Discussion Question

Imagine a world where everyone is equally risk-averse, and where there are two assets available: You can hold stock in an umbrella company, or you can hold stock in a sunscreen company. Depending on the (quite unpredictable) weather, one of these stocks is sure to gain value at 100% a year while the other is sure to lose value at 95% a year, but it’s impossible to know which is which.

Given this, the smart thing to do is to hold a balanced portfolio of the two assets and earn a comfortable 5% per year. Most people in this imaginary world are smart enough to figure this out. But a small number are stupid enough to put all their eggs in one or the other basket. Half these people are quickly wiped out; the other half become super-rich.

Now we have a society in which nobody smart is especially rich, and everyone rich is especially dumb.

Question: Does this parable contribute anything useful to understanding some aspect (obviously not all aspects!) of the wealth distribution in the world we inhabit? Discuss.

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32 Responses to “Discussion Question”

  1. 1 1 Roger

    The rich will say that they got rich by doing something smart, and it will be hard to refute that argument. Maybe they were smart.

  2. 2 2 Jonathan Kariv

    Well toy models are usually pretty good places to start thinking about things (your writing has done a lot to convince me of that).

    In this model imagine 1024 stupid people who over 10 years pick a stock at random. The 1 guy will win all 10 times and have 1024x (where x is the original portfolio value). 10 guys will win 9 times and lose 1 and will hold 512/20 x, 55 will win 8 and lose 2 holding 256/400. The rest of the dummies will be pretty much wiped out. Of course this analysis assumes the dummies pick at random instead of dogmatically holding to a belief. If half pick sunscreen to hold for 10 years and half pick umbrellas and both stocks come out on top somewhere in the 4-6 range (pretty likely) we’ll see all the dumb people coming out poor.

    The next question is weather any smart people can do anything with a). predicting weather or b). selling some kind of derivative of umbrellas and sunscreen.

    Also are we assuming that everyone knows one of those 2 cases will happen? Maybe it’s worth seeing what happens when people at different levels of intelligence have different distributions in mind. Let’s call sunscreen goes up 100% and umbrellas down 95% S and the reverse scenario U. Maybe bright people think S and U are equally likely. Medium people think one or the other has a 75% chance of happening and dumb people think one or the other has 1005 chance of happening.

    What if people can hold cash and possibly spend some. With smarter people earning more.

  3. 3 3 Mike Bravo

    An interesting parable which sounds rather plausible.

    Although your linkage between being rich and “especially dumb” can only be true because of the equal risk-aversion assumption. “Dumb” presumably meaning that they are not adhering to the “wisdom” of modern portfolio theory.

    By relaxing that risk aversion assumption – the rich might then be able to demonstrate that they are not so dumb. (By being rich that is.)

    So a lot depends on your equal risk-aversion assumption – which I think would be where behavioral economics would disagree. Kahneman’s Prospect Theory being an example for instance. Market participants’ risk aversion appears to change over time and change under certain conditions.

  4. 4 4 Harold

    Yes. People tend to attribute good outcomes to good their own skill and judgement, even if it was blind chance. The stupid rich people in your world are likely to believe themselves smart – and others will also believe them. No reason why this would not occur in the real world also. If these sorts of scenarios exist in the real world, then the distribution of wealth is likely to be less well correlated with smartness than we think it is.

  5. 5 5 Andy

    If I have 100 worth of each stock then by year 2 I will have 200 worth of one and only 5 of the other. Are you assuming the smart are also smart (and diligent) enough to rebalance this back to 50/50 every year? If they don’t then some people will also end up holding effectively only 1 stock but they came from the smart group to begin with. (I’m assuming no impact of rebalancing on the two prices). I think in the real world many people who are smart enough to hold a balanced portfolio do not actually rebalance it very frequently, primarily because they don’t look at their investments very frequently (pension fund holdings etc.).

  6. 6 6 Andy

    By the way doesn’t that make the annual return 2.5%? I might be missing something…

  7. 7 7 Pete

    I have done very well with a limited number of stocks over the years, I guess I’m in the dumb luck camp.

    This is something I often complain about to anyone who’ll listen. Most of the time you look at what stocks a mutual fund owns, it’s usually greater than thirty. When you have that many, you are approaching the diversification of just owning the whole S&P (yes the number is much smaller than 500, but at thirty stocks, you’re getting almost all of the effect). And from all this, most mutual funds give slightly worse results than the S&P 500. And then they charge you lots of fees for the brilliant active management they provided.

    If you’re going to own the market, own the market and pay the tiny fees charged for an index fund.

  8. 8 8 FC

    I like this, even though I may not be able to add much. A simple case, then we can add in other elements to see their effect. I’ll be watching this thread.

    Restricting yourself 100% to your example only, I feel there is very little argument for re-distribution. Probably most minimal opinions will be swayed by how they interpret your loaded term “dumb” (someone who has an IQ of 60 and takes the all-in position and someone with a 140 IQ but too lazy to think both fit the dictionary description of “dumb”).

    But more extensive arguments I think will come similar to a Rorschach test as people “see” other contextual elements you did not include. To grossly simplify what I think the major arguments are for redistribution, and elements inferred for these:

    (i) The fact that you can own stock in the umbrella co etc reflect that you are using infrastructure provided by society (concept of a company, someone cannot take you money away or your factory, roads to/from factory, army to protect your miners raping some third world company for sunscreen mud etc). So then re-distribution reflects payback to everyone for that. Now, what is the true cost of that infrastructure …

    (ii) Since they are risk averse, you may want to penalize the dumb guy (NOT risk – taker) since his behavior may impose penalties on others. That pre-supposes we don’t let the schmuck die in the street the next year. Again, what should that penalty be?

    Other tweaks that can change what one may decide whether (or how much) to redistribute
    (a) people able to repeat the game many times
    (b) different utility functions – dumbness/ignorance vs knowingly taking risk

  9. 9 9 Doctor Memory

    Careful there. An impressionable mind might, based on this, form the idea that it was less than ideal to distribute economic and political power based on people’s success (or, perhaps more pertinently, their ancestors’) at a game of chance. Who knows where such thoughts could lead…

  10. 10 10 David Pinto

    Where did the people get the money to buy stocks in the first place? They have to be working, and some are even making umbrellas or sun screen! If the sun screen workers are using their hard earned money to buy umbrella stock, I assume they know something others don’t, and are therefore smarter.

    Also, what if the sunscreen company finds a way to make their product much cheaper, so they still make a profit even in rather sunless years?

    Finally, umbrellas last a lot longer than sunscreen. A good umbrella is useful for years. Sunscreen has an expiration date. So I buy sun screen every year, even if I haven’t used if all from last season. I’ve hand the same umbrella for 10 years. So anyone smart will buy and hold more sunscreen than umbrellas, and look smarter.

  11. 11 11 Manfred

    I like this parable.
    But I quibble with one statement:
    “But a small number are stupid enough to put all their eggs in one or the other basket.”
    I think they may not be dumb, they just have a different (lower) aversion to risk (which violates your premise in your fist sentence, I know). But it seems to me that this is exactly what hedge fund managers, Bill Gates, Zuckerberg, and other investors have done. They became hyper-rich by investing in a small number of eggs. What we do *not* see are the failures – those who lost the 95% in your parable.
    However, the overwhelming majority, as in your parable, just follows a diversified market risk with average market return.

  12. 12 12 nobody.really

    All else being equal, wouldn’t we expect the umbrella company to perform better due to its relative advantages in minimizing taxes and avoiding liability?

  13. 13 13 Josh

    But it’s not like gates and zuckerberg would have been poor and on the streets if their ideas had not taken off. They were both Harvard educated and ambitious in general so they likely would have lived a nice upper middle class or even upper class existence. In other words, they were not one trick ponies, and were just generally intelligence people, ‘which may be a better and more encompassing term than having your eggs in one basket.

  14. 14 14 Seth

    I can’t imagine a world where everyone is equally risk averse.

  15. 15 15 nobody.really

    What conclusions can we draw from this parable?

    1. As others have remarked, the presumption of equal risk-aversion weighs heavily on this parable. It requires us to assume that the people who bet entirely on one stock do so out of ignorance.

    2. Yet the ignorant can do fabulously productive things precisely because they fail to see – and thus fail to heed – the risks of their plans. I surmise many (most?) entrepreneurs fall into this category. Columbus would be the archetypical example: a man attempting to reach Asia via a means that informed people knew would not work.

    3. But here is arguably one huge lesson of this parable: The lesson we draw depends on what we value.

    A. If we value average per-capita wealth, and we (costlessly) reallocate society’s wealth from the rich to the poor to ensure the poor people’s survival, then any individual investment strategy seems as good as any other, provided society has a balanced portfolio.

    B. If we value average per-capita wealth and we don’t reallocate, then we draw a very different conclusion: Diversity is the ultimate social virtue. Sure, some people will lose everything. But the good news is that they’ll die – and won’t influence the per-capital wealth equation anymore! From this perspective, the real drags on the economy are all those people who have balanced portfolios: They neither become rich, nor do they die; rather, these bastards simply hang on and drag down the average.

    I presume Spain financed Columbus’s voyage not out of abject ignorance, but as a wager: In the unlikely event that Columbus’s plan worked, this would be wildly lucrative for Spain. And if Columbus’s plan didn’t work … well, that’s a shame. But the Crown had no intension of reallocating social resources to compensate Columbus or his crew in the event of a bad outcome.

    Ironically, a libertarian philosophy that purports to promote the value of individuals ends up sacrificing individuals to maximize an aggregate social goal. A risk-pooling philosophy that purports to focus on large social dynamics ends up promoting the (survival) interest of more individuals (at least, relative to the libertarian philosophy).

    For it was written: He who serves others ultimately serves himself. He who serves himself merely serves others. Which is why you should avoid self-service cafeterias. Amen.

  16. 16 16 CC

    “When you have that many, you are approaching the diversification of just owning the whole S&P (yes the number is much smaller than 500, but at thirty stocks, you’re getting almost all of the effect). ”

    Pete- If you randomly pick 30 stocks, then yes (though you would probably end up with a small-cap tilt.) But a portfolio manager probably has some systematic bias — I mean strategy — behind his picks. For instance, he might think tech will outperform utilities or something like that, so he’s long a bunch of tech and skipped over utilities. He could very easily generate a lot of tracking error relative to the broad index.

  17. 17 17 Bennett Haselton

    Yes, I believe this is closer to our reality than many people are comfortable believing. In fact, there is one simple argument that superstar success is almost certainly *not* the result of hard work, intelligence, etc. without a lot of luck.

    And that is: If super-success were really the result of hard work, intelligence, and other personal attributes, then venture capitalists and other investors would find those people, invest in their projects, and double or triple their investment every month. This does not happen — some studies show that VC-backed projects succeed only around 5% of the time — which suggests that no matter how smart and hard-working your beneficiaries are, there’s always going to be some luck involved. (In the case of Google, one of Sergei’s and Larry’s lucky breaks came when they tried to sell the company early on for $1.6 million, and *couldn’t* find any buyers!)

    By contrast, consider med school students. For people following that path and doing the requisite work, success will come to *most* of them, not just a lucky few, and so med school loan officers feel comfortable lending them money, confident that most of them will be able to pay it back, with interest. This suggests that success as a med school student and subsequently as a doctor, has a lot less to do with luck.

  18. 18 18 Tjd


    Am I correct that because of the weather the winner is different each year ?

    In that case everybody will get terribly poor.
    Imagine a series of years where the weather alternates

    Post Year1 ( Bought 100 stocks of each )
    A value 200
    B value 5

    Post Year2 ( Bought no stocks )
    A value 10
    B value 10

    Post Year2 ( Bought no stocks )
    A value 20
    B value 0.5

    Etc. Nobody wins in this game ?

  19. 19 19 Tjd

    Nevermind, as per another commenter you have to rebalance.. I guess the moral of this story is that I would create an HFT company ‘to provide liquidity’

  20. 20 20 Roger

    @Bennett, the VCs do in fact invest in those people with those super attributes. Your comparison of success rates is not very meaningful. It is like saying that baseball hitter success is mainly luck, because the good hitters only hit about .300.

  21. 21 21 Pete


    I absolutely love your point. However, could that not be solved with ETFs? I guess you’d have to pay a manager to choose the right ETF based on the market, and that payment should be worth just a bit less than the amount they beat the market by.

    My gut is there’s a reason a bias doesn’t justify managers, but I haven’t been able to think of one for the past few minutes.

    Empirically, most managers are bad at their jobs when compared to the market, but my original point doesn’t necessarily lead to this outcome; the outcome is just an anecdote that I may be right.

    Thank you very much for giving me something to think about! Even if I do come up with a response, I think you’re going to force me to qualify it more than I would have though.

  22. 22 22 Mark

    Fun. However, if we could go back to a state of nature, and everyone’s representative acted behind a veil of uncertainty, we would all have agreed that any differences in outcomes must make the least of us as best off as we could be. Given that we’re all risk averse, this would entail a redistribution of the wealth so that everyone has exactly the same amount of money.

    Not that I agree with this, but the assumption of risk aversion plays well into Rawls’ theory of justice.

  23. 23 23 Phil

    Here’s what the parable illustrates:

    If you are certain that you have a perfect understanding of how the economy works, you will believe that rich people only got that way because of stupidity and luck.

  24. 24 24 Advo

    Applied to a different context, the thought model explains why it’s always the biggest banks that blow up when a credit bubble ends.
    As long as there is no liquidity crunch, it’s the banks which are run by the greedy idiots which grow fastest.

  25. 25 25 Mark B

    A few thoughts:

    1. In this model, as others have indicated, the rich are bold/reckless but lucky, the poor are bold/reckless but unlucky

    2. Whether or not bold/reckless also means stupid depends on the information available at the time. If long-range weather forecasts say we’re in for a heatwave, investing everything in a sunscreen company is bold, possibly reckless, but perhaps not stupid

    3. Where the rich sit on the bold-reckless-stupid spectrum therefore depends on the information available at the time. It also depends on how that information is available. If everyone knows there will be a heatwave, the price of sunscreen company shares will rocket and that of the umbrella company will plummet, so sinking everything into the former will generate only ordinary returns, but everyone sensible will do it since (in the model) we can deduce that the umbrella company will not survive into the next period

    4. Things start to get interesting when you consider the possibility that information is unequally distributed. In that scenario, Joe Average splits his money equally between sunscreen and umbrella and gets a mildly disappointing return (umbrella company is wiped out by a heatwave Joe didn’t see coming). Meanwhile the modestly smart investor (think someone in actively managed investment trusts, or with access to broker notes) gets a moderately pleasing return (100% allocation to sunscreen, but the price he pays to invest is driven up because he is not alone in knowing it faces a positive trading period and the alternative will be wiped out). Meanwhile the hedgie with prior access to metereological forecasts buys sunscreen and shorts umbrella before the prices reflect the forecast, and makes a killing

    5. The model also assumes everyone starts with the same amount of capital, let’s say $1000. Assuming that the claimed 5% (actually 2.5%) return offered by allocating half of that sum to each company in the model is what a person needs to live on, someone who has more than $1000 need not be fully allocated to shares at any point in time. Equally, if he or she has assets other than cash or income other than that generated from investing the $1000, it may be possible to borrow against the assets or future income if the market falls, to take short positions and generally to benefit from being at an advantage compared with the ‘blind’ investor who must be fully invested and diversified to survive

    6. Throw in the fact that most companies can survive a single period of poor trading and that, even if they can’t, their assets and goodwill are generally available to be purchased at less than replacement cost, and you can see that there is truth in the adage that every cloud has a silver lining – at least for those with sufficient wealth to benefit from others’ misfortune. Even without privileged information, the wealthy investor is able to more than recoup losses sustained by investing in the umbrella company by also investing in a turnaround/distress investment vehicle that acquires umbrella co’s assets when it becomes insolvent

    For all the above, the general principle remains that a combination of random walk, attitudinal difference and unequal access to both information and capital account for a high proportion of difference in wealth in the model, and I would suggest, in life.

    I believe the key question for the next 20-30 years is how society allocates effort and resource between ex-ante efforts to equalise the variables that create inequality and ex-post redistribution to mitigate its effects. I believe we underplay the former and overdo the latter, but explaining why would be a blog in itself, not a comment on someone else’s.

  26. 26 26 Bennett Haselton

    Well yes VCs do invest in those people but if they still only manage about a 5% success rate, that requires a lot of luck.

    The difference from baseball players, I think, is that you get so many at-bats over your career, that if you’re averaging .300, that’s still a useful contribution to your team. Whereas if you have personal attributes that give you a 5% chance of your VC-backed project being a success, you’re probably not going to be successful, because you only get a handful of “at-bats” at most in that system.

  27. 27 27 Flocccina

    OT: If Democrats are so concerned with inequality why don’t they end the the state lotteries.

  28. 28 28 Flocccina

    A Democrat might argue for high taxes on high net earnings so as to nudge the stupid people away risk but I would let it go. I am not a very talented person myself but I understand that risk plus randomness can put a person like me on top and I get a little pleasure from that kind of thought.

  29. 29 29 Daniel

    I like the parable about the “smart” people incorrectly computing a simple return.

  30. 30 30 Kevin Erdmann

    The biggest problem with your puzzle is the simple one-one-step decision tree. In a world filled with uncertainty, you can’t make one decision and then wait to see the binary result (outside of Vegas). Take a look at a firm like PATK. They’ve had a tremendous run over the past couple of years. Imagine you were lucky enough to put all your cash in it at $2 in October 2011. How do you know when to sell? If you held the entire amount until today at $40, a $50,000 stake could have earned you a decent retirement. But there were dozens of decision points between $2 and $40. So, even among people who would have started at exactly the right time, if half sold at every decision point, a small fraction of a percent would have gotten the golden ticket. And for every PATK, there are 20 stocks that went to $10 and fell back to $2 if you were holding for $40.
    Luck is a lot easier in a textbook decision tree than in real life where the decision tree is compounded daily.

  31. 31 31 Al V.

    This reminds me of the discussion a coworker and I had in the early 90s. At the time there were many companies making PCs (Compaq, Dell, Wyse, etc.), and I made the point that it was hard to product which would be successful in the long run, and which would fail. I made the suggestion that it would be smart to put, say, $1,000. in each of 10 companies, betting that some would fail, but those that succeeded would make up for the failures.

    For me, it was an idle discussion, but Jerry (who had more free cash) acted on the idea. And he is retired now, while I am still working. Most of those companies are now out of business, but $1,000 in Dell at the time peaked at above $1,000,000 a few years ago, although it is about 20% of that peak now.

  32. 32 32 iceman

    This actually seems ‘progressive’ in the sense that the dumb people who do well would’ve otherwise been poor.

    Plus if they spend it foolishly it will flow back to smart people (who can run a real business).

    And in terms of judging distributions, a question is is dumb luck in some way ‘unjust’?

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