I Was Told There Would Be No Maths

Published in Investing on 23 February 2012

Miscalculating your way to financial mistakes.

A version of this article originally appeared on our US site, Fool.com.

In a 2009 NBC/Wall Street Journal poll, 8 in 10 Americans said they were concerned about the federal deficit and growing national debt.

But a separate poll that same year asked, "How many millions are in a trillion?" and 79% of Americans either answered wrong or didn't know.

Think about that. Eight in 10 Americans are worried about the national debt, but the same number can't accurately put the numbers into context. How do you know if $15 trillion of debt is dangerous if you don't know what a trillion is?

Deficits are something to be concerned about. But a bigger threat to your personal finances exists: innumeracy.

In a recent paper titled "Numeracy, Financial Literacy, and Financial Decision-Making," Dartmouth economist Annamaria Lusardi came to a shocking conclusion: Most young baby boomers about to enter retirement struggle with basic, real-life financial arithmetic. And those who need the most financial knowledge tend to be the most innumerate.

Here's an example:

"Let's say you have 200 dollars in a savings account. The account earns 10 percent interest per year. How much would you have in the account at the end of two years?"

Take your time. Feel free to use a calculator. What's your answer?

When asked, 82.2% of those age 51 to 56 couldn't produce the right answer ($242). Of those who answered wrong, about half erred by ignoring that interest accrues on both principal and interest -- compound interest.

That was one example of many. Given three basic questions on interest, division, and percentages, only a small fraction of those about to enter retirement could answer all correctly.

"These are pretty dismal findings, considering the complexities of the calculations involved in many financial decisions," Lusardi writes.

Dismal and scary. In 1979, 38% of private-sector workers were covered by an employer-provided pension plan that required minimal planning on their part. By 2008, just 15% were. At the same time, defined-contribution plans that require workers to plan and manage their own funds ballooned, covering 43% of workers in 2008 from 17% in 1979, according to the Employee Benefit Research Institute. Unlike the past half-century, Americans' "retirement security will depend ever more on their own decisions" going forward, Lusardi writes. And yet look at where we are. 

But what's fascinating about all of this is that the standard response -- that we need more financial education and more emphasis on financial literacy -- may not be the complete answer. Lauren Willis at Loyola Law School has shown (link opens PDF) that financial-literacy programs can actually be harmful to people's financial wellbeing. 

How? For some, it increases confidence without improving ability. You can imagine someone taking a one-day class on derivatives trading and suddenly thinking they're George Soros, only to watch their portfolio disintegrate through hyperactive and ill-informed trades. That's an extreme example, but it captures how people actually behave. Put simply, there is "no reliable empirical evidence that financial-literacy programs are effective," Willis writes.

The key to getting people to make smarter choices with their money, then, may not be financial literacy or numeracy in itself. It's combing literacy with a proper understanding of the softer sides of financial knowledge -- things like behavioural finance, psychology, and emotional intelligence. Widespread innumeracy is a sign that financial education is lacking. But it's the emotions of finance that really influences how people manage their money.

Take a well-known example. In 1998, the hedge fund Long Term Capital Management, staffed thick with Ph.D.s and two Nobel laureates, exploded under an almost incomprehensible amount of leverage. Behind the failure was management's utter lack of emotional control. "The young geniuses from academe felt they could do no wrong," wrote Roger Lowenstein in the book When Genius Failed.

Warren Buffett later said this about the firm's 16-person management team:

"They probably have as high an average IQ as any sixteen people working together in one business in the country ... just an incredible amount of intellect in that group. Now you combine that with the fact that those sixteen had extensive experience in the field they were operating in ... in aggregate, the sixteen probably had 350 or 400 years of experience doing exactly what they were doing. And then you throw in the third factor: that most of them had virtually all of their very substantial net worths in the business. ... And essentially they went broke. That to me is absolutely fascinating."

The managers of LTCM had higher financial literacy and were more numerate than almost anyone on the planet. And they literally went bankrupt.

On the contrary, three years ago I interviewed hedge fund manager Mohnish Pabrai, whose track record puts him among the top money managers of the past decade. Pabrai doesn't use analyst teams. He doesn't use complex spreadsheets. There are no Bloomberg terminals in his office. I'd be surprised if he owns a calculator. When I asked him what his edge was, he replied, "Control over my emotions." That's it? I asked. "It's huge. You'd be surprised."  

Pabrai understands finance, of course. He's quite numerate. But it's the emotional intelligence he applies to that knowledge that allows him to make smart financial decisions while so many others make mistake after mistake. That speaks volumes about what a useful financial education should include.

So what's the solution? We do need more financial education that teaches basic numeracy, but that education should first and foremost teach the emotional constraints of finance. After all, it doesn't help to know what APR is unless also taught that bankers selling loans rarely have your best interest at heart. 

Knowing how to read a balance sheet doesn't help unless you also appreciate the biases that cause investors to buy high and sell low. And understanding compound interest won't help without conquering the social pressures that prevent people from saving money in the first place. We must focus on fixing America's innumeracy. But it's like Aristotle said: Intelligence without wisdom is worthless.

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Comments

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goodlifer 23 Feb 2012 , 10:47am

Ah, the serene beautiful magic of 'e' and of compounding!

I've read somewhere that those who don't understand it end up paying all their money to those who do.

Hannibalis 23 Feb 2012 , 3:32pm

Interesting that the maths question on interest (how much is $200 worth in 2 years @ 10%?) ignored *tax*. As well as being able to calculate percentages and yields, you need to know how to avoid paying tax on the income. That makes the difference between a good return and a great return.

In addition to avoiding tax, it is also sometimes possible to get the taxman to actually give you money.
http://www.the-diy-income-investor.com/2011/01/avoid-tax-legally.html

tux222 23 Feb 2012 , 5:37pm

Interesting also that the questioner thought (presumably) that 242 was right and 240 was wrong. The question as reported here didn't even say "compounded annually" or "with interest paid annually". Personally I'd call $240 "right enough".

Surely the real worry is how many people said "haven't a clue" or gave answers wildly different from $240. People like that were allowed to get mortgages that they couldn't afford and couldn't work out that they couldn't afford, and the rest is recent history.

I recently had a checkout operative try to give me £17.23 change from a £10 note -- and argued with me when I pointed out his mistake! "Till says £17". Oh dear.

tux222 23 Feb 2012 , 5:51pm

By the way, as well as tax you have to consider inflation. the simplest calculation is 10% interest (I wish!) taxed at 20% is 8%. Subtract inflation of (say) 4% and you have 4% real per annum. Over two years your real return is about 8% and youy get back money *worth* something like $216 in today's money. Compounding is irrelevant compared to uncertainties of future inflation and tax rates, which you have to guess at.

For a realistic UK savings account paying 4% the rate after 20% tax is 3.2%, the rate after inflation is minus 0.8%, and after two years you get back money worth about 197 today.

ANuvver 23 Feb 2012 , 6:16pm

goodlifer:

The rules of 72 and 69 should be taught at secondary level! Speaking of which, it amuses me that, while you can get into the stratosphere with higher maths if you wish, all you really need as an investor is + - / *, basic algebra and the concept that percent means "over 100".

Hannibalis:

Literal: in your second par you mean "(and by State in the US)".
There are certain investments that are offshore but ISA-eligible - ie income comes gross and HMRC can go jump.
And from a CGT perspective, an ISA wrap is a natural place for people to indulge their multi-bagging lust.

tux:

Ah yes, till dependency... When I used to work in West End bars you had to memorise the price list and be tested on it before you even started the job. Even when itemised till systems came in later, you had to tot up the round in your head before you went near the till.

And the ability to ask: "same again?" on a 12-drink order was guaranteed to bring a tip!

Still, probably less important now that most people pay by card or run tabs. I was surprised to learn recently that my local boozerie only carries a cash float of £80.

ANuvver 23 Feb 2012 , 6:21pm

tux:

Oh and your checkout person should be introduced to the old practice of leaving the clip up on the relevant note drawer while issuing change. Training these days...

goodlifer 23 Feb 2012 , 11:48pm

Thank you, ANuvver

Ashamed to say I'd never heard of the rule of 69.
When would you prioritise it over the rule of 72?
Why aren't there rules of 70 or 71?
Or are there?

Perhaps they should also be shown how easy it is to get a precise answer by using the log buttons on their calculators.

breelander 24 Feb 2012 , 12:58am

Why aren't there rules of 70 or 71? Or are there?
70 is ok, but 71 is a prime so not much use. Now, 69.3, that's a nice rule... :-)


Ok, ok, I had to look it up in Wikipedia...
http://en.wikipedia.org/wiki/Rule_of_72

spinquark 24 Feb 2012 , 1:06am

Isnt the bigger point here that the idea of self provision and self managed pensions is actually a very bad idea for the majority of the population because the majority lack the competences needed to make effective long term pension decisions and will always do so.

In the end people who get their self provision wrong will have to be bailed out by the rest of us through the tax and benefit system.

What we really need is a system where essential pension provision and management is provided through say an employer funded arrangement managed by a properly qualified and representative set of trustees. Oh dear seems I am describing good employer provided defined benefit arrangements - just what politicians have selfishly destroyed over the last 15 years.

ANuvver 24 Feb 2012 , 1:52am

goodlifer:

69 is generally more accurate, 72 is best around 8% or so. But 72's good enough as damnit and is so deliciously factorable...

I suspect it's a bit much to expect people to cope with:

0.3 / log (1.08)
eg for 8% increase

for the exact result.

goodlifer 24 Feb 2012 , 11:23pm

Have to admit I've always used 70 or 72.
Between them they're multiples of every number up to 14, apart from 11and 13.

69's only good for 3 and 23; 3's covered by 72, and not many us actually need 23.

My calculator says the actual time for 3% to double is something like 23 years, 23 weeks, 3days, 6 hours, 42 minutes and 12.7 seconds.

So 69 is, as ANuvver says, more accurate than 72, but only by a whisker.

Is it really sensible to expect such accuracy from simple rules of thumb?
:

ANuvver 25 Feb 2012 , 4:33pm

Oh sure, thumbs are thumbs. I agree that 72 and 70 are far more useful.

Bit like the old Celsius-Fahrenheit deal. Multiply by 9/5 is all very well if the numbers fall conveniently, but there's nowt wrong with "double it and knock off a bit"!

I'd venture that a lot of schooldkids these days would guess that a logarithm is a sub-genre of drum'n'bass favoured by those who indulge in spliffs of industrial proportions. e, of course, has already been dealt with.

Ah yes, the 23 problem would be a lovely one to have. Unless we're talking about inflation, in which case it's beans'n'guns time...

goodlifer 26 Feb 2012 , 9:58am

While we're on the subject, does anyone know a rule of thumb to tell us how long it takes to treble?

goodlifer 26 Feb 2012 , 12:59pm

ANuvver

"I suspect it's a bit much to expect people to cope with:

0.3 / log (1.08)
eg for 8% increase

for the exact result"

Something fishy about this, shurely?
Where does that 0.3 come from?

What's wrong with log (2)/log (1.08)?

ANuvver 26 Feb 2012 , 3:30pm

I stand corrected. log (2) is 0,30103 - half a rule of thumb.

ANuvver 26 Feb 2012 , 3:55pm

Rule of 114 gives tripling time, apparently.

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