Time Diversification actually DOES reduce stock risk

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Lbill
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Time Diversification actually DOES reduce stock risk

Post by Lbill » Mon Jun 13, 2011 4:23 pm

There are many articles, such as this oneby John Norstad that dispute the concept of "time diversification;" i.e., that equity investment risk is reduced over long time horizons. However, Time Diversification actually does work in theory, but in practice it doesn't. This isn't because time diversification doesn't work; rather it is because, for most investors, the dollar amount that they have invested in stocks is heavily skewed toward the latter years of their investment accumulation horizon. This is the natural result of the fact that their portfolio grows (hopefully) over time because of investment gains as well as new savings contributions that are being made over time.

The argument against time diversification can be traced back to Paul Samuelson's paper "Risk and Uncertainty: A fallacy of large numbers." In the paper, Samuelson gives the example of betting $100 on a coin toss at 2:1 odds. Suppose you refuse to take the bet since, for you, the pain of losing $100 would be greater than the satisfaction of winning $200. Should you be more willing to accept the outcome of a series of similar bets (or "trials")? Based on the "law of averages", the reasoning goes that over the long run, wins and losses should even out, thereby making it almost certain that you'll come out ahead. But Samuelson shows this reasoning is fallacious and the answer is "No."

Imagine, for example, that you have the luckiest series of outcomes possible, winning the first 99 of a series of 100 coin tosses. You have accumulated 99 X $200, or $19,800, with one toss to go. You still have a 50:50 chance of losing the entire $19,800 on the final toss in the series, which is exactly the same as if you had been willing to take the intial single-trail bet with $19,800 at stake instead of $100. But you refused that bet, so logically you should also refuse a bet based on the outcome of a series of similar bets as well. Therefore, applying Samuelson's metaphor to stock investing, the idea that you can reduce your risk of loss (increase your odds of winning) by "staying in the casino" longer and placing more bets (time diversification) is wrong.

However, Samuelson points out that, instead of multiplying your $100 bet with a series of similar bets, you should subdivide your original stake into several similar bets with each piece. For example, you could bet $1 on each of 100 trials. In this way, the "law of averages" would work in your favor and you should end up winning close to $100, (50 wins @2) while losing $50 (50 losses @$1) overall and coming out ahead. If you do this, then "time diversification" (ie., making a series of bets sequentially) will actually work in your favor. How can you do this investing in stocks? In order to take advantage of time diversification for stock investing, Mr. Investor should try to have nearly the same dollar amount of money at stake in the stock market each year for as many years as possible. This is equivalent to subdividing a stake of $100 into a series of several equal-sized dollar bets (e.g. 100 bets of $1 each).

Let's imagine that Mr. Investor has a sum of money from an inheritance he wants to invest into the stock market. In order to have the same dollar amount of money at risk over as many years as possible, Mr. Investor should invest the entire amount immediately as a lump sum. Furthermore, as the dollar value of his stock investment grows, he should liquidate stocks to maintain the original dollar amount he invested. In addition, if the dollar value of his stock investment declines he should move money into stocks to maintain his original investment amount. All this can be accomplished most easily if Mr. Investor simply invests his inheritance into a portfolio of stocks and fixed-income and rebalances annually between them. However, he should rebalance in order to maintain the same dollar amount in stocks (adjusted for inflation) rather than the same percentage amount in stocks. For example, if Mr. Investor's puts $100,000 into stocks, representing 75% of his inheritance, and his portfolio grows to $250,000 (real), then rebalancing to 75% would be $187,500. He has much more at risk in dollar amount than the $100,000 he began with. The benefit of time diversification will not be as great for Mr. Investor if he allows the dollar amount of his stake to become significantly skewed over time.

So, this example illustrates that time diversification works for the special case in which the investor has the same dollar amount at stake over time. It also works to a degree when the same percentage allocation to stocks is maintained over time, but the benefits are overwhelmed and washed out by the fact that most investors have the their greatest stake in the market toward the end of their investment accumulation horizon. Whatever the market does during this relatively short timeframe of 10 years or so will overwhelm (for good or evil) most of the benefits of time diversification from having owned stocks even over a much longer run.
Last edited by Lbill on Mon Jun 13, 2011 5:13 pm, edited 1 time in total.
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Post by stratton » Mon Jun 13, 2011 4:52 pm

You plan on retiring at the end of 2008 and reality happens. Oops. Big loss and you don't have enough money. This is what's wrong with holding constant equities all the way through. Shit happens. :twisted:

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Re: Time Diversification actually DOES reduce stock risk

Post by Opponent Process » Mon Jun 13, 2011 4:57 pm

Lbill wrote:Whatever the market does during this relatively short timeframe of (the last) 10 years or so will obliterate most of the advantages of having owned stocks even over a much longer run.
how do you know that it will be obliterated? isn't it equally possible that the last ten years could also cause a much bigger return from stocks relative to earlier years? you can't predict this one way or the other.

your coin-toss example also assumes that equity markets go to zero, which they don't, although in theory they could. the main point of time diversifiers is that, even given an equity market downturn at the end, the overall equity returns will still be larger that those obtained with bonds. riskier, yes, but also more money, which is what you want.
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Post by jimkinny » Mon Jun 13, 2011 4:59 pm

stratton wrote:You plan on retiring at the end of 2008 and reality happens. Oops. Big loss and you don't have enough money. This is what's wrong with holding constant equities all the way through. Shit happens. :twisted:

Paul
Yes: can not predict when shit happens.

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Post by Majormajor78 » Mon Jun 13, 2011 5:00 pm

My goodness... what a horrible idea. I understand the math but, not to be too blunt, it completely castrates the power of compounding. Nobody who followed this scenario would be able to reach any reaonable retirement goal unless thier savings rate was phenomenal. It's an interesting academic argument but if an investor wishes to divorce himself almost completely from both the risks and rewards of stock investing why wouldn't they just go 100% treasuries to begin with?
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Post by yobria » Mon Jun 13, 2011 5:03 pm

Personally I reduce my stock allocation as I age to mitigate this issue.

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Post by chaz » Mon Jun 13, 2011 5:07 pm

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Post by Lbill » Mon Jun 13, 2011 5:15 pm

how do you know that it will be obliterated? isn't it equally possible that the last ten years could also cause a much bigger return from stocks relative to earlier years? you can't predict this one way or the other
Yeah. Poor choice of wording on my part. I edited to make my intended meaning clearer.
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Post by Lbill » Mon Jun 13, 2011 5:32 pm

My goodness... what a horrible idea. I understand the math but, not to be too blunt, it completely castrates the power of compounding
That's certainly a valid point. I'm not necessarily proposing a strategy - just trying to point out that I think time diversification rests on a defensible foundation. As for compounding, unfortunately that cuts both ways. The more compounded gains you accumulate over time, the more you have at stake to lose in the market. Unless you reduce your stock allocation pretty significantly during the latter years of your accumulation period, you are setting up for potentially huge dollar losses in the homestretch. If I lose 50% of my much smaller equity stake at age 30, it will hurt lot less than if I lose 50% of a much bigger pile at age 60. If it were possible, it would be nice to have a larger stake at the front end of accumulation and be able to reduce that dramatically as retirement nears. At least we know that if you win the lottery or are in Leona Helmsley's will you should probably go ahead and put it all (or as much as you're comfortable with) in the market as a lump sum. That way, the whole magillah gets to start compounding right off the bat. DCA won't do that for you.
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Post by Opponent Process » Mon Jun 13, 2011 5:53 pm

yobria wrote:Personally I reduce my stock allocation as I age to mitigate this issue.

Nick
yes, but the paradox is that to the extent we do that, we reduce the time diversification benefit of stocks. in theory, we need to hold them for very long periods of time (i.e., as you age), undiluted as it were, for time diversification to work.

I would say that even the people who believe in the strong form of time diversification do not practice it. I believe in it but I don't practice it, or I practice a weaker form, because it does have implications for balanced portfolios. I view my 60/40 portfolio as a current, ongoing, daily bet on an equity risk premium. I put the odds at 60/40 every day. should I change this (make it more conservative) as I get older? with regard to the time diversification argument, I'm not sure I should. I think I should stick with it, in theory. will I do that? probably not.
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Post by RobG » Mon Jun 13, 2011 6:34 pm

stratton wrote:You plan on retiring at the end of 2008 and reality happens. Oops. Big loss and you don't have enough money. This is what's wrong with holding constant equities all the way through. Shit happens. :twisted:

Paul
You missed the point: stocks are very unpredictable in the short term so don't hold them if you need the money shortly! On the other hand, if your timeframe is long, then "time diversification" will increase your odds of beating less risky investments.

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Post by ThePrune » Mon Jun 13, 2011 7:17 pm

Lbill,

Thanks for taking the time to write a rather lengthy but well written addition to the ongoing discussion on time diversification. I enjoyed it and, even better, had my thinking on the topic taken deeper! :D It was a nice counterpoint to John Norstadt's article on time diversification in a pure equity portfolio (which I had read several years ago).
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Post by Lbill » Mon Jun 13, 2011 7:36 pm

As a retiree, my situation is akin to the investor with an inheritance or lottery jackpot to invest. Retirees essentially have a "lump sum" stash to deal with, where the benefit of "time diversification" may be realizable. Because of decumulation, the total portfolio value is diminishing, or not growing very significantly, from investment growth or new contributions. "Growth compounding" is turned 180-degrees into "loss compounding." To take advantage of time diversification over one's 20-30 year retirement horizon, I believe that one should determine the appropriate level of stock allocation (based on ability, willingness, and need) and then try to maintain that allocation as evenly as possible in real dollars throughout retirement. Of course, I believe that a periodic review of one's allocation should be done, and adjusted accordingly, if necessary. That's why I don't believe in the age-based, or "age-in-bonds" guideline, because it mindlessly reduces equity allocation using the "birthday rule" instead of a better thought-out strategy that increases the odds of improving risk-adjusted returns during retirement.
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Post by 555 » Mon Jun 13, 2011 7:49 pm

Lbill, is there any connection between what you are saying and what Samuelson is saying? (I'm more interested in what he would think than what you think.)

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Post by umfundi » Mon Jun 13, 2011 8:08 pm

stratton wrote:You plan on retiring at the end of 2008 and reality happens. Oops. Paul
Yes, I retired November 1, 2008. More excitement than I really wanted.

So, I have learned a lot about time diversification here, some of it surprising. But, practically, what can you do? As a practical matter, no one (who is accumulating) is able to keep a constant dollar amount invested. (If that were good advice, I should have stopped after the first $200 of savings I put in a mutual fund thirty years ago.)

Suppose I plan to work 30 years and save $10,000 per year. Is there anything more rational than to pick a diversified asset allocation and rebalance periodically?

And, by the way, is the tossing the dice question an inside joke? I'd appreciate at least a link to an explanation.

Thank you,

Keith

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Re: Time Diversification actually DOES reduce stock risk

Post by SP-diceman » Mon Jun 13, 2011 8:49 pm

Lbill wrote:
The argument against time diversification can be traced back to Paul Samuelson's paper "Risk and Uncertainty: A fallacy of large numbers." In the paper, Samuelson gives the example of betting $100 on a coin toss at 2:1 odds. Suppose you refuse to take the bet since, for you, the pain of losing $100 would be greater than the satisfaction of winning $200. Should you be more willing to accept the outcome of a series of similar bets (or "trials")? Based on the "law of averages", the reasoning goes that over the long run, wins and losses should even out, thereby making it almost certain that you'll come out ahead. But Samuelson shows this reasoning is fallacious and the answer is "No."

Imagine, for example, that you have the luckiest series of outcomes possible, winning the first 99 of a series of 100 coin tosses. You have accumulated 99 X $200, or $19,800, with one toss to go. You still have a 50:50 chance of losing the entire $19,800 on the final toss in the series, which is exactly the same as if you had been willing to take the intial single-trail bet with $19,800 at stake instead of $100.
With 2 to 1 odds and a 50-50 bet your optimum bet is 25% of your money.

Your first bet with $100 should have been $25.
If a win, the next bet $37.50 (150*.25)
If a loss, the next bet $18.75 (75*.25)

The problem with the $19,800 isn’t the casino odds, its the fact that its all your money.

One cant change the casino odds, but they can reduce their equity exposure.
(what a gambler would call his bankroll)


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SP-diceman

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Re: Time Diversification actually DOES reduce stock risk

Post by wintermute » Mon Jun 13, 2011 10:58 pm

Lbill wrote:Whatever the market does during this relatively short timeframe of 10 years or so will overwhelm (for good or evil) most of the benefits of time diversification from having owned stocks even over a much longer run.
That's why accumulating a floor of bonds to cover your basic expenses (in addition to SS) is a good idea. If you can swing that.

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Post by jidina80 » Tue Jun 14, 2011 12:52 am

If we were to chart the importance of stock/bond allocation versus the amount of new money invested or money spent throughout a typical investor's life we would find this:

1) Early Investing Years: Amount invested each year has a greater impact than returns on the asset balance.

2) Late Investing Years: Returns have a greater impact than amount invested each year.

3) Early Retirement Years: Returns have a greater impact than amount spent.

4) Late Retirement Years: Spending has a greater impact than returns.

It's a hill that we have to acknowledge because our asst balance is highest in our late investing and early retirement years. This is why it makes sense to have a high stock allocation until we enter our retirement years.

Vanguard's Target Retirement Funds provide a good cross-check on our allocation, as I believe they have some great research behind their allocations.

Just.

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Re: Time Diversification actually DOES reduce stock risk

Post by chaster86 » Tue Jun 14, 2011 10:23 am

Lbill wrote:For example, if Mr. Investor's puts $100,000 into stocks, representing 75% of his inheritance, and his portfolio grows to $250,000 (real), then rebalancing to 75% would be $187,500. He has much more at risk in dollar amount than the $100,000 he began with.
This isn't true because the fact that the stocks have grown to $250,000 means that the risk of owning the stock has decreased. Therefore, Mr Investor does not have more at risk after rebalancing to $187,500 (in fact he has even less at risk than the initial $100,000).

This is why investment advisors have begrudgingly upped the percentage stock allocations they have recommended for investors over the years. But if you simply buy and hold (without rebalancing) than the market will automatically decrease your stock allocation when risk increases and increase your stock allocation when risk decreases.

Although I don't know how one would implement time diversification in light of this insight.

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Post by ladders11 » Tue Jun 14, 2011 12:04 pm

So time diversification works but is not possible for anyone to actually implement. Great job with the math.
Majormajor78 wrote:My goodness... what a horrible idea. I understand the math but, not to be too blunt, it completely castrates the power of compounding. Nobody who followed this scenario would be able to reach any reaonable retirement goal unless thier savings rate was phenomenal.
Compounding is magic because it is not reality. When you use random rates to plan your retirement, or a "monte carlo" simulation, you find that compounding does not work right a lot of the time: it depends when the bad years come. The only solution is to "save more" which makes me angry.

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Post by Lbill » Tue Jun 14, 2011 1:01 pm

So, I have learned a lot about time diversification here, some of it surprising. But, practically, what can you do? As a practical matter, no one (who is accumulating) is able to keep a constant dollar amount invested. (If that were good advice, I should have stopped after the first $200 of savings I put in a mutual fund thirty years ago.)
Yes, as a practical matter I think you're right. But I wanted to try to point out that it's not because the concept of time diversification is wrong - which is the common conclusion that is often expressed and that I accepted also. It's really the fact that most people aren't able to implement the concept during the portfolio accumulation/growth period. As has been said, investing the long run works; however, when you have the long run you don't have the money to invest and when you have the money to invest you don't have the long run. Maybe the best the accumulator can do is to try to get as much as possible into stocks as early as possible and keep it there, but be careful to reduce the allocation to stocks pretty significantly as they approach the end of their accumulation period. Unfortunately, for lots of reasons, most people end up investing relatively little in the first 20 years of their career (at least that's what I did). Then they start cramming as much as possible into stocks for the last 20 years. If you can even it out just a little more over the years, it's a little better than nothing.
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Post by ladders11 » Tue Jun 14, 2011 4:20 pm

I think the moral of the story is to invest immediately once you can. Not easy. Yet to be honest, I must suggest that most individuals' income reaches 75% of their max year when they are only between 25 and 35. Traditionally they are saving for the purpose of buying a house (bad investment) or having kids (Bad Investment).

If your 20 years of cramming money into stocks is between age 30 and 50, you will know where you stand while you can still walk. This is useful.

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Post by Lbill » Tue Jun 14, 2011 6:36 pm

In an up-post, I suggested that maintaining an equal-dollar allocation to stocks throughout retirement drawdown (annually adjusted for inflation) would be a way to implement the portfolio diversification benefit. Allocation is usually discussed in terms of percentage allocation, rather than dollar amount. So, I set out using the data from Simba's spreadsheet to see how that would have worked out. I have to admit that I was surprised, even shocked by what I found.

I compared two $1,000,000 retirement portfolios over the period of 1972-2010 with annual withdrawals of 4% of the initial value ($40,000) in real, or inflation-adjusted dollars. Both portfolios were initially equally divided between stocks (TSM) and bonds (TBM); i.e., $500K each or a 50/50 allocation.

Portfolio #1 was annually rebalanced in order to maintain a constant 50/50 allocation throughout the 1972-2010 time period. With annual withdrawals of $40k (real), the residual value of this portfolio at the end of 2010 would have been $326,574, a net decumulation of 67.2%.

Portfolio #2 was annually rebalanced in order to maintain the same $500K initial (real) allocation to stocks over the same time period. This is the "time diversification" portfolio. With annual $40K withdrawals the residual value of this portfolio would have been an astounding $1,234,507, a net gain of 23.5%.

I examined the allocation of Portfolio #2 over the 1972-2010 period and found that it had an average allocation to stocks of 58% vs. the 50% for Portfolio #1. Could this have accounted for the difference in residual values? Well, no. When I plugged in a 58/42 allocation for the entire period, the residual value would have been $403,094. So it's quite apparent that the "time diversification" portfolio #2 beats the "fixed allocation" portfolio #1 even when they both held the same average allocation to stocks.

Well, surely my findings are based on one time period and require further study and confirmation. But, even so, I have to admit that I didn't expect to find this kind of support for the "time diversification" strategy in any time series. So I thought it was worth reporting. I'm going to check my figures and dig deeper but I'm sure thinking about following some version of this approach with my retirement portfolio, with an initial stock allocation that's probably closer to 25% than 50%
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Post by Cloud » Tue Jun 14, 2011 7:18 pm

I can't wait to hear your follow up. I would love to know is this works for other time periods.

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Post by umfundi » Wed Jun 15, 2011 12:46 am

I compared two $1,000,000 retirement portfolios over the period of 1972-2010 with annual withdrawals of 4% of the initial value ($40,000) in real, or inflation-adjusted dollars. Both portfolios were initially equally divided between stocks (TSM) and bonds (TBM); i.e., $500K each or a 50/50 allocation.
Your result is quite astonishing, to me. Especially when I realize that your ending allocation for Portfolio 2 is 40% stocks and 60% bonds. (End value = $1,234,507, stocks = $500,000.)

I will refrain from theorizing, but it would be interesting to see the following scatter plots for Portfolio 2. ("Rebalance" means restore stocks to $500,000):

1. Y axis: % allocation in stocks immediately after rebalancing to $500,000. X axis: % allocation in stocks immediately prior to rebalancing.

(See below. Plot (x, y) = (c, b).)

2. Y axis: % change in stock allocation before / after rebalancing, the difference in the quantities plotted in chart 1. X axis: % change in the over the previous year. In other words:

Value a = % allocation to stocks after rebalancing, year n.
Value b = % allocation to stocks before rebalancing, year n+1.
Value c = % allocation to stocks after rebalancing, year n+1.

Plot (x, y) = (c-b, b-a)

Keith

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Post by letsgobobby » Wed Jun 15, 2011 1:46 am

Lbill wrote:In an up-post, I suggested that maintaining an equal-dollar allocation to stocks throughout retirement drawdown (annually adjusted for inflation) would be a way to implement the portfolio diversification benefit. Allocation is usually discussed in terms of percentage allocation, rather than dollar amount. So, I set out using the data from Simba's spreadsheet to see how that would have worked out. I have to admit that I was surprised, even shocked by what I found.

I compared two $1,000,000 retirement portfolios over the period of 1972-2010 with annual withdrawals of 4% of the initial value ($40,000) in real, or inflation-adjusted dollars. Both portfolios were initially equally divided between stocks (TSM) and bonds (TBM); i.e., $500K each or a 50/50 allocation.

Portfolio #1 was annually rebalanced in order to maintain a constant 50/50 allocation throughout the 1972-2010 time period. With annual withdrawals of $40k (real), the residual value of this portfolio at the end of 2010 would have been $326,574, a net decumulation of 67.2%.

Portfolio #2 was annually rebalanced in order to maintain the same $500K initial (real) allocation to stocks over the same time period. This is the "time diversification" portfolio. With annual $40K withdrawals the residual value of this portfolio would have been an astounding $1,234,507, a net gain of 23.5%.

I examined the allocation of Portfolio #2 over the 1972-2010 period and found that it had an average allocation to stocks of 58% vs. the 50% for Portfolio #1. Could this have accounted for the difference in residual values? Well, no. When I plugged in a 58/42 allocation for the entire period, the residual value would have been $403,094. So it's quite apparent that the "time diversification" portfolio #2 beats the "fixed allocation" portfolio #1 even when they both held the same average allocation to stocks.

Well, surely my findings are based on one time period and require further study and confirmation. But, even so, I have to admit that I didn't expect to find this kind of support for the "time diversification" strategy in any time series. So I thought it was worth reporting. I'm going to check my figures and dig deeper but I'm sure thinking about following some version of this approach with my retirement portfolio, with an initial stock allocation that's probably closer to 25% than 50%
I'll admit, I'm not sure I totally understand what you did. But it seems to me that in any long period in which stocks ultimately reached substantially new highs, maintaining higher stock exposure (in this case, higher than 50/50 rebalancing called for) would naturally have resulted in higher total returns (higher ending value). And the fact that this portfolio, with an average stock exposure of 58%, outperformed a 58/42 portfolio, should not be surprising, either, because the 58% was purely an average; in fact, starting in 1972, there would have been at least 2 occasions (late 1974 and mid 1982) when, because of the huge decline in stock values leading up to those points, maintaining a constant $500,000 of stocks would have meant equity allocations of much greater than 58%. In other words, these portfolios would have been over-rebalanced. Amazingly/ironically/coincidentally, these times would have occurred at long-term lows of PE10 (about 8 in 1974, about 5 in 1982). Said another way, isn't "constant value of stocks" really just another way of overbuying stocks at times of low valuation? And hasn't that always worked in the United States? Hasn't that always worked in any diversified global equity portfolio?

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Post by letsgobobby » Wed Jun 15, 2011 1:47 am

oops
Last edited by letsgobobby on Wed Jun 15, 2011 8:31 am, edited 1 time in total.

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Post by letsgobobby » Wed Jun 15, 2011 1:48 am

oops
Last edited by letsgobobby on Wed Jun 15, 2011 8:25 am, edited 1 time in total.

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Post by Lbill » Wed Jun 15, 2011 7:29 am

And the fact that this portfolio, with an average stock exposure of 58%, outperformed a 58/42 portfolio, should not be surprising, either, because the 58% was purely an average; in fact, starting in 1972, there would have been at least 2 occasions (late 1974 and mid 1982) when, because of the huge decline in stock values leading up to those points, maintaining a constant $500,000 of stocks would have meant equity allocations of much greater than 58%. In other words, these portfolios would have been over-rebalanced. Amazingly/ironically/coincidentally, these times would have occurred at long-term lows of PE10 (about 8 in 1974, about 5 in 1982). Said another way, isn't "constant value of stocks" really just another way of overbuying stocks at times of low valuation?
Yes, that's exactly what happened. But the reverse happened also (underbalancing). The percentage allocation to stocks ranged from a low of 38%(1999-2001) to a high of 89% (1982). Of course, the percentages don't mean anything per se - it's the growth of the overall value of the portfolio. There was never a single year where Port #2 had a lower real value than Port #1. It started ahead right out of the box in 1973 (they had the same value in 1972 of course) and just kept pulling ahead. The starting time was undoubtedly fortuitous since this led to systematically overbalancing stocks throughout that period, culminating in an 89% allocation in 1982. I want to see what happens if you don't start at 1972.

[Added Edit: Actually, as I think about it, maintaining a fixed real dollar allocation to a decumulating portfolio would cause stocks to become a larger and larger percentage of the portfolio over time. If this happens to coincide with a bull market, then this overbalancing toward equities will work in your favor. From 1972-1982 there was actually a bear market, which caused you to overbalance even more dramatically toward equities, just in time for the bull market that followed from 1982-2000. So, the results I observed are surely the result of a very fortuitous series of market returns - a bear market followed by a huge bull market in equities. Very important to examine what happens over different time periods that are less "lucky" for this strategy.]
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Re: Time Diversification actually DOES reduce stock risk

Post by LH » Wed Jun 15, 2011 8:09 am

Lbill wrote:There are many articles, such as this oneby John Norstad that dispute the concept of "time diversification;" i.e., that equity investment risk is reduced over long time horizons. However, Time Diversification actually does work in theory, but in practice it doesn't. This isn't because time diversification doesn't work; rather it is because, for most investors, the dollar amount that they have invested in stocks is heavily skewed toward the latter years of their investment accumulation horizon. This is the natural result of the fact that their portfolio grows (hopefully) over time because of investment gains as well as new savings contributions that are being made over time.

The argument against time diversification can be traced back to Paul Samuelson's paper "Risk and Uncertainty: A fallacy of large numbers." In the paper, Samuelson gives the example of betting $100 on a coin toss at 2:1 odds. Suppose you refuse to take the bet since, for you, the pain of losing $100 would be greater than the satisfaction of winning $200. Should you be more willing to accept the outcome of a series of similar bets (or "trials")? Based on the "law of averages", the reasoning goes that over the long run, wins and losses should even out, thereby making it almost certain that you'll come out ahead. But Samuelson shows this reasoning is fallacious and the answer is "No."

Imagine, for example, that you have the luckiest series of outcomes possible, winning the first 99 of a series of 100 coin tosses. You have accumulated 99 X $200, or $19,800, with one toss to go. You still have a 50:50 chance of losing the entire $19,800 on the final toss in the series, which is exactly the same as if you had been willing to take the intial single-trail bet with $19,800 at stake instead of $100. But you refused that bet, so logically you should also refuse a bet based on the outcome of a series of similar bets as well. Therefore, applying Samuelson's metaphor to stock investing, the idea that you can reduce your risk of loss (increase your odds of winning) by "staying in the casino" longer and placing more bets (time diversification) is wrong.

However, Samuelson points out that, instead of multiplying your $100 bet with a series of similar bets, you should subdivide your original stake into several similar bets with each piece. For example, you could bet $1 on each of 100 trials. In this way, the "law of averages" would work in your favor and you should end up winning close to $100, (50 wins @2) while losing $50 (50 losses @$1) overall and coming out ahead. If you do this, then "time diversification" (ie., making a series of bets sequentially) will actually work in your favor. How can you do this investing in stocks? In order to take advantage of time diversification for stock investing, Mr. Investor should try to have nearly the same dollar amount of money at stake in the stock market each year for as many years as possible. This is equivalent to subdividing a stake of $100 into a series of several equal-sized dollar bets (e.g. 100 bets of $1 each).

Let's imagine that Mr. Investor has a sum of money from an inheritance he wants to invest into the stock market. In order to have the same dollar amount of money at risk over as many years as possible, Mr. Investor should invest the entire amount immediately as a lump sum. Furthermore, as the dollar value of his stock investment grows, he should liquidate stocks to maintain the original dollar amount he invested. In addition, if the dollar value of his stock investment declines he should move money into stocks to maintain his original investment amount. All this can be accomplished most easily if Mr. Investor simply invests his inheritance into a portfolio of stocks and fixed-income and rebalances annually between them. However, he should rebalance in order to maintain the same dollar amount in stocks (adjusted for inflation) rather than the same percentage amount in stocks. For example, if Mr. Investor's puts $100,000 into stocks, representing 75% of his inheritance, and his portfolio grows to $250,000 (real), then rebalancing to 75% would be $187,500. He has much more at risk in dollar amount than the $100,000 he began with. The benefit of time diversification will not be as great for Mr. Investor if he allows the dollar amount of his stake to become significantly skewed over time.

So, this example illustrates that time diversification works for the special case in which the investor has the same dollar amount at stake over time. It also works to a degree when the same percentage allocation to stocks is maintained over time, but the benefits are overwhelmed and washed out by the fact that most investors have the their greatest stake in the market toward the end of their investment accumulation horizon. Whatever the market does during this relatively short timeframe of 10 years or so will overwhelm (for good or evil) most of the benefits of time diversification from having owned stocks even over a much longer run.
the whole thing completely loses me. How does the example, which I take as a series of "all in bets" each time, at 2:1 odds, have anything to do with investing?

Each bet, risk of going to zero?

vs

Passive indexing in stock/bond split?

To extrapolate much of anything from that example, and relate it to investing, seems bizzarre.

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Post by letsgobobby » Wed Jun 15, 2011 8:24 am

Lbill wrote:
And the fact that this portfolio, with an average stock exposure of 58%, outperformed a 58/42 portfolio, should not be surprising, either, because the 58% was purely an average; in fact, starting in 1972, there would have been at least 2 occasions (late 1974 and mid 1982) when, because of the huge decline in stock values leading up to those points, maintaining a constant $500,000 of stocks would have meant equity allocations of much greater than 58%. In other words, these portfolios would have been over-rebalanced. Amazingly/ironically/coincidentally, these times would have occurred at long-term lows of PE10 (about 8 in 1974, about 5 in 1982). Said another way, isn't "constant value of stocks" really just another way of overbuying stocks at times of low valuation?
Yes, that's exactly what happened. But the reverse happened also (underbalancing). The percentage allocation to stocks ranged from a low of 38%(1999-2001) to a high of 89% (1982). Of course, the percentages don't mean anything per se - it's the growth of the overall value of the portfolio. There was never a single year where Port #2 had a lower real value than Port #1. It started ahead right out of the box in 1973 (they had the same value in 1972 of course) and just kept pulling ahead. The starting time was undoubtedly fortuitous since this led to systematically overbalancing stocks throughout that period, culminating in an 89% allocation in 1982. I want to see what happens if you don't start at 1972.

[Added Edit: Actually, as I think about it, maintaining a fixed real dollar allocation to a decumulating portfolio would cause stocks to become a larger and larger percentage of the portfolio over time. If this happens to coincide with a bull market, then this overbalancing toward equities will work in your favor. From 1972-1982 there was actually a bear market, which caused you to overbalance even more dramatically toward equities, just in time for the bull market that followed from 1982-2000. So, the results I observed are surely the result of a very fortuitous series of market returns - a bear market followed by a huge bull market in equities. Very important to examine what happens over different time periods that are less "lucky" for this strategy.]
exactly right. If one started in 1982, one's portfolio would have progressively underrebalanced stocks right up to the 2000 peak, and would likely underperform a 50/50 portfolio to that time. However, I wonder what would happen if you extend out to the present, having now experienced a decade long sideways market with 2 severe declines. I can't do the math on so many moving parts in my head.

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Post by Lbill » Wed Jun 15, 2011 9:59 am

exactly right. If one started in 1982, one's portfolio would have progressively underrebalanced stocks right up to the 2000 peak, and would likely underperform a 50/50 portfolio to that time.
makes sense. But beginning in 2000, you would have benefitted by having an underbalanced stock allocation when the market went south. It takes a bit of time to cobble together all the data for a given time period, but I want to do it starting in 1982 to 2010. Have to travel next couple of days, but will post results when I get this accomplished. Another consideration is that a retired investor is probably not going to have the stomach to let his allocation drift to an 89% stock allocation if he started with 50%. With that high allocation you are exposed to a lot of risk. The strategy I'm thinking about is to maybe cap the stock allocation. The question then becomes how valuable the benefit is from "underbalancing" stocks during a bull market. I'll take a look at this too.
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Post by letsgobobby » Wed Jun 15, 2011 10:19 am

Lbill wrote:
exactly right. If one started in 1982, one's portfolio would have progressively underrebalanced stocks right up to the 2000 peak, and would likely underperform a 50/50 portfolio to that time.
makes sense. But beginning in 2000, you would have benefitted by having an underbalanced stock allocation when the market went south. It takes a bit of time to cobble together all the data for a given time period, but I want to do it starting in 1982 to 2010. Have to travel next couple of days, but will post results when I get this accomplished. Another consideration is that a retired investor is probably not going to have the stomach to let his allocation drift to an 89% stock allocation if he started with 50%. With that high allocation you are exposed to a lot of risk. The strategy I'm thinking about is to maybe cap the stock allocation. The question then becomes how valuable the benefit is from "underbalancing" stocks during a bull market. I'll take a look at this too.
the ideal compromise between risk and return (as discussed in fredflinstone's thread about PE10) is to allow much greater range in stock allocation at a younger age, and narrowing that cone down as one's longevity decreases. So, for example, at age 20 you let your allocation run the whole range; by age 50 you cap on both the up- and down-side; by age 80 you ignore this and PE10 altogether and stick with a pure, risk tolerance-driven asset allocation (say, age in bonds).

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Coin tosses and the market

Post by efmoody » Wed Jun 15, 2011 10:58 am

You cannot put a coin toss rationale in with the variability of the financial market.

Coin tosses have a finite gaussian distribution. Finance variability has an infinte number of distributions. 1987 was a 10 to the 50th power reality check. That is at least 23 sigmas.

Any discussion with the two is way out of context

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Re: Time Diversification actually DOES reduce stock risk

Post by Lumpr » Wed Jun 15, 2011 1:01 pm

SP-diceman wrote:
Lbill wrote:
The argument against time diversification can be traced back to Paul Samuelson's paper "Risk and Uncertainty: A fallacy of large numbers." In the paper, Samuelson gives the example of betting $100 on a coin toss at 2:1 odds. Suppose you refuse to take the bet since, for you, the pain of losing $100 would be greater than the satisfaction of winning $200. Should you be more willing to accept the outcome of a series of similar bets (or "trials")? Based on the "law of averages", the reasoning goes that over the long run, wins and losses should even out, thereby making it almost certain that you'll come out ahead. But Samuelson shows this reasoning is fallacious and the answer is "No."

Imagine, for example, that you have the luckiest series of outcomes possible, winning the first 99 of a series of 100 coin tosses. You have accumulated 99 X $200, or $19,800, with one toss to go. You still have a 50:50 chance of losing the entire $19,800 on the final toss in the series, which is exactly the same as if you had been willing to take the intial single-trail bet with $19,800 at stake instead of $100.
With 2 to 1 odds and a 50-50 bet your optimum bet is 25% of your money.

Your first bet with $100 should have been $25.
If a win, the next bet $37.50 (150*.25)
If a loss, the next bet $18.75 (75*.25)

The problem with the $19,800 isn’t the casino odds, its the fact that its all your money.

One cant change the casino odds, but they can reduce their equity exposure.
(what a gambler would call his bankroll)


Thanks
SP-diceman
Kelly Criterion?

For what it is worth, Samuelson was an ardent opponent of the Kelly Criterion. Frankly, I've never been convinced by Samuelson's arguments against KC.

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Re: Coin tosses and the market

Post by LH » Wed Jun 15, 2011 3:40 pm

efmoody wrote:You cannot put a coin toss rationale in with the variability of the financial market.

Coin tosses have a finite gaussian distribution. Finance variability has an infinte number of distributions. 1987 was a 10 to the 50th power reality check. That is at least 23 sigmas.

Any discussion with the two is way out of context
Yeah, ditto.

Could someone respond to this? Because unlike most of what I read on this board, I have utterly zero clue how the example relates to the stock market. A series of all or nothing bets, compared to passive investing? It does not even appear to be in the same ballpark, it does not even appear to be conflation. Its not even apples to oranges, its more like squid to oranges, or nuetron star to oranges, to dip into hyperbole myself with the nuetron star thing...... I hesitate to use words like "nonsensical" so someone please explain.

completely lost,

LH

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Post by Lbill » Wed Jun 15, 2011 4:06 pm

Could someone respond to this? Because unlike most of what I read on this board, I have utterly zero clue how the example relates to the stock market.
Have you even read the Samuelson paper, or any of the other published articles dealing with the subject? You might want to start there. Samuelson's paper referenced in my up-post is the basis of most of the work on the topic, so it's important to understand what he said and didn't say about event risk.
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Post by Lbill » Wed Jun 15, 2011 8:10 pm

I have the results of comparing the constant-dollar (CD) and the fixed-percentage (FP) retirement decumulation portfolios for 1982-2010. This was a bull market period for 18 years, followed by the "Lost Decade" for stocks. Both portfolios started with $1M split 50/50 between stocks and bonds. The fixed-percentage port was rebalanced annually to the 50/50 allocation. The constant-dollar portfolio maintained a constant real dollar allocation to stocks throughout ($500K). For both portfolios an annual $40K (real dollars) draw is taken.

At the end of 2010, the fixed-percentage portfolio had a residual value that was 19% higher than for the constant-dollar portfolio. As expected, the stock allocation in the CD port systematically declined during the bull market period; it began at 50% and declined to 17% at the end. The average allocation to stocks for the CD portfolio over the entire 1982-2010 period was 26%, or about half of the allocation for the FP portfolio.

It's clear that the reason the FP port outperformed was its higher allocation to stocks during this period. The poor stock market returns in 2000-2002 and in 2008 were not enough to knock it out of the lead that it built up from 1982-1999.

However, the CD port has a better risk-adjusted return than the FP portfolio over the period. The ratio of annualized average return to the annualized standard deviation for the CD port was 67%, while the ratio was 49% for the FP portfolio. Comparing apples-to-apples, if we match the FP stock allocation over the period to the CD port average allocation (26%), the return/SD ratio was 56%. So it's apparent that the CD port is a more efficient portfolio, even though it has a lower absolute return over the period because of it's much lower allocation to stocks.

As in my up-post, for a given level of overall average stock exposure, a constant-dollar exposure to stocks annually seems to provide a higher risk-adjusted return than a corresponding static or fixed-percentage exposure. However, the absolute return can differ based on market price trends.
Last edited by Lbill on Thu Jun 16, 2011 8:37 am, edited 2 times in total.
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Post by renditt » Wed Jun 15, 2011 8:27 pm

I'm with LH, I'm lost.

So I read the Norstead paper, but somehow I don't think it addresses the critical question. For me the central question when discussing this issue is the following: if I want to achieve a certain minimum return, which I need for retirement and let's say that return is 5%, am I more or less likely to do that with a longer time horizon? Surely the answer is that I am more like to do so with a 30 year horizon than 1 year.

The fact that I may lose a lot of money in year 29 is irrelevant, as long as I still achieve my target return and my target portfolio value in year 30.

What am I missing?

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Post by dbr » Wed Jun 15, 2011 8:46 pm

renditt wrote:I'm with LH, I'm lost.

So I read the Norstead paper, but somehow I don't think it addresses the critical question. For me the central question when discussing this issue is the following: if I want to achieve a certain minimum return, which I need for retirement and let's say that return is 5%, am I more or less likely to do that with a longer time horizon? Surely the answer is that I am more like to do so with a 30 year horizon than 1 year.

The fact that I may lose a lot of money in year 29 is irrelevant, as long as I still achieve my target return and my target portfolio value in year 30.

What am I missing?
It is certainly true that one can still reach one's objective even after losing half one's investment in the last year. Having twice what is needed in the year just prior is sufficient for that. Sometimes one wonders what point people are trying to make. One might well ask, however, what happens if one meets the objective at year thirty, then loses half one's money at year 31 . . . then recovers from that loss by year 35? What was the plan as to what to be done with the money at the end of year thirty . . . invest in something with no uncertainty?

The other part of your question is that whether or not thirty years is more likely to produce a 5% CAGR than one year does depends on the properties of what one is invested in. You don't say, so who knows?

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Post by grayfox » Wed Jun 15, 2011 8:47 pm

renditt wrote:If I want to achieve a certain minimum return, which I need for retirement and let's say that return is 5%, am I more or less likely to do that with a longer time horizon? Surely the answer is that I am more like to do so with a 30 year horizon than 1 year.

The fact that I may lose a lot of money in year 29 is irrelevant, as long as I still achieve my target return and my target portfolio value in year 30.

What am I missing?
OK, I've seen a lot of discussion of this quesiton, so today I finally got around to thinking about this question myself. I set up a spreadsheet with some ultra simple models of the source of stock returns, and looked at IRR over various time periods. I'll just state my conclusion:
To the extent that real GDP growth rate and corporate profit margins are random variables whose mean values are constant and known, stock returns have less variance and are more predictable with longer holding periods and, therefore, stocks become less risky to hold in the long run.
See Are Stocks Less Risky in the Long Run?

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Post by umfundi » Wed Jun 15, 2011 9:31 pm

To be sure, I'm learning a lot. But, I think the discussion has strayed into one of stocks only. What about the rest of your diversified AA portfolio? There is a gambling / flipping the coin analogy for stocks, but not for precious metals?

So what if, by some definition of risk, stocks are risky in the long run? If you are young and the long run (to accumulate) is 40 years, what should you do? If you are retired, like me, and the long run (to deplete) is maybe 20 years, what should you do?

What I have learned in the last couple of weeks is:

1. When you do start depleting, do not foolishly take 4% of your portfolio's starting value per year forever. Take 4% of the per year value, and see how that goes.

2. When you are depleting, and there are big market moves, consider over-rebalancing. I am still trying to get my head around this.

By the way, I am an engineer, and so I believe there is no correct answer. There is only the best decision you can make, based on the evidence. Collecting the evidence is up to you.

Keith

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Post by renditt » Wed Jun 15, 2011 9:51 pm

dbr wrote:
renditt wrote:
It is certainly true that one can still reach one's objective even after losing half one's investment in the last year. Having twice what is needed in the year just prior is sufficient for that. Sometimes one wonders what point people are trying to make. One might well ask, however, what happens if one meets the objective at year thirty, then loses half one's money at year 31 . . . then recovers from that loss by year 35? What was the plan as to what to be done with the money at the end of year thirty . . . invest in something with no uncertainty?

The other part of your question is that whether or not thirty years is more likely to produce a 5% CAGR than one year does depends on the properties of what one is invested in. You don't say, so who knows?
Sorry, wasn't clear. Meant investing in stocks. Haven't done any testing with historical data, but would assume a 5% CAGR is a fairly safe assumption for stocks.

If you hit your number, then yes, you will invest in something safe in year 30. In reality, you may likely achieve higher returns than 5% in the first for example 15 years, in which case you may decide to sell a portion of your stocks and buy bonds, as the need to take risk has decreased.

In a different scenario, the first 10-15 years offer very poor returns (think 2000 onwards), in which case you may have to stick with 100% stocks until the end. That's obviously a scary scenario as another serious downturn could then truly put your goal out of reach.

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Post by grayfox » Thu Jun 16, 2011 8:35 am

renditt wrote:if I want to achieve a certain minimum return, which I need for retirement and let's say that return is 5%, am I more or less likely to do that with a longer time horizon? Surely the answer is that I am more like to do so with a 30 year horizon than 1 year.

The fact that I may lose a lot of money in year 29 is irrelevant, as long as I still achieve my target return and my target portfolio value in year 30.

What am I missing?
So my answer to your question is that, YES you are more likely to get 5% return over 30 years than over 1 year, provided that some conditions are met. Namely, that GDP growth rate and corporate profit margins have mean values that are known constants. I think that these are sufficient conditions for the variance of return to decrease over longer periods. I don't know if they are necessary conditions.

What are you missing? Well, what if those conditions aren't met. Then I think it gets more complicated. It may not necessarily be true that holding for the longer period is more likely to have less uncertain results.

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Post by renditt » Thu Jun 16, 2011 8:55 am

grayfox wrote:
So my answer to your question is that, YES you are more likely to get 5% return over 30 years than over 1 year, provided that some conditions are met. Namely, that GDP growth rate and corporate profit margins have mean values that are known constants. I think that these are sufficient conditions for the variance of return to decrease over longer periods. I don't know if they are necessary conditions.

What are you missing? Well, what if those conditions aren't met. Then I think it gets more complicated. It may not necessarily be true that holding for the longer period is more likely to have less uncertain results.
Just curious: what were historically the lowest returns (both nominal and real) in the US stock market over a 30 year time period?

Thanks

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Post by renditt » Thu Jun 16, 2011 9:05 am

Actually just looked it up on the Shiller website: if you invested at the peak in 1929, you had a nominal CAGR of 2-3% and a real return of basically 0 over the next 30 years.

Wow, that's pretty poor.

Edit: this is excluding dividends, so including dividends I would have even then met the 5% target, at least on a nominal basis. Not that terrible after all.

Still curious if someone knows the exact return including dividends.

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Post by dbr » Thu Jun 16, 2011 9:59 am

renditt wrote:
dbr wrote:
renditt wrote:
It is certainly true that one can still reach one's objective even after losing half one's investment in the last year. Having twice what is needed in the year just prior is sufficient for that. Sometimes one wonders what point people are trying to make. One might well ask, however, what happens if one meets the objective at year thirty, then loses half one's money at year 31 . . . then recovers from that loss by year 35? What was the plan as to what to be done with the money at the end of year thirty . . . invest in something with no uncertainty?

The other part of your question is that whether or not thirty years is more likely to produce a 5% CAGR than one year does depends on the properties of what one is invested in. You don't say, so who knows?
Sorry, wasn't clear. Meant investing in stocks. Haven't done any testing with historical data, but would assume a 5% CAGR is a fairly safe assumption for stocks.

If you hit your number, then yes, you will invest in something safe in year 30. In reality, you may likely achieve higher returns than 5% in the first for example 15 years, in which case you may decide to sell a portion of your stocks and buy bonds, as the need to take risk has decreased.

In a different scenario, the first 10-15 years offer very poor returns (think 2000 onwards), in which case you may have to stick with 100% stocks until the end. That's obviously a scary scenario as another serious downturn could then truly put your goal out of reach.
One thing to consider is that the person arriving at the end of the thirty years probably has as his objective retiring at that point and supplying some amount of income from there on out. Therefore the risk that needs to be analyzed for different strategies is the risk that needed income cannot be supplied. How relevant to that is the question of variability of returns of stocks? The answer depends on what one does to manage the risk to one's income.

If one expects to supply that income via withdrawals from a portfolio of stocks and bonds one enters the marvelous world of retirement withdrawal studies. There is much to be learned there, but some general trends include the ideas that the result (riskwise) is driven by withdrawal rate and luck of history and not very much by allocation. It seems that the trade-off of expected return with volatility for stocks is offsetting over a fairly wide range of asset allocation for reasonable withdrawal rates. It seems also that too little stock investment is risky. The coming and going of market booms and busts does not much affect safe withdrawal rates. A major risk in depending on SWR approaches is that one ends up with massive unspent wealth due to the conservatism that had to be imposed to defend against the worst case outcome. One can look at what TIPS can do to reduce that uncerainty but not to increase the withdrawal rate by a huge amount.

On basic financial terms there is no doubt that the best risk management tool for income in retirement and the optimum tool for rate of income is inflation indexed fixed immediate annuities, whether of the purchased type, the pension type, or the Social Security type. The risks include agency risk concerning insurance companies, one's employer, and future of SS. A mitigating strategy is diversification among supplies and of timing. Also one cannot annuitize everything, so one goes back to an emergency fund concept. One must also manage legacy concerns if one has such.

I think seriously volatility in stock investing is a smaller part of a larger picture than most people have it in mind in conversations like these.

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Post by dbr » Thu Jun 16, 2011 10:12 am

renditt wrote:
Sorry, wasn't clear. Meant investing in stocks. Haven't done any testing with historical data, but would assume a 5% CAGR is a fairly safe assumption for stocks.
Interestingly as an academic example, an absolutely secure bond could be an example where one year is certain and uncertainty increases as years go by. It would work this way. Invest in a thirty year bond paying 5%. At the end of the first year 5% would be paid out. In fact that happens at the end of every year. The uncertainty is that the payout would have to be reinvested at 5% or more each year or 5% compound growth would not be achieved. Furthermore that 5% reinvestment would have to be in bonds that would mature in shorter and shorter time period to all be recovered at the end of thirty years. It is entirely possible that starting with a 5% bond one would be unable to find compound growth for thirty years at 5%.

As for stocks, if one invests in something with an expected return of 5%, then the likelihood of falling short of 5% in any given time period compared to the likelihood of exceeding 5% would depend on the shape of the distribution of end point wealth for that time period. Expected return is a statistic which is taken to be the average of the outcomes. If the probability distribution of outcomes is symmetric, then there are as many outcomes above the average as below. If the distribution is not symmetric there can be more chances of ending up at less or more than the average value rather than the opposite. If the expected return is greater than 5% then the effects of skew would be offset and likely the number of outcomes exceeding 5% would increase in time, and the opposite if expected return is less than 5%. These things depend entirely on what the actual statistics are and it is not simple.

yobria
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Post by yobria » Thu Jun 16, 2011 10:40 am

renditt wrote:I'm with LH, I'm lost.

So I read the Norstead paper, but somehow I don't think it addresses the critical question. For me the central question when discussing this issue is the following: if I want to achieve a certain minimum return, which I need for retirement and let's say that return is 5%, am I more or less likely to do that with a longer time horizon? Surely the answer is that I am more like to do so with a 30 year horizon than 1 year.

The fact that I may lose a lot of money in year 29 is irrelevant, as long as I still achieve my target return and my target portfolio value in year 30.
That's true, though keep in mind:

-You may actually need that money before year 30 (eg you become disabled).

-Taking your comment literally, losing a lot of money in year 29 is of course relevant, since you won't have time to recover in a year

-While 30 year underperformance is less likely than single year, it's certainly possible. Japan will be lucky to get 0% from 1989-2019, for example.

Nick

dbr
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Post by dbr » Thu Jun 16, 2011 10:51 am

yobria wrote:
-Taking your comment literally, losing a lot of money in year 29 is of course relevant, since you won't have time to recover in a year


Nick
Indeed, correct, but also not correct. Assuming by taking literally one means that one has just reached the threshold before the crash, then, yes, there might be a problem. In reality when banking on hitting a certain threshold based on expected return there will be many outcomes coming out far above and many outcomes far below. The single instance where one of the far belows is just exactly being on target at year 29 and losing half in year thirty would be possible but highly unlikely. There are far more and some worse outcomes where needing 5% growth based on expected return of 5% would fail. Probably to be highly certain of getting 5% would require operating on an expected return of 7% or 8%, and in that case most outcomes could still tolerate a 50% loss in the last year.

But there is more involved than that. If the next step is to just continue to stay invested and start withdrawing some money, one does have precisely the time needed to recover from the loss. A position like that would very likely put that investor in one of the worst case scenarios for retirement ruin, but the whole point of retirement ruin studies is to establish what the worst cases are that one still survives, so it is not a given that disaster has occurred.

I think these simplistic scenarios about "losing half the investment" in the "last" year are not well enough defined to say anything with certainty one way or the other. In fact the concept of arriving at retirement with a target wealth is too simplistic as an analysis of the problem.

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