An Introduction to Retirement Investing for Scientists

After spending a number of afternoons and evenings with friends and family over the last few months reviewing their retirement planning and investments, I’ve gone and done something a little bit crazy: I suggested to the GSC at Caltech that maybe I could give a talk on retirement investing to the grad student/postdoc population.  Incredibly, they thought this sounded like a good idea, and so now I’m scheduled to give a talk in a couple of weeks.  I’m going to try and write it up here in prose form first, to get it organized.  It’s gotten to be a bit long… so I’m going to break it up.

Main Points:

  1. Taking responsibility for funding your own retirement is arguably more important now than it has been for a couple of generations.  100 years ago we had much more in the way of traditional (family, community) support in old age, and the systems that we put in place after the Depression (corporate pensions demanded by organized labor, social security) show few signs of being fixed any time soon.  Generally today you do not even have the option of signing up for a “defined benefit” plan.  It’s a 401(k) or the highway.
  2. Investment returns are for all practical purposes random, unpredictable events, and because of this there’s really no such thing as an “expert investor” in the sense that most people selling their investment management services try and imply.  Nobody can reliably beat the broad markets, but you can do a perfectly good job of managing your own retirement funds if you’re willing to spend about 4 hours per year on it, say the other half of the day you spend doing your taxes.
  3. To maximize your chances of success, you must habituate yourself to spending less than you earn, making investing as automatic as possible, starting early and aggressively, and continuing throughout your entire career, regardless of what life and the markets throw at you.  Because returns are exponential and not linear, the difference between starting to save at age 23 and age 32, assuming roughly an 8% rate of return, can be on the order of a factor of two in the final value of your retirement funds.  Being comfortable living well below your apparent means makes it possible not only to save money now, but also reduces the amount of money you need in order to have “enough” in retirement, where “enough” means about 25 times your expected annual withdrawals, as you can take about 4% of your money out each year indefinitely.
  4. Maximizing the returns on your investments largely comes down to managing investment costs: how much you pay the people doing the actual investing (i.e. the mutual fund companies), and how much you pay in taxes.  The difference between paying 0.2% and 2% in fees and taxes each year might not seem huge, but over the course of 35 years of investing, it makes roughly a factor of two difference in the amount of money you end up with.
  5. The two most important tools you have in managing investment risk are diversification and asset allocation.  Diversification reduces the overall impact of many kinds of unpredictable events (high oil prices, the demise of the newspaper industry, war between India and Pakistan, collapse of the Icelandic currency… etc.) reducing the overall volatility of your portfolio.  Asset allocation (mainly the split between stocks and bonds) allows you to choose what kind of financial risk you are exposed to, and to shift it over time as you get closer to actually needing to live off your investments.  With stocks, you get the potential for future growth, at the expense of having to put up with wild fluctuations in their value.  With bonds, you get less price fluctuation and less potential for growth, but the ability to draw a reliable income stream.  With cash you get little to no price fluctuation, but essentially zero potential for real (inflation adjusted) growth.

What is retirement?

Somehow over the last century people in the industrialized nations got the idea that it would be nice at some point in their lives to be able to stop working, or at least to have more freedom to choose what kind of work they do, and how much of it.  It’s a nice idea.  Actually implementing it reliably for hundreds of millions of people over many decades has turned out to be somewhat challenging.  To make it work, you have to somehow smuggle wealth to yourself forward through time.  That means both deferring present consumption, and somehow at least preserving, and preferably increasing, the real value of the wealth you are smuggling, en route to the future.

The first part (deferring consumption) is hard because we are generally impatient and at least a little greedy, and also because there are plenty of organizations with large advertising budgets that would like to encourage us to give in to that impatience.  The second part (the smuggling) is hard because society and its institutions are at least a little less stable than we like to tell ourselves, and so it’s hard to know where to place your bets.  Wars, plagues, famines and floods do happen.  We develop and deploy technologies which disrupt the pre-existing natural and social orders.  We are prone en masse to bouts of both irrational exuberance and apocalyptic pessimism.  All these things happen on timescales comparable to that of your likely investing career, which will be on the order of half a century long.  Think of the world in 1900 (Jules Verne, pre-WWI, Moulin Rouge, bicycles just invented) compared to the world of 1950 (post-WWII, nuclear weapons), or 1925 (population: 2 billion, before Lindbergh’s flight, before cars were common) next to 1975 (population: 4 billion, Apollo had already been canceled, OPEC-induced global economic mess).  Avoid the temptation to think of the US experience over the last century as normal, or likely to indicate what the next century will be like.

Imagine being a babushka who remembers vaguely but personally the Russian Revolution and civil war, and who watches her pension evaporate along with the Soviet Union.  Imagine being a gray haired resident of modern, glittering Shanghai or Shenzhen, and having also actually fought in Mao’s guerrilla war against the nationalists.  This, or possibly even more, is the scale of change that is possible over your lifetime.  The future self you are trying to smuggle this wealth to lives in a world with between 7 and 12 billion human inhabitants, in which the northwest passage might be open for business all summer long, and sea levels have risen between 0.1 and 1.0 meters.  A world in which probably everyone living in a developed nation has had their genome sequenced, many of the younger folks before they were even born.  And I dare you to make a list of which nations we’ll even consider “developed” in 2050, or whether such a designation will even still make sense.  Those are the kinds of changes you should expect as a matter of course, ignoring for the moment the possibility of anything really truly weird happening, like human lifespans doubling, or the emergence of a powerful artificial intelligence.

But if you’re willing to buy in to the premise of investing at all: that buggy-whip manufacturers will go bankrupt, and Ukranian bot-herders will go public to take their place, and that somehow the whole process will result in the net creation of wealth, then the goal of retirement investing is this: to one day have enough money set aside that you can reasonably expect that for the rest of your life, what you do with your time each day will be a choice you make unconstrained by the need to be employed.  If we naïvely take historical returns to be indicative, generally, of what we might expect to be able to earn on our investments 30-50 years from now, then this means building up savings of roughly 25 times your expected annual living expenses in retirement, as you have historically been able to safely draw an income worth about 4% of your capital indefinitely.

Investing should be like brushing your teeth.

Managing your own retirement investments, if done correctly, should be a lot like brushing your teeth.  Neither should take very much time or expertise.  Both require a little discipline and regular if uninspired attention.  Nobody really expects brushing their teeth to be very exciting or intellectually stimulating, but most of us do it anyway, because the consequences of not doing it are pretty ugly.  Planning for retirement is no different.

Maybe the biggest difference between brushing your teeth and investing is that there’s no multi-billion dollar industry dedicated to trying to convince you that their particular mysterious and proprietary tooth brushing technique will lead to fewer cavities, and that you should therefore pay them handsomely to brush your teeth for you.

Why should you listen to me?

The short answer is that you probably shouldn’t, at least not as if I were some kind of “authority”.  I’m just some dude with a tie and a laptop.  I’m not an economist, I’m not a Certified Financial Planner or Analyst, and I’m not really giving you “financial advice” in the legal sense.  However, I’d humbly like to suggest that you also ought to resist the urge to listen to most people who do claim to be experts.  They may be professional advisers, but that’s different from being experts, and often they are not working for you.  They are also, metaphorically, just dudes with ties and laptops.

Like the Buddha said:

Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense.

Or as physicist and statistician W. Edwards Deming was fond of saying:

In God we trust; all others must bring data.

What I am is an enthusiastic amateur adviser, and I’m giving this talk because I’ve been disturbed at how few of the very smart people I’ve talked to have put any energy into understanding this topic, which is actually not that complex, and fairly important to us as individuals.  If we bring the same skepticism, empiricism, and analytical skills to investing that we would bring to a department seminar we should be fine.  Or at least as fine as anybody else is.

The Grand Casino: Asset Classes by Analogy

But before I bring you the data, I want to describe the two most general hypotheses about investing which you are likely to encounter.  I will use a version of what is probably the most dangerously over-used analogy in probability and statistics: the casino.  I say it’s dangerously over-used because real-world probability distributions having to do with social and other complex non-linear phenomena, like markets, are never anywhere close to as well defined as the probability distributions you’ll encounter in a casino.

Wall St. and Las Vegas differ from each other in important ways.  Casinos in Nevada are very reliably and aggressively regulated.  You know the odds going in, and you know they’re stacked against you.  Wall St. on the other hand is like a casino in which the odds have historically been stacked in your favor overall, but where the house can and will cheat as much as you let them.  There are also no table limits on Wall St., and strangely in this casino occasionally a random fluctuation in the Earth’s magnetic field will cause all the dice to come up snake eyes, and all the roulette wheels to come up double-ought for a few hours, and there’s nothing you can do about it.

So without succumbing to the Ludic Fallacy, imagine you’re in a casino, and there are several versions of the same game on offer.  In the first you put down your stake and your friendly croupier Trent flips a coin.  If heads comes up, your stake is increased by 30%.  Tails, and you go down 10%. Alternatively, you can also opt to play a couple of similar games, but with different payoffs, either +60%/-25% or +10%/-2%.  However, there’s a catch: the coins are flipped only once a night.  Which game should you play?  If you’re at the beginning of a (very) long vacation, and you’re going to be playing the game many times, then clearly the +60/-25 game is the best bet to start with, as over the long run, its expected payoff will be 9.5% per night, versus 8.2% at the +30/-10 table, or the paltry 3.8% return of the +10/-2 table.

However, as you near the end of your stay, the sensible choice changes, depending on how much you need the money, and whether or not you can change the date of your ticket home, since you have a 25% chance of losing 44% of your money over the last two nights (or any consecutive two nights) if you keep playing the high risk, high reward game.  On the other hand, it’s worth noting that if you happen to owe a guy with a baseball bat named Fat Tony $15,000 tomorrow, and all you’ve got is $10,000, then the high risk table looks pretty good even over the short term, because at least there you’ve got a 50/50 chance of going home with your kneecaps intact.

One night you wander in a bit of a drunken haze into the alleyway behind the Casino.  Here in the shadows you find a bunch of other games to play.  You meet a guy named Mallory, who offers you the same kind of bet you’ve been making every night so far, but his payoffs are +58/-26.  At first, even through your free cocktail induced buzz, this doesn’t seem like a particularly good deal given that you can get the same average payoff (8.1%) inside the casino, with a lot less risk, but then Mallory leans close and assures you “Don’t worry.  I just flipped this coin ten times, and it came up heads every single time.”  The other gamblers gathered round his table nod in agreement.  Is it a loaded coin, or does Mallory just know how to flip it so it always comes up heads?  You put down your stake, he flips the coin, and you lose 26%.

There’s a relevant story that’s sometimes told about Enrico Fermi.  When he first came to the US and started working on the Manhattan project, he had a lot of meetings with high ranking military officers.  At some point he was told “So-and-so is a great general.”

“What is the definition of a great general?” Fermi asked the officer.
“I guess it’s a general who’s won many consecutive battles”
“How many?”
After some back and forth they settled on five.
“What fraction of American generals are great?”
After some more back and forth, they settled on a few per cent.

But imagine, Fermi rejoined, that there is no such thing as a great general, that all armies are equally matched, and that winning a battle is purely a matter of chance.  Then the chance of winning one battle is one out of two, or 1/2; two battles 1/4, three 1/8, four 1/16 and five consecutive battles 1/32, which is about three per cent.  You would expect a few per cent of American generals to win five consecutive battles, purely by chance.  Now has any of them won ten consecutive battles?

In the game you lost above, Mallory wasn’t lying to you outright, but he wasn’t telling you the whole truth either.  Beneath his table, he’s got a bag filled with about a thousand other coins, and he’s just flipped each of them ten times, in the hopes that one of them would come up heads ten times in a row so that he could tell you with a straight face that the coin you bet on had a good record.

The Casino in general is the markets, and the three games described above might in real life represent Emerging Markets or Small Cap Stocks (+60/-25), the US Stock Market (+30/-10) and the US Bond Market (+10/-2).

Mallory is a malicious mutual fund manager, operating well within the bounds of the law, and the ethical standards that most of the industry holds itself to.

Many state and corporate pensions, and not a few individual investors, have either catastrophically underfunded their retirement accounts, or took on too much risk too close to needing the money, and now find themselves owing Fat Tony a whole lot more than they’ve got, and so they no longer feel they have any choice but to roll the high-risk dice.

Aside from actually being willing to defer consumption — to live well below your means and invest the difference — the most important thing to understand from this talk is that market returns are functionally random.  The odds and payoffs are not as straightforward as the above cartoon description, but all honest empirically minded attempts to demonstrate that investors can do better than chance would predict at choosing investments have so far failed.  That doesn’t mean it’s necessarily impossible (proving a negative statement is generally a pretty tough task…), but it does mean that for all practical purposes it’s not something you’d want to stake your retirement plans on.  You wouldn’t after all decide only to buy electricity today that had been generated by a nuclear fusion reactor just because it might in theory be possible to build one.  And so whenever you feel yourself being drawn into a story about why one investment (blue chips, tech stocks, real estate, commodities, whatever…) is better than another, it may help to remember the serenity prayer:

God, grant me the serenity
To accept the things I cannot change;
The courage to change the things that I can;
And the wisdom to know the difference.

What I am asserting is that you can change how much you save and spend; you can affect how much you pay in fees and taxes; you can choose and maintain an asset allocation, but you must simply accept the returns the markets provide.  In the next post, I’ll present the data which supports this assertion.

Updated 2/25/2010 to correct the average returns to be geometric means, not arithmetic means, and fix the stated probabilities to get the point I intended across. Whoops!

10 thoughts on “An Introduction to Retirement Investing for Scientists”

  1. I’d like to note that your way of calculating average payoffs seems wrong for the purpose at hand. In the limit as you play the game infinitely often, you will almost certainly have more money if you play the game “give me 1.2% regardless” than if you play the +60/-36 game (as Sqrt(1.6*0.64)<1.012).

    Of course for each finite n there is a very small, yet positive chance of getting awfully disgustingly rich playing the +60/-36 game, which makes the expectation value of the money you win large when playing the high stakes game, but it seems that for retirement investing you'd usually want to disregard this possibility.

    I'm more interested in the dilemma: "With high probability you'll be better of playing the +30/-10 game instead of +10/-2, but there is a small change you're totally screwed".

  2. Whoops, you’re absolutely right, it should be the geometric mean not the arithmetic mean. The point I was trying to get across was that you have several choices available, and those with higher expectation values (average returns) also have much more variability in those returns. A better high risk/reward game would have been +75/-25, which has a geometric mean return of 9.5%, vs. 8.2% for +30/-10 and 3.8% for +10/-2.

    Part of the point of the talk is that there’s always a small chance you’re going to be totally screwed. You can try and minimize it, but it’s always there, even if you just use a money-market/savings account, which will barely keep up with inflation and require you to save ~50% of your take-home pay if you want to safely retire at 65.

    The thing to do is to play more than one table at a time. Early in your stay, you put a larger proportion of your stake down on the high-risk table each night, and late in your stay, you put more of it on the low-risk table. And that’s about all there is to asset allocation.

  3. Nicely done. I like your mutual fund manager analogy. And I did not see the Ukranian bot-herders coming.

    Of course, now that you have me hooked, I want to see the data and the conclusions!

  4. Hi Zane.

    I really appreciated your talk today (/45 minutes ago). I have a pretty severe aversion to all things finance so this approach is basically perfect for me. Many thanks.

    P.S. That internship at the Fed consisted mostly of napping and eating delicious subsidized cookies 😉

  5. Glad you thought it was useful! I hope I didn’t inadvertently send anybody off in some weird unexpected direction…

    I really want to understand where all these aversions to financial things I keep running into with people I talk to about this stuff are coming from. I mean, if someone with a background in quantitative finance, math and stats, doing a PhD in SS and interning at the Fed doesn’t want to deal with their retirement accounts… the general public is totally screwed!

  6. Haha, well, I haven’t met a lot of micro-economists who don’t have some degree of this aversion as well. But I can’t say where it comes from. Maybe because finance seems more like macro, and macro is completely baffling (and vaguely menacing) to us?

    Plus my background is a bit misleading. When I was at the Fed I was basically involved with a very micro-oriented economic history project in the research division. So in fact I’ve had very little academic exposure to macro and almost zero exposure to finance. There is so much noise out there about this, and so many possibly sketchy people giving advice, so the natural (and lazy) thing to do is to just tune out everything indiscriminately. Which might not be super rational, but here at Caltech we’re all about relaxing rationality assumptions 🙂

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