plastic is effective and beneficial for most consumers. The exception is if you are a “travel hacker” beating the credit card issuers at their own game. If you have to ask, you’re not a travel hacker. Simplifying the equation by avoiding the potential for making bad choices is worth losing a few benefits that are, by comparison, small. In some industries, all the major players violate this rule. However, when there an alternate option is available, it should usually be preferred (e.g., Vanguard, cash or debit cards instead of credit cards, etc.).

4. Inculcate a Habit of Inquiry

The squeaky wheel gets the grease.

There is plenty of information available easily via web search. For example, you can easily learn about investing, retirement accounts, or strategies for convincing your bank to waive an overdraft fee by searching Google. However, many people are not in the habit of seeking information nor asking for special consideration from a lender, bank, et cetera. There are differences between how subject-matter experts and novices seek information; novices may not know where to begin, and are typically unfamiliar with the jargon of personal finance, insurance, taxes, credit cards, mortgages, student loans, credit-reporting bureaus, and more. Therefore, it is unfair to blame them for failing to seek out information. Instead, we should educate them in the basics and encourage them to build a habit of inquiry, so they less likely to be shortchanged in their financial dealings.

In addition to educating others, we should lobby for laws and regulations that compel employers and financial institutions to conduct business in ways that do not unfairly disadvantage the non-wealthy (e.g., comprehension rules), and advocate for prosocial behaviors among employers, financial institutions, corporations, and governments that benefit the poor. For instance, it is unfair that many government benefits are not received by the most needy, due to being difficult to claim.

5. Focus on Long-Term Lifestyle Strategy

But, give tactical advice when appropriate.

Reducing bills, increasing income, and changing one’s habits is important. There are many forums and other websites about living frugally. In some ways this overlaps with Item 4; for example, one can save quite a bit on a car, phone or cable bill, rent, or terms of debt service by inquiring with sellers, service providers, landlords, and lenders. Responsible financial educators should encourage learners to (a) reduce expenses as a way of life (e.g., smaller living space, more roommates, no dining out, etc.), (b) focus on significantly increasing income by leveraging education, skills, et cetera, and (c) eliminate debts, save, and invest.

Financial education appears to be more effective when it either focuses on norms and general principles or is given tactically (i.e., “just-in-time“). The best time to tell someone how to write a check is immediately before they need to write a check. Financial advisers can serve as financial educators by offering key information and advice soon before significant financial events such as shopping for a house and mortgage. On the other hand, if this advice is offered many months or years in advance, it is neither remembered nor followed.