Fallacy of time diversification

Discuss all general (i.e. non-personal) investing questions and issues, investing news, and theory.
protagonist
Posts: 6093
Joined: Sun Dec 26, 2010 12:47 pm

Re: Fallacy of time diversification

Post by protagonist » Tue Jan 14, 2020 8:31 pm

lazyday wrote:
Tue Jan 14, 2020 12:32 pm
protagonist wrote:
Tue Jan 14, 2020 12:06 pm
You are confusing risk with predictable loss. Cash is much more predictable than stocks- you know you will probably gradually lose to inflation Thus by definition it is much less risky. (Though inflation is unpredictable and becomes more so over time so the degree of risk of cash does, as with stocks, increase over time). Risk is a function of predictability.
Are you viewing upside unpredictability as a risk?

Imagine two investments. One will return between 5% and 20%. The second will return between -2% and 0%.

Which is riskier?
If you are referring to "real" risk (relative to inflation), the first scenario presents zero risk, because no matter what, you predictably win. Let me know if you find such an investment....I want in.

The second investment is predictably stupid, unless it is your best option. No matter what, you lose (or if you are lucky you break even). The maximum amount you can lose is small and defined- thus the risk is present but not huge,
Last edited by protagonist on Tue Jan 14, 2020 8:33 pm, edited 1 time in total.

jmk
Posts: 547
Joined: Tue Nov 01, 2011 7:48 pm

Re: Fallacy of time diversification

Post by jmk » Tue Jan 14, 2020 8:33 pm

deleted
Last edited by jmk on Wed Jan 15, 2020 10:28 am, edited 2 times in total.

protagonist
Posts: 6093
Joined: Sun Dec 26, 2010 12:47 pm

Re: Fallacy of time diversification

Post by protagonist » Tue Jan 14, 2020 8:39 pm

jmk wrote:
Tue Jan 14, 2020 8:33 pm
Geologist wrote:
Tue Jan 14, 2020 8:28 am
This quotation from Malkiel that nisiprius included is very important: "Certainly the variability of the final value of your portfolio does increase the longer you hold your stocks."

William Bernstein refers to this as Terminal Wealth Dispersion and he provided a graph in The Four Pillars of Investing (from Jeremy Siegel's data) showing the real end wealth of $1 invested in U.S. Stocks over 30 year periods ending 1901-2000 ranged from roughly $2 to $21. That's a big range.
But while the dispersion of returns increases, the probability of those extremes does not. If you follow a 25th percentile line, for instance, you'll see that it increase over time. In fact the 25th and 75th percentile converge, as do the other percentiles.
The range of possibilities over the next century are losing 100% on the down side and unlimited on the up side. The range of 30 year returns within the 20th century on $1 may have ranged from $2 to $21, but that only represents a bit over 3 independent data points (during a remarkable century), which is statistically meaningless for the future. Even if past returns predict future performance, there is far too little data to make any meaningful prediction. It is the statistical equivalent of saying that if the range of 1 day stock returns over the past 3 days was always positive, you should feel confident that the stock market will rise tomorrow. How I wish that method of market timing worked!!!

Seasonal
Posts: 641
Joined: Sun May 21, 2017 1:49 pm

Re: Fallacy of time diversification

Post by Seasonal » Wed Jan 15, 2020 3:20 am

lazyday wrote:
Tue Jan 14, 2020 6:31 am
Seasonal wrote:
Tue Jan 14, 2020 5:34 am
If over some period of time stocks are not riskier than bonds, why should we believe they will perform better than bonds over that period?
Maybe the average dollar in stocks is invested by someone who cares more about shorter term returns.
I suppose anything is possible, but there should be trading or hedging strategies to deal with that possibility.

thx1138
Posts: 1014
Joined: Fri Jul 12, 2013 2:14 pm

Re: Fallacy of time diversification

Post by thx1138 » Wed Jan 15, 2020 8:53 am

The “fallacy” is in most folks ignoring the utility function Samuelson uses in his paper. It is a utility function that I can’t imagine any real investor ever actually having. Samuelson makes a salient and important point about the behavior of returns over time and how they are frequently represented incorrectly in the investing world. But the conclusion about an investor being indifferent to the time horizon is built on the particular utility function he uses to make the math easy and again no sane person in the world has such a utility function for their retirement investments so the claim is as academic as academic can be. A numerical curiosity otherwise completely irrrelevant to the real world.

Topic Author
UberGrub
Posts: 115
Joined: Wed Aug 21, 2019 3:47 pm

Re: Fallacy of time diversification

Post by UberGrub » Wed Jan 15, 2020 8:58 am

thx1138 wrote:
Wed Jan 15, 2020 8:53 am
The “fallacy” is in most folks ignoring the utility function Samuelson uses in his paper. It is a utility function that I can’t imagine any real investor ever actually having. Samuelson makes a salient and important point about the behavior of returns over time and how they are frequently represented incorrectly in the investing world. But the conclusion about an investor being indifferent to the time horizon is built on the particular utility function he uses to make the math easy and again no sane person in the world has such a utility function for their retirement investments so the claim is as academic as academic can be. A numerical curiosity otherwise completely irrrelevant to the real world.
Could you explain to me what utility function Samuelson assumes (as in what that actually looks like) and why you don’t think it applies to any sane person?

I’m not well versed on the subject and could use some dumbing down, thanks!

thx1138
Posts: 1014
Joined: Fri Jul 12, 2013 2:14 pm

Re: Fallacy of time diversification

Post by thx1138 » Wed Jan 15, 2020 10:00 am

UberGrub wrote:
Wed Jan 15, 2020 8:58 am
thx1138 wrote:
Wed Jan 15, 2020 8:53 am
The “fallacy” is in most folks ignoring the utility function Samuelson uses in his paper. It is a utility function that I can’t imagine any real investor ever actually having. Samuelson makes a salient and important point about the behavior of returns over time and how they are frequently represented incorrectly in the investing world. But the conclusion about an investor being indifferent to the time horizon is built on the particular utility function he uses to make the math easy and again no sane person in the world has such a utility function for their retirement investments so the claim is as academic as academic can be. A numerical curiosity otherwise completely irrrelevant to the real world.
Could you explain to me what utility function Samuelson assumes (as in what that actually looks like) and why you don’t think it applies to any sane person?

I’m not well versed on the subject and could use some dumbing down, thanks!
Sure. Samuelson uses the "isoelastic utility function". Peeling away lots of math Wikipedia gives a good distillation of the salient feature of it:

In theoretical models this often has the implication that decision-making is unaffected by scale. For instance, in the standard model of one risk-free asset and one risky asset, under constant relative risk aversion the fraction of wealth optimally placed in the risky asset is independent of the level of initial wealth.

Source: https://en.wikipedia.org/wiki/Isoelastic_utility

This is of course a rather ridiculous assumption for retirement planning. For almost everyone the whole point to saving for retirement is to have "enough" and well "enough" immediately implies that scale isn't irrelevant but rather the whole point! At some point you have "enough" and you quickly have no utility in taking on risk for additional money you don't need.

User avatar
siamond
Posts: 5142
Joined: Mon May 28, 2012 5:50 am

Re: Fallacy of time diversification

Post by siamond » Wed Jan 15, 2020 10:08 am

thx1138 wrote:
Wed Jan 15, 2020 8:53 am
The “fallacy” is in most folks ignoring the utility function Samuelson uses in his paper. It is a utility function that I can’t imagine any real investor ever actually having. Samuelson makes a salient and important point about the behavior of returns over time and how they are frequently represented incorrectly in the investing world. But the conclusion about an investor being indifferent to the time horizon is built on the particular utility function he uses to make the math easy and again no sane person in the world has such a utility function for their retirement investments so the claim is as academic as academic can be. A numerical curiosity otherwise completely irrrelevant to the real world.
Exactly. What boggles my mind is that many intelligent people I respect fall for this. Some academics really made an atrocious mess of defining 'risk'.

jmk
Posts: 547
Joined: Tue Nov 01, 2011 7:48 pm

Re: Fallacy of time diversification

Post by jmk » Wed Jan 15, 2020 10:14 am

A picture makes the issue clearer for me to give specifics to vague notions like "risk". Compare a bootstrapped monte carlo (1930-2019 Shiller data) 10,000 runs of Sp500 versus Cash. (It doesn't reflect auto-correlation, but will work for this issue.)

Cash:
Image

SP500:
Image

To state the obvious, the dispersion of portfolio value for stocks in terms of inflation adjusted dollars is much higher than the dispersion of value of cash. (If that matters to you.) The volatility risk of each asset over short time periods is evident. But over long terms, while the dispersion of stocks is much more than cash, the "worst case" of stocks is actually better than the worst case of cash. More importantly, the middle range of cases (25th-75th percentiles--returns between the green and red lines) of Stock portfolio value rise quickly over time and are much better than Cash's 25th-75th percentile results. So in a very practical sense, stocks are much safer than cash even though they are riskier assets in any short time period.

Topic Author
UberGrub
Posts: 115
Joined: Wed Aug 21, 2019 3:47 pm

Re: Fallacy of time diversification

Post by UberGrub » Wed Jan 15, 2020 10:32 am

thx1138 wrote:
Wed Jan 15, 2020 10:00 am
UberGrub wrote:
Wed Jan 15, 2020 8:58 am
thx1138 wrote:
Wed Jan 15, 2020 8:53 am
The “fallacy” is in most folks ignoring the utility function Samuelson uses in his paper. It is a utility function that I can’t imagine any real investor ever actually having. Samuelson makes a salient and important point about the behavior of returns over time and how they are frequently represented incorrectly in the investing world. But the conclusion about an investor being indifferent to the time horizon is built on the particular utility function he uses to make the math easy and again no sane person in the world has such a utility function for their retirement investments so the claim is as academic as academic can be. A numerical curiosity otherwise completely irrrelevant to the real world.
Could you explain to me what utility function Samuelson assumes (as in what that actually looks like) and why you don’t think it applies to any sane person?

I’m not well versed on the subject and could use some dumbing down, thanks!
Sure. Samuelson uses the "isoelastic utility function". Peeling away lots of math Wikipedia gives a good distillation of the salient feature of it:

In theoretical models this often has the implication that decision-making is unaffected by scale. For instance, in the standard model of one risk-free asset and one risky asset, under constant relative risk aversion the fraction of wealth optimally placed in the risky asset is independent of the level of initial wealth.

Source: https://en.wikipedia.org/wiki/Isoelastic_utility

This is of course a rather ridiculous assumption for retirement planning. For almost everyone the whole point to saving for retirement is to have "enough" and well "enough" immediately implies that scale isn't irrelevant but rather the whole point! At some point you have "enough" and you quickly have no utility in taking on risk for additional money you don't need.
I’m confused. Bogleheads are notorious for recommending an asset allocation independent of wealth. If you got 10M or 1M, they might still recommend a 50/50. This only seems consistent with isoelastic utility. You’resaying this kind of advice is not sane?

thx1138
Posts: 1014
Joined: Fri Jul 12, 2013 2:14 pm

Re: Fallacy of time diversification

Post by thx1138 » Wed Jan 15, 2020 10:41 am

UberGrub wrote:
Wed Jan 15, 2020 10:32 am
thx1138 wrote:
Wed Jan 15, 2020 10:00 am
UberGrub wrote:
Wed Jan 15, 2020 8:58 am
thx1138 wrote:
Wed Jan 15, 2020 8:53 am
The “fallacy” is in most folks ignoring the utility function Samuelson uses in his paper. It is a utility function that I can’t imagine any real investor ever actually having. Samuelson makes a salient and important point about the behavior of returns over time and how they are frequently represented incorrectly in the investing world. But the conclusion about an investor being indifferent to the time horizon is built on the particular utility function he uses to make the math easy and again no sane person in the world has such a utility function for their retirement investments so the claim is as academic as academic can be. A numerical curiosity otherwise completely irrrelevant to the real world.
Could you explain to me what utility function Samuelson assumes (as in what that actually looks like) and why you don’t think it applies to any sane person?

I’m not well versed on the subject and could use some dumbing down, thanks!
Sure. Samuelson uses the "isoelastic utility function". Peeling away lots of math Wikipedia gives a good distillation of the salient feature of it:

In theoretical models this often has the implication that decision-making is unaffected by scale. For instance, in the standard model of one risk-free asset and one risky asset, under constant relative risk aversion the fraction of wealth optimally placed in the risky asset is independent of the level of initial wealth.

Source: https://en.wikipedia.org/wiki/Isoelastic_utility

This is of course a rather ridiculous assumption for retirement planning. For almost everyone the whole point to saving for retirement is to have "enough" and well "enough" immediately implies that scale isn't irrelevant but rather the whole point! At some point you have "enough" and you quickly have no utility in taking on risk for additional money you don't need.
I’m confused. Bogleheads are notorious for recommending an asset allocation independent of wealth. If you got 10M or 1M, they might still recommend a 50/50. This only seems consistent with isoelastic utility. You’resaying this kind of advice is not sane?
I've not seen most Bogleheads recommending that at all. There are endless discussions on here about AA when you've "reach your number" or "won the game". Both those turns of phrase imply utility far different than isoelastic. And the standard Boglehead AA recommendation is one that varies over time so again implies not isoelastic. So near as I can tell all the standard Boglehead advice on the wiki and the typical discussions here on Bogleheads strongly indicate that Bogleheads at least clearly don't have isoelastic utility or at the very least take actions and give recommendations that do not imply isoelastic utility.

And yes I'd say not having a spending goal which then implies a wealth goal is not sane at all. Trying to get to 10M when you plan to spend only $50K/yr is not sane. Calling yourself done at 1M when you plan to spend $200K/yr is not sane. Saying everyone should be at a static AA their entire life is not really insane but is very much not a Boglehead recommendation.

Now, if you look at the typical savings rates for most people, the typical retirement age for most people and the typical retirement spending in relation to pre-retirement saving for most people then you can indeed form a blanket pretty good recommendation that is independent of wealth. Mostly this is down to the fact that people who make lots of money tend to spend lots of money both pre and post retirement. And even in this condition the recommendation is an AA glideslope that is incorporated with variations into every target date retirement fund around. Which again implies not isoelastic utility.
Last edited by thx1138 on Wed Jan 15, 2020 10:43 am, edited 1 time in total.

muffins14
Posts: 74
Joined: Wed Oct 26, 2016 4:14 am

Re: Fallacy of time diversification

Post by muffins14 » Wed Jan 15, 2020 10:43 am

It’s also not a single-variable problem. Someone with 1M at 20 years of age would likely get a more aggressive recommendation than someone with 1M at age 75 ... because of the time horizon of each investor

User avatar
gmaynardkrebs
Posts: 1760
Joined: Sun Feb 10, 2008 11:48 am

Re: Fallacy of time diversification

Post by gmaynardkrebs » Wed Jan 15, 2020 10:44 am

Much of the risk in Treasury bonds in the Siegel data was due to inflation. If TIPS had existed way back when, I would think the historical advantage he computed for equities in would have been less. I have only the 1994 edition of his book. Does anyone know if he ran a hypothetical series with TIPS instead of nominal Treasuries in later editions?

Topic Author
UberGrub
Posts: 115
Joined: Wed Aug 21, 2019 3:47 pm

Re: Fallacy of time diversification

Post by UberGrub » Wed Jan 15, 2020 10:56 am

thx1138 wrote:
Wed Jan 15, 2020 10:41 am
UberGrub wrote:
Wed Jan 15, 2020 10:32 am
thx1138 wrote:
Wed Jan 15, 2020 10:00 am
UberGrub wrote:
Wed Jan 15, 2020 8:58 am
thx1138 wrote:
Wed Jan 15, 2020 8:53 am
The “fallacy” is in most folks ignoring the utility function Samuelson uses in his paper. It is a utility function that I can’t imagine any real investor ever actually having. Samuelson makes a salient and important point about the behavior of returns over time and how they are frequently represented incorrectly in the investing world. But the conclusion about an investor being indifferent to the time horizon is built on the particular utility function he uses to make the math easy and again no sane person in the world has such a utility function for their retirement investments so the claim is as academic as academic can be. A numerical curiosity otherwise completely irrrelevant to the real world.
Could you explain to me what utility function Samuelson assumes (as in what that actually looks like) and why you don’t think it applies to any sane person?

I’m not well versed on the subject and could use some dumbing down, thanks!
Sure. Samuelson uses the "isoelastic utility function". Peeling away lots of math Wikipedia gives a good distillation of the salient feature of it:

In theoretical models this often has the implication that decision-making is unaffected by scale. For instance, in the standard model of one risk-free asset and one risky asset, under constant relative risk aversion the fraction of wealth optimally placed in the risky asset is independent of the level of initial wealth.

Source: https://en.wikipedia.org/wiki/Isoelastic_utility

This is of course a rather ridiculous assumption for retirement planning. For almost everyone the whole point to saving for retirement is to have "enough" and well "enough" immediately implies that scale isn't irrelevant but rather the whole point! At some point you have "enough" and you quickly have no utility in taking on risk for additional money you don't need.
I’m confused. Bogleheads are notorious for recommending an asset allocation independent of wealth. If you got 10M or 1M, they might still recommend a 50/50. This only seems consistent with isoelastic utility. You’resaying this kind of advice is not sane?
I've not seen most Bogleheads recommending that at all. There are endless discussions on here about AA when you've "reach your number" or "won the game". Both those turns of phrase imply utility far different than isoelastic. And the standard Boglehead AA recommendation is one that varies over time so again implies not isoelastic. So near as I can tell all the standard Boglehead advice on the wiki and the typical discussions here on Bogleheads strongly indicate that Bogleheads at least clearly don't have isoelastic utility or at the very least take actions and give recommendations that do not imply isoelastic utility.

And yes I'd say not having a spending goal which then implies a wealth goal is not sane at all. Trying to get to 10M when you plan to spend only $50K/yr is not sane. Calling yourself done at 1M when you plan to spend $200K/yr is not sane. Saying everyone should be at a static AA their entire life is not really insane but is very much not a Boglehead recommendation.

Now, if you look at the typical savings rates for most people, the typical retirement age for most people and the typical retirement spending in relation to pre-retirement saving for most people then you can indeed form a blanket pretty good recommendation that is independent of wealth. Mostly this is down to the fact that people who make lots of money tend to spend lots of money both pre and post retirement. And even in this condition the recommendation is an AA glideslope that is incorporated with variations into every target date retirement fund around. Which again implies not isoelastic utility.
The BH wiki on Asset Allocation doesn’t have a single mention as to how to vary AA based on your own wealth. It’s all recommendations of % that you apply to whatever savings you have.

User avatar
305pelusa
Posts: 1330
Joined: Fri Nov 16, 2018 10:20 pm

Re: Fallacy of time diversification

Post by 305pelusa » Wed Jan 15, 2020 10:59 am

thx1138 wrote:
Wed Jan 15, 2020 10:41 am
UberGrub wrote:
Wed Jan 15, 2020 10:32 am
thx1138 wrote:
Wed Jan 15, 2020 10:00 am
UberGrub wrote:
Wed Jan 15, 2020 8:58 am
thx1138 wrote:
Wed Jan 15, 2020 8:53 am
The “fallacy” is in most folks ignoring the utility function Samuelson uses in his paper. It is a utility function that I can’t imagine any real investor ever actually having. Samuelson makes a salient and important point about the behavior of returns over time and how they are frequently represented incorrectly in the investing world. But the conclusion about an investor being indifferent to the time horizon is built on the particular utility function he uses to make the math easy and again no sane person in the world has such a utility function for their retirement investments so the claim is as academic as academic can be. A numerical curiosity otherwise completely irrrelevant to the real world.
Could you explain to me what utility function Samuelson assumes (as in what that actually looks like) and why you don’t think it applies to any sane person?

I’m not well versed on the subject and could use some dumbing down, thanks!
Sure. Samuelson uses the "isoelastic utility function". Peeling away lots of math Wikipedia gives a good distillation of the salient feature of it:

In theoretical models this often has the implication that decision-making is unaffected by scale. For instance, in the standard model of one risk-free asset and one risky asset, under constant relative risk aversion the fraction of wealth optimally placed in the risky asset is independent of the level of initial wealth.

Source: https://en.wikipedia.org/wiki/Isoelastic_utility

This is of course a rather ridiculous assumption for retirement planning. For almost everyone the whole point to saving for retirement is to have "enough" and well "enough" immediately implies that scale isn't irrelevant but rather the whole point! At some point you have "enough" and you quickly have no utility in taking on risk for additional money you don't need.
I’m confused. Bogleheads are notorious for recommending an asset allocation independent of wealth. If you got 10M or 1M, they might still recommend a 50/50. This only seems consistent with isoelastic utility. You’resaying this kind of advice is not sane?
I've not seen most Bogleheads recommending that at all. There are endless discussions on here about AA when you've "reach your number" or "won the game". Both those turns of phrase imply utility far different than isoelastic. And the standard Boglehead AA recommendation is one that varies over time so again implies not isoelastic. So near as I can tell all the standard Boglehead advice on the wiki and the typical discussions here on Bogleheads strongly indicate that Bogleheads at least clearly don't have isoelastic utility or at the very least take actions and give recommendations that do not imply isoelastic utility.

And yes I'd say not having a spending goal which then implies a wealth goal is not sane at all. Trying to get to 10M when you plan to spend only $50K/yr is not sane. Calling yourself done at 1M when you plan to spend $200K/yr is not sane. Saying everyone should be at a static AA their entire life is not really insane but is very much not a Boglehead recommendation.

Now, if you look at the typical savings rates for most people, the typical retirement age for most people and the typical retirement spending in relation to pre-retirement saving for most people then you can indeed form a blanket pretty good recommendation that is independent of wealth. Mostly this is down to the fact that people who make lots of money tend to spend lots of money both pre and post retirement. And even in this condition the recommendation is an AA glideslope that is incorporated with variations into every target date retirement fund around. Which again implies not isoelastic utility.
An AA glide path is entirely consistent with an isoelastic utility if the person is earning an income.

In fact, that’s a common misconception. The glide path isn’t because you have a long time horizon and want to be more aggressive at first. The glide path is done because a worker has lots of human capital and so should overinvest in stocks early on to try to make it up. In fact, Samuelson, who assumes isoelastic utility, would recommend a glide path if you have an income (and of course, a constant allocation of there are no plans to add to the nest egg)

User avatar
nisiprius
Advisory Board
Posts: 39783
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

Re: Fallacy of time diversification

Post by nisiprius » Wed Jan 15, 2020 11:11 am

We've had this discussions like this in forum before and it seems to me that it always comes down to this, in a rough but useful way.

Let's use the phrase "range" to refer to fairly bad and good cases. Not the literal extremes but, let's say 10% and 90% percentiles. For example, when I was using it, the Fidelity Retirement Income Planner used the 10% percentile of stock market returns for projections.

Well, for stocks and bonds, the bottom end of the range is about the same, but the median and average are much higher for stocks, and the upper end is much much higher.

So us prudent/fraidycat/pessimistic types prefer to plan for the bottom end of the range, because we want to have enough even if the stock market does poorly. And that leads to the conclusion that you must save about the same amount no matter what your asset allocation is. You cannot safely take advantage of the higher expected return of stocks to justify slacking off on savings and making up for it with a more aggressive asset allocation.

In this case, we see that a) more stocks does not enable you to save less, and b) the spread of outcomes increases, not decreases with time.

The optimists observe, correctly, that the extra spread is upward from the same bottom, and object to calling this "risk" when the only uncertainty is by how much stocks will beat bonds.

But a meaningful question is how people really act. Based on past historical statistics as always, if high-stocks investors save just as much as low-stocks investors, then it would seem that they are getting the equivalent of free lottery tickets. Free, because it doesn't cost them any more to invest in stocks. Lottery tickets, because there is no guarantee that they will actually do better than they would have done in bonds.

The problem is that I doubt people act this way. I think high-stocks investors tend to count on the higher historical averages, making only partial allowance for it's just being an average, and base this on an incorrect belief that the bounds on outcomes pull in and narrow for longer holding periods, so that it becomes safe to count on getting the average, rather than allowing for the wide range.

This impression could be the result of the wide publication of poisonous charts like this one (Burton Malkiel, A Random Walk Down Wall Street, 2015 edition.

Image

This chart is poisonous in three ways. One is that because it is not inflation-corrected, it gives the impression that a fifteen-year holding period eliminated the risk of loss. One is that for unstated reasons, it throws out the worst periods for stocks in the US, and, guess what? all investments look good if you throw out the times when they looked bad. But, most serious of all, it's a chart of annualized average returns, CAGR. But if you hold an investment for 25 years, you don't get the CAGR, you get the CAGR compounded over 25 years. If you replace the chart with one that shows the results of compounding, those narrowing bars explode right back out again.

It isn't productive to argue about "what is risk," etc. What is important is that:
  • Increasing the length of the holding period does not pull in and narrow the spread. Hence, it does not improve the certainty or reliability of outcome.
  • Assuming the same savings rate, increasing stock allocation widens the spread but it's all up from the bottom. The bottom stays put.
  • Assuming the same savings rate, stocks give you "free lottery tickets" with a darn good chance at a jackpot, but you can't count on that jackpot and shouldn't plan for it.
  • If you unwisely cut your savings rate in the belief that you can count on an average return, believing that long holding periods narrow the range and make stocks less uncertain, then you have changed the situation to one in which increasing stock stock allocation makes the range spread outward from the center. Your bidirectional risk has increased, down as well as up. The bidirectionality is not intrinsic to stocks, but is due to combination of stocks and the plans you have voluntarily chosen to follow. If the facts are that savers with high stock allocations customarily save enough for a comfortable retirement regardless of stock allocation, then, of course, I've set up a straw man.
Last edited by nisiprius on Wed Jan 15, 2020 11:21 am, edited 2 times in total.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

User avatar
willthrill81
Posts: 15207
Joined: Thu Jan 26, 2017 3:17 pm
Location: USA

Re: Fallacy of time diversification

Post by willthrill81 » Wed Jan 15, 2020 11:19 am

Ferdinand2014 wrote:
Mon Jan 13, 2020 11:23 pm
Stocks are just as risky tomorrow whether you have owned them 1 year or 10 if measured by volatility. However, if you have purchased stocks month after month over many years, the likelihood is the compounded returns from unrealized capital gains and dividends reinvested will overwhelm any loss tomorrow if you have held the stocks for a long time. Also, it depends on what you mean by risk. I do not think of volatility as a good measure of risk. I consider risk running out of money when you need it.
:thumbsup

100% agree. The risk of losing to inflation has clearly decreased as the holding period for stocks has lengthened.

I don't understand how anyone could claim that an investment with returns ranging from 3% to 12% is riskier than another investment with returns ranging from 1% to 3%.
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

User avatar
Tyler9000
Posts: 479
Joined: Fri Aug 21, 2015 11:57 am

Re: Fallacy of time diversification

Post by Tyler9000 » Wed Jan 15, 2020 12:26 pm

DK666 wrote:
Tue Jan 14, 2020 4:27 am
The “fallacy of time diversification” is a reference to the difference between %s and $s.
Exactly. As your investing timeframe grows, you have greater confidence in the average return but greater uncertainty in the final compounded result. It's a tricky concept to understand if you're used to thinking only in terms of simple averages, but this article helps explain it with a few charts.

PluckyDucky
Posts: 196
Joined: Tue Jan 15, 2019 8:29 pm

Re: Fallacy of time diversification

Post by PluckyDucky » Wed Jan 15, 2020 12:42 pm

If a coin flip was 60/40 in your favor, then yes, playing 30 games is better than playing one.

Topic Author
UberGrub
Posts: 115
Joined: Wed Aug 21, 2019 3:47 pm

Re: Fallacy of time diversification

Post by UberGrub » Wed Jan 15, 2020 12:45 pm

PluckyDucky wrote:
Wed Jan 15, 2020 12:42 pm
If a coin flip was 60/40 in your favor, then yes, playing 30 games is better than playing one.
But what Roger is saying is different. He’s not saying one is better or not. He’s saying that you might not want to play once but if you’re given the opportunity to play it 30 times, that THEN you’d be willing to play.

That makes zero sense to me. If the coin was biased and you’d be willing to play the game 30 times, then surely you’d be willing to play it once too. The tosses are independent any ways so expressing willingness to play 30 times implies you’re willing to play it once as well.

User avatar
305pelusa
Posts: 1330
Joined: Fri Nov 16, 2018 10:20 pm

Re: Fallacy of time diversification

Post by 305pelusa » Wed Jan 15, 2020 12:57 pm

Yeah people in this thread are just not getting the point. Like Uber says, Roger claims a, say, 80/20 allocation is to risky to invest it for the short term but might be ok if you’re allowed to hold it long term.

If market returns are independent, this is completely illogical since the long term is simply a series of short terms.

Presumably you don’t want to hold say, 100% because you’d be uncomfortable with, say, a 50% loss of principal. Well guess what. With a St Dev of 20% and expected return of 6% Over 30 years, an 80/20 allocation is MORE likely to lose half of your principal than over 1 year.

The fallacy of time diversification is thinking that it becomes LESS likely because the good years will cancel out the bad (I.e mean reversion aka market return are not independent). If you do believe market returns are independent (a big if but one Roger DOES agree with) then it appears to me like he’s committing the fallacy.

glorat
Posts: 359
Joined: Thu Apr 18, 2019 2:17 am

Re: Fallacy of time diversification

Post by glorat » Wed Jan 15, 2020 1:01 pm

UberGrub wrote:
Wed Jan 15, 2020 12:45 pm
PluckyDucky wrote:
Wed Jan 15, 2020 12:42 pm
If a coin flip was 60/40 in your favor, then yes, playing 30 games is better than playing one.
But what Roger is saying is different. He’s not saying one is better or not. He’s saying that you might not want to play once but if you’re given the opportunity to play it 30 times, that THEN you’d be willing to play.

That makes zero sense to me. If the coin was biased and you’d be willing to play the game 30 times, then surely you’d be willing to play it once too. The tosses are independent any ways so expressing willingness to play 30 times implies you’re willing to play it once as well.
This is such a fantastic example of the point because although it makes zero sense to you it makes perfect sense to me. I indeed might play 30 times but not only 1 time under this scenario.

It depends how I measure the risk/reward of the outcome

PluckyDucky
Posts: 196
Joined: Tue Jan 15, 2019 8:29 pm

Re: Fallacy of time diversification

Post by PluckyDucky » Wed Jan 15, 2020 1:39 pm

UberGrub wrote:
Wed Jan 15, 2020 12:45 pm
PluckyDucky wrote:
Wed Jan 15, 2020 12:42 pm
If a coin flip was 60/40 in your favor, then yes, playing 30 games is better than playing one.
But what Roger is saying is different. He’s not saying one is better or not. He’s saying that you might not want to play once but if you’re given the opportunity to play it 30 times, that THEN you’d be willing to play.

That makes zero sense to me. If the coin was biased and you’d be willing to play the game 30 times, then surely you’d be willing to play it once too. The tosses are independent any ways so expressing willingness to play 30 times implies you’re willing to play it once as well.
I disagree.

If I bet $10 once and lose it, I'm done.

But knowing I get to bet 30 times, I know that my expected value after 30 trials is better. It is a different bet than betting once. Even though the trials are independent, you can consider the 30 trials their own event with different probabilities for different results than just the original coinflip.

For example, a 60/40 coin, with a win doubling your money and a loss losing your bet, and betting the same amount each trial, has over a 90% chance of just breaking even (15 wins) after 30 trials

So looking at the 30 trials in total as ONE event, it is 90/10 chance to double my per-trial bet or lose it, quit different odds than participating in 1 trial.

This is the game casinos play. The edge of each trial is in the house's favor. They know that over time, they will win.

I view the "time diversification" of the stock market similarly, much like the Malkiel chart someone posted earlier.

The argument people seem to be making is not that long-run investors will go bust, but that they just won't be as rich as they thought, because their long-run CAGR might be lower than the historical average.

Still better than holding cash, as another poster showed with his charts.

Image
Last edited by PluckyDucky on Wed Jan 15, 2020 2:05 pm, edited 4 times in total.

User avatar
firebirdparts
Posts: 527
Joined: Thu Jun 13, 2019 4:21 pm

Re: Fallacy of time diversification

Post by firebirdparts » Wed Jan 15, 2020 1:41 pm

UberGrub wrote:
Wed Jan 15, 2020 12:45 pm
That makes zero sense to me.
There you have it. I am not sure anybody but you can really help you with that. It's not easy to follow statistics, which is really the only math in play here. There are several brazen misstatements in this thread, and just plain ol' crazy ways of thinking. Honestly, we get that a lot. People will take some old worn out half-true platitude and change one word to a synonym, and then you have a sentence that is basic insanity, being presented as some sort of thermodynamic law.

Thought experiments usually are pretty easy, but once in a while, you get really bound up.

Like I said, you make an awful lot of money somehow. Maybe you can figure out how that is happening, and that might shed some light on it.
Last edited by firebirdparts on Wed Jan 15, 2020 1:50 pm, edited 1 time in total.
A fool and your money are soon partners

User avatar
305pelusa
Posts: 1330
Joined: Fri Nov 16, 2018 10:20 pm

Re: Fallacy of time diversification

Post by 305pelusa » Wed Jan 15, 2020 1:50 pm

PluckyDucky wrote:
Wed Jan 15, 2020 1:39 pm
UberGrub wrote:
Wed Jan 15, 2020 12:45 pm
PluckyDucky wrote:
Wed Jan 15, 2020 12:42 pm
If a coin flip was 60/40 in your favor, then yes, playing 30 games is better than playing one.
But what Roger is saying is different. He’s not saying one is better or not. He’s saying that you might not want to play once but if you’re given the opportunity to play it 30 times, that THEN you’d be willing to play.

That makes zero sense to me. If the coin was biased and you’d be willing to play the game 30 times, then surely you’d be willing to play it once too. The tosses are independent any ways so expressing willingness to play 30 times implies you’re willing to play it once as well.
I disagree.

If I bet $10 once and lose it, I'm done.

But knowing I get to bet 30 times, I know that my expected value after 30 trials is better. It is a different bet than betting once. Even though the trials are independent, you can consider the 30 trials their own event with different probabilities for different results than just the original coinflip.

For example, a 60/40 coin, with a win doubling your money and a loss losing your bet, and betting the same amount each trial, has over a 90% chance of just breaking even (15 wins) after 30 trials

So looking at the 30 trials in total as ONE event, it is 90/10 chance to double my per-trial bet or lose it, quit different odds than participating in 1 trial.

This is the game casinos play. The edge of each trial is in the house's favor. They know that over time, they will win.

I view the "time diversification" of the stock market similarly, much like the Malkiel chart someone posted earlier.

The argument people seem to be making is not that long-run investors will go bust, but that they just won't be as rich as they thought, because their long-run CAGR might be lower than the historical average.

Still better than holding cash, as another poster showed with his charts.
Let me ask you this. I present two bets.
Bet 1: Has an expected return of 18.5%. And an standard deviation of 34%
Bet 2: Has an expected return of 129.5%. But an standard deviation of 124%.

Which one would you be more inclined to take? Really thinking about it and the distributions and risks or whatever else and just try to answer honestly.

User avatar
305pelusa
Posts: 1330
Joined: Fri Nov 16, 2018 10:20 pm

Re: Fallacy of time diversification

Post by 305pelusa » Wed Jan 15, 2020 1:51 pm

glorat wrote:
Wed Jan 15, 2020 1:01 pm
UberGrub wrote:
Wed Jan 15, 2020 12:45 pm
PluckyDucky wrote:
Wed Jan 15, 2020 12:42 pm
If a coin flip was 60/40 in your favor, then yes, playing 30 games is better than playing one.
But what Roger is saying is different. He’s not saying one is better or not. He’s saying that you might not want to play once but if you’re given the opportunity to play it 30 times, that THEN you’d be willing to play.

That makes zero sense to me. If the coin was biased and you’d be willing to play the game 30 times, then surely you’d be willing to play it once too. The tosses are independent any ways so expressing willingness to play 30 times implies you’re willing to play it once as well.
This is such a fantastic example of the point because although it makes zero sense to you it makes perfect sense to me. I indeed might play 30 times but not only 1 time under this scenario.

It depends how I measure the risk/reward of the outcome
Let me ask you the same thing. I present two bets.
Bet 1: Has an expected return of 18.5%. And an standard deviation of 34%
Bet 2: Has an expected return of 129.5%. But a standard deviation of 124%.

Which one would you be more inclined to take? Really thinking about it and the distributions and risks or whatever else and just try to answer honestly and personally. Which one looks more attractive to you?

PluckyDucky
Posts: 196
Joined: Tue Jan 15, 2019 8:29 pm

Re: Fallacy of time diversification

Post by PluckyDucky » Wed Jan 15, 2020 2:00 pm

305pelusa wrote:
Wed Jan 15, 2020 1:50 pm
...
Let me ask you this. I present two bets.
Bet 1: Has an expected return of 18.5%. And an standard deviation of 34%
Bet 2: Has an expected return of 129.5%. But an standard deviation of 124%.

Which one would you be more inclined to take? Really thinking about it and the distributions and risks or whatever else and just try to answer honestly.
Since my debt is dischargeable in bankruptcy, bet 2. 68% chance of 1% to 250% return (assuming normal). If I'm risking going beyond bust, might as well go big!

User avatar
305pelusa
Posts: 1330
Joined: Fri Nov 16, 2018 10:20 pm

Re: Fallacy of time diversification

Post by 305pelusa » Wed Jan 15, 2020 2:08 pm

PluckyDucky wrote:
Wed Jan 15, 2020 2:00 pm
305pelusa wrote:
Wed Jan 15, 2020 1:50 pm
...
Let me ask you this. I present two bets.
Bet 1: Has an expected return of 18.5%. And an standard deviation of 34%
Bet 2: Has an expected return of 129.5%. But an standard deviation of 124%.

Which one would you be more inclined to take? Really thinking about it and the distributions and risks or whatever else and just try to answer honestly.
Since my debt is dischargeable in bankruptcy, bet 2. 68% chance of 1% to 250% return (assuming normal). If I'm risking going beyond bust, might as well go big!
Just to confirm, that’s honestly what you’d pick with your entire life savings? I can’t tell if you’re being funny or serious.
EDIT: Based on the tone of your response I mean.

PluckyDucky
Posts: 196
Joined: Tue Jan 15, 2019 8:29 pm

Re: Fallacy of time diversification

Post by PluckyDucky » Wed Jan 15, 2020 2:14 pm

305pelusa wrote:
Wed Jan 15, 2020 2:08 pm
...
Just to confirm, that’s honestly what you’d pick with your entire life savings? I can’t tell if you’re being funny or serious.
EDIT: Based on the tone of your response I mean.
I wouldn't pick either bet. The max loss in both scenarios makes me negative. If I'm forced to choose between 2 bets that might make me be in significant debt, I will pick the choice that has the best chance of not being in debt (bet 2) and also the best chance of larger gain (bet 2).

Your bet 1 is significantly negative within one standard deviation of the average while bet 2 is not.
Last edited by PluckyDucky on Wed Jan 15, 2020 2:17 pm, edited 1 time in total.

GAAP
Posts: 1015
Joined: Fri Apr 08, 2016 12:41 pm

Re: Fallacy of time diversification

Post by GAAP » Wed Jan 15, 2020 2:16 pm

For "Time Diversification" to actually work in your favor, you have to assume that a series of random positive and negative results will somehow non-randomly end with a net positive result.

I know of no particular reason why such a sequence MUST occur, and am therefore unwilling to count on it.

The sequence can be negative for longer periods of time than most individual plans require. Even if you have a 30-year plan, a 10-year bad sequence can make a really big difference. For example, a simple simulation of 30-year results with only a 10-year SOR problem: https://www.portfoliovisualizer.com/mon ... nt=1000000.
“Adapt what is useful, reject what is useless, and add what is specifically your own.” ― Bruce Lee

User avatar
305pelusa
Posts: 1330
Joined: Fri Nov 16, 2018 10:20 pm

Re: Fallacy of time diversification

Post by 305pelusa » Wed Jan 15, 2020 2:18 pm

PluckyDucky wrote:
Wed Jan 15, 2020 2:14 pm
305pelusa wrote:
Wed Jan 15, 2020 2:08 pm
...
Just to confirm, that’s honestly what you’d pick with your entire life savings? I can’t tell if you’re being funny or serious.
EDIT: Based on the tone of your response I mean.
I wouldn't pick either bet. The max loss in both scenarios makes me negative. If I'm forced to chose between 2 bets that make me be in significant debt, I will pick the choice that has the best chance of not being in debt (bet 2) and also the best chance of larger gain (bet 2).
What makes you say that bet 1 has a significant chance of getting you into debt? It’s almost a 4 standard deviation event to get a -100% return on bet 1. That’s happens with less than 0.05% chance.

PluckyDucky
Posts: 196
Joined: Tue Jan 15, 2019 8:29 pm

Re: Fallacy of time diversification

Post by PluckyDucky » Wed Jan 15, 2020 2:19 pm

GAAP wrote:
Wed Jan 15, 2020 2:16 pm
For "Time Diversification" to actually work in your favor, you have to assume that a series of random positive and negative results will somehow non-randomly end with a net positive result.

I know of no particular reason why such a sequence MUST occur, and am therefore unwilling to count on it.

The sequence can be negative for longer periods of time than most individual plans require. Even if you have a 30-year plan, a 10-year bad sequence can make a really big difference. For example, a simple simulation of 30-year results with only a 10-year SOR problem: https://www.portfoliovisualizer.com/mon ... nt=1000000.
The ordering in the sequence does not matter unless you have something that makes your whole portfolio go to 0 in one trial. SORR is irrelevant without withdrawals.

Thus, what matters is simply that the positives outweigh the negatives.

Historically, over time, they do in the US stock market.

Past performance does not predict future results. yada yada yada

GAAP
Posts: 1015
Joined: Fri Apr 08, 2016 12:41 pm

Re: Fallacy of time diversification

Post by GAAP » Wed Jan 15, 2020 2:28 pm

PluckyDucky wrote:
Wed Jan 15, 2020 2:19 pm
The ordering in the sequence does not matter unless you have something that makes your whole portfolio go to 0 in one trial. SORR is irrelevant without withdrawals.

Thus, what matters is simply that the positives outweigh the negatives.

Historically, over time, they do in the US stock market.

Past performance does not predict future results. yada yada yada
So, as long as it doesn't go to 0 before you retire, you're fine? What if 30 years later, it only sits at $1? Still fine?

The PV chart I linked is simple/simplistic, yet there is an 11:1 difference in the ending balance between the 10th and 90th percentiles. Even the 50th percentile is ~3.5 times bigger than the 10th percentile. If you use the "standard" 4% withdrawal rate, the 10th percentile will provide an income of about $71K in real dollars while the 50th percentile provides about $258K -- that would certainly matter to me.

And keep in mind, that was only a 10-year SOR problem...,
“Adapt what is useful, reject what is useless, and add what is specifically your own.” ― Bruce Lee

PluckyDucky
Posts: 196
Joined: Tue Jan 15, 2019 8:29 pm

Re: Fallacy of time diversification

Post by PluckyDucky » Wed Jan 15, 2020 2:34 pm

GAAP wrote:
Wed Jan 15, 2020 2:28 pm
PluckyDucky wrote:
Wed Jan 15, 2020 2:19 pm
The ordering in the sequence does not matter unless you have something that makes your whole portfolio go to 0 in one trial. SORR is irrelevant without withdrawals.

Thus, what matters is simply that the positives outweigh the negatives.

Historically, over time, they do in the US stock market.

Past performance does not predict future results. yada yada yada
So, as long as it doesn't go to 0 before you retire, you're fine? What if 30 years later, it only sits at $1? Still fine?

The PV chart I linked is simple/simplistic, yet there is an 11:1 difference in the ending balance between the 10th and 90th percentiles. Even the 50th percentile is ~3.5 times bigger than the 10th percentile. If you use the "standard" 4% withdrawal rate, the 10th percentile will provide an income of about $71K in real dollars while the 50th percentile provides about $258K -- that would certainly matter to me.

And keep in mind, that was only a 10-year SOR problem...,
So what are you doing about it?

The US Stock Market has never gone to 0.

PluckyDucky
Posts: 196
Joined: Tue Jan 15, 2019 8:29 pm

Re: Fallacy of time diversification

Post by PluckyDucky » Wed Jan 15, 2020 2:37 pm

305pelusa wrote:
Wed Jan 15, 2020 2:18 pm
PluckyDucky wrote:
Wed Jan 15, 2020 2:14 pm
305pelusa wrote:
Wed Jan 15, 2020 2:08 pm
...
Just to confirm, that’s honestly what you’d pick with your entire life savings? I can’t tell if you’re being funny or serious.
EDIT: Based on the tone of your response I mean.
I wouldn't pick either bet. The max loss in both scenarios makes me negative. If I'm forced to chose between 2 bets that make me be in significant debt, I will pick the choice that has the best chance of not being in debt (bet 2) and also the best chance of larger gain (bet 2).
What makes you say that bet 1 has a significant chance of getting you into debt? It’s almost a 4 standard deviation event to get a -100% return on bet 1. That’s happens with less than 0.05% chance.
I misread your SD as +- that SD, not +- SD*ER.

I'd go with Bet 1 if that is what you meant (so +- 6.29 so 1SD is 12.21 to 24.79 return %).

What's your point?

User avatar
305pelusa
Posts: 1330
Joined: Fri Nov 16, 2018 10:20 pm

Re: Fallacy of time diversification

Post by 305pelusa » Wed Jan 15, 2020 2:44 pm

PluckyDucky wrote:
Wed Jan 15, 2020 2:37 pm
305pelusa wrote:
Wed Jan 15, 2020 2:18 pm
PluckyDucky wrote:
Wed Jan 15, 2020 2:14 pm
305pelusa wrote:
Wed Jan 15, 2020 2:08 pm
...
Just to confirm, that’s honestly what you’d pick with your entire life savings? I can’t tell if you’re being funny or serious.
EDIT: Based on the tone of your response I mean.
I wouldn't pick either bet. The max loss in both scenarios makes me negative. If I'm forced to chose between 2 bets that make me be in significant debt, I will pick the choice that has the best chance of not being in debt (bet 2) and also the best chance of larger gain (bet 2).
What makes you say that bet 1 has a significant chance of getting you into debt? It’s almost a 4 standard deviation event to get a -100% return on bet 1. That’s happens with less than 0.05% chance.
I misread your SD as +- that SD, not +- SD*ER.

I'd go with Bet 1 if that is what you meant (so +- 6.29 so 1SD is 12.21 to 24.79 return %).

What's your point?
I’m still not sure we’re on the same page.
The SD doesn’t multiply with ER. It adds or substracts.

So 1 SD in bet 1 means a return between -15% and +52.5%.

You’d need around 4 SDs (4*-34) to create a -100% loss on bet 1, and hence “go negative” (end up with less than you started with and hence bankrupt). It takes fewer SD for that to be the case with bet 2.

Does that make sense now?

User avatar
Phineas J. Whoopee
Posts: 9041
Joined: Sun Dec 18, 2011 6:18 pm

Re: Fallacy of time diversification

Post by Phineas J. Whoopee » Wed Jan 15, 2020 3:09 pm

PluckyDucky wrote:
Wed Jan 15, 2020 2:34 pm
...
The US Stock Market has never gone to 0.
If we include the former Confederate States of America, now reconstructed into the rest of the US, a lot of assets there did go to zero, including good drops to zero like pretend-owned human beings. (It is my contention that it is inherently impossible for one human being to own another. It's possible to coerce another. It's possible to kidnap another. It's possible and all too common to exploit another. It's possible to physically harm another. It's possible to credibly threaten their family and carry out the threat. But ownership, I contend, is inherently impossible.)

PJW
Last edited by Phineas J. Whoopee on Wed Jan 15, 2020 8:13 pm, edited 1 time in total.

azanon
Posts: 2633
Joined: Mon Nov 07, 2011 10:34 am

Re: Fallacy of time diversification

Post by azanon » Wed Jan 15, 2020 3:28 pm

UberGrub wrote:
Mon Jan 13, 2020 11:03 pm
Hello,
I read that stocks do not actually get safer over time. So stocks aren't necessarily a better choice based on a long time horizon. I think I read a quote from Paul Samuelson at some point that he thought it was silly that people would not play a game if you could only bet once but would play if they could bet many times. In other words, the concept that you shouldn't use stocks for short term but should use them if you can hold them for many years seemed debunked.
This is the correct version. In this video, Dr. Zvi Bodie spends about 5 minutes explaining the fallacy of time diversification in easy-to-understand, layman's terms: https://www.youtube.com/watch?v=vXtoAgm ... bgWg6UgUAI

GAAP
Posts: 1015
Joined: Fri Apr 08, 2016 12:41 pm

Re: Fallacy of time diversification

Post by GAAP » Wed Jan 15, 2020 5:16 pm

PluckyDucky wrote:
Wed Jan 15, 2020 2:34 pm
GAAP wrote:
Wed Jan 15, 2020 2:28 pm

So, as long as it doesn't go to 0 before you retire, you're fine? What if 30 years later, it only sits at $1? Still fine?

The PV chart I linked is simple/simplistic, yet there is an 11:1 difference in the ending balance between the 10th and 90th percentiles. Even the 50th percentile is ~3.5 times bigger than the 10th percentile. If you use the "standard" 4% withdrawal rate, the 10th percentile will provide an income of about $71K in real dollars while the 50th percentile provides about $258K -- that would certainly matter to me.

And keep in mind, that was only a 10-year SOR problem...,
So what are you doing about it?

The US Stock Market has never gone to 0.
What am I doing? Not counting on one asset class or specific economy, diversifying within asset classes, minimizing costs, etc. -- basically, controlling what I can, and attempting to manage the risks of the things I can't control.

Until it happened, the equivalent markets in China and Russia didn't go to zero either...
“Adapt what is useful, reject what is useless, and add what is specifically your own.” ― Bruce Lee

PluckyDucky
Posts: 196
Joined: Tue Jan 15, 2019 8:29 pm

Re: Fallacy of time diversification

Post by PluckyDucky » Wed Jan 15, 2020 6:38 pm

GAAP wrote:
Wed Jan 15, 2020 5:16 pm
What am I doing? Not counting on one asset class or specific economy, diversifying within asset classes, minimizing costs, etc. -- basically, controlling what I can, and attempting to manage the risks of the things I can't control.

Until it happened, the equivalent markets in China and Russia didn't go to zero either...
And what does that have to do with the "fallacy" that 30-yr returns of the us market (or TSM) or any broad index have a smaller spread of CAGR than 1-yr returns?

User avatar
gmaynardkrebs
Posts: 1760
Joined: Sun Feb 10, 2008 11:48 am

Re: Fallacy of time diversification

Post by gmaynardkrebs » Wed Jan 15, 2020 7:24 pm

This is what Samuelson on this in "Risk and Uncertainty: A Fallacy of Large Numbers
https://www.google.com/url?sa=t&rct=j&q ... 7E3UMRUoNq
Thus. if you would always refuse to take favorable odds on a single toss, you must rationally refuse to participate in any (finite) sequence of such tosses.

The Iogic of the proof can be briefly indicated. If you will not accept one toss, you cannot accept two - since the latter could be thought of as consisting of the (unwise) decision to accept one plus the open decision to accept a second. Even if you were stuck with the first outcome, you would cut your further (utility) losses and refuse the terminal throw. By extending the reasoning from 2 to 3 = 2 + 1, . . . . and from n-l to n, we rule out any sequence at all.

User avatar
willthrill81
Posts: 15207
Joined: Thu Jan 26, 2017 3:17 pm
Location: USA

Re: Fallacy of time diversification

Post by willthrill81 » Wed Jan 15, 2020 7:33 pm

gmaynardkrebs wrote:
Wed Jan 15, 2020 7:24 pm
This is what Samuelson on this in "Risk and Uncertainty: A Fallacy of Large Numbers
https://www.google.com/url?sa=t&rct=j&q ... 7E3UMRUoNq
Thus. if you would always refuse to take favorable odds on a single toss, you must rationally refuse to participate in any (finite) sequence of such tosses.

The Iogic of the proof can be briefly indicated. If you will not accept one toss, you cannot accept two - since the latter could be thought of as consisting of the (unwise) decision to accept one plus the open decision to accept a second. Even if you were stuck with the first outcome, you would cut your further (utility) losses and refuse the terminal throw. By extending the reasoning from 2 to 3 = 2 + 1, . . . . and from n-l to n, we rule out any sequence at all.
That so-called 'proven' logic is quite flawed.

The historic odds of U.S. stock falling behind inflation in a one year period were 31%.

The historic odds of U.S. stock falling behind inflation in a ten year period were 11%.

The historic odds of U.S. stock falling behind inflation in a twenty year period were 1%.

Yet Samuelson would have us believe that these odds are irrelevant and/or meaningless. :oops:
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

User avatar
305pelusa
Posts: 1330
Joined: Fri Nov 16, 2018 10:20 pm

Re: Fallacy of time diversification

Post by 305pelusa » Wed Jan 15, 2020 8:03 pm

It’s kinda funny for OP to open a thread asking posters if they think X writer committed the time fallacy of diversification, only to find most don’t think so... precisely because they themselves commit it.

I didn’t realize this fallacious thinking was so pervasive in BHs.

thx1138
Posts: 1014
Joined: Fri Jul 12, 2013 2:14 pm

Re: Fallacy of time diversification

Post by thx1138 » Wed Jan 15, 2020 9:00 pm

UberGrub wrote:
Wed Jan 15, 2020 10:56 am
The BH wiki on Asset Allocation doesn’t have a single mention as to how to vary AA based on your own wealth. It’s all recommendations of % that you apply to whatever savings you have.
From the Wiki on AA:

The need to take risk is determined by the rate of return required to achieve financial objectives.

That is, once you achieve your financial objectives you don't need to take risk. Thus not isoelastic.

thx1138
Posts: 1014
Joined: Fri Jul 12, 2013 2:14 pm

Re: Fallacy of time diversification

Post by thx1138 » Wed Jan 15, 2020 9:01 pm

305pelusa wrote:
Wed Jan 15, 2020 10:59 am
An AA glide path is entirely consistent with an isoelastic utility if the person is earning an income.

In fact, that’s a common misconception. The glide path isn’t because you have a long time horizon and want to be more aggressive at first. The glide path is done because a worker has lots of human capital and so should overinvest in stocks early on to try to make it up. In fact, Samuelson, who assumes isoelastic utility, would recommend a glide path if you have an income (and of course, a constant allocation of there are no plans to add to the nest egg)
Excellent point, thanks for the correction!

langlands
Posts: 100
Joined: Wed Apr 03, 2019 10:05 pm

Re: Fallacy of time diversification

Post by langlands » Wed Jan 15, 2020 9:55 pm

willthrill81 wrote:
Wed Jan 15, 2020 7:33 pm
gmaynardkrebs wrote:
Wed Jan 15, 2020 7:24 pm
This is what Samuelson on this in "Risk and Uncertainty: A Fallacy of Large Numbers
https://www.google.com/url?sa=t&rct=j&q ... 7E3UMRUoNq
Thus. if you would always refuse to take favorable odds on a single toss, you must rationally refuse to participate in any (finite) sequence of such tosses.

The Iogic of the proof can be briefly indicated. If you will not accept one toss, you cannot accept two - since the latter could be thought of as consisting of the (unwise) decision to accept one plus the open decision to accept a second. Even if you were stuck with the first outcome, you would cut your further (utility) losses and refuse the terminal throw. By extending the reasoning from 2 to 3 = 2 + 1, . . . . and from n-l to n, we rule out any sequence at all.
That so-called 'proven' logic is quite flawed.

The historic odds of U.S. stock falling behind inflation in a one year period were 31%.

The historic odds of U.S. stock falling behind inflation in a ten year period were 11%.

The historic odds of U.S. stock falling behind inflation in a twenty year period were 1%.

Yet Samuelson would have us believe that these odds are irrelevant and/or meaningless. :oops:
To be fair to Samuelson (a brilliant economist), he's not making the mistake you're indicating (which would be very embarrassing). Samuelson was well aware of the law of large numbers (hence referencing it in the title of his paper) and knows that as you increase the time period or the number of bets, the probability of a good outcome approaches 1.

But just because the outcome from doing X is better than the outcome from doing Y 99.99% of the time doesn't automatically make X a better proposition. What's missing here is...the utility function. If in that 0.01% of the time in which X does worse than Y, your utility is much much worse, that tail event bad outcome can swing the decision in favor of Y. In that paper, Samuelson assumed that the person's utility is such that if he would reject a bet at one wealth level, then he would reject it at all wealth levels. This is an extremely stringent condition and almost no one has a utility function that risk averse. Hence while his result is true mathematically, it has a very narrow range of applicability. Perhaps he should have made this clearer, but academics always want to oversell their results...
Last edited by langlands on Wed Jan 15, 2020 11:53 pm, edited 2 times in total.

fwellimort
Posts: 134
Joined: Tue Feb 12, 2019 9:41 am

Re: Fallacy of time diversification

Post by fwellimort » Wed Jan 15, 2020 9:58 pm

The fallacy of time diversification presumes each year's return in the stock market to be completely random (aka independent from one another).

Whether "completely random" exists in the real world or not is another debate in itself but if it is mostly random, then yes, the fallacy can still have some truths.

However, empirically (out of sheer luck or maybe cause stock market returns year by year have some sort of relationships with one another: e.g. P/E ratio, etc.) in the US, the markets have awarded those who put money for longer periods of time.

Conclusion: It is most likely the case that the returns of the stock market are highly dependent to the other years' returns. Either that or you truly believe US' historical stock market returns was a fluke.


It really depends how you model the stock market. If you believe the US stock market year by year return is almost completely independent, then yes, this fallacy should not be overlooked. If not, then this mathematics is not worth fretting much over.

Same idea with "compound interest", "logarithmic growth", etc. For all we know, experts could all be over fitting with past data.

Topic Author
UberGrub
Posts: 115
Joined: Wed Aug 21, 2019 3:47 pm

Re: Fallacy of time diversification

Post by UberGrub » Wed Jan 15, 2020 10:10 pm

fwellimort wrote:
Wed Jan 15, 2020 9:58 pm
The fallacy of time diversification presumes each year's return in the stock market to be completely random (aka independent from one another).

Whether "completely random" exists in the real world or not is another debate in itself but if it is mostly random, then yes, the fallacy can still have some truths.

However, empirically (out of sheer luck or maybe cause stock market returns year by year have some sort of relationships with one another: e.g. P/E ratio, etc.) in the US, the markets have awarded those who put money for longer periods of time.

Conclusion: It is most likely the case that the returns of the stock market are highly dependent to the other years' returns. Either that or you truly believe US' historical stock market returns was a fluke.


It really depends how you model the stock market. If you believe the US stock market year by year return is almost completely independent, then yes, this fallacy should not be overlooked. If not, then this mathematics is not worth fretting much over.

Same idea with "compound interest", "logarithmic growth", etc. For all we know, experts could all be over fitting with past data.
I completely agree with you.

The only reason why I'm "fretting over it" is that I get the distinct impression from Roger Gibson's book that he believes the market is a random walk. That future returns are uncorrelated with past returns. And at no point in that discussion did I see a mention about reversion to the mean.

Interestingly, Jeremy Siegel does talk about how holding stocks for the long run is not as risky. But he explicitly says that's only because stocks have shown mean reversion.

User avatar
willthrill81
Posts: 15207
Joined: Thu Jan 26, 2017 3:17 pm
Location: USA

Re: Fallacy of time diversification

Post by willthrill81 » Wed Jan 15, 2020 10:27 pm

UberGrub wrote:
Wed Jan 15, 2020 10:10 pm
The only reason why I'm "fretting over it" is that I get the distinct impression from Roger Gibson's book that he believes the market is a random walk. That future returns are uncorrelated with past returns. And at no point in that discussion did I see a mention about reversion to the mean.

Interestingly, Jeremy Siegel does talk about how holding stocks for the long run is not as risky. But he explicitly says that's only because stocks have shown mean reversion.
If stocks followed a random walk, they would be equally likely to drop in value by 50% before a decline of 50% as they would be after a decline of 50%. I don't know that many experts believe that at all.
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

fwellimort
Posts: 134
Joined: Tue Feb 12, 2019 9:41 am

Re: Fallacy of time diversification

Post by fwellimort » Wed Jan 15, 2020 10:31 pm

UberGrub wrote:
Wed Jan 15, 2020 10:10 pm
The only reason why I'm "fretting over it" is that I get the distinct impression from Roger Gibson's book that he believes the market is a random walk. That future returns are uncorrelated with past returns. And at no point in that discussion did I see a mention about reversion to the mean.

Interestingly, Jeremy Siegel does talk about how holding stocks for the long run is not as risky. But he explicitly says that's only because stocks have shown mean reversion.
Stock markets (from maybe our pure luck with 'overfitting' uncorrelated data <shrugs>) have behaved quite predictably in the past.
And not just in the US, but also in other developed nations including Japan.

There's a good reason why people around the world always talk about P/E ratio and all.

Let's extrapolate 1 individual stock. First, understand a stock is representative of a portion of a company (in the US). It's not a random piece of paper that has random chance. A stock at end of day is backed by an entity and that entity, might give a "real" return aka dividends.

Say this company earns $100 a year and has 100 shares (and issues dividends) [assume stock price never goes up and inflation doesn't exist].
Each share gets say $1 and say this company is very healthy and will most likely not disappear tomorrow (e.g.: Microsoft -rated AAA by Moody's-).

There's near 0 probability people will sell a share that gives $1 a year for $0. If there were, sign me up! My friends and I are going to buy all those damn stocks hence creating demand.
At the same time, there's also near 0 probability people will buy that share for $10000000000000000000000000 in the real world.
Why? Because the laws of an individual stock fundamentally is not "purely random".

If US Treasuries give 0.5% a year, then this stock might trade for say < $200 a year.
However, if US Treasuries give 10% a year, then this stock might trade for say < $10 a year (because you take more risks with a stock).

Already, you see a relationship of the stock market playing with the bond market. This in and of itself shows the stock market is not "completely random".

So I would honestly throw this "fallacy of time diversification" out the window.
You should view US stocks more as "a shareholder of a company", and not a "piece of a paper that goes up and down randomly with no reasons".

That's all I'll say. Having stated that, do not also forget that stocks are generally formulated through intrinsic price of stock + speculation.
Unfortunately, "speculation" portion is something none of us can control. However, that's a complete different argument as "speculation" is something else entirely.


Also, it is because stocks overall have "dividends" that stocks cannot be completely random in price. If it didn't
hand out dividends, stocks would in general have near no value (outside the ability to control the company). Stocks are backed by ability to control company + cash (dividends) unlike many other 'products' like cryptocurrencies in which their only backing is hope.

Post Reply