Fallacy of time diversification

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UberGrub
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Fallacy of time diversification

Post by UberGrub »

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.

However, I was reading Asset Allocation and found this in a chapter:
"In summary, volatility swamps the expected payoff from stocks in the short run, making them a risk not worth taking. But in the long run, stocks emerge as the winner because of the convergence of average re- turns toward stocks’ higher return growth path coupled with the miracle of compound interest."

Is he basically making this mistake? It's too risky to hold stocks for short-term reasons but much better idea to hold them for long-term liabilities?

Any help on the subject is greatly appreciated!
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Re: Fallacy of time diversification

Post by Ferdinand2014 »

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.
“You only find out who is swimming naked when the tide goes out.“ — Warren Buffett
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Post by hdas »

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Last edited by hdas on Wed Jan 29, 2020 9:52 pm, edited 1 time in total.
....
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Re: Fallacy of time diversification

Post by ohai »

Ferdinand2014 wrote: Mon Jan 13, 2020 11:23 pm I consider risk running out of money when you need it.
Good way of putting it. The problem is, say you retire tomorrow. So you better have money tomorrow specifically. The risk is your spending timing, not just the stocks' volatility.
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UberGrub
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Re: Fallacy of time diversification

Post by UberGrub »

One more passage:
"It is more difficult to identify bad five- and ten-year periods [of the stock market] since good years invariably become averaged in with the bad years. The passage of time therefore mitigates the risk posed by volatility while giving an opportunity for the equity risk premium to compound its advantage."

This literally sounds like the fallacy of time diversification no? That over long periods of time, the good times will average out the bad and that time "mitigates (as Roger puts it) the risks.

Roger Gibson is clearly very well prepared that it's kind of surprising to read this. Am I misinterpreting his writing?

Thanks.
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Re: Fallacy of time diversification

Post by ohai »

hdas wrote: Mon Jan 13, 2020 11:31 pm
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.
False, just a simple inspection of the data will contradict this. Cheers :greedy
Stocks held over longer periods will certainly have a wider distribution of final price. However, I think what you are saying is that positive exponential drift will eventually dominate volatility of returns that follow a distribution sigma*sqrt(time).
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Re: Fallacy of time diversification

Post by 1789 »

It is very easy to distinguish good 5-10 years from bad ones when looking at past, but it is not possible for future. The belief that stocks are long term plays are rooted in the positive direction of economy over long periods (businesses growth, increasing dividend payments, etc..) I think one can make use of this trend over (say 10+) years by constantly buying whatever market does. This helps to load stock shares if we have bad 5-10 years of period along the way and so compounding brings the benefit over time. Let me know if i understood you correct
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Re: Fallacy of time diversification

Post by firebirdparts »

UberGrub wrote: Mon Jan 13, 2020 11:03 pm Hello,
I read that stocks do not actually get safer over time.
You make an awful lot of money somehow, investing in diversified funds.

It is true that individual companies don’t get safe over time. They sure don’t. Not at all.

Perhaps it depends on what you call “stocks”.
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Re: Fallacy of time diversification

Post by rbaldini »

Flip three coins. What is the probability that they all come up tails? How about thirty coins? Three hundred coins?
langlands
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Re: Fallacy of time diversification

Post by langlands »

I think there's a lot of confusion over the "fallacy of time diversification" because the question "Do stocks get safer as you stay invested longer?" is vague and ill-defined. Very roughly, the intuition that stocks are in fact safer over time is that your CAGR (Cumulative annualized growth rate) will converge to a positive number in the long run. What this means is that after 100 years, your investment return is overwhelmingly likely to be very good. The intuition that stocks are not safer over time is that the longer you stay invested, the higher the probability of a truly catastrophic event (like losing 99.999% of your capital). Basically, the veracity of the "fallacy of time diversification" depends on your utility function and how risk averse you are. I think for most normal people, it's false (i.e. time diversification is a real thing).

Ross has a nice paper https://www.cambridge.org/core/journals ... 42B27CE740 that addresses this issue. He gives the following example of the type of person for which the "fallacy of time diversification" might be true:
To put this in perspective, imagine an individual with a total wealth of $25,000
facing a 50-50 gamble of losing 90% of his wealth, $22,500, or winning $22,500.
The premium to insure against this bet is 81% of total wealth, or $20,250. In other
words, this individual is so risk averse that, despite having a current wealth level
of only $25,000, he would pay up fully $20,250 of it, leaving him with $4,750
for sure to avoid having a 50% chance of having $2,500 and a 50% chance of
having $47,500. Such behavior is certainly possible and one can imagine unusual
circumstances where it would occur, but it does not seem to be a reasonable description of the behavior of economic everyman to pay 80% of his wealth to avoid a 50% chance of losing 90% and pass up a 50% chance of nearly doubling.
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Re: Fallacy of time diversification

Post by rossington »

OP,
What investment over time do YOU think in your analysis will give you the greatest return over the long term?
I am very interested in your decision.
"Success is going from failure to failure without loss of enthusiasm." Winston Churchill.
DK666
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Re: Fallacy of time diversification

Post by DK666 »

The “fallacy of time diversification” is a reference to the difference between %s and $s.

Over time the annual rate of return tends to have lower volatility (purely a mathematical fact of averages). People use this as a reference to time diversification.

The counter point is that it’s a fallacy because risk increases in absolute $s. Which is a function of compound returns.

Think of a 6.5% compound return over 40 years vs 6%. Difference seems small enough to make the case for time diversification but if you compound it out it’s 12.42 vs 10.29 which is nearly 20% less.

Cheers.
Last edited by DK666 on Tue Jan 14, 2020 4:31 am, edited 1 time in total.
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Re: Fallacy of time diversification

Post by danielc »

langlands wrote: Tue Jan 14, 2020 2:49 am I think there's a lot of confusion over the "fallacy of time diversification" because the question "Do stocks get safer as you stay invested longer?" is vague and ill-defined. Very roughly, the intuition that stocks are in fact safer over time is that your CAGR (Cumulative annualized growth rate) will converge to a positive number in the long run. What this means is that after 100 years, your investment return is overwhelmingly likely to be very good. The intuition that stocks are not safer over time is that the longer you stay invested, the higher the probability of a truly catastrophic event (like losing 99.999% of your capital).
No. The reason why stocks "don't get safer" with time is that, while the CAGR might converge, the final value of your portfolio does not become any more predictable. Consider two examples:

1) $1,000 invested for 10 years with a CAGR between 7.1773% and 14.8698% will give you a final value between $2,000 and $4,000.

2) $1,000 invested for 100 years with a CAGR between 7.8972% and 8.6477% will give you a final value between $2M and $4M.

The 100-year investment needs a much smaller uncertainty in CAGR to produce the same factor-of-two uncertainty in the final portfolio value. That is the main sense in which one could say that stocks don't get safer with time. The convergence of CAGR creates the illusion that the portfolio value becomes more predictable, but it clearly does not.

If I wanted to argue that stocks become safer, the argument that I would make is that I could measure risk as the probability of not having enough. The longer stocks are allowed to compound, the lower the probability that my portfolio will not be large enough.
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Re: Fallacy of time diversification

Post by Seasonal »

The theoretical basis for stocks outperforming bonds is that they are riskier. 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?
sambb
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Re: Fallacy of time diversification

Post by sambb »

past performance doesnt indicate future results. look at japan.
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Re: Fallacy of time diversification

Post by lazyday »

Seasonal wrote: Tue Jan 14, 2020 5:34 amIf 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.
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Re: Fallacy of time diversification

Post by UpperNwGuy »

sambb wrote: Tue Jan 14, 2020 6:20 am past performance doesnt indicate future results. look at japan.
Here we go again....
Ferdinand2014
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Re: Fallacy of time diversification

Post by Ferdinand2014 »

hdas wrote: Mon Jan 13, 2020 11:31 pm
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.
False, just a simple inspection of the data will contradict this. Cheers :greedy
If you have held stocks for 1 or 100 years or whether 10,000 becomes 1,000 or 1 million does nothing to predict the volatility tomorrow. My statement is certainly true from a volatility standpoint. Another way to state it: roll dice 10,000 times and get 1-6. The 10,001 time cannot be predicted by the previous 10,000. Again, if you are looking at it from a risk of not having enough money instead of volatility, over time your compounded returns will tend to overwhelm any volatility as time gets longer. As others have said, this depends on a general upward trend of the market. If your 10,000 grows to 1,000,000 vs 10,000,000 and it drops 50% the next day, but you needed the 10,000 to be at least 500,000 you are still ok from having enough standpoint.


“Investing is an activity in which consumption today is foregone in an attempt to allow greater consumption at a later date. “Risk” is the possibility that this objective won’t be attained.”

“I want to quickly acknowledge that in any upcoming day, week or even year, stocks will be riskier – far riskier – than short-term U.S. bonds. As an investor’s investment horizon lengthens, however, a diversified portfolio of U.S. equities becomes progressively less risky than bonds”

Warren Buffett 2017 Shareholder letter
Last edited by Ferdinand2014 on Tue Jan 14, 2020 12:50 pm, edited 3 times in total.
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Re: Fallacy of time diversification

Post by nisiprius »

I'm not sure exactly what book you are referring to with the words "Asset Allocation." But, yes, my opinion is that the idea that stocks get safer with longer holding periods is a myth that is so convenient and so attractive to people who are trying to sell stocks to risk-averse customers that it never dies.

However, Jeremy Siegel, author of Stocks for the Long Run, is often misrepresented as saying that stocks become safer over time. But his book title refers to a comparison with bonds, not a claim that stocks become safer with longer holding periods. Siegel made this clear.
...many of you who have gone to my presentations have probably seen that slide before. Now, one thing I should make very clear, I never said that that means stocks are safer in the long run.... What I pointed out here is that the standard deviation for stocks goes down twice as much— twice as fast as random walk theory would predict. In other words, they are relatively safer in the long run than random walk theory would predict. Doesn’t mean they’re safe. The whole point is that they are relatively safer.
And you're right, Paul Samuelson vigorously rejected the idea of safety in longer holding periods:
Many analysts argue that when you average over many investment periods, so favorable are the long-run returns of stocks that while you are still young, you should borrow substantially to hold large positions in stocks and you should do so because some kind of “stochastic dominance” is supposed to justify it.

Now, when I read such things, my eyebrows arch upwards. I think I have written 27 articles rebutting this idea—with at least one article completely in one syllable words, except for the word “syllable” itself.
Unfortunately, the article written in "one-syllable words" is not really that easy to understand, but here it is: Why We Should Not Make Mean Log of Wealth Big Though Years to Act are Long.

In A Random Walk Down Wall Street Malkiel says the same thing; I'm quoting from the 2015 and I think this is an addition or clarification from earlier editions. I've boldfaced some words.
A substantial amount (but not all) of the risk of common-stock ownership and sticking to it through thick and thin... I do not mean to argue that stocks are not risky over long holding periods. Certainly the variability of the final value of your portfolio does increase the longer you hold your stocks.
Here is the elephant in the room: Pastor, Lubos and Stambaugh, Robert F., Are Stocks Really Less Volatile in the Long Run? (March 22, 2011). EFA 2009 Bergen Meetings Paper; AFA 2010 Atlanta Meetings Paper.
According to conventional wisdom, annualized volatility of stock returns is lower over long horizons than over short horizons, due to mean reversion induced by return predictability. In contrast, we find that stocks are substantially more volatile over long horizons from an investor's perspective. This perspective recognizes that parameters are uncertain, even with two centuries of data, and that observable predictors imperfectly deliver the conditional expected return. Mean reversion contributes strongly to reducing long-horizon variance, but it is more than offset by various uncertainties faced by the investor, especially uncertainty about the expected return. The same uncertainties reduce desired stock allocations of long-horizon investors contemplating target-date funds.
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Re: Fallacy of time diversification

Post by Call_Me_Op »

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
A misinterpretation. Stocks are always risky at any point in time. However, if you buy a basket of stocks today, chances are very high that in 20 years that basket will be worth more than it is today. In that sense, stocks get less risky with (holding) time.
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Re: Fallacy of time diversification

Post by junior »

UberGrub wrote: Mon Jan 13, 2020 11:03 pm Hello,
I read that stocks do not actually get safer over time.
There are models that show stocks to not get safer over time. The logic seems to go that risk= volatility and since stocks change in value a lot even if you've had them over time they aren't safer, as measured by volatility.

This model seems "off" to me but I believe it's considered a "good" model by many academics.

I will say that this forum has a huge bias towards the idea that investing in stocks is a good thing and the idea that the 21st century will be like the 20th but with better phones.

If history happens, say a meteor blows up the west coast of the United States or whatever, those bogleheads who survive will find the value of their stocks evaporate. Investing heavily in stocks is a bet that this will not occur.
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Re: Fallacy of time diversification

Post by Geologist »

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.
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Re: Fallacy of time diversification

Post by SandysDad »

If you consider stocks random wo an upward trend then time acts as a diversifier and reduces risk. But the premise is untrue. Stocks go up over the long haul assuming f earnings increase over the long haul. Therefore short term randomness is overtaken by long term increases. So time diversification lowers average returns
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Re: Fallacy of time diversification

Post by Kenkat »

John Norstad anyone?

viewtopic.php?t=245914
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UberGrub
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Re: Fallacy of time diversification

Post by UberGrub »

nisiprius wrote: Tue Jan 14, 2020 6:44 am I'm not sure exactly what book you are referring to with the words "Asset Allocation." But, yes, my opinion is that the idea that stocks get safer with longer holding periods is a myth that is so convenient and so attractive to people who are trying to sell stocks to risk-averse customers that it never dies.

However, Jeremy Siegel, author of Stocks for the Long Run, is often misrepresented as saying that stocks become safer over time. But his book title refers to a comparison with bonds, not a claim that stocks become safer with longer holding periods. Siegel made this clear.
...many of you who have gone to my presentations have probably seen that slide before. Now, one thing I should make very clear, I never said that that means stocks are safer in the long run.... What I pointed out here is that the standard deviation for stocks goes down twice as much— twice as fast as random walk theory would predict. In other words, they are relatively safer in the long run than random walk theory would predict. Doesn’t mean they’re safe. The whole point is that they are relatively safer.
And you're right, Paul Samuelson vigorously rejected the idea of safety in longer holding periods:
Many analysts argue that when you average over many investment periods, so favorable are the long-run returns of stocks that while you are still young, you should borrow substantially to hold large positions in stocks and you should do so because some kind of “stochastic dominance” is supposed to justify it.

Now, when I read such things, my eyebrows arch upwards. I think I have written 27 articles rebutting this idea—with at least one article completely in one syllable words, except for the word “syllable” itself.
Unfortunately, the article written in "one-syllable words" is not really that easy to understand, but here it is: Why We Should Not Make Mean Log of Wealth Big Though Years to Act are Long.

In A Random Walk Down Wall Street Malkiel says the same thing; I'm quoting from the 2015 and I think this is an addition or clarification from earlier editions. I've boldfaced some words.
A substantial amount (but not all) of the risk of common-stock ownership and sticking to it through thick and thin... I do not mean to argue that stocks are not risky over long holding periods. Certainly the variability of the final value of your portfolio does increase the longer you hold your stocks.
Here is the elephant in the room: Pastor, Lubos and Stambaugh, Robert F., Are Stocks Really Less Volatile in the Long Run? (March 22, 2011). EFA 2009 Bergen Meetings Paper; AFA 2010 Atlanta Meetings Paper.
According to conventional wisdom, annualized volatility of stock returns is lower over long horizons than over short horizons, due to mean reversion induced by return predictability. In contrast, we find that stocks are substantially more volatile over long horizons from an investor's perspective. This perspective recognizes that parameters are uncertain, even with two centuries of data, and that observable predictors imperfectly deliver the conditional expected return. Mean reversion contributes strongly to reducing long-horizon variance, but it is more than offset by various uncertainties faced by the investor, especially uncertainty about the expected return. The same uncertainties reduce desired stock allocations of long-horizon investors contemplating target-date funds.
The book is by Roger Gibson. I forgot to mention it on the OP but said it on my other post.


Thank you everyone for your response. I already understand that the annualized volatility decreases with longer time horizon but the terminal wealth becomes much more uncertain.

My only question in this thread is whether Roger Gibson is committing the fallacy of time diversification in these passages that is all. Because if he isn’t, then perhaps I don’t quite understand what he’s saying
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Re: Fallacy of time diversification

Post by 3funder »

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.
+1
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Re: Fallacy of time diversification

Post by lazyday »

Geologist wrote: Tue Jan 14, 2020 8:28 amreal end wealth of $1 invested in U.S. Stocks over 30 year periods ending 1901-2000 ranged from roughly $2 to $21
With bonds, the low end wasn't more than $0.55 of real wealth, also according to Bernstein:

http://www.efficientfrontier.com/t4poi/Ch1.htm
in the 30 years from 1952 ... bonds returned only 2.3%, while inflation annualized out at 4.3%
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Re: Fallacy of time diversification

Post by mimiesg »

So what is the way around this , I have been struggling with this exact question and I came to understand that having an asset allocation that lets you sleep well is the way.

The other ideas that I originally had was buying regularly over a large time period there by getting diversification of time but another poster debunked that it doesn't reduce anything and we go back to asset allocation...

In this sense I like Target date funds since they take care of everything for newbies like me

But on a taxable account, what is the newbie to do?
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Re: Fallacy of time diversification

Post by lazyday »

junior wrote: Tue Jan 14, 2020 8:23 amIf history happens, say a meteor blows up the west coast of the United States or whatever, those bogleheads who survive will find the value of their stocks evaporate. Investing heavily in stocks is a bet that this will not occur.
You could say the same for investing in bonds, or holding cash.

Maybe someone remembers from Credit Suisse Yearbooks or from Triumph of the Optimists, what the record has been on total or near total losses with stocks vs with bonds.

W Bernstein's Deep Risk also touches on this, as I recall.
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Re: Fallacy of time diversification

Post by rbaldini »

I had to look up the fallacy of time diversification because I had not seen the term before. It’s a strange term, I think.

The fallacy as stated seems to be based on confusing mean annualized return in percent with total return in absolute dollars. When investing in a random walk, the longer one holds, more one’s annualized return over that period resembles the CAGR. But the variance in the total amount of money one has at the end only increases linearly with the amount of time invested. The fallacy, I think, is in thinking that your long term wealth absolutely converges close to some $ amount at the end of your investing period. It certainly does not. Nonetheless your average annualized return will probably be something close to the CAGR.

From what you posted, it’s not clear that anyone made this fallacy. I don’t see it.

You might find it more useful to consider the following. Let’s say you have $x now. If you invest it in a stock index, what’s the probability that you will be, say, 30% poorer *than you are now* next year? In 10 years? In 40 years? The exact probabilities will depend on your model, but historically they decrease the longer you hold. In your 40th year, you might well lose 30% of your money, but by then you will almost certainly have more than $x, so you still come out ahead in the long run.
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Re: Fallacy of time diversification

Post by randomguy »

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.
Anyone who thinks that playing a game once and a game 1000s times is the same has a very poor understanding of mathematics and I would hesitate to take financial advice from them. Maybe the quote is missing some context.

Now if you want to debate if the stock market is playing the game 1000s of times or once is a bit more debatable.
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Re: Fallacy of time diversification

Post by rbaldini »

I decided to do some simulating to hopefully shed light here. Suppose you took $1 and invested it into a random walk fund that has an expected log normal return of 0.1 and standard deviation of 0.3. I simulate out a million such cases and show the 10th and 90th percentile of total value and annualized return across years.

Parentheses are (10th percentile, 90th percentile)

Year 1
Total value of fund: (0.75, 1.62)
Annualized growth: (0.75, 1.62)

Year 5
Total: (0.70, 3.89)
Annualized: (0.94, 1.31)

Year 10
Total: (0.81, 9.18)
Annualized: (0.98, 1.25)

Year 20
Total: (1.33, 41.11)
Annualized: (1.01, 1.20)

Year 40
Total: (4.77, 620.47)
Annualized: (1.04, 1.17)

You can see...
1. the range of the total return increases over time
2. The range of the annualized return decreases over time
3. After a few years, the 10th percentile of total value starts increasing with time. This is what most people mean when they say stocks get safer over time.

The numbers shown are not meant to be realistic values for the stock market. Just the overall behavior of a random walk.
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Re: Fallacy of time diversification

Post by protagonist »

langlands wrote: Tue Jan 14, 2020 2:49 am . What this means is that after 100 years, your investment return is overwhelmingly likely to be very good.
What basis do you have to come to this conclusion? A single data point, representing the outcome since 1920? Or at most two, from the dawn of the industrial revolution?

In any complex nonlinear system (such as the stock market), noise compounds far more than signal over time. This is why, if you bet that the stock market will not lose 50% of its value tomorrow and not recover you are making a very safe bet, but if you say that it will not lose 50% of its value over the next 100 (or 1000. or million) years and not recover you are just wild guessing.

Stocks don't get safer over time. Nothing does. Their performance becomes less predictable. It is an illusion based on recency bias, as we are fortunate enough to have lived in what probably represents the greatest period of economic growth in the history of civilization.

I'm not too worried about losing half my money in the stock market over the next minute. But over the next 10, 20, 30, 100, 1000, 1 million years it is a distinct possibility, as the future becomes less and less predictable with increasing time.
Last edited by protagonist on Tue Jan 14, 2020 11:30 am, edited 3 times in total.
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Re: Fallacy of time diversification

Post by lazyday »

protagonist wrote: Tue Jan 14, 2020 11:05 amStocks don't get safer over time. Nothing does.
How about the added risk of using stocks instead of cash, or instead of bonds?

It's clearly risky to own stocks instead of cash for a period of one year. How about 30 or 50 years?
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Re: Fallacy of time diversification

Post by protagonist »

lazyday wrote: Tue Jan 14, 2020 11:18 am
protagonist wrote: Tue Jan 14, 2020 11:05 amStocks don't get safer over time. Nothing does.
How about the added risk of using stocks instead of cash, or instead of bonds?

It's clearly risky to own stocks instead of cash for a period of one year. How about 30 or 50 years?
I doubt that you will lose 50% or more of your money if you hold stocks for a minute . In fact, I am very confident of that, and would happily bet on it.
You probably won't if you hold them for a year, though I am a bit less sure of that. There is a greater risk of it happening than if you hold them for a minute or a day.
I have no clue whether you will or not if you hold them for 30 or 50 years.
Last edited by protagonist on Tue Jan 14, 2020 11:32 am, edited 5 times in total.
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Re: Fallacy of time diversification

Post by Unladen_Swallow »

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.
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Re: Fallacy of time diversification

Post by lazyday »

protagonist wrote: Tue Jan 14, 2020 11:23 amThere is a greater risk of it happening than if you hold them for a minute or a day.
I'm thinking that it's risky to own cash for 50 years, and it's probably less risky to own stocks for 50 years.
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Re: Fallacy of time diversification

Post by protagonist »

lazyday wrote: Tue Jan 14, 2020 11:55 am
protagonist wrote: Tue Jan 14, 2020 11:23 amThere is a greater risk of it happening than if you hold them for a minute or a day.
I'm thinking that it's risky to own cash for 50 years, and it's probably less risky to own stocks for 50 years.
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.

For example, if you buy a new car, you know it will depreciate, and you have a good idea how much it will depreciate year to year. You have a pretty good idea that , for example, if you buy Model X for $20K today it will be worth about $10-12K in 2023. You are taking very little risk in making that purchase- you know what it will be worth within a narrow range.

With stocks you stand to make a fortune over time, and for that chance you accept the risk of losing a lot as well.
Last edited by protagonist on Tue Jan 14, 2020 12:12 pm, edited 1 time in total.
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Re: Fallacy of time diversification

Post by lazyday »

protagonist wrote: Tue Jan 14, 2020 12:06 pmYou 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?
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Re: Fallacy of time diversification

Post by alluringreality »

mimiesg wrote: Tue Jan 14, 2020 9:43 amThe other ideas that I originally had was buying regularly over a large time period there by getting diversification of time but another poster debunked that it doesn't reduce anything and we go back to asset allocation...
Aside from a scenario that makes all stocks worthless, buying stocks over time will tend to have different results than lump-sum buying stock today. For example I have the ability to borrow money today against projected future earnings, by using our house as collateral, and buy more stocks lump-sum right now. I can also just use my future earnings to buy stocks over time, essentially dollar cost averaging. If the future 30 years happen to follow similar trends as the recent US stock market then borrowing against future earnings may be a good idea in relation to my attempts to have more capital at a later date. If the stock market in the future happens to follow a less than ideal scenario, like Japan for the past 30 years, then borrowing against future earnings to buy stocks could end up being a terrible idea compared to buying across time. Basically I question how practical these sorts of discussions tend to be without additional items being included, like future earnings, so I tend to wonder if some discussion might fall outside the original context as suggested in the following.
https://www.soa.org/globalassets/assets ... e-myth.pdf
Last edited by alluringreality on Tue Jan 14, 2020 12:57 pm, edited 1 time in total.
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Re: Fallacy of time diversification

Post by TonyDAntonio »

randomguy wrote: Tue Jan 14, 2020 9:59 am
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.
Anyone who thinks that playing a game once and a game 1000s times is the same has a very poor understanding of mathematics and I would hesitate to take financial advice from them. Maybe the quote is missing some context.

Now if you want to debate if the stock market is playing the game 1000s of times or once is a bit more debatable.
Yep. There is a reason casinos limit the max bet on their games of chance. If you could continue to place bets that cover all your losses plus some amount of profit you would never lose... assuming the game isn't rigged. Not quite the stock market but similar in some respects. Until that meteor hits. :(
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Re: Fallacy of time diversification

Post by langlands »

protagonist wrote: Tue Jan 14, 2020 11:05 am
langlands wrote: Tue Jan 14, 2020 2:49 am . What this means is that after 100 years, your investment return is overwhelmingly likely to be very good.
What basis do you have to come to this conclusion? A single data point, representing the outcome since 1920? Or at most two, from the dawn of the industrial revolution?

In any complex nonlinear system (such as the stock market), noise compounds far more than signal over time. This is why, if you bet that the stock market will not lose 50% of its value tomorrow and not recover you are making a very safe bet, but if you say that it will not lose 50% of its value over the next 100 (or 1000. or million) years and not recover you are just wild guessing.

Stocks don't get safer over time. Nothing does. Their performance becomes less predictable. It is an illusion based on recency bias, as we are fortunate enough to have lived in what probably represents the greatest period of economic growth in the history of civilization.

I'm not too worried about losing half my money in the stock market over the next minute. But over the next 10, 20, 30, 100, 1000, 1 million years it is a distinct possibility, as the future becomes less and less predictable with increasing time.
The "fallacy of time diversification" is a mathematical result and is based on certain mathematical assumptions. The usual one applied to stocks is lognormal growth. I suppose I should have made this clear in my post.

I agree that the real world is much more complex. Whether time actually does diversify fully is impossible to answer, since no one can accurately model the world. If you think the probability of nuclear holocaust or other catastrophic events from which the stock market will never recover is high, then certainly time in the market will not diversify your returns to your liking. But my post was geared toward a "vanilla" scenario of lognormal growth, an academic assumption that you could view as completely useless if you wish.
Last edited by langlands on Tue Jan 14, 2020 3:44 pm, edited 2 times in total.
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Re: Fallacy of time diversification

Post by langlands »

danielc wrote: Tue Jan 14, 2020 4:30 am
langlands wrote: Tue Jan 14, 2020 2:49 am I think there's a lot of confusion over the "fallacy of time diversification" because the question "Do stocks get safer as you stay invested longer?" is vague and ill-defined. Very roughly, the intuition that stocks are in fact safer over time is that your CAGR (Cumulative annualized growth rate) will converge to a positive number in the long run. What this means is that after 100 years, your investment return is overwhelmingly likely to be very good. The intuition that stocks are not safer over time is that the longer you stay invested, the higher the probability of a truly catastrophic event (like losing 99.999% of your capital).
No. The reason why stocks "don't get safer" with time is that, while the CAGR might converge, the final value of your portfolio does not become any more predictable. Consider two examples:

1) $1,000 invested for 10 years with a CAGR between 7.1773% and 14.8698% will give you a final value between $2,000 and $4,000.

2) $1,000 invested for 100 years with a CAGR between 7.8972% and 8.6477% will give you a final value between $2M and $4M.

The 100-year investment needs a much smaller uncertainty in CAGR to produce the same factor-of-two uncertainty in the final portfolio value. That is the main sense in which one could say that stocks don't get safer with time. The convergence of CAGR creates the illusion that the portfolio value becomes more predictable, but it clearly does not.

If I wanted to argue that stocks become safer, the argument that I would make is that I could measure risk as the probability of not having enough. The longer stocks are allowed to compound, the lower the probability that my portfolio will not be large enough.
Why is the "factor-of-two uncertainty in the final portfolio value" the metric by which you measure the risk of a portfolio? Why is it important that you should be able to measure your ending portfolio value accurately? I'm not familiar with any utility function for which this would be the primary metric. By this logic, you'd prefer a lottery ticket that paid between $2000 and $4000 over one that paid between $1M and $1B just because the first one has a factor of 2 uncertainty and the second one has a factor of 1000.

I agree with your last paragraph, but I think that's the same reason I gave for why stocks are safer. The reason that when stocks are allowed to compound, the lower the probability that the portfolio will not be large enough is exactly that the CAGR converges, and thus the probability of a good outcome becomes overwhelmingly likely (and hence the probability of a poor outcome becomes vanishingly small). The only reason such a proposition could possibly be unpalatable to an investor is that he is so risk averse as to not want the increased probability of a truly catastrophic outcome. As I replied to the previous poster, the basic assumption here is that you can model the stock market as independent flips of a coin with bounded variance, which results in a lognormal functional form for stock price.
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Re: Fallacy of time diversification

Post by danielc »

langlands wrote: Tue Jan 14, 2020 3:37 pm Why is the "factor-of-two uncertainty in the final portfolio value" the metric by which you measure the risk of a portfolio?
...
I agree with your last paragraph, but I think that's the same reason I gave for why stocks are safer.
It's not a metric. It's a convenient example. It makes the math easy. The point is that the uncertainty in the final dollar value doesn't decrease with time. If anything, it increases. I'm just trying to justify why a reasonable person could reasonably take the view that stocks don't get safer with time. In my last paragraph I gave a counter-argument. If that is what you intended to say, then perhaps I misunderstood your post.
langlands wrote: Tue Jan 14, 2020 3:37 pm The reason that when stocks are allowed to compound, the lower the probability that the portfolio will not be large enough is exactly that the CAGR converges, and thus the probability of a good outcome becomes overwhelmingly likely (and hence the probability of a poor outcome becomes vanishingly small).
But you see, even re-reading your post, I don't think that what you are saying is correct. I think you are saying that the probability of a poor outcome decreases because CAGR converges. I don't agree with that. The probability of a poor outcome decreases because, with more years of compounding, you don't need as high a return to avoid a poor outcome.
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Re: Fallacy of time diversification

Post by langlands »

danielc wrote: Tue Jan 14, 2020 4:01 pm
langlands wrote: Tue Jan 14, 2020 3:37 pm Why is the "factor-of-two uncertainty in the final portfolio value" the metric by which you measure the risk of a portfolio?
...
I agree with your last paragraph, but I think that's the same reason I gave for why stocks are safer.
It's not a metric. It's a convenient example. It makes the math easy. The point is that the uncertainty in the final dollar value doesn't decrease with time. If anything, it increases. I'm just trying to justify why a reasonable person could reasonably take the view that stocks don't get safer with time. In my last paragraph I gave a counter-argument. If that is what you intended to say, then perhaps I misunderstood your post.
langlands wrote: Tue Jan 14, 2020 3:37 pm The reason that when stocks are allowed to compound, the lower the probability that the portfolio will not be large enough is exactly that the CAGR converges, and thus the probability of a good outcome becomes overwhelmingly likely (and hence the probability of a poor outcome becomes vanishingly small).
But you see, even re-reading your post, I don't think that what you are saying is correct. I think you are saying that the probability of a poor outcome decreases because CAGR converges. I don't agree with that. The probability of a poor outcome decreases because, with more years of compounding, you don't need as high a return to avoid a poor outcome.
Yes, I agree the uncertainty in the dollar amount will increase. I think we're on the same page on this point.

Regarding your second paragraph, I'm assuming geometric brownian motion: https://en.wikipedia.org/wiki/Geometric_Brownian_motion
The important point is that according to this model, your investment will grow by a factor of

exp( (mu - sigma^2/2)t + sigma*B_t)

where mu is your average annual return, sigma is the annual volatility, t is the investment time period, and B_t is a standard normal with standard deviation sqrt(t). The CAGR is then simply mu - sigma^2/2 + (sigma*B_t)/t. As t goes to infinity, the second term sigma*B_t/t goes to 0 since B_t only on the order of sqrt(t). Thus, assuming mu - sigma^2/2 is positive, you are overwhelmingly likely to have a positive CAGR. If the second term didn't become negligible (if the CAGR didn't converge), then you wouldn't be able to make such a conclusion. That's why I say that the probability of a poor outcome decreasing is a result of CAGR converging.

I hope that was clear. Unfortunately, I'm beginning to realize that Bogleheads might not be the best venue for this kind of technical discussion. However, it doesn't seem that there's any other forum that discusses investment theory with the same level of financial sophistication that this one does.




Edit: The below doesn't bear directly on your post (I was confused for a second about what you said). It is an explanation for why one might not want to time diversify, even knowing that the probability of a poor outcome decreases with more years of compounding.

Even though the probability of a poor outcome decreases, the probability of a truly catastrophic outcome increases. So the probability distribution of outcomes moves to the right, but spreads out. Good outcomes become much more likely (and hence bad outcomes become much less likely), but the really bad outcomes also become much more likely.

As a concrete example, consider a normal distribution with mean 1 and standard deviation 1 vs. a distribution with mean 100 and standard deviation 10. It is overwhelmingly likely that you'll draw a larger number from the second distribution than the first. But what's the probability of getting lower than -100? In the first distribution, that's a 100 stdev. event. In the second, that's only a 20 stdev. event. It's way way more likely to get lower than -100 with the second distribution than the first. So with a super super risk averse utility function, one might still choose the first distribution over the second. If you find that ridiculous, it's because you find that utility function ridiculous, which most people do. And hence why time diversification works for most people who don't have insanely risk averse utility functions.
Last edited by langlands on Tue Jan 14, 2020 4:43 pm, edited 2 times in total.
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Re: Fallacy of time diversification

Post by anoop »

The US is in a very unique position in that anything goes wrong, the fed steps in aggressively. Previously, they waited for a correction before stepping in, but now it looks like they're stepping in on a daily basis well before any problem of any sort happens. Where this leads to is anybody's guess, but the bears have been proven 100% wrong so far, and even a lot of bulls have been proven wrong because the market has returned way beyond anyone's imagination (Q for everyone: Tell the truth, did you foresee the Dow had any chance of hitting 30,000 in 10 years back in 2009?). As dessert, the fed has pretty much served up the death fixed income investing. So mathematics, study of the past, etc. no longer works.

But from an academic standpoint, Zvi Bodie said the same thing.
https://www.semanticscholar.org/paper/O ... f7df9a0454
He's not too active these days, but he follows his own advice -- he is 100% in TIPS.
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Re: Fallacy of time diversification

Post by Oicuryy »

Kenkat wrote: Tue Jan 14, 2020 8:37 am John Norstad anyone?

viewtopic.php?t=245914
Under the model in appendix A of Norstad's post the probability of stocks underperforming the bank account goes down over time. Stocks get safer over time but never get as safe as the bank account.

Here are the excel formulas for the probability of stocks underperforming the bank account over 1, 10, 20, 30 and 40 year periods using Norstad's model.

42%=LOGNORMDIST(1.06^1, 0.09707*1,0.194756*SQRT(1))
26%=LOGNORMDIST(1.06^10, 0.09707*10,0.194756*SQRT(10))
19%=LOGNORMDIST(1.06^20, 0.09707*20,0.194756*SQRT(20))
14%=LOGNORMDIST(1.06^30, 0.09707*30,0.194756*SQRT(30))
10%=LOGNORMDIST(1.06^40, 0.09707*40,0.194756*SQRT(40))

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Re: Fallacy of time diversification

Post by siamond »

The only real fallacy here is the fallacy of the fallacy of time diversification... Just an utterly misguided definition of risk(s)...
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Re: Fallacy of time diversification

Post by Oicuryy »

This article by an actuary talks about the misapplication of Samuelson's paper.
https://www.soa.org/essays-monographs/i ... e-myth.pdf

Do you have an isoelastic utility function?

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Re: Fallacy of time diversification

Post by protagonist »

langlands wrote: Tue Jan 14, 2020 3:17 pm
protagonist wrote: Tue Jan 14, 2020 11:05 am
langlands wrote: Tue Jan 14, 2020 2:49 am . What this means is that after 100 years, your investment return is overwhelmingly likely to be very good.
What basis do you have to come to this conclusion? A single data point, representing the outcome since 1920? Or at most two, from the dawn of the industrial revolution?

In any complex nonlinear system (such as the stock market), noise compounds far more than signal over time. This is why, if you bet that the stock market will not lose 50% of its value tomorrow and not recover you are making a very safe bet, but if you say that it will not lose 50% of its value over the next 100 (or 1000. or million) years and not recover you are just wild guessing.

Stocks don't get safer over time. Nothing does. Their performance becomes less predictable. It is an illusion based on recency bias, as we are fortunate enough to have lived in what probably represents the greatest period of economic growth in the history of civilization.

I'm not too worried about losing half my money in the stock market over the next minute. But over the next 10, 20, 30, 100, 1000, 1 million years it is a distinct possibility, as the future becomes less and less predictable with increasing time.
The "fallacy of time diversification" is a mathematical result and is based on certain mathematical assumptions. The usual one applied to stocks is lognormal growth. I suppose I should have made this clear in my post.

I agree that the real world is much more complex. Whether time actually does diversify fully is impossible to answer, since no one can accurately model the world. If you think the probability of nuclear holocaust or other catastrophic events from which the stock market will never recover is high, then certainly time in the market will not diversify your returns to your liking. But my post was geared toward a "vanilla" scenario of lognormal growth, an academic assumption that you could view as completely useless if you wish.
The problem is that nobody knows the probability of catastrophe of unknown origin or severity (or even of one of many known origins such as your example of nuclear holocaust) within a given time frame. There is no way to compute it. There is no way to compute even the probability of a relatively minor known event like the 2008 crash within any given time interval. Likewise, nobody knows the probability of a continuing "vanilla" scenario over the next 1,10, 100, 1000 years....only that the probability of the latter continuing will decrease with time and the probability of the former happening will increase with time. How much time is anybody's guess...if we had a way to determine that we would all be rich.
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