Guest Post: Don’t Buy Too Much Insurance!

Editor’s Note:  Lars Kroijer, semi-regular contributor here and author of Investing Demystified, offers one of the two most important principles of Insurance: Namely, don’t buy too much of it. In this post he uses the simple example of auto insurance – which because of state laws in the US we must buy – to argue that less insurance is generally better. Even though we cannot avoid auto insurance altogether, we can apply this same principal to other types of insurance. Take it away, Lars…

lars_kroijer

In very rough terms the world of insurance is divided into life and non-life insurance.  Non-life insurance is for things like your car, house, travel, company, and other non-life things.  We all know how it works.  You pay $500 to insure your car against a number of things, including for example theft.  Let’s say it is a $10,000 value car.  In simple terms, the probability of making a claim against the full value of the car in any one year has to be 5%.  Without necessarily doing it in those terms, most buyers of insurance probably consider that about right and therefore worth it.

The reason I would not prefer to buy the $500 insurance on my $10,000 car – other than the insurance that is required by law – has to do with my knowledge of the insurance company’s combined ratio.  The combined ratio is the sum of the claims and expense ratio.  The claims ratio is exactly that – what the company pays out in claims to people whose cars were stolen or damaged.  And the expense ratio is all the other costs of the insurance company; marketing, administration, overhead, etc.  Insurance companies can have combined ratios over 100%; if claims don’t come due for a while the insurers earn an interest on the premiums they collected until the claim falls due.  But since car insurance is typically a one year policy the combined ratio for this policy should be below 100%, in order for the insurance policy to be profitable for the insurance company.

For car insurance the risks are somewhat predictable and the insurance company are likely to have a good idea of the number of claims and expenses they will face (insurers can reinsure risks they don’t wish to hold fully themselves).  Using very rough numbers the insurance company might have a combined ratio of 95% for these policies made up of a 70% claims ratio and 25% expense ratio (my friends in insurance will bemoan this simplification).  So essentially if you are an average risk customer, for every time you pay $100 in premium on your car insurance you get $70 back in claims and it costs $25 for the insurance company to make it all happen, and they take a $5 profit.  Put in other words, you are paying $30 for the peace of mind of having the insurance.

When I describe it this way, I am simplifying the amounts and the process. You obviously don’t get $70 back.  Most of the time you get nothing back as you didn’t make a claim on the insurance company, and then when misfortune strikes you get your $10,000 back; on average you get $70 back.

So the reason I don’t buy extra insurance above what’s required by law is that I don’t want to pay the 30% in cases where I can afford the loss (25% expenses plus 5% profit to the insurance company).  Obviously it would really stink to have my car stolen or damaged to the tune of the full $10,000, but I see this as a risk I can afford to bear and don’t need to pay to protect against.  Importantly I don’t think that I save the full $500 in annual car insurance.  I think that I save the 30% difference between what I paid and the average claims.  In my view the insurance company knows as much about my risk as buyer of insurance as I do, and if they set the average pay-out for me at 70% of a $500 policy then that is probably about right.  So using this case of car insurance to extrapolate how I think about insurance in general, on average over all the insurance policies I don’t buy I would expect to have a loss of $350 (70% of $500) on my car in any one year, and have saved $150 by not buying insurance (30% of $500).

porsche_savings_from_low_cost_mutual_funds

Not buying insurance against things we can afford to replace or have happen does not mean that those things don’t happen.  It just means that instead of having the small bleed of constantly paying small premiums for lots of small things we will once in a while be paying out larger replacements amounts for things we did not insure against.  Personally I also think the whole hassle of keeping track of insurance policies is a pain I would rather avoid and I also seem to constantly hear stories about insurance companies that either fought claims or made claiming on a policy a huge headache.

Without being scientific about it including all insurance forms that I don’t buy (including life insurance) I think I save about $500 per year in expense ratio and insurance company profit.  Assuming that I took this money every year for the next 30 years and invested it in the broader equity markets and was able to return 5% on that money, my savings from not buying insurance over the period would amount to around $35,000 in present money.  This is money I have, instead of it being in the insurance company’s pockets in 30 years.  Importantly this saving does not assume that I do not have accidents or have my car stolen.  In fact it assumes that I am at risk of those things exactly with the same probability that the insurance companies assume.

Investment advice typically has an “always seek expert advice” or “don’t try this at home” disclaimer, but here it really applies.  You should not save on insurance premium payments in instances where you can’t afford the loss; and everyone is different in terms of what they can afford to lose.  Most people could not afford to lose their house in a fire so they should insure against this possibility (you probably couldn’t get a mortgage if you didn’t). Most people in countries without national health services couldn’t afford bad health reverses and should get health insurance.  Many can’t afford to have bad things happen to their car or their homes broken in to, so they should insure against that.

Try to save your money from all these nice folks
Try to save your money from all these nice folks

But, importantly, most people can afford to lose their mobile phone, having to cancel a flight or vacation, or an increase in the price of their electricity bill, and they should not insure against those things.  And even if there are things you need to buy insurance for you should always get a high deductible which in turn will lower the cost of the insurance policy.  Over time having no insurance or a high deductible when you do will save you quite a bit of money, and that should make you sleep better at night.

Similarly there are many instances where life insurance makes sense.  As with the case of annuities many life products have an investment component to them, but obviously also a life component.  If you are in a situation where your death or disability will cause unbearable financial stress on your descendants then the premium you pay on these policies make sense.  As with the example of car insurance, you should do so when you or your descendants can’t afford the loss.  Whether they can or not is obviously a highly individual thing, but bear in mind that as with all insurance products there is a tangible financial cost to the intangible peace of mind many people cherish in insurance.  Make sure it is worth it.

 

Please see related posts:

Insurance Part I – Risk Transfer Only

Insurance Part II – The Good, The Optional, The Bad

Insurance Part III – Life Insurance Calculations

Book Review: Investing Demystified by Lars Kroijer

Audio Interview with Lars Kroijer, Part I – Global Diversification

Audio Interview with Lars Kroijer, Part II – On Having an Edge in Investing

Guest Post by Lars Kroijer: You don’t have an investing edge

Also, see book review about an author obsessed with auto insurance, in My Vast Fortune by Andrew Tobias

 

 

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Book Review: Diary Of A Very Bad Year


I’ll admit to two large biases before praising Diary of a Very Bad Year: Confessions of an Anonymous Hedge Fund Manager.

First, I prefer a personal account by a financial practitioner, rather than a financial journalist’s perspective, nearly every time. This preference, after all, underpins my idea with the Bankers Anonymous site itself.

The acronymic jargon of an ordinary financial practitioner’s presentation, however, typically overshadows his story for the lay reader. Who, except the specialist, can unpack the Re-Remics from the Reverse Repos, the positive carry from the negative basis trades, or FX forwards from a commodity curve in backwardation? Only the rare financier knows his craft so well that he can explain complexity while using language we can all understand.

Second, the Anonymous Hedge Fund Manager (HFM) featured in the book was a client of mine for a short while when I sold bonds on the emerging markets desk for Goldman. His clear language and thinking made a strong impression at that time.

Which explains why, when I read a review of this book a few years ago, I immediately thought of my ex-client. Was he the unidentified HFM? An email query and reply a few hours later confirmed it, yes.

Through a series of interviews with a journalist, HFM gives a wide-ranging but personal perspective on his experience between September 2007 and August 2009, covering the periods of the deepest dive and steepest financial recovery. His interests, while inescapably specific and technical, frequently veer to the philosophical and big picture.

In the free-fall period of late 2008 – when even the most plugged-in hedge fund manager was overwhelmed with unexpectedly bad developments – we experience a real existential question for financial markets: If all private banks were at risk of implosion without the backing of the US Government, what happens when the US Government defaults? Who is insuring it and how do you hedge that risk? Martians were not offering credit default swaps to earthlings.

Diary of a Very Bad Year will not tell you everything you need to know about the Credit Crisis of 2008. It will tell you what a large hedge fund manager experienced, in real time, in a way no journalist on the outside could ever tell you.

It’s the best book I’ve ever read on the Crisis.

I read this a few years ago but was reminded of it because my wife just read Diary of a Very Bad Year this past week. She found it somewhat technical for the non-finance expert – as terms like leverage, credit default swaps, FX crosses, and even ‘hedge fund,’ get thrown around without explanation or definition. But she also appreciated the brilliance and humor of HFM in describing those two awful years, in real time.

The final chapter reveals HFM’s plan to quit New York City and move to Austin, TX with his fiancé.

He’s burned out on the stress of the Crisis and the responsibility of managing a large team and complex portfolio at his New York hedge fund. He dreams of eliminating his management responsibilities, simplifying his life, and shifting his balance, away from working, and more toward living.

When I checked in with him for lunch in Austin a few years ago, he had followed his plan exactly.

diary of a very bad year

 

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Book Review: Flash Boys by Michael Lewis

The Rise of the Machines

Michael Lewis wrote Flash Boys to alert the non-finance world about the scourge of high frequency traders front-running investors and fracturing traditional capital markets.

Lewis does not distinguish between quantitative (or algorithmic) trading strategies and high frequency trading firms (HFTs), although it’s helpful to define these terms first.

Quantitative strategies – of which HFTs form a subset – are computer-driven trading models, in which the human input all occurs prior to a market’s opening bell. The human instructions come from computer programmers who tell the model to look for certain signals in the way securities trade to prompt a buy or sell order. HFTs are a type of quantitative strategy that rely on speed, in milliseconds, to successfully execute trades. A good primer generally on quant trading and HFTs from someone inside that world is Rishi Narang’s Inside The Black Box, which I reviewed recently.

Lewis points to at least four simultaneous innovations that have led to the profitable opportunity for high frequency trading firms over the past decade.

  • First, an investor-protection law from 2005 called Reg NMS demanded that investors receive the ‘best’ price visible on a stock exchange, even though sophisticated investors know that large investment purchases or sales may get a best overall price if done quietly ‘off-market’ without alerting the rest of the investment community. Following Reg NMS, HFTs can play games with the ‘visible’ market price by posting, say, 100 shares for purchase or sale, only to cancel that price as soon as a real order hits the market. In Lewis’ telling, the 100 share order from the HFTs becomes an electronic trip-wire to signal certain types of large investors are making a move, and allowing the HFTs to front-run that investor through superior trading speed.
  • Second, the fracturing of the equity markets into more than a dozen major electronic exchanges and 40 (or so) broker-dealer created ‘dark pools’ for anonymous electronic trading has created multiple opportunities for risk-less arbitrage between exchanges, for those HFTs who execute trades in milliseconds.
  • Third, the privatization of US stock exchanges like the Nasdaq and New York Stock Exchange led the exchanges to seek their own profit through fee arrangements with HFTs at the expense of investor-oriented protections, which would have limited the access of HFTs.
  • Fourth, technology – between lightning-fast software and speed-of-light fiber optic cable – created a haves and haves-not unfair playing field between investors in many markets.

Lewis’ narrative follows the evolution of his protagonist Brad Katsuyama who figures out just enough of the HFT game to become inspired to shut it down – first because it interferes with his job trading equities for the Royal Bank of Canada, and later because he’s a self-appointed evangelist for protecting real investors from the HFTs.

Bill Murray

Katsuyama and his plucky rag-tag group of Wall Street castoffs – and here Flash Boys most closely resembles the plot of every early Bill Murray movie like Meatballs and Stripes – set out to build a better exchange known as the Investors Exchange (IEX),[1] which through slow trading will box out the HFTs and their nasty algorithms.

 

The moralistic tone, and why it matters

Flash Boys differs from Lewis’ earlier finance books in the introduction of his moralistic tone – he seems genuinely outraged by the activities of high frequency trading firms. This moral outrage differs from the way that he was previously mostly amused by disgusting mortgage traders, stupid Icelandic Viking financiers, or Sub-prime CDO structurers.

In Liar’s Poker, Boomerang, and The Big Short Lewis distinguished himself from other financial journalists by adopting a knowing attitude toward Wall Street’s greedy ways. Whereas other financial journos portray a fairy tale world of virtuous small-time investors and evil greedy bullies, Lewis worked on Wall Street for a few years and knew better than to fall into that trap.

Lewis usually celebrates – at least up to a certain extent – those who outwit the competition to earn themselves a big payout.

Lewis’ bad guys in those earlier tales typically would receive a kind of satirical treatment for their excessive attitudes. Lewis found ways to laugh at his antagonists because he spent time enough with them to understand their strengths, weaknesses, and the right distinguishing characteristic to turn their unattractiveness into humor.

Lewis does not seem to have spent any time getting to know high frequency traders for Flash Boys, however, and here his moral tone – rather than knowing satire -exposes a weakness.

I’m not saying Lewis shouldn’t be upset about high frequency trading. He makes a compelling case that we should all take a much harder look at whether all of their activity acts like a massive, hidden, tax on capital markets. What I am saying is that the moral tone – which resembles the style of weaker financial journalists – exposes the fact that he hasn’t spent enough time getting to know actual high frequency traders.

flash_boys

If he had spent time with some, we would have gotten some funny anecdotes and satirical send-ups – That Russian programmer with the bad breath and an unhealthy obsession with Miley Cyrus! Ha! The South African technologist who keeps twenty cats in his office and eats only vegetables that start with the letter T! You can’t believe how funny these guys are! That kind of thing.

The humor is amusing in its own right of course, but the humor also tells us that Lewis was there, and got to know these people. Unique among journalists he has a track record of actually going out and finding the stories rather than create fairy tales based on preconceived moral views. The Good Guys = Brad Katsuyama & Team versus Bad Guys = Faceless & Nameless HFTs formula makes me suspect we only got a portion of the full story.

I’m thinking about Lewis’ apparent failure to talk to HFT folks because a friend of mine from the HFT industry thinks Lewis totally blew it when describing his world.

I do not know HFTs myself well enough to judge, but I know my friend has a moral compass and wants the HFT story portrayed accurately.

(And you should see his 20 cats! Just kidding.)

I’m hoping in coming weeks to learn enough to judge better the accuracy of Flash Boys. More importantly than judging the book, I’d like to know to what extend HFTs really threaten the system, as Lewis argues.

More questions than answers

For my own future reference, but also perhaps other readers, here’s my beginning list of further questions to explore and answer after reading Flash Boys.

rise_of_the_machines
We have got to stop SkyNet
  1. Lewis leaves practically unanswered what I think is the much greater problem of quantitative and high frequency trading: As computer algorithms constitutes 50-80% of all trading volume on US exchanges, what are we doing to shore up the system against massive technical fails like the Flash Crash of 2010, or like the Crash of ’87, for that matter? We haven’t seen The Big One yet but I’m pretty worried about it, and I hope regulators have a plan in place to prevent it. In other words, WE MUST PREVENT SKYNET! WHERE IS OUR JOHN CONNOR?
  2. If Katsuyama’s IEX is a better mousetrap and a solid protection against HFT front-running, as Lewis believes, how has it fared in the subsequent months since opening in October 2013? I’ll be curious to know if it has begun to siphon off volume from other exchanges and the broker-created dark pools. If investors are self-interested, they should want to participate in the IEX far more than the shark-infested dark pools.
  3. Lewis mentions only two HFT strategies that I can see, in simplest form: Strategy #1: Set up 100 share trip-wires inside these exchanges. When those get tripped, quickly front-run the direction of the market ahead of a big order. Strategy #2: Gain arbitrage opportunities by seeing an order in one exchange and then quickly executing in another exchange based on that order. Strategy #1 is borderline illegal so it strikes me as something that regulators could address. Strategy #2 is theoretically (marginally) ‘creating efficiencies,’ although not if the HFTs are, as they seem to be doing, seeing order flow to some exchanges faster than everyone else. IEX could put that strategy #2 out of business. But something tells me there are many dozens to hundreds more HFT strategies not described in this book. What are they?
  4. Whatever happened to the high-speed line built by Spread Networks from New Jersey to Chicago mentioned in the early chapters? And was it made obsolete by the microwave towers mentioned in the Epilogue, or is that part of the same network?
  5. My friend from the HFT firm mentioned this one to me: Lewis relays a very fishy anecdote about a hedge fund trader typing a buy order into his computer, only to watch the market suddenly shift away from him before he hits enter to execute the trade. This is, basically, impossible – unless the HFTs have hacked into the hedge fund guy’s computer – to see his trades before he even sends them to the exchange. Even I’m not that paranoid about Skynet yet. So, Lewis, what’s up with that anecdote?
  6. Can we, and should we, distinguish between quantitative trading – relying on computer algorithms rather than human input to execute trades – and HFTs in a meaningful way when it comes to regulation and treatment in a market exchange?

 

That’s my short list of questions. More to come later.

Please see related posts:

Book Review of Pete Kovac’s Flash Boys: Not So Fast

Book Review of Rishi Narang’s Inside The Black Box

Book Reviews of Michael Lewis’ previous books on finance:

Liar’s Poker

Boomerang

The Big Short

Crashes happen when quants take over the markets, in Rise of The Machines

 

 

[1] Fun fact: They didn’t use the full URL of the exchange name because, you know, investorsexchange.com could be interpreted a variety of ways.

 

 

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Book Review: All The Math You Need To Get Rich

I learned from my wife the concept of the “feedback sandwich,” by which she means if you want to give someone an important piece of critical advice, it’s often most strategic to cushion the blow with a compliment to start, and a compliment to finish, with the criticism nestled in between.

Michael Scott in Scranton, PA might have given feedback this way.

“Hey, I love your ability to file those papers alphabetically!”

“Everyone here in the office has just one word for you: halitosis.”

“Also, cool green shirt you have on today!”

In reviewing Robert L. Hershey’s All The Math You Need To Get Rich I have had recourse to the feedback sandwich. First, I will list some examples from the book that I quite liked. In the middle, a couple of important concerns. Finally, some kind words about how I would use this book if I taught math to high school kids

What works

Hershey presents basic, essential, practical, financial math and then follows it up with numerous word problems at the end of each chapter to help lock in the knowledge.

Two examples in particular stood out as excellent, and paraphrasing them from Hershey’s book illustrates the importance of Hershey’s project.

Example 1

Two twin brothers, each of whom wants to get rich in 45 years, pursues two different paths toward their goal.

The first brother (aptly named Lucky), in a hurry for wealth, decides to buy lottery tickets. He makes a plan to buy $10 of lottery tickets every day, six days a week, for the next 45 years.

The second brother (named Tim) decides to invest exactly half of the amount spent by brother Lucky in a balanced portfolio of market securities, such as stocks and mutual funds.

How much does Lucky bet and spend over course of 45 years, and what is the probable outcome? How much does Tim invest over the course of 45 years, and what is the probable outcome?

While results may vary, we can calculate the expected value of each of these brothers’ behaviors.

To calculate Lucky’s results, we need to know that lotteries return an expected value of $-0.50 per $1 bet. The point of a lottery, after all, is to raise money for the lottery organizer, and to return about half the money over time to the players.

Lucky bets $3,120 per year ($10 x 6 x 52)

And a total of $140,400 over the 45 years ($3,120 x 45)

Since he loses an expected amount of $0.50 per $1 bet, we can quickly see that Lucky loses $70,200 over the course of his 45 years of lottery playing. Lucky might win $10 here, $100 there, and occasionally $1,000, but the odds in the long run mean he’ll burn up an estimated $70,200 over the years, nearly guaranteed.

What about Tim’s results?

Tim invests $5/day, 6 days a week, 52 weeks per year. His annual investment is $1,560 ($5 x 6 x 52).

Hershey (the book’s author) assumes a 10% gain on investments[1] to calculate Tim’s results after 45 years. Aggregating the compounded returns of annual $1,560 investments at 10%, we can see Tim’s net worth climbs to $1,121,492 after 45 years.

Tim’s a millionaire using just half of the money Lucky ‘invested’ in lottery tickets, while Lucky has a zero net worth.

Now, that’s what I call a useful mathematical comparison.

all the math you need book

Example number two that I loved from the book

A recent college graduate named Patience is thinking of taking a trip to Europe, which will require her to max out her $5,000 credit card and pay the 18% annual interest charges on the card. Realistically she knows she will stay maxed out for 10 years, so she will have to pay that 18% interest all the while for the next ten years. How much is that?

Alternatively, Patience considers not making the trip to Europe, and instead may invest the amount of the unspent interest in an S&P500 index fund. Hershey assumes a 15% annual return[2] on that investment. How much money would she have then at the end of 10 years?

The annual finance charge, following the trip to Europe, would be $900 ($5,000 x 18%). Over ten years Patience would end up paying $9,000 in interest charges, and still owe $5,000 at the end of ten years.

If, instead, she invested $900 per year in the mutual fund that earns 15% per year, we can calculate – using the magic of compound interest – that she would have $18,274 in her fund.[3] Her positive net worth from investing beats the $5,000 deficit by a long shot. And just as importantly, the interest charge on the credit card ends up costing more than the original trip itself.

My critical thoughts – the bologna in the feedback sandwich

First concern – Who reads this?

One concern I maintain with a book like this – which I fretted about earlier in a review of another math-book-for-non-math-types Innumeracy – is who, honestly, will ever pick up this book? Will people who already feel uncertain about their math skills, however theoretically eager to learn the mysteries of numbers or tempted by the chance to “Get Rich,” actually dig past the first few paragraphs to learn what they do not know?

I don’t know. I doubt it. Math-oriented people enjoy confirming their own math aptitude with a book like this, and they may be able to expand their skills into useful finance applications with this book. I have a harder time picturing non-math folks picking up and actually working their way through the instructions and sample problems, however accessible this book may be. I think Hershey has made this as approachable as possible, but I still question the draw of those who are the intended audience.

Second concern – No way to teach compound interest (my pet peeve)

Every finance-math for non-experts book that I’ve ever read relies on a terrible crutch when it comes to teaching compound interest: The table in the Appendix with compound interest multiplication “factors.” I hate this.

What a proper book on compound interest should teach is the formula FV = PV * (1+Y/p)^N, with definitions of each variable and multiple examples to shows its application. That formula, once understand, can solve any compound interest problem flexibly, and precisely.

This book’s appendix features a y-axis listing the number of compounding terms from 1 to 100, for example (the N in the formula), while the x-axis shows ascending percentages of yield (the Y in the formula). At the end of every example in the book that references these tables, Hershey is forced to say: “That’s not exactly the answer, but it’s close enough.”

I can’t endorse this. I refuse.

All The Math You Need to Get Rich was first published in 1982, the same year in which my fifth grade teacher introduced us to the Timex Sinclair 2000.

[10: Print “Mike” ; 20: Goto 10 ; Run]

At that point in 1982, text appendices of compound interest tables made perfect sense.

Not in 2014, though.

Any reader of a book in 2014 also has use of an Excel spreadsheet program that sits on their desktop or laptop, and can be used to good effect with the formula above.

The text-based, imprecise, crutch of an Appendix table, which no person will carry with them, ever, gets in the way of anyone who ever wanted to actually learn how the compound interest formula really works, in real life.

Phew, got that off my chest.

Back to the complimentary thoughts

If I was assigned a high school math class as a substitute teacher and given 1 month to teach the kids something useful, I would pick a book like All The Math You Need To Get Rich as a textbook. Here are real-life skills for understanding interest rates, percentages, probabilities, and dealing with orders of magnitude – in short most of the things households, investors and citizens need to use on a daily basis to get by. Certainly these help most of us think much more, and much more often, about useful math applications, than the traditional courses – Geometry, Trigonometry, quadratic equations, and Calculus – that make up the majority of traditional high school math curricula.

Not only do these relatively accessible concepts come in handy more often, I would hope – as their substitute teacher – that I could impress upon the unruly high schoolers their own self-interest.

“Learn this about probabilities” I would exhort, “and save yourself thousands over your lifetime by not buying lottery tickets or gambling.”

“Deeply understand interest rates and percentages,” I would urge, “and use your powers for good (getting wealthy) instead of evil (making credit card companies richer).”

This is a fine book and I may use it for teaching my girls what they need to know in the future.


See related book reviews:

Innumeracy by John Allen Paulos

Master Math: Business and Personal Finance Math by Mary Hansen

 

 

 

[1] Astute readers will argue that 10% is too high an assumed return from a portfolio of stocks for 45 years, and I agree. Using a 6% return, Tim’s net worth at the end of 45 years climbs to $331,880. This doesn’t have quite the ring of ‘millionaire’ that the author Hershey probably wanted, but it still isn’t anything to sneeze at, for the cost of a daily Starbucks addiction.

[2] I know I know, too high, but still, work with me here a little bit.

[3] If we assume a more modest 6% return, she would have $11,863.

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Cash Transfers and Inequality

conditional cash transfersMarkets work great, if the goal is to

1. Maximize total output;

2. Encourage innovation;

3. Reward maximum effort;

4. Reward talent; and

5. Use resources most efficiently.

As a result, limiting markets tends to impair one of more of the above, valuable, outcomes. Also, non-market solutions to problems often produce sub-optimal results in one or more of the above areas.

Markets work poorly, however, if the goal is to

1. Make sure that the maximized output gets distributed equitably, or justly.

What I mean by that is that while some people control hundreds, thousands, or millions of times more resources than other people, its hard to argue from an equity, or justice, standpoint that some people are hundreds, or thousands, or millions of times more ‘worthy’ of the world’s resources than others. Especially if you include in your analysis of the efficacy of markets the estimated 870 million people on this planet in poverty, at the lowest end of resources, without basic survival necessities such as food, water, and shelter, sanitation, or protection from destructive elements.

Markets also work poorly to

2. Overcome inter-generational barriers to human development over long periods of time, where the upfront costs only get paid out over, for example, decades. For those aforementioned 870 million people in poverty, for example, its not enough to just say “let the markets be free,” because that’s not likely to help. The real long-term solution of human development for the most impoverished requires the investment of extraordinary resources today, right now, in order to make it possible to lift the next generation (or more distant generations) up to a standard at which a market economy even has a chance of working, through such things as education, skills training, and connection to productive economic networks. That extended ‘payoff’ over decades basically doesn’t work for markets or capitalists. I mean that markets don’t invest well in communities to achieve a return on human capital 50 years from now, even though realistically, that is what is needed.

I’m thinking about all of this after reading a review in The Economist about experiments with transfer payments, especially for the word’s poorest.

Discussing ‘transfer payments’ in the United States often degrades quickly into political name calling, with pro-market folks mistrustful of social democratic or socialistic approaches to alleviating inequality. Outside of the US – or more specifically in areas of extreme poverty – it becomes perhaps easier to discuss the efficacy and theory of transfer payments. Clearly a ‘market solution’ is not happening right away in situations of extreme poverty, or fast enough to alleviate clear human suffering, so a taboo solution like ‘transfer payments’ in some contexts (the developed world) becomes easier to discuss, I think, across a broader spectrum of ideologies, for basic practical reasons. People are dying and suffering right now, so in a sense we can leave aside the ideology and theory, and try to discuss what works.

Cash Transfers

The Economist ran this interesting review last year of programs known as Unconditional Cash Transfers (UCT).

UCTs are typically philanthropic programs that drop unexpected money on very needy people – a rural villager in Kenya identified by a Google satellite image by his lack of electricity in one example, with the hope that even small amounts of money can catalyze higher standards of living and human development in very efficient ways. Targeted UCTs may seek out mothers in a certain region, with the credible theory that mothers can best decide how to feed, clothe, and educate their children, if they only had a boost in resources to do so.

UCTs contrast with a more conventional development model of Conditional Cash Transfers. CCTs typically seek to influence and incentivize behaviors, around vaccinations, or education, for example. If the children attend school, the parent receives cash, for example

The UCTs provide a tantalizing alternative to the paternalism of CCTs, by requiring less resources to administer and enforce. Imposing conditions means the philanthropy or government behind the transfer has to build a structure of monitorig compliance with its rules.

So far, The Economist reports, the CCTs show more effectiveness at addressing the root causes of poverty. Still, the rise of UCTs will bring in more data over time to continue the comparisons. Even though these fall firmly in the ‘non-market solution’ category, the competition between the styles should lead to improvemnent.

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Rapunzel and Compound Interest

Rapunzel
Trapped in the tower for the Summer, learning Compound Interest

“Daddy,” began the little princess plaintively, “I’m bored.” The poor thing is trapped in her tower for the Summer months. Wizarding school ended the first week of June, and will not start again until next Fall.

Also, it’s a Sunday and her 4-year old sister, the other little princess trapped in the tower, naps deeply on the couch.

“Oh is that so?” replied the wizard, looking up from his desktop computer, the glass desk table strewn with envelopes with coffee mug circles, and toast crumbs.

“Yeah, there’s nothing to do.”

“Huh. Sounds like we need to do some math magic. Would you like to do that?”

“Ok!” she brightens.

“Can I show you how to spin ordinary straw into gold, so you can be very rich 50 years from now?

“Daddy…” she gives the wizard her stop-pulling-my-leg look.

“What?” the wizard looks back innocently, eyebrows raised.

“Ok fine, show me.”

It turns out the sweet thing will do anything to escape the existential prison-tower called Summer. The wizard cackled silently to himself.

 

Calculating Annual Returns

“Let’s take this magical spell step by step. We have to build up the magic in small pieces to be able to do all of it.

Do you remember last Fall, when you invested $500 in shares of Kellogg?”

“Yes, you took all my savings and risked them in the market,” The princess looked up reprovingly.

“That’s right. Well, I’m sure that must have been magical money – received over eight years from Godparents, Santa Claus, and the Tooth Fairy – because look what’s happened to your $500.”

With that, the wizard took out his magical iPhone and pressed the ‘Stocks’ App, which showed a closing price of 68.91 for ticker symbol K.

“The stock is up 11% since September last year,” pointed out the wizard. And since it’s been less than one year, so far you’ve grown your money at an annual rate of 15%.”

“But that might not last, right? Because you said it could always go down?”

“That’s true. It still might, and it probably will go down at some point. But in the long run, it probably continues to go up. And since you don’t need the money for a long time, you can think about what’s going to happen in the long run.”

“Ok.”

 

Calculating one year’s annual growth

“The magic spell I want to show you – how to spin ordinary straw into pure gold – happens over a long time. In fifty years, when I’m over ninety, and a very old wrinkled wizard, you will be a very rich princess. But first, let’s talk about how to figure out the growth of your money in one year

Do you remember how we talked about percents?

To figure out how your money can grow over one year, you have to multiply your original amount by the percent growth, and then add it to the original amount.

So to do the first part of this spell, you need to calculate 15% of $500, and then add that to $500. Let’s see how much money you could have after one year.”

With that, the princess took her blue-ink wand in hand and scratched out the runes on a paper notepad. After a half-minute of spell-casting, she looked up.

“$75 more. So after one year I would have $575 if it grows by 15%.”

 

Calculating Compound Returns in multiple years

“Very well done. Now I’ve got two more intermediate steps that you will find too hard, but after you try it and can’t do it, I’ll help you through the magic.

Tell me how much you would have after 2 years and 3 years, if you start with $500, and achieve 15% growth each year, for 2 years, and then for 3 years.

The princess began to puzzle over this. Her magic didn’t seem to be working. She wrote some runes, and then some more runes, and then scratched them out. Some heavy sighing followed. She held her golden head in her left hand, while working magic with her right. Finally, with a little prompting, she came up with $150 in extra money, over two years.

“$650 after two years?” she looked up hopefully.

“Close, but not quite,” replied the wizard. “The difference is that when you compound growth at 15% for two years in a row, you have to start the second year’s growth from the previous year’s ending point. With this, the wizard quickly showed how the magic spell gets cast.

“One year’s growth gets you to $575, and then the second year’s growth will be 15% of the $575, or $86.25. When you add that to $575, you end up with $661.25.”

The princess looked up, a little unsure where this was going, or why the difference mattered much.

The wizard plowed ahead anyway.

“Can you show me how you’d get to the third year?” asked the wizard.

This time, the young princess had the right insight.

“Multiply the $661.25 times 15%, and then add that to $661.25?”

“Exactly!” The wizard pulled out his magical iPhone, pressed the calculator App, performing a mystical ritual involving intricate numerical symbols.

“Accio Numericus!” he exclaimed as he pressed the “=” on his calculator with a flourish.

“Daddy.” eye-rolled the princess. The wizard turned the magical iPhone face toward her so she could read it.

“760.44,” she read.

“That’s not the real trick though,” warned the wizard.

 

Do you want to see something really magical?

“Ok,” said the wizard conspiratorily, lowering his voice a little bit. “Do you want to see the whole magic spell? We had to learn the basic magic before you could handle this.”

“What if you could keep compounding your 15% return over the next 50 years? When I’m a wrinkled old wizard, that $500 of straw you invested could become gold. But how much gold? This magical spell tells you.”

Calculating long-term compound growth of an existing investment

The wizard added to the tension in the room by slowly checking over his right shoulder, then over his left. Seeing no prying eyes of elves, orcs, or bad wizards, he returned to the pad of paper in front of them.

There, he wrote a mysterious series of letters:

FV = PV * (1+Y)^N

The wizard looked up, wide-eyed, expectant.

Here, finally, some powerful magic to impart to the young magi princess.

The princess giggled.

The wizard frowned.

“That is totally confusing!” she exclaimed. “Why are there so many letters?”

“No, no, no, you can understand all of this math. Let me just tell you what everything means and you’ll see.

Writing “FV” on the pad, he said “FV just means “Future Value,” which is what our magic is going to calculate. That’s our magical answer – what we’re working towards, how much gold you’ll have in fifty years.”

And now writing “PV” on the paper, the wizard continued, “PV is just Present Value, which is the amount we started with. For you, that’s the $500 you invested in Kellogg.”

“The magic symbol ‘Y’ in this spell,” the wizard went on, is the annual return that we’re working with. Since we’re trying to figure out the answer to a problem with a 15% annual return, we can use 15% for Y in this formula. Since 15% can also be written as a decimal 0.15, we’ll end up turning (1+Y) in the formula into 1.15 for our magical calculation.

“But Daddy you’ve never told me anything about an N. N doesn’t make any sense to me.”

“N is just the number of years. And it has the little carot symbol to show that it means ‘raised to the power of,’ do you remember that?”

“I think so.”

“Right, so when we did 3 raised to the power of 2, we wrote it 3 times 3. And 5 raised to the power of 4 we wrote it 5 times 5 times 5 times 5. In this magical spell, we’re going to have 1.15 times 1.15 times 1.15, but multiplied by itself for a total of 50 times. Which we’re not going to do in our heads, but rather with the magical and mystical iPhone calculator App.”

“Ok,” came the princess’ reply, a little skeptically.

“Are you ready for the magic?” intoned the wizard, upping the drama once again. “First, I want you to guess how big your $500 straw can grow into spun gold in 50 years, when I’m an old wrinkled wizard.”

“I don’t know.”

“Just guess. Something big.”

“I don’t know, maybe $2,700.”

“No, bigger. I said you’d be rich.”

“Ok. How about $9,000.”

“Let’s see what the magical iPhone calculator app tells us. First, we turn it horizontally to be able to see additional calculator functions, in particular the ‘X raised to the power of Y’ button. Now, remember to always say ‘Accio Powerzoom Numericus’ when you input numbers like this.”

Sigh from the Princess. Half an eye-roll.

“No, you have to say it. Say it with me.”

“Accio Powerzoom Numericus!”

The wizard theatrically pressed buttons while describing his process.

“First, enter 1.15, then the ‘X^Y ’ button, and then 50, for the number of years, and then hit the “=” sign.

Now multiply that result by our original PV of $500.

There’s your answer: $541,828.72”

“That’s a lot of money, Daddy.”

“Yes, and do you know what you have to do to make that gold come to you?”

“What?”

“Nothing. Absolutely nothing. Just never sell. The people who work for Kellogg do all the hard work. They sell cereal and whatever else and keep growing their business. You do no more work than you ever did to put that $500 into that stock.”

“Whoa. That’s cool. But what if it only goes up by 10%?”

“It might. So we can use the same magic formula to see what happens then. We can make Y just 10%, so then our “(1+Y)” is 1.1 instead. We raise that to the power of the same N, 50. Then we multiply it by our original present value amount of $500.

And don’t forget:

“Accio Powerzoom Numericus!”

“Boom! At 10% annual return you’d only have $58,695.43.

Which, for not doing any work for the next 50 years, would also be a lot. Most people I know would like to have an extra $58 thousand dollars right now.”

“Yeah, that’s still a lot. Daddy, can my sister and I go outside to play on the porch now?”

“Sure kiddo. Great work there.”

Boom! Mischief managed.

mischief_managed
Mischief Managed!

The front door banged closed, and the wizard cackled quietly to himself.

Once she was out of earshot he rehearsed the following under his breath:

“I don’t mind if you go out to the porch this time, but just promise me one thing, my sweet girl?” in his gentlest wizard tone.

“Sure, anything, what do you need, Daddy?” he answered quietly to himself, in a little princess falsetto.

“NEVER ASK. TO LEAVE THIS TOWER. AGAIN.”

 

Please also see related posts:

Compound Interest and Wealth

Book Review: Make Your Kid a Millionaire

Daddy I need an Allowance – Teaching Compound Interest

The Allowance Experiment gets even better

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