Book Review: Innumeracy, by John Allen Paulos

In Innumeracy – Mathematical Illiteracy And Its Consequences  John Allen Paulos launches himself against the tide of mathematical illiteracy both as a polemicist and as a teacher.

 His stated purpose is to appeal to innumerates with enjoyable and illuminating examples of everyday, as well as fanciful, uses of mathematics.  I enjoyed the book, and some Bankers Anonymous readers would as well.

 The problem: only the numerate will read the book.  All innumerates – the intended audience – will put the book down by the 3rd paragraph of the first chapter.

 Probability and Coincidences

Paulos provides a valuable example of the stock market promoter who sends out a newsletter to 32,000 potential customers, predicting a specific upward or downward movement in a stock.  At the end of 6 such random predictions, this promoter will have been right 6 times in a row to approximately 500 astonished people.  At this point, the promoter can offer a $500 subscription to those remaining 500 people.  If they pay up, he pockets $250,000. 

A variation of this classic example is explained well in Nassim Taleb’s Fooled by Randomness as well, and should be kept in the forefront of the minds of everyone who interacts with the Financial Infotainment Industrial Complex.

Just as coin tosses of a completely fair coin frequently run in hot streaks in seemingly improbable ways, many of the patterns we think we see in financial markets are more noise than signal.

 Pseudoscience

Pseudoscience will fool people who don’t have numbers fluency.  Seemingly improbable ‘coincidences’ turn out to be less miraculous with a little bit of math.  Highly unlikely events become highly likely – given enough chances. 

I appreciate that Paulos repeats a great piece of wisdom my college advisor once told me: Any system of orthodox thought ,like Freudian psychology or Marxism, which cannot be criticized – without exposing oneself to counterclaims of ‘neuroses’ or ‘class-blindness – is a pseudoscience. 

Real systems of thought, however powerful, are open to criticism from the outside.  It’s a simultaneously humbling but empowering idea.  No system of thought, however powerful, is without its weaknesses.

A useful book – but who will read it?

 Paulos fills his book with examples of how we can be easily misled about numerical scale.

 I find this is true in personal finance – not understanding the incredible scalable power of compound interest, for example, or in public finance – not grasping the power of large numbers when it comes to the national debt.

 Innumeracy is probably most fun for people who already understand 95% of the math Paulos uses.  The book then becomes for readers a confirmatory exercise in ‘Look at me and the math I already understand,’ rather than fulfilling his stated purpose of ‘More people should be relatively numerate and I’m going to make that case, at the same time helping innumerates get started on a better math path.’  I don’t see his supposed intended audience – innumerates – making it through from start to finish.

 I’m not making this critical argument about a book that came out 25 years ago in order to point out a flaw in something few people have read.  What I’m doing in reviewing Innumeracy is thinking out loud (ok, in print) about the problem I face with personal-finance writing.  Namely, how do you convince an audience of smart-but-non-finance folks that:

A. They should want to understand finance better for their own good, and

B. They should read my stuff to help them get started down the learning-finance path.

 I fear that my personal finance writing attracts people already comfortable and fluent with financial topics, seeking confirmation of their relative sophistication.  “Look at me, I understand finance and I read stuff by a former Wall Streeter still in recovery from his finance profession,” readers may say, rather than, “I’m an educated but non-finance person eager to get started in better understanding my world through a financial lens.” 

Obviously I want both kinds, or rather all kinds, of readers.  But my highest value-added proposition, in terms of a personal finance book, is for the non-expert reader.

Reviewing Innumeracy, which, in my opinion, fails in its stated goal, reminds me of the challenge ahead.

 Suggestions on this present conundrum, from all kinds of readers, are welcome!

innumeracy

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Book Review: The Only Investment Guide You’ll EVER Need

It pains me to write this[1], but Andrew Tobias’ hyperbolically titled[2] The Only Investment Guide You’ll EVER Need actually lives up to the name.

Tobias delivers solid personal financial advice, but in a playful tone.

He enlivens an entire chapter on saving money – the world’s dreariest subject – with anecdotes about his own fetishistic ways to scrimp.[3]

In the chapter about beginning to invest, Tobias delivers the punch-line early on: Trust No One, while offering fairly hilarious ways in which his younger, more gullible self, failed to head his own good advice.

In the stock-investing chapter, he hits the essential notes which readers of my earlier posts and reviews will know by now:

  1. The vast majority of individuals, could do a lot worse than just buying low-cost index mutual funds and never selling, as advocated by Nick Murray in Simple Wealth, Inevitable Wealth.
  2. Some money managers out of a large group will appear to ‘beat the market’ for an improbable-seeming time, but this type of result can be replicated with a coin toss experiment, as described by Nassim Nicholas Taleb in Fooled by Randomness.
  3. The intrinsic value of a stock derives from an enterprise’s ability to generate current and future cash flow, as Benjamin Graham’s Intelligent Investor explains.
  4. Investing your first slug of savings through an IRA or 401K vehicle is a no-brainer.  But even outside of tax-advantaged vehicles, the tax code heavily favors stock investing as a way to get rich.

 

Tobias made money early in his life – through best-selling books and then more significantly through best-selling personal finance software – so he managed to quickly accumulate a lifetime’s worth of successful and unsuccessful investment experience.  He spins his unsuccessful experiences into memorable and hilarious ‘How-Not-to-Invest’ stories throughout the book.

But the best part of the book, Tobias saves for last.  He comes up with an amazing way to teach kids about the power of compound interest, a personal obsession of mine.

Tobias suggests three versions of a Cookie Jar Experiment, which over a month can viscerally and intuitively teach the magic of compound interest to your kids.

 

  1. Version One.  Offer your kid $1 on day one, and put it in the cookie jar.  Offer to add 10% per day in interest growth on that original $1.  Thereafter – Day 2: $1.10 in the jar, Day 3: $1.21, Day 4, $1.33.  After a month you’ve got $17.45 in the jar, which shows how powerful 10% compounding can be, even if you begin with just $1.  Tobias suggests you probably won’t continue the experiment to the end of Month 3 ($5,313) or Month 6 ($28 million) but of course, that’s up to you and your own resources.  While ‘real life’ doesn’t let you compound that quickly on a daily basis, the experiment lets you demonstrate the amazing power of compound growth. [NOTE: I have since done this experiment with my oldest daughter, which I wrote about here.  And then a follow-up post on the same topic here, as this allowance experiment is even better than I first realized.

 

  1. Version Two.  Between your two kids, you offer the same deal, with a twist.  If one of them is willing to skip the first three days of interest accrual, they can get something desirable like a chocolate bar.  After they finish fighting over the chocolate, you run the experiment for two months.  The kid who went hungry has $304, while the ‘lucky’ kid who got the chocolate only has $228 in the Cookie Jar at the end of 60 days.  Lesson: Start saving early because it’s the earliest accruing period that matters the most.

 

  1. Version Three.  Run the same experiment, but use the interest rate associated with many credit cards, like 20%.  Start adding money to the $1 at a 20% growth rate and label this ‘Credit Card’ growth.  On day 19 the ‘credit card’ account has grown to $32, versus the $6 that the original savings at 10% per day grew to.  If you run the comparison all the way to day 35, the difference is $590 for the credit card account versus $28 for the ordinary 10% growth account.  The key to this version is pointing out that some people scrimp and save and achieve some growth on their savings, while others pay huge amounts to credit card companies.

 

I taught a personal finance course last Spring, for bright college students, and I plan to do the same next Spring.  One of my frustrations was with the textbook we used, a dry-as-dirt tome written by CPAs, seemingly for CPAs.  My co-teacher and I ended up hardly ever referring to it, because how can you expect anyone to read such a thing?

Unless I can come up with something better real soon, the students will get assigned Tobias’ book.  I think it’s all they need.[4]

Please see related post: All Bankers Anonymous Book Reviews in one place.

 

Only Investment Guide You'll EVER Need
Only Investment Guide You’ll EVER Need

[1] It doesn’t actually pain me to say this.  I use that turn of phrase to capture the sense of the Oscar Wilde aphorism “Every time a friend succeeds, a little something in me dies.”  And Tobias is not a friend, but rather, I am jealous because I’m attempting to write a personal finance book, and Tobias has done such a good job with his.

[2] Tobias is a fan of the hyperbolic title, such as his excellent and funny My Vast Fortune, which I reviewed last month.

[3] He apparently carries Crystal Light powdered packets when he travels to save on beverages, buys canned goods by the pallet at Costco, rarely accelerates his car (to save on gas), checks his bank statements for errors every month, and has substituted cubic zirconium for diamonds in any jewelry purchases he ever made.  In a related story, his net worth is above 99% of the people reading this right now.

[4] Until my book comes out, of course.

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Mortgages Part III – 15-year vs. 30-year Mortgages

Why are 15 year mortgages cheaper than 30 year mortgages?

The answer has to do with the interest-rate curve.  Contrary to what some may believe, the economy does not have one interest rate, but rather an infinite number of market-based rates, and dozens of important benchmark rates that determine the cost of money to different groups of borrowers.

interest rate curve

Mortgage interest rates respond to market-based interest rates, which may be seen as an upward-sloping curve on a graph, showing a Y-axis of % interest rates and an X-axis of different loan “terms” that represent the cost of money for time periods from 1 day, to 3 months to 30 years.

Generally, 15-year mortgage interest rates trade somewhat below 30-year rates, as lenders charge less to lend money for 15 years than 30 years.

For that matter, generally 3, 5, and 7 year mortgage rates are lower than 15-year or 30-year rates, which is where the ‘teaser’ rates for adjustable-rate mortgages (ARMs) come from, before those interest rates float upwards at the end of a their 3, 5, and 7-year fixed period. 

Mortgage borrowers historically refinanced after the fixed period, making it statistically reasonable – in pre-2008 crisis times – to charge lower rates for 3, 5, and 7-year interest rates.  The fact that ARMs got combined in a toxic manner with sub-prime lending temporarily gave ARMs a bad name, although I think they’re great products, and I got a 5-year ARM in 2001 and a later a 3-year ARM in 2006.

Please see related Mortgage posts:

Part I – I refinanced my mortgage and today I’m a Golden God

Part II – Should I pay my mortgage early?

Part IV – What are Mortgage Points?  Are they good, bad or indifferent?

Part V – Is mortgage debt ‘good debt’ A dangerous drug?  Or Both?

Part VI – What happens at the Wall Street level to my mortgage?

Part VII – Introduction to Mortgage Derivatives

Part VIII – The Cause of the 2008 Crisis

 

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Book Review: The Millionaire Next Door – The Surprising Secrets of America’s Wealthy

 It seems overly dramatic1 to write that Thomas Stanley and William Danko’s book The Millionaire Next Door changed my life, but actually it kind of did.

Let me dispense with the major flaw in the book first.

The authors conducted a study in the 1990s of close to 350 millionaires, with an average net worth of $3.7 million, surveying them on their behaviors, spending patterns, lifestyle choices, and attitudes.  From that review Stanley and Danko describe a composite “average millionaire” and explain the lifestyle factors correlated with US millionaires.

The real point of the book, the only reason to purchase it, is to learn how we, the readers, can replicate their success.

Yet the caustic financial critic Nassim Nicholas Taleb blasted their book in his own Fooled by Randomness for a statistical flaw.  As Taleb points out, simply interviewing 350 millionaire ‘winners’ does not take into account the possibly thousands or millions of people who might have behaved in ways similar to the 350 but who did not end up millionaires.  The study underlying The Millionaire Next Door suffers from “survivorship bias.”

This same “survivorship bias” leads to our thinking that all hedge fund managers in 2013 are rich – and have good investment track records – because we only look at surviving hedge fund managers, not the tens of thousands who have disappeared from the investment scene or gone out of business.2

Having pointed out the logical scientific flaw in their method, however, I would argue that Stanley and Danko are still worth reading.  Even if their research does not rise to the level of a randomized placebo-controlled double-blind study that you’d require for true science, their correlations seem useful and right.

So what do Stanley and Danko say about millionaires?

They live below their means. 

They allocate their time, energy and money efficiently, in ways conducive to building wealth.

They believe that financial independence is more important than displaying high social status

Their parents did not provide economic outpatient care

Their adult children are economically self-sufficient

They are proficient in targeting market opportunities

They chose the right occupation.

 

An enduring image from the book, introduced in Chapter 1, is the ‘big hat, no cattle’ phrase referring to people who appear wealthy, but really have little actual wealth.  They spend money on showy things but finance their purchases with debt.  (Now that I live in Texas, I enjoy hat and cattle references more.)

They state this point, re-state it, and then argue it some more, that the appearance of wealth – a fancy car, expensive trips, a three-story house in the right zip code – are not wealth itself but in fact – in many ways – the opposite of wealth.  To the extent these raise the cost of people’s lifestyle, wealth is harder to achieve for those with expensive needs rather than ordinary needs.

One of the great things about Stanley and Danko’s “steps to being the millionaire next door” – in fact the key attraction of their best-seller – is the applicability to everyone’s life.  “Live within your means,” as a step 1, works for anyone, with either $999,000 saved – or just starting out.

Please see related post The Millionaire Mind, by Thomas Stanley

Please see related post: All Bankers Anonymous Book Reviews in one place.

 millionaire-next-door-book-review

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  1. And leaves me feeling uncool and easily teased.  It’s kind of like admitting that Huey Lewis and the News was my favorite band in 1986.  It just doesn’t make me look good.  Forget I even said it, ok?  But Sports – in its 30th Anniversary Year! – is a really good album.
  2. What? Are you talking to me? Are you TALKIN’ to me?

Ask an Ex-Banker: Mortgages Part II – Should I Pay My Mortgage Early?

mortgage or invest

Dear Banker,

Most months we manage to cover our costs and have a little extra left over.  Sometimes I send the bank an extra $500 or $1,000 toward paying down our mortgage balance, which has another 21 years to go.  Once I sent close to $5,000.  Does this make sense?  — Manny T., Chicago, IL

Dear Manny,

Congratulations on doing the first-order hardest thing in personal finance – produce a monthly surplus in your household.  Wealth for you – while not inevitable – is made possible by this monthly surplus.

I appreciate your question whether you should – or anyone should — pay off a mortgage early with small interim payments of principal.

This perennial question generates as many strongly held opinions as there are mortgage holders.  There’s a thoughtful discussion to a similar question prompted on this personal finance site.

Like most interesting personal finance questions, the answer depends on a combination of personal psychology and finance math.[1]  Your own personal relative weighting of this combination may lead you to a different ‘correct’ answer than that of someone else.[2]

My own short answer is that while paying off your mortgage principal in small early increments does not make much sense from a pure financial math perspective, it can be the totally correct thing for certain psychological reasons.

Therefore, while I don’t advocate paying off a mortgage this way, I fully acknowledge that for people with a different psychological approach than me, the incremental payments make plenty of sense.

The math side of things – forward rates

First, it’s helpful to understand mechanically what happens when you make an extra, partial, principal payment on your mortgage.

After making your regular monthly payment, let’s say you send an additional $1,000 to the bank for principal.  The bank – actually the mortgage servicing company, but let’s not nitpick – applies that principal to the furthest-away-in-time mortgage payment.  In Manny’s case, his $1,000 payment gets applied toward a payment due 21 years from now.

In other words, Manny’s total mortgage principal gets reduced by $1,000, but not in any way that affects his current monthly mortgage costs.  He’s still obligated to make regular mortgage payments next month.[3]

You may have read, not entirely incorrectly, that when you pay debt principal early you get a guaranteed return on your money equal to your interest rate.  If you have a 6% mortgage, the conventional wisdom goes, you get a 6% “return on investment” when you pay off your mortgage.

But this is not entirely correct either, in purely financial math terms.

I’m going to assume Manny’s mortgage (obtained 9 years ago) has a 6% interest rate.  Since he’s eliminated by early payment the obligation to pay 6% interest on his borrowed money 21 years from now, we could more precisely say he’s invested the equivalent of $1,000 at “6% interest rate, 21 years forward.”

That may seem like an odd turn of phrase, except that the bond markets operate precisely this way – on today’s interest rate (you might call this the ‘spot’ rate) as well as tomorrow’s forward rates (incorporating the idea for example, of 1 year interest rates, one year from now, stated as “1 year rates, 1 year forward.”)

We don’t all have to be bond geeks to make good decisions about early mortgage payments, nor do we need to know exactly what I mean with this clarification, except you should understand the following:  We don’t know with very much precision what prevailing interest rates will be 21 years from now.  As a result, it’s not as obviously a ‘good trade’ to pay off your mortgage at 6%, precisely because it’s not actually true that you’re locking in a “6% return” on your money today.

21 years from now a 6% mortgage interest rate may be extraordinarily high or it may be extraordinarily low (I’m agnostic on the issue) but the imprecision around the question of forward rates makes it less obvious what your effective ‘return on investment’ really is, or what you should reasonably expect to earn on your money 21 years from now.

One major and obvious exception to my clarification on “forward rates” is that if you pay off your full mortgage balance early – entirely eliminating the need to make future monthly payments – then indeed you did lock in a 6% ‘return’ on your money.[4]

Inflation scenario as an illustration of forward rates

To return to the problem of unknown forward rates for a moment, it may be helpful to think of specific, possibly extreme, scenarios.  I’ve written before that the combination of home ownership with a mortgage can be a very powerful inflation hedge.  One way of seeing that is through the concept of forward rates.

A future high inflation rate can illustrate the ‘forward rates’ problem.  If future inflation, say 10 years from now, runs at an annual 15% rate, with prevailing mortgage interest rates around 18%, then it becomes obvious that locking in a 6% return on your money in the final years of your mortgage was not a good idea, from a personal financial math perspective.  In my example you might have earned 18% just leaving your money parked in a money market account.  That kind of future interest rate can show us why we should be less sure of ourselves that earning a 6% return by paying of a mortgage early is the right decision, from a purely mathematical perspective.

More on the math side of things – comparative rates of return

I have not yet addressed the most common financial math reason why people claim you should not pay off your mortgage in small early chunks of principal payment.

Specifically, many argue that you may be able to earn a higher return on your money “in the market” than you can by eliminating personal debt and locking in the rate of return of your mortgage’s interest rate.

This is possibly true, although it depends on specific scenarios, like the following:

·         If you are talking about credit card debt – with interest rates between 9% and 29.99% – it’s clear to me that paying off your debt offers a better return than you could reasonably expect from another investment “in the market.”

·         If instead you are talking about current prevailing mortgage rates – like my newly refinanced 15-year mortgage at 2.75%! – then I heartily agree that a better return is quite likely available “in the market” rather than through paying down personal debt.

·         If you are able to invest in a tax-advantaged 401K or IRA vehicle, and you have a sufficiently long time horizon to invest in risky assets, then you can stack the odds mightily in your favor to earn a better return “in the market” rather than paying down debt.[5] 

The Psychological approach – Arguing against myself

So I’ve made the case that locking in a specific return on your money – by paying down mortgage debt – is not as clear-cut as it first appears, from a purely finance-math perspective.

However, I do think the psychological aspect of making early mortgage payments should not be forgotten.  We are all humans,[6] responding irrationally to myriad inputs.  For many of us, money left on a monthly basis in the checking account gets spent, so the key to not spending is to not leave extra money lying around.

If Manny’s realistic choice every month is between sending $1,000 to the bank to pay his mortgage early or instead – like many of us – to spend $150 more on Amazon Prime downloads, $300 on jewels in Farmville and $273 on One Direction concert tickets, leaving just a $277 surplus at the end of the month, then the choice is clearer. 

All the possible market returns in the world cannot undo the simple fact that paying off debt guarantees an incremental increase in net worth.  If you can’t stop yourself from spending your surplus – and this really comes down to the psychological imperative: “know thyself” – then paying off the mortgage in small extra increments makes total, perfect, unassailable sense.

And then there’s risk tolerance

In addition, there’s the “know thyself” imperative applied to risk tolerance. 

Investing money in the market – instead of paying down debt – makes an increase in net worth possible, even likely, but has no guarantee.  If you hate losing any amount of money ever, then by all means pay down all of your debts before investing in anything risky.

Earning a 6% return by paying off your mortgage[7] early may sound much better than shooting for a possible 10% compound annual return but with a possibility of a 25% sudden loss in any given year.

Few investments in the long run are worth 3AM insomnia.  A fully paid-off mortgage may do more for encouraging restful sleep than all the Posturepedic  mattresses in the world.

Please see related posts:

On Mortgages Part I – I Am a Golden God

Part III – 15 yr vs. 30 yr mortgages

Part IV – What are Mortgage Points?  Are they good, bad or indifferent?

Part V – Is mortgage debt ‘good debt’ A dangerous drug?  Or Both?

Part VI – What happens at the Wall Street level to my mortgage?


[1] My bond sales mentor memorably told me once that bond sales consists of 5% bond math and 95% child psychology.  Personal finance strikes me as a similar deal, although probably even more weighted toward the psychology part of the spectrum.

[2] And since I’m always looking for an excuse to quote Jack Handey, let’s review this gem: “Instead of having ‘answers’ on a math test, they should just call them ‘impressions,’ and it you got a different ‘impression,’ so what, can’t we all be brothers?”

[3] I’m assuming for the purposes of this example that Manny has sent the money to the bank to be applied to principal since that’s how his question is phrased, rather than specifying something like ”I’m paying the next 3 months early.”  Presumably that’s also possible, but non germane to the question.

[4] At this point further math geeks will point out that the tax-deductibility of mortgage interest means that your effective interest rate is probably closer to the 4% than 6% rate, making your effective ‘return on investment’ lower than it seems.

[5] As always, if you can get an employer match for 401K contributions then that use of money trumps everything except paying off high interest-rate credit card debt.

[6] All of us, that is, except for my Rihanna-bot, who takes care of me in my old age, on my hovercraft.  She’s not human, just human-like.

[7] Yes, closer to 4% after taxes, and yes, actually “6% 21 years forward.”

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Book Review: Suze Orman’s The Money Book for the Young, Fabulous, and Broke


I admire Suze Orman’s delivery of a financial fix-up book to an important group that needs help.  The target audience – described succinctly in the title – clearly needs advice from somewhere.

In The Money Book for the Young, Fabulous & Broke she addresses the educated twenty-something who’s just started a working-career but has dug him or herself a financial hole early-on.   As I am in the process of writing a personal finance book for a similar demographic, I paid particular attention to her techniques and knowledge.

I can’t fault the advice – pay off high-interest credit cards, try to find meaningful work you don’t hate, remember to ask for a raise, scrimp and save wherever you can, know your FICO score, and try to avoid bankruptcy if you possibly can because the consequences are long-lasting and serious. 

All this seems basically correct.  The advice is sound. 

In addition, she fills at least half of every chapter with an accessible question-and-answer format – “I’m thinking of filing bankruptcy, here’s my balance sheet, etc, should I?”  “I co-signed for my friend’s credit card account, now the collection agencies are calling, etc, what should I do?”  All good and useful.

Here’s the problem: I would personally never pick up this book, and it’s mostly because of the tone.  I find her ‘hipness’ robotic and forced.  Not that I am hip personally and have a hip platform from which to judge others’ hipness, but I’d like to think I at least own my non-hipness.[1]   

Suze Orman’s hipness seems to be a calculated, search-engine optimized, consultant-approved uber-casual hipness that sounds the opposite of casual.  You know those fifty-somethings who use the lingo wrong?  Or slightly too earnestly?  That’s the tone of Young Fabulous & Broke.

I’m not even the youthful audience she’s addressing, and I found this to be nails-on-the-chalkboard annoying. 

How can I explain this off-putting tone problem?  Ah, I have found a way! 

The applicable cliché:  A picture is worth a thousand words.[2]  

Check out the cover of this book.

Suze Orman Book

This is all so funny and hip my smile is frozen in place. 

Maniacal laugh.  Maniacal laugh.

 

Please see related post: All Bankers Anonymous Book Reviews in one place.


[1] How about I call myself ‘nerd-chic?’  Would that be ok?

[2] Another applicable phrase, borrowed from Jack Handey: “The face of a child says it all.  Especially the mouth part of the face.”

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