Surviving Rates versus Half Failure Rates

Research on Safe Withdrawal Rates

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JWR1945
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Surviving Rates versus Half Failure Rates

Post by JWR1945 »

I have noticed that plots of Half Failure Withdrawal Rates are very similar to those with Historical Surviving Withdrawal Rates. Here is my explanation.

Gummy's Safe Withdrawal Rate Equation can be written in this form:
Balance(N) / Initial Balance = RETURN0*(1 - w/WFAIL) where
Balance(N) is the portfolio's balance after N years, RETURN0 is the total return when there are no withdrawals whatsoever, w is the withdrawal rate and WFAIL is the withdrawal rate that fails at N years (i.e., it has a zero balance).

Notice that RETURN0 is not an annualized return. It is the ratio of the portfolio's balance after N years to its initial balance provided that there are no additions or withdrawals. If the annualized return is r, then (1+r)^N = RETURN0.

Both RETURN0 and WFAIL change as N, the number of years, changes.

It is not immediately obvious that Half Failure Withdrawal Rates and Historical Surviving Withdrawal Rates would be tied closely together. It is not automatically guaranteed that the relevant number of years N would be the same in both cases. But upon reflection, it is quite plausible that they should be closely related and that N is always the portfolio lifetime (30 years) being examined.

Although a portfolio's balance can dip down and then increase before its lifetime (30 years) is up, our procedure requires us to increase withdrawal rates until a failure or half failure occurs. It is hard to conceive of how a portfolio's balance could drop below 50% in any year without our already being at or above the half failure rate.

This means that N equals the total lifetime under investigation, in our case 30 years.

By the time that 30 years has occurred, the annualized return is close to the 6.5% to 7.0% long-term rate of the market as a whole. [Strictly speaking, the portfolio's rate of return is not that of stocks alone, but that of a combination of stocks and bonds or commercial paper.] This means that RETURN0 is of the order of (1.065)^30 = 6.614.

Now look at what happens when RETURN0 is of the order of 6.614 or so. Dividing both sides of the equation by RETURN0:
( [Balance(N) / Initial Balance] / RETURN0 ) = 1 - w/WFAIL.

When we look at Half Failure Withdrawal Rates, [Balance(N) / Initial Balance] = 0.5. If RETURN0 equals 6.614, then the left-hand side is very small, equal to (0.5/6.614) = 0.0756. This leaves us with an equation:

w/WFAIL = 1 - (a small number close to 0.0756)

or

w = WFAIL*(a number just slightly less than 1).

This means that the Half Failure Withdrawal Rates should be equal to the Historical Surviving Withdrawal Rates times a number close to, but slightly smaller than, one.

Translating this into our curve fitting equations: to a first approximation, both the slopes and intercepts should be just a little bit smaller for the Half Failure Withdrawal Rates as compared to the Historical Surviving Withdrawal Rates. This is strictly true of HFWR50 but not of HFWR80. HFWR80 has a slope very close to that of HDBR80, but slightly larger, and an intercept that is much, much smaller than that of HDBR80.

I have presented enough to show that it is reasonable to expect some similarity between Half Failure Withdrawal Rates and Historical Surviving Withdrawal Rates. The relationship is not strong enough to prevail under all circumstances.

Have fun.

John R.
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Post by hocus2004 »

"This means that the Half Failure Withdrawal Rates should be equal to the Historical Surviving Withdrawal Rates times a number close to, but slightly smaller than, one. "

The Half-Failure Withdrawal Rate calculation could in some circumstances have significant strategic implications, in my view. I have observed over the years that there are a good number of people who are not aware that the REHP study's SWR number presumes complete depletion of the portfolio at the end of 30 years. The study clearly states that this is the presumption on which its calculations are based. But lots of people use studies without reading them with care. My sense is that there are a good number of people who do not intuitively view a strategy that calls for complete depletion of one's portfolio in 30 years as a "100 percent safe" one. So they jump to the conclusion that the study, which purports to offer a means of achieving a safe investment strategy, is insuring something better than seeing one's portfolio completely depleted at the end of 30 years.

I think these people are right to be skeptical of the real-world value of calculations based on such a presumption. For many, early retirement means retirement at age 50 or 55. There is a good chance that someone who retires at age 50 or 55 is going to live more than 30 years. Those people should not be using a number that calls for complete depletion of their portfolios in 30 years to put together their plans.

I am not saying that we should not employ the 30-year complete-depletion presumption in our work on this board. We need to do so to make our numbers comparable to the conventional methodology numbers. However, I think it would be a good idea for us to supplement the findings that we come up with from use of the complete portfolio depletion presumption with numbers that provide greater safety than the scenario purported in the conventional studies to reveal what is "100 percent safe."

The obvious way to provide a more realistic SWR would be to calculate what take-out number would insure the early retiree not just of not going bust in 30 years but of maintaining the real value of his portfolio after 30 years. For stocks at today's valuation levels, this would be a very low number.

The current SWR for stocks is 2.5 percent (I am using the number from the "Calculated Rates for the Past Decade" thread). The take-out number that would work presuming zero real growth over 30 years is 3.3 percent (a TIPS paying zero real return would permit you a take-out of 3.3 percent per year without depletion of your portfolio for 30 years). So It appears to me that the 2.5 percent SWR that applies for an 80 percent S&P portfolio today suggests that a returns sequence as bad the worst that we have seen in the past (but not worse than that) translates into a negative return on stocks for the next 30 years (for those in the distribution stage rather than the accumulaton stage of their investing lives).

Is it mathematically correct to determine the take-out number that insures against portfolio loss at the end of 30 years by subtracting 3.3 percent from the SWR? I don't know how the numbers work well enough to say . But if that is so, it means that those with 80 percent stock portfolios who retire today cannot be sure that taking 0 percent out per year will leave them at the end of 30 years with the same level of financial independence as they possess today.

It seems to me that the calculation discussed in the thread-starter might provide an alternate means of pursuing the general goal being pursued by calculating the withdrawal rate that insures against portfolio loss for 30 years. I believe that the Half Failure Withdrawal Rate would not insure the retiree that he would not suffer portfolio loss over 30 years. But in some circumstances it might offer a not-bad level of protection against the negative consequences of a reasonably high percentage of the returns sequences that have turned up in the historical record.

This calculation might provide an aspiring early retiree a means of putting together a strategy that offers greater safety than the purported (but illusory) "100 percent safe" conventional methodology stratagy but less safety than the belt-and-suspenders stratagy of using the number that even in the worst-case scenario insures against portfolio loss for 30 years. My sense from reading posts on these questions for over five years now is that this middle-ground is the level of safety that many (but not all or necessarily even most) aspiring early retirees are seeking when looking to SWR analysis to help with the crafting of their plans.

I am not saying that the Half Failure Rate would be a good number for a lot of retirees to take as their overall take-out number. The take-out number would be too low for most and the risk factor too high (given the depletion factor that applies with an unadjusted Half Failure Rate). But it might work to take this number for 50 percent of one's portfolio (comprised of 80 percent stocks and 20 percent fixed-income) while taking the higher SWR that applies for TIPS for the other 50 percent of the portfolio. This would translate into an overall stock allocation of 40 percent. I believe that it would yield an overall SWR of less than 4 percent, but I believe it would be a higher number than the number you would get for 80 percent stocks. A benefit of this approach is that it would incorporate the long-term growth potential that many early retirees find lacking in TIPS without requiring reliance on a switching strategy.

Another benefit is that this approach protects against the emotional pressure to sell stocks when their prices are low that follows from reliance on the conventional methodology approach. The conventional methodlogy numbers assume that the retiree will maintain his 74 percent stock allocation even if stock prices fall by 90 percent (the highest percentage drop in the historical record). I find this assumption to be extremely far-fetched. In the approach described above, the retiree would be starting out with a stock allocation of only 40 percent. So he would feel less pressure to lower his stock allocation when faced with price drops. Also, his take-out number would be lower than the take-out number being used by those relying on the conventional studies. So the risk to the long-term success of his plan that he would suffer with a drop in stock prices would be less, according to the historical data. And he would have steady income coming in from his TIPS investments. These realities (perhaps combined with some reductions in spending) would translate into a far greater ability to get through the experience of large price drops without feeling strong emotional pressures to sell stock shares when their prices are low.

Please don't take the details of the stratagy I am outlining here too seriously. I have not studied the numbers in enough depth to say with precision how a stratagy along these lines should be constructed. My goal is just to think through at a surface level of understanding how an early retiree might make use of the Half-Failure Rate in construction of a plan. I am confident that there are lots of possibilites other than the one I have outlined above. I am just trying to get one possible strategic use out there so that people can mull it over a bit and get a sense of how the Data-Based SWR Tool can be put to use in a variety of circumstances to serve a variety of different sorts of strategic purposes.
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Post by JWR1945 »

hocus2004 (out of sequence):
Please don't take the details of the strategy I am outlining here too seriously. I have not studied the numbers in enough depth to say with precision how a strategy along these lines should be constructed.
Please break your post into many specific sections and expand on each. Please put together many details so that I can take them seriously even though that was not your original intent. There is so much data gathering and data analysis power in the latest Deluxe Calculator V1.1A02 that we can easily answer many questions previously considered totally unreasonable because of the effort required.

As far as the use of 30-year lifetimes in our investigations: that is a compromise that is good for analysis purposes without being entirely unreasonable to retirees. It turns out to be necessary to include 30 years of data in any investigation so that sequences include both good times and bad times for starting retirement. Shorter sequences typically include either good times or bad times but not both.

Using longer sequences causes two data analysis problems. The first is that you end up with a final decade similar to the first. Portfolios can fail because of an early sequence or because of a sequence that starts 30+ years later. For example, the 1930s and the 1960s were both difficult times for retirement portfolios. The other problem is that you end up with fewer complete sequences to analyze. With a 30-year lifetime, the last complete sequence starts in 1972. With a 40-year lifetime, the last complete sequence starts in 1962. The 1960s turn out to be critically important in our research. Using a 30-year lifetime is an accommodation.
Is it mathematically correct to determine the take-out number that insures against portfolio loss at the end of 30 years by subtracting 3.3 percent from the SWR? I don't know how the numbers work well enough to say. But if that is so, it means that those with 80 percent stock portfolios who retire today cannot be sure that taking 0 percent out per year will leave them at the end of 30 years with the same level of financial independence as they possess today.
No. The 80% stock portfolio is unsafe at 3.3%, but it is safe at 0.0%. Subtracting does not work. However, the 80% stock portfolio has reduced the amount that can be withdrawn safely to 2.5% (with a small, residual risk of 5% remaining) when compared to TIPS or ibonds at an interest rate of zero percent.
I am not saying that the Half Failure Rate would be a good number for a lot of retirees to take as their overall take-out number. The take-out number would be too low for most and the risk factor too high (given the depletion factor that applies with an unadjusted Half Failure Rate). But it might work to take this number for 50 percent of one's portfolio (comprised of 80 percent stocks and 20 percent fixed-income) while taking the higher SWR that applies for TIPS for the other 50 percent of the portfolio. This would translate into an overall stock allocation of 40 percent.
Here are two things to keep in mind: 1) we normally rebalance our portfolios in our investigations (although I am beginning to wonder whether it is worthwhile to do so) and 2) previous investigations have always come back showing that working with a single portfolio is better than working with two portfolios that start out with the same number of dollars.

OTOH, we can easily talk in terms of selecting a withdrawal rate between the two numbers and applying it to a single portfolio and seeing what happens. There will be a different number for the lowest balance. There will be a new range of final balances as well.

We can look at mixed withdrawal strategies such as taking a portion from stock dividends and second, different percentage from TIPS interest. We can take a portion from the portfolio's overall balance and a second, different percentage from TIPS interest.

There are numerous possibilities. In addition, we can start investigating what happens when we don't rebalance the portfolio. That situation has not been examined very much. We can now take a fixed percentage of TIPS interest while taking another portion from the portfolio as a whole. Suddenly, a portfolio without rebalancing becomes more interesting. Essentially, we are using the TIPS to provide a support level until stocks begin to grow. We might wish to look at how the amount withdrawn varies under such circumstances.

Have fun.

John R.
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Post by hocus2004 »

Please break your post into many specific sections and expand on each.

I'll aim to get to this sometime next week.

Subtracting does not work. However, the 80% stock portfolio has reduced the amount that can be withdrawn safely to 2.5% (with a small, residual risk of 5% remaining) when compared to TIPS or ibonds at an interest rate of zero percent.

Are you able to say what the take-out number is that would insure the retiree of having the same amount of buying power at the end of 30 years as he possessed on his date of retirement?

Say that the portfolio is $1,000,000. Say that the valuation level is what it is today, a level at which the SWR for an 80 percent S&P portfolio is 2.5 percent. That 2.5 percent take-out number insures you that, even in a worst-case scenario, you will have at least $1 in your portfolio at the end of 30 years. Can you say what take-out number assures you that you will have $1 million in inflation-adjusted dollars in your portfolio at the end of 30 years?
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Post by JWR1945 »

hocus2004 wrote:Are you able to say what the take-out number is that would insure the retiree of having the same amount of buying power at the end of 30 years as he possessed on his date of retirement?
Yes. I have just posted a complete set of results for 80% stocks:
CTVR80 versus Earnings Yield dated Sat Aug 07, 2004.
http://nofeeboards.com/boards/viewtopic ... 059#p23059

Have fun.

John R.

[Edited to change CVTR to CTVR.]
Last edited by JWR1945 on Sun Aug 08, 2004 7:08 am, edited 1 time in total.
hocus2004
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Post by hocus2004 »

"Yes. I have just posted a complete set of results for 80% stocks:
CVTR80 versus Earnings Yield dated Sat Aug 07, 2004.
http://nofeeboards.com/boards/viewtopic ... 059#p23059

I responded on the new thread.
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Post by hocus2004 »

"Please break your post into many specific sections and expand on each. "

JWR1945:

My goal was not to put forward any one particular scenario and see what the numbers were for that scenario. I was trying to suggest some of the strategic possibilities of the tool.

One of the problems we face in getting across to people the power of the Data-Based SWR Tool is getting them to look at SWR analysis in a new way. When you use the conventional methodology, SWR analysis appears to be useful but not all that exciting. Even if the conventional methodology were analytically valid, it would only answer one or two questions (important questions, to be sure) about how to invest. The reality is that there are more than two questions that need to be examined in crafting an effective investment strategy. Because the data-based tool is rooted in the realities of the historical data, it is able to provide insights on a host of investing questions. It is a more flexible tool. Its reach is far greater than the reach of the conventional methodology tool.

Our focus for the first 26 months has been the valuation question. The failure to take into account the effect of changes in valuations is the most serious flaw of the conventional methodology. But it is not the only serious flaw of that methodology. Another flaw of the REHP study (and I presume some other conventional methodology studies) is that it gives you the take-out number that works if you are willing to allow your portfolio value to dimish to zero at the end of 30 years. This is NOT an appropriate way to determine what take-out number is "100 percent safe," in my view.

The number that is "100 percent safe" is the number that stands a very good chance of working. A number that may leave you with zero assets at the end of 30 years is not providing 100 percent safety, but something a good bit less than that. I am not saying that we should be using time-periods of greater than 30 years in our research. The 30-year time-span makes sense for a number of reasons. What I am saying is that we need to keep in mind that finding the number that leaves at least one dollar in the portfolio at the end of 30 years is only part of a complete SWR analysis. We also need to address the question of what the retiree is going to do when the 30 years expires. An examination of that question needs to be part of any well-constructed investment plan.

You say on the other thread that the retiree attains an assurance of retaining his full starting-point portfolio value by reducing his withdrawal rate from 2.5 percent (the SWR for a high-stock portfolio at today's valuation level) to 1.9 percent. Doing that would obviously provide sufficient cover. But most retirees don't need to go all the way down to 1.9 percent. If you retire at age 50, you will be 80 at the end of 30 years. You don't need as much in your portfolio at age 80 as you do at age 50. Being sure of retaining at least 50 percent (or some other percentage less than 100 percent but more than 0 percent) might be enough to insure "100 percent safety" in your particular circumstances. Knowing the 1.9 percent number helps. Perhaps the number for a particular aspiring retiree is 2.2 percent, the number halfway between the 1.9 percent number and the 2.5 percent number.

This thread focuses on a third of the various moving pieces. In the thread-starter above, you are focusing on the question of what number assures you of not suffering more than a 50 percent loss in portfolio value. The safety concern at play there is the concern that big drops in portfolio value will cause you to sell stocks at the worst possible time (when prices are low). The failure to take this factor into consideration is a third flaw of the conventional methodology. The conventional methodology assumes (with no support in the historical data whatsoever) that investors will retain their high-stock-percentage portfolios even if they suffer a 90 percent drop in prices (as happened in 1929). This is madness, in my view. I would not be too surprised to learn that there was not a single investor who retained a stock allocation of 74 percent when stock prices fell by 90 percent. Yet the conventional methodology assumes that all investors using conventional methodology studies will do this, that it is "100 percent safe" to assume this.

Somewhere down the road we will need to examine what sorts of assumptions re retention of starting-point stock percentages are realistic. Your thread-starter here provides important clues. Using this research, an investor who feels comfortable with an assumption that he will not sell stocks unless their prices drop by more than 50 percent can learn what sort of take-out number he should be taking to achieve "100 percent safety" (or whatever other safety level he prefers). So both of the recents threads provide us with important clues to solving the puzzle of how to go about constructing effective Retire Early investing plans.

Ultimately, we need to explore how to combine the various insights. Say that TIPS were paying a return of 4.1 percent real (as they were not too long ago andn which translates into an SWR of 5.85 percent) and that stocks were providing a SWR of 2 percent or less (as they were not too long ago). One way to construct a plan would be to put roughly half of one's portfolio in TIPS and half in stocks. It is my sense that you have indicated that there are complexities to dividing up portfolios in this way. Those complexities ultimately need to be addressed, but I don't expect that they will stand in the way of exploration of the strategic goal of using the insights we have developed for purposes of successful portfolio construction. I'm not aiming to deal with the complexities today, just to put forward a suggestion as to how some of the insights can be combined into highly effective overall portfolio construction stratagies.

A 50/50 portfolio might have a overall SWR of something in the neighborhood of 4 percent in the scenario described above. This would be lower than the 5.85 percent SWR that could be obtained from TIPS alone, but it would provide the long-term growth potential offered by stocks. So it might have some appeal to those concerned about financing life in the years on the other side of the intiial 30-year period. There would be a problem with this portfolio, however. The TIPS portion would be entirely depleted in 30 years. In a worst-case returns sequence, the stock portion would be too. The portfolio descirbed is not a "100 percent safe" portolio in a real-world sense.

Lower the take-out from the stock portion to where you are assured of retaining the full starting point portfolio value, and you may have solved the problem. You would then be assured of retaining 50 percent of the overall starting-point value. That's probably enough at age 80.

Again, I am not endorsing this particular strategy. Whether a strategy is a good one or not always depends on the particular life goals and financial circumstances of the aspiring retiree for whom the strategy is being developed. There are also some complexities that I am side-stepping for the time-being. My goal is not to say "do this" or "do that" or "do the other thing." It is to suggest considerations that might be taken into account when developing a plan, to give people who have never used the tool a sense of its possibilities.

SWR analysis is not just about determining take-out numbers. That is important, but there is a whole lot more that SWR analysis can do. People have come to think that it is a tool of narrow usefulness only because they have been misled by the conventional methodology studies into thinking that the historical data generates la-la land numbers. Actually, the historical data generates numbers much in line with what your common sense would lead you to expect. The advantage over common sense that is provided by an analytically valid SWR analysis is that it quantifies your common sense impressions. It gives you hard numbers to work with. In construction of a plan, you need numbers to plug in, and SWR analysis takes the vague impressions provided by common sense and transforms them into actionable information bits.

I wasn't hoping to have you do any additional calculations in response to my earlier post. I was aiming to get people who read the post to begin to think about the promise of SWR analysis in a different way. SWR analysis is a far more powerful tool than people who have come to know it from seeing the results of conventional methodology studies realize. We are still in an early stage of our explorations of this wonderful new investing tool.
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Post by JWR1945 »

A Survey with Stocks and TIPS

I have included many data analysis capabilities in the Deluxe Calculator V1.1A02 which seemed worthwhile but for which I did not have an immediate need. I am making brief surveys to determine what kinds of investigations offer promise.

This survey was inspired by hocus2004's vague speculations about complementary goals for a portfolio of stocks and TIPS.

These results surprised me.

General Description

All portfolios included 50% in stocks and 50% in TIPS or Ibonds at a 2.5% (real) interest rate.

In all cases I withdrew 80% of the interest, which starts out at 1% of the portfolio's initial balance.

In all cases I withdrew 4.20% in investment expenses. By interpretation, this would consists of withdrawals of 4% of the portfolio's current balance (not of the initial balance) and 0.20% in regular expenses.

I made no other withdrawals.

This corresponds to a base withdrawal 1% from interest (initially) and 4% from the portfolio's initial balance. This is consistent with a commonly investigated strategy of withdrawing 5% of a portfolio's current balance. It is the most commonly investigated alternative to withdrawing 4% of a portfolio's initial balance plus adjustments to match inflation.

Calculator Inputs

I set B4, the Initial Balance, to $100000.
I set B6, the Stock Allocation, to 50%.
I set B7, the Fixed Income Series to 4 (TIPS) or 5 (Ibonds).
I set H8, the interest coupon rate, to 2.50%.
I set B9, the Initial Withdrawal Rate, to 0.00%.
I set B15, the Investment Expenses, to 4.20%.
I set B16, which answers ReBalance Portfolio?, as appropriate.
I set B17, the Percentage Gains Removed, to 0%.
I set B22, the Dividends Reinvested, to 100%.
I set B23, the Interest Reinvested, to 20%.
I set M1, the initial year in the data summary tables, to 1921.
I set M2, the final year in the data summary tables, to 1975. (I could not use 1980 because of the effects of dummy data.)

Special Remarks about TIPS

The balance of a TIPS holding can decrease in nominal dollars during times of deflation. This shows up as a negative interest rate whenever deflation overcomes the coupon rate.

Under normal conditions, 100% of the interest is reinvested. If less than 100% is reinvested and if deflation is high enough, what would normally be interest withdrawals become interest replacements.

For example, if TIPS principal falls by $500 because of deflation and if the coupon produces $400 of interest, the TIPS balance decreases by $100 (net). The calculator treats this $100 as a negative net interest rate. If only 20% of the interest is withdrawn, the TIPS balance in the calculator falls by only $20. The other $80 is a negative withdrawal. That is, the other $80 is replaced externally.

The combination of deflation in the early 1930s and the stock market crash of 1929 combine to produce heavy damage to portfolio withdrawals. TIPS have negative withdrawals. Reductions in the stock market affect the TIPS balances because the 4.2% (of the current balance) that is withdrawn applies to the entire portfolio, not just to stocks. The net Total Amount Withdrawn in year 4 of the 1929 sequence fell to $34.

That is why I included Ibonds in this investigation. Ibonds never lose principal. Their net interest rate is never negative.

Results

TIPS without rebalancing

Minimum Portfolio Balances within:
10 years: $42331 in year 9 of the 1973 sequence.
20 years: $31866 in year 16 of the 1966 sequence.
30 years: $31866 in year 16 of the 1966 sequence.

Minimum Portfolio Balance after:
10 years: $43080 with the 1972 sequence.
20 years: $33895 with the 1962 sequence.
30 years: $50200 with the 1965 sequence.

Minimum Total Amount Withdrawn within:
10 years: $34 in year 4 of the 1929 sequence.
20 years: $34 in year 4 of the 1929 sequence.
30 years: $34 in year 4 of the 1929 sequence.

Minimum Total Amount Withdrawn within if 1929 is excluded:
10 years: $2949 in year 10 of the 1940 sequence.
20 years: $1973 in year 18 of the 1965 sequence.
30 years: $1973 in year 18 of the 1965 sequence.


TIPS with rebalancing

Minimum Portfolio Balances within:
10 years: $43601 in year 9 of the 1973 sequence.
20 years: $32000 in year 17 of the 1965 sequence.
30 years: $31872 in year 30 of the 1965 sequence.

Minimum Portfolio Balance after:
10 years: $44054 with the 1972 sequence.
20 years: $32138 with the 1962 sequence.
30 years: $31872 with the 1965 sequence.

Minimum Total Amount Withdrawn within:
10 years: $645 in year 3 of the 1929 sequence.
20 years: $645 in year 3 of the 1929 sequence.
30 years: $645 in year 3 of the 1929 sequence.

The Minimum Total Amount Withdrawn remains low until 1932 is excluded.

Ibonds without rebalancing

Minimum Portfolio Balances within:
10 years: $42331 in year 9 of the 1973 sequence.
20 years: $31866 in year 16 of the 1966 sequence.
30 years: $31866 in year 16 of the 1966 sequence.

Minimum Portfolio Balance after:
10 years: $43080 with the 1972 sequence.
20 years: $33895 with the 1962 sequence.
30 years: $50200 with the 1965 sequence.

Minimum Total Amount Withdrawn within:
10 years: $2949 in year 10 of the 1940 sequence.
20 years: $1973 in year 18 of the 1965 sequence.
30 years: $1973 in year 18 of the 1965 sequence.

Ibonds with rebalancing

Minimum Portfolio Balances within:
10 years: $43601 in year 9 of the 1973 sequence.
20 years: $32000 in year 17 of the 1965 sequence.
30 years: $31872 in year 30 of the 1965 sequence.

Minimum Portfolio Balance after:
10 years: $44054 with the 1972 sequence.
20 years: $32138 with the 1962 sequence.
30 years: $31872 with the 1965 sequence.

Minimum Total Amount Withdrawn within:
10 years: $2918 in year 10 of the 1940 sequence.
20 years: $2177 in year 18 of the 1965 sequence.
30 years: $2096 in year 30 of the 1962 sequence.

The Special Insight

These numbers argue against rebalancing.

Rebalancing offers its benefits at a great penalty.

Looking at the various numbers, we find that rebalancing props up a minimum balance here and there. It helped a little bit with deflation in 1929, but it dragged the problem out for a few more years. But what jumps out and grabs my attention are the balances at the end of 30 years.

It takes about three decades for our investment portfolios to cycle through everything, the good and the bad together. Given a chance to grow, stock holdings do exceptionally well after 30 years. Rebalancing stunts that growth by clipping off the peaks. It does not give back enough for what it takes away. Starting from $100000 and without rebalancing, you would have $50200 after 30 years even with the 1965 sequence. Starting from the same $100000 but with rebalancing, you are condemned to $31872 because of the 1965 sequence.

Have fun.

John R.
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Post by Mike »

I think this means that with 50% initial equity, and 5% of current balance withdrawn, not rebalancing produces more return . This makes sense. Starting with low initial equity exposure protects against downdrafts in the first years of retirement, and gradually increasing equity as time goes on increases return. Taking a percentage of of current portfolio forces a person to cut back when things are not going well early on.
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Post by JWR1945 »

This might help people understand these results.

Suppose that stocks return 6.5% and that TIPS return 2.5% in real (i.e., inflation adjusted) dollars. If there are no additions or withdrawals, the expected or average return is between these rates according to their proportions. If the proportions are 50% stocks and 50% TIPS, their expected return is 0.5*6.5% + 0.5*2.5% = 4.5%.

Consider two cases that are very similar but different. In the first, you have two investments that both return 4.5%. In the other, you have equal allocations of stocks and TIPS which, when taken together, start out returning 4.5%.

Rebalancing brings about a rebalancing bonus. The actual return (assuming that the investments are not highly correlated and behave somewhat differently) is a little bit above 4.5%. It the first case, the actual return is higher than either individual investment. In the second case, the actual return is higher than the proportions would have indicated, but it is less than the 6.5% from stocks by themselves.

In the first case, whether you rebalance or do not rebalance your portfolio, the individual proportions will remain the same (sampled over long-periods of time). In the second case, whether you rebalance or do not rebalance your portfolio produces radically different results.

Rebalancing always causes the percentage of stocks to return to 50%. Not rebalancing, however, allows the proportion of stocks to increase over time because of their higher long-term return. Eventually, they dominate the portfolio. As their proportion comes closer to 100% of the portfolio [it can never equal 100%], the expected return of the portfolio climbs closer and closer to 6.5%.

A rebalanced portfolio of 50% stocks and 50% TIPS consistently yields a little bit more than 4.5% every year. More precisely, its expected or average return is just a little bit above 4.5% every year.

A portfolio without rebalancing starts out with an expected or average return of 4.5% in the first year. It is inferior in the first year. As time passes, the expected or average return grows closer to 6.5% as stock values dominate the total portfolio.

[The concept of an increasing expected or average return is a little bit difficult. Averaged with respect to what? The averaging is with respect to a large number of possible sequences. The expected return for the first year, averaged over the first year all of the possible sequences, is 4.5%. The expected return for the second year is averaged from the second year of the possible sequences. It is higher that 4.5%. The expected return for the third year is averaged from the third year of the possible sequences. It is even higher. And so on.]

The analysis becomes more difficult when there are additions or withdrawals. We have observed empirically that choosing not to rebalance has resulted in a bigger 30-year minimum balance.

Have fun.

John R.
hocus2004
Moderator
Posts: 752
Joined: Thu Jun 10, 2004 7:33 am

Post by hocus2004 »

"We have observed empirically that choosing not to rebalance has resulted in a bigger 30-year minimum balance. "

My guess is that rebalancing might make more sense when you are starting out with a high-risk plan than when you are starting out with a low-risk plan or a moderate-risk plan.

Your calculations show an SWR in the year 2000 of 1.6 percent for a portfolio of 80 percent stocks. At the time, people were being told that the SWR for a high-stock portfolio was 4 percent, and some were saying that they did not require 100 percent safety, so they were going to take 5 percent. Your calculations have shown that a 5 percent withdrawal was a high risk withdrawal in those circumstances.

Say that, in the early years of such a retirement, the price of stocks went up. Should the retiree rebalance? My guess is that he should. It is true that a big price drop in the early years of a retirement raises the possibility of a worst-case returns sequence coming up, and the fact that this retiree has gotten through the first few years without a price drop means that his risk profile is better than what it was when he was starting out. One could thus argue that he does not need to rebalance to retain the same level of safety that he had starting out. But his risk profile was so great starting out that my guess is that he should rebalance. Rebalancing in these circumstances might allow him to take advantage of the luck he experienced in the first few years of his retirement by lowering his long-term risk profile.

It's different when you are dealing with a portfolio allocation that was safe to start with. If your plan was safe enough on the first day of retirement, and you then got through the early years without any big price drops, your portfolio is now safer than just safe enough. That means that you can afford a move in the direction of greater risk. You can afford to increase your alliocation to the asset class that generally provides both high risk and high long-term return potential.

It is my sense that the reason why rebalancing is called for in the conventional studies is that those studies are trying to push the stock allocation up as high as the historical data will permit it to be pushed without the portfolio going bust. This allocation--the highest possible stock allocation that does not cause the portfolio to go bust in a worst-case returns sequence--is referred to as the "optimal" allocation. Rebalancing may be necessary to retain even moderate levels of safety when you are pushing things to the limit in this way. When you are failing to take into account a critical variable (the effect of changes in valuation), the allocation that appears to be pushing things to the limit is in reality pushing them beyond the limit. So it would seem to me that you would not want to be increasing your stock allocation in these circumstances, even if getting through the first few years of your retirement without a price drop served to lower your risk profile a bit from where it was starting out.
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Post by JWR1945 »

These are preliminary results. I will provide more details in the next few days.

The advantage of not rebalancing is critically tied in with my choosing to strip off 80% of the interest. If I had reinvested all interest, which is the normally investigated situation, there would have been a minor advantage in favor of rebalancing.

These effects are true with both 2.5% ibonds and with commercial paper.

These effects are true with 80% stocks and with 50% stocks. Arguably, they are a little bit more pronounced with 50% stocks.

These effects are true whether withdrawals are a percentage of the initial balance plus inflation (the conventional approach) or of the current balance (the most commonly investigated alternative).

Have fun.

John R.

P.S. Examining this is easy to do. The 30-year (real) balances are in column AB, rows 15 through 124. Put in your conditions, scroll over to column AB, copy the final balances and paste-special them onto a spreadsheet.
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Post by JWR1945 »

Rebalancing Surveys

Here are a host of surveys with and without rebalancing.

All balances are at 30-years. They are in real dollars. They are read from calculator column AB and rows 15-124. Unless stated otherwise, there are no conventional withdrawals. The investment expenses when there are conventional withdrawals are 0.20%. Conventional withdrawals are adjusted annually to match inflation. Conditions without rebalancing are indicated by an N such as CTVR80N. Interest was either entirely reinvested (100%) or 20% was reinvested, as indicated.

Use caution when examining sequences starting after 1972. The calculator has dummy data for 2003-2010 with large losses in stocks.

Results without rebalancing are in the center column. Results with rebalancing are on the right column.

The data show higher balances in the right column during the 1960s whenever the all of the interest was reinvested. They show higher balances in the center column during the 1960s whenever only 20% of the interest was reinvested. WARNING: There are many instances in which comparisons from the 1960s differ from those of the 1930s or 1940s.

Have fun.

John R.
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Post by JWR1945 »

All Interest Reinvested

Conditions

Code: Select all


Final Balances: 30 Years
80% Stocks / 20% commercial paper
3.3% withdrawal rates
100% Reinvested Interest
1871-1920

Code: Select all


Year   CTVR80N   CTVR80
1871    657886    672903
1872    661865    675041
1873    579982    592115
1874    508928    525767
1875    550007    561808
1876    599956    606253
1877    666102    659674
1878    468934    477076
1879    509408    513380
1880    374858    384996
1881    291204    303179
1882    331174    344384
1883    297877    309711
1884    264660    275018
1885    272699    280249
1886    228974    235849
1887    198630    204863
1888    150410    157475
1889    129780    135337
1890    115827    120335
1891    114908    119999
1892    109982    115833
1893    112037    117408
1894    143701    143879
1895    168978    166276
1896    187540    180587
1897    210469    200795
1898    221656    210819
1899    252804    240430
1900    258836    250744
1901    162007    167561
1902     99591    111935
1903     89673    102814
1904    196481    210862
1905    106157    119266
1906    104509    117944
1907    133851    146956
1908    201426    211317
1909    148325    159551
1910    103553    114189
1911    101707    111716
1912     94897    104681
1913    100836    110252
1914    144928    151859
1915    207431    208056
1916    202792    203596
1917    192950    197720
1918    331457    321369
1919    384108    374075
1920    431250    418930
1921-1980

Code: Select all


1921    608635    543980
1922    569284    499993
1923    474571    425413
1924    481208    431017
1925    527830    466095
1926    503086    446462
1927    442763    397338
1928    234801    227308
1929    123456    125507
1930    154087    151194
1931    248014    220117
1932    680648    485598
1933    720936    509592
1934    455570    335810
1935    660534    469333
1936    354097    265305
1937    176653    139782
1938    466410    333928
1939    391874    284648
1940    342561    258991
1941    474056    356297
1942    714257    523887
1943    718344    534701
1944    451247    366046
1945    274124    240674
1946    253290    225231
1947    413180    358033
1948    396642    354029
1949    385346    345508
1950    335060    305640
1951    289031    270959
1952    212899    209350
1953    224639    220577
1954    256671    250451
1955    154590    156774
1956    124900    128624
1957    154850    157832
1958    179955    182460
1959    111288    116193
1960    117302    122188
1961    104867    110553
1962     90230     96055
1963    112490    117698
1964     77509     82957
1965     51313     56396
1966     51042     56063
1967    103715    107860
1968     96949    100480
1969    116848    118340
1970    225305    214675
1971    210252    203302
1972    153184    153581
1973    105491    109793
1974    171918    173765
1975    246919    242941
1976    138068    142496
1977    108732    114549
1978    117096    123378
1979     93901     99718
1980     77232     81668
All Interest Reinvested

Conditions

Code: Select all


Final Balances: 30 Years
80% Stocks / 20% commercial paper
3.8% withdrawal rates
100% Reinvested Interest
1871-1920

Code: Select all


Year   CTVR80N   CTVR80
1871    604188    618626
1872    606266    619083
1873    526337    538167
1874    462725    478748
1875    498027    509600
1876    546705    553395
1877    608811    603273
1878    428149    435561
1879    473484    477434
1880    331887    341537
1881    254666    265611
1882    291522    303745
1883    258459    269427
1884    228192    237780
1885    242150    249094
1886    195304    201620
1887    169408    175167
1888    128034    134413
1889    108880    113940
1890     97140    101328
1891     96921    101492
1892     91665     96987
1893     84684     89608
1894    119151    119217
1895    141719    139363
1896    155369    149431
1897    177763    169358
1898    179569    171180
1899    203413    194783
1900    206853    201802
1901    121260    127275
1902     73139     83820
1903     59277     70418
1904    157519    170395
1905     71835     82973
1906     59598     71140
1907     75230     87755
1908    161629    170117
1909    108268    117795
1910     56522     64933
1911     62256     70305
1912     65371     73471
1913     68279     76364
1914    107492    114040
1915    166765    168154
1916    156877    159224
1917    161726    166822
1918    302801    293755
1919    355460    346527
1920    394589    384043
1921-1980

Code: Select all


1921    562615    502622
1922    526360    462169
1923    432335    388093
1924    440401    394973
1925    476290    422032
1926    440127    393402
1927    382846    346717
1928    184585    182830
1929     62404     70916
1930     85415     91491
1931    174285    158832
1932    594105    419354
1933    652114    456428
1934    382768    278701
1935    580671    408025
1936    275947    203133
1937    110037     83600
1938    391298    273821
1939    318464    225038
1940    283555    209102
1941    422236    312701
1942    659491    478429
1943    659875    485840
1944    409585    328487
1945    246159    213629
1946    224922    198039
1947    383077    329538
1948    370632    328550
1949    359522    320093
1950    313282    284082
1951    266150    248156
1952    193467    189306
1953    202677    198189
1954    232772    226237
1955    131513    133230
1956     99518    102899
1957    124527    127532
1958    151662    154022
1959     81349     85967
1960     84486     89304
1961     74549     79967
1962     54476     60202
1963     76658     82069
1964     40371     45816
1965     16244     20899
1966      8634     13532
1967     53506     58998
1968     38178     43761
1969     46320     51716
1970    146789    143226
1971    139404    137826
1972     95489     98359
1973     63533     67944
1974    139107    141099
1975    220096    216001
1976    117427    120991
1977     92800     97687
1978    104814    110243
1979     84501     89659
1980     69434     73424
All Interest Reinvested

Conditions

Code: Select all


Final Balances: 30 Years
80% Stocks / 20% commercial paper
4.2% expenses only
100% Reinvested Interest
1871-1920

Code: Select all


Year   CTVR80N   CTVR80
1871    300841    306441
1872    305754    310373
1873    277586    281786
1874    241872    248477
1875    265413    269367
1876    282750    283849
1877    310333    306676
1878    219358    223210
1879    221854    223076
1880    195688    199658
1881    158210    163788
1882    176197    182059
1883    165841    171058
1884    150183    154772
1885    140963    144396
1886    134090    137230
1887    116348    119130
1888     88590     92036
1889     79563     82190
1890     71078     73042
1891     69430     71961
1892     68614     71390
1893     86949     89420
1894     90859     91132
1895    103687    102203
1896    118836    114779
1897    126699    121334
1898    148426    140404
1899    172008    160985
1900    178885    170517
1901    128069    128817
1902     81481     88413
1903     86271     94099
1904    134814    142040
1905     98870    106632
1906    119150    126856
1907    154761    159793
1908    137921    143613
1909    122650    129318
1910    123023    130548
1911    107608    114426
1912     86117     92328
1913     93825     99235
1914    116499    119310
1915    141411    140097
1916    150328    147538
1917    118588    119365
1918    154713    149671
1919    170343    165203
1920    200071    192930
1921-1980

Code: Select all


1921    271146    242787
1922    253377    222782
1923    223880    199630
1924    223049    198791
1925    257959    224946
1926    273001    236757
1927    249107    217375
1928    168275    154795
1929    156441    144377
1930    180489    162037
1931    218324    185623
1932    372029    274249
1933    349245    255723
1934    278188    211814
1935    352949    259732
1936    258521    200794
1937    183163    151739
1938    285940    217134
1939    260450    201516
1940    217543    174823
1941    242527    191399
1942    319690    244857
1943    328166    254745
1944    215823    182454
1945    136317    124574
1946    130916    120271
1947    181838    162295
1948    168894    155189
1949    165173    152533
1950    142291    133117
1951    130777    125254
1952    101386    101530
1953    109837    109467
1954    123157    121926
1955     91208     92772
1956     86906     88684
1957    105496    106336
1958    108976    110004
1959     91796     93819
1960     99228    100814
1961     90632     92849
1962     96945     98869
1963    103713    104861
1964     95880     97504
1965     84037     86386
1966     98351    100083
1967    129305    127894
1968    144088    141111
1969    173064    165848
1970    220963    203942
1971    201449    188847
1972    158691    153957
1973    113650    114715
1974    115449    115713
1975    125993    125040
1976     81517     84530
1977     63565     67115
1978     58891     62431
1979     46344     49365
1980     38248     40440
More follows.
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Post by JWR1945 »

All Interest Reinvested

Conditions

Code: Select all


Final Balances: 30 Years
80% Stocks / 20% commercial paper
5.2% expenses only
100% Reinvested Interest
1871-1920

Code: Select all


Year   CTVR80N   CTVR80
1871    221265    225384
1872    224879    228275
1873    204161    207250
1874    177894    182752
1875    195208    198117
1876    207959    208767
1877    228246    225557
1878    161335    164168
1879    163171    164070
1880    143926    146846
1881    116361    120464
1882    129591    133902
1883    121974    125811
1884    110458    113833
1885    103676    106201
1886     98622    100931
1887     85573     87618
1888     65157     67691
1889     58518     60450
1890     52277     53722
1891     51065     52927
1892     50465     52506
1893     63950     65767
1894     66825     67026
1895     76260     75169
1896     87402     84418
1897     93186     89240
1898    109165    103266
1899    126510    118403
1900    131568    125413
1901     94193     94743
1902     59929     65027
1903     63451     69209
1904     99154    104469
1905     72718     78427
1906     87633     93301
1907    113825    117526
1908    101439    105626
1909     90208     95112
1910     90482     96016
1911     79144     84159
1912     63338     67906
1913     69007     72986
1914     85684     87751
1915    104006    103040
1916    110564    108513
1917     87220     87792
1918    113790    110081
1919    125285    121505
1920    147150    141898
1921-1980

Code: Select all


1921    199424    178567
1922    186356    163853
1923    164661    146825
1924    164050    146209
1925    189726    165445
1926    200789    174132
1927    183215    159877
1928    123765    113850
1929    115061    106188
1930    132748    119176
1931    160575    136523
1932    273623    201707
1933    256865    188081
1934    204604    155787
1935    259590    191030
1936    190139    147682
1937    134715    111602
1938    210306    159700
1939    191558    148213
1940    160000    128580
1941    178376    140772
1942    235128    180090
1943    241362    187362
1944    158735    134193
1945    100260     91623
1946     96287     88458
1947    133740    119366
1948    124219    114140
1949    121483    112186
1950    104653     97906
1951     96185     92123
1952     74568     74674
1953     80784     80512
1954     90581     89675
1955     67082     68233
1956     63918     65226
1957     77591     78209
1958     80150     80906
1959     67515     69003
1960     72981     74147
1961     66658     68289
1962     71302     72717
1963     76279     77124
1964     70519     71713
1965     61808     63536
1966     72336     73610
1967     95102     94065
1968    105975    103786
1969    127286    121980
1970    162516    149997
1971    148163    138895
1972    116715    113234
1973     83588     84372
1974     84911     85105
1975     92667     91965
1976     59955     62171
1977     46751     49362
1978     43313     45917
1979     34086     36307
1980     28131     29744

All Interest Reinvested

Conditions

Code: Select all


Final Balances: 30 Years
50% Stocks / 50% commercial paper
3.8% withdrawal rates
100% Reinvested Interest
1871-1920

Code: Select all


Year   CTVR50N   CTVR50
1871   521723    540861
1872   521287    537602
1873   454417    469640
1874   404240    426371
1875   410095    423682
1876   435686    440882
1877   451969    439546
1878   324352    330255
1879   356326    356794
1880   274567    285921
1881   236262    252063
1882   264448    281619
1883   231516    246677
1884   196029    208802
1885   195371    203492
1886   163858    171797
1887   144409    151840
1888   111142    119909
1889    90205     96773
1890    78555     83787
1891    75556     81047
1892    76104     83259
1893    61079     67015
1894    76315     74662
1895    87423     82558
1896    88269     79199
1897   101063     88812
1898    97903     86579
1899   121909    108896
1900   122058    113191
1901    78092     83675
1902    59573     73854
1903    48346     63846
1904   103088    115500
1905    52351     66076
1906    46244     60166
1907    48851     61648
1908    97269    102168
1909    74840     84132
1910    38897     48167
1911    38903     47149
1912    43630     52299
1913    43311     51478
1914    62350     66594
1915    94258     90086
1916    96015     92972
1917   107914    108390
1918   194865    172635
1919   234426    210299
1920   257737    229888
1921-1980

Code: Select all


1921   337983    246931
1922   310885    217384
1923   256120    188607
1924   259084    189803
1925   277319    196367
1926   253024    181205
1927   218548    160248
1928   109141     96272
1929    45643     47830
1930    48082     46140
1931    79462     54436
1932   283524    104970
1933   326969    120919
1934   175035     67900
1935   280406    103055
1936   118130     43080
1937    38099      7704
1938   181637     59990
1939   142295     44612
1940   131952     47745
1941   220731     94338
1942   360171    153069
1943   359218    159171
1944   226467    122316
1945   140402     90519
1946   133618     93197
1947   232396    156531
1948   229773    165467
1949   221009    160495
1950   196134    150321
1951   169114    139402
1952   128753    117651
1953   132135    121220
1954   149222    135238
1955    87624     87629
1956    67603     70994
1957    82314     84920
1958   100662    101837
1959    58443     63978
1960    59668     65319
1961    54378     61098
1962    42890     50019
1963    55544     61816
1964    35153     41945
1965    21779     28263
1966    19951     26410
1967    45581     50996
1968    41404     46258
1969    50437     53153
1970   101027     91084
1971    97636     90376
1972    75584     75288
1973    58867     62907
1974   100883    100234
1975   150881    140460
1976    92108     94534
1977    79582     84946
1978    90028     95618
1979    79556     85917
1980    72011     77581
All Interest Reinvested

Conditions

Code: Select all


Final Balances: 30 Years
50% Stocks / 50% commercial paper
5.2% expenses
100% Reinvested Interest
1871-1920

Code: Select all


Year   CTVR50N   CTVR50
1871   193786    199159
1872   193959    198068
1873   176104    179842
1874   158535    165221
1875   164764    167876
1876   170313    169941
1877   182041    176387
1878   134922    137823
1879   131409    131058
1880   122104    125400
1881   104981    110703
1882   115915    121826
1883   108264    113436
1884    97757    102273
1885    90163     93357
1886    85281     88148
1887    74130     76689
1888    58965     62519
1889    51472     54028
1890    45021     46809
1891    44951     47423
1892    45388     48217
1893    54491     56669
1894    54121     53778
1895    59592     57170
1896    66159     60841
1897    69791     63045
1898    80382     70649
1899    91860     78776
1900    97113     86534
1901    74212     73673
1902    54707     61909
1903    59822     68288
1904    80210     85927
1905    62963     70518
1906    71259     77763
1907    87154     89334
1908    78303     81516
1909    71529     76461
1910    72678     78693
1911    63799     69350
1912    51872     57269
1913    54800     58891
1914    64686     65074
1915    75688     70948
1916    79564     72965
1917    64165     62080
1918    81139     72259
1919    89526     80175
1920   104628     92493
1921-1980

Code: Select all


1921   135599    101392
1922   125620     89951
1923   111767     82789
1924   111328     82370
1925   127265     89169
1926   134355     92867
1927   122890     86193
1928    85188     67660
1929    79387     63561
1930    90374     68008
1931   107162     71392
1932   177094     85880
1933   166062     79259
1934   133605     70595
1935   168303     81927
1936   125150     69918
1937    90720     59143
1938   138112     74020
1939   126493     70943
1940   106868     65402
1941   118439     69499
1942   154751     84611
1943   159530     90147
1944   108214     74363
1945    71432     58231
1946    68994     56953
1947    93901     72785
1948    88954     73413
1949    87374     72914
1950    76225     65467
1951    72158     65282
1952    59579     58933
1953    63877     62570
1954    70795     68420
1955    56396     57569
1956    54485     55971
1957    63588     63786
1958    65873     66256
1959    58301     60078
1960    61694     62873
1961    57745     59743
1962    60425     61974
1963    63231     63819
1964    59535     60763
1965    54105     56320
1966    60598     61878
1967    74923     72400
1968    81934     77558
1969    95240     86085
1970   117364     98049
1971   108462     93655
1972    88598     82135
1973    67092     67212
1974    67524     66786
1975    72805     70722
1976    52322     55226
1977    43882     47745
1978    41430     45361
1979    35285     38915
1980    31710     34610
More follows.
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Post by JWR1945 »

Only 20% of Interest Reinvested

Conditions

Code: Select all


Final Balances: 30 Years
80% stocks / 20% commercial paper
4.2% expenses
20% Reinvested Interest
1871-1920

Code: Select all


Year   CTVR80N   CTVR80
1871    272877    242996
1872    279116    247234
1873    253629    225350
1874    218693    199336
1875    244542    216581
1876    263050    228378
1877    291014    246511
1878    202613    179009
1879    207430    179177
1880    179920    160123
1881    142436    131332
1882    159177    146210
1883    150213    137343
1884    136222    124474
1885    128659    116281
1886    122649    110607
1887    106426     96265
1888     79792     74163
1889     72354     66191
1890     65061     58711
1891     63045     57659
1892     61815     57126
1893     79909     72013
1894     84847     73355
1895     97865     82239
1896    113238     92645
1897    121075     97850
1898    142484    113132
1899    165695    129373
1900    171552    137045
1901    120562    103662
1902     73082     71063
1903     76605     76068
1904    126189    115603
1905     90706     87141
1906    111623    104358
1907    147631    132601
1908    131431    120183
1909    116160    108620
1910    116290    110376
1911    101745     97291
1912    81206     78947
1913     89307     85496
1914    112306    103479
1915    137471    122119
1916    146556    129089
1917    115197    104917
1918    151328    132705
1919    166687    147283
1920    196182    173426
1921-1980

Code: Select all


1921    267967    220524
1922    250791    203064
1923    221449    182463
1924    220713    182393
1925    255715    207011
1926    270746    218211
1927    246987    200426
1928    166353    142946
1929    154670    133654
1930    178730    150098
1931    216696    171981
1932    370574    254863
1933    347881    236885
1934    276708    195337
1935    351303    238323
1936    256704    182941
1937    181186    137126
1938    283806    194875
1939    258132    178881
1940    215027    152950
1941    239883    166180
1942    316643    211414
1943    324619    217742
1944    211932    153042
1945    132403    103190
1946    126890     99025
1947    177037    132832
1948    163486    125621
1949    159514    121881
1950    136764    104885
1951    124353     96689
1952     94254     76760
1953    102362     82065
1954    115080     90280
1955     82858     67986
1956     78453     64635
1957     96680     77332
1958     99676     79358
1959     82217     67119
1960     89598     71769
1961     80940     65664
1962     87380     69901
1963     94332     74175
1964     86553     68919
1965     74674     60827
1966     89037     70532
1967    119930     90283
1968    134592     99768
1969    163616    117873
1970    211494    145904
1971    191964    135372
1972    149375    110748
1973    104904     83162
1974    107076     85281
1975    117462     93108
1976     73076     63176
1977     55294     50382
1978     50898     47330
1979     38727     37876
1980     30739     31422
Only 20% of Interest Reinvested

Conditions

Code: Select all


Final Balances: 30 Years
80% stocks / 20% commercial paper
2.8% conventional withdrawals
20% Reinvested Interest
1871-1920

Code: Select all


Year   CTVR80N   CTVR80
1871    628350    555560
1872    636951    561076
1873    562293    497056
1874    489337    442964
1875    540380    475106
1876    593323    511529
1877    665216    555602
1878    462187    401035
1879    501328    427886
1880    370541    326821
1881    281945    258483
1882    321444    293331
1883    292423    265317
1884    262331    236837
1885    268832    238667
1886    229727    203943
1887    199310    177778
1888    149157    136313
1889    131030    117533
1890    117793    104207
1891    116209    103455
1892    110470     99805
1893    121087    105716
1894    151889    125501
1895    179266    143936
1896    202593    157679
1897    225489    173607
1898    242993    184103
1899    276517    209097
1900    283164    218647
1901    177999    148825
1902    104296     99726
1903     96678     94661
1904    209415    186416
1905    117439    110600
1906    123477    114539
1907    163904    145743
1908    220145    194603
1909    166145    151901
1910    127517    118406
1911    122169    113888
1912    109306    104164
1913    118571    111670
1914    167287    151050
1915    232878    202158
1916    231440    201419
1917    210463    190379
1918    347220    300695
1919    398828    349544
1920    452564    397761
1921-1980

Code: Select all


1921    641369    521059
1922    600893    480778
1923    505758    413913
1924    511637    420166
1925    567447    459420
1926    552392    448794
1927    490290    402748
1928    274557    242615
1929    173996    157839
1930    214016    187331
1931    314580    253435
1932    761753    507054
1933    785168    516888
1934    523436    357459
1935    734905    481547
1936    426476    292704
1937    237953    171884
1938    535476    348131
1939    459018    299840
1940    395234    265161
1941    518802    342437
1942    760405    486173
1943    766805    492403
1944    482631    333146
1945    292296    217395
1946    271408    202878
1947    430044    310630
1948    407729    301476
1949    395518    289964
1950    341341    251628
1951    294263    219520
1952    213588    166434
1953    226614    173553
1954    258345    193153
1955    156020    121231
1956    128212     99834
1957    160273    121331
1958    182001    136872
1959    114731     87775
1960    122044     91475
1961    107702     81523
1962     95679     70971
1963    117538     85656
1964     82947     60463
1965     55847     41007
1966     57889     40956
1967    113943     78040
1968    109550     73429
1969    134569     88274
1970    251769    160719
1971    233149    152499
1972    168787    115870
1973    114444     84325
1974    177681    133539
1975    247740    185806
1976    135210    109900
1977    102772     88295
1978    107988     95301
1979     83299     77869
1980     65648     64558
More follows.
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Post by JWR1945 »

Only 20% of Interest Reinvested

Conditions

Code: Select all

Final Balances: 30 Years
80% stocks / 20% ibonds (2.5%)
4.2% expenses
20% Reinvested Interest
1871-1920

Code: Select all


Year   CTVR80N   CTVR80
1871   271761    238228
1872   278106    242733
1873   252905    222106
1874   218024    196622
1875   244042    214088
1876   262622    225982
1877   290644    244185
1878   202292    177244
1879   207237    177801
1880   179564    158495
1881   142087    129990
1882   158666    144238
1883   149875    135963
1884   135990    123510
1885   128501    115588
1886   122570    110170
1887   106502     96408
1888    79985     74765
1889    72660     67211
1890    65426     59999
1891    63388     58776
1892    62172     58213
1893    80255     73256
1894    85168     74770
1895    98184     83889
1896   113572     94624
1897   121404     99926
1898   142794    115333
1899   165980    131683
1900   171762    138580
1901   120796    104855
1902    73316     71734
1903    76801     76541
1904   126449    116680
1905    91004     88115
1906   111972    105729
1907   148013    134461
1908   131868    122314
1909   116598    110490
1910   116700    112005
1911   102193     99034
1912    81745     80915
1913    89887     87777
1914   112919    106415
1915   138111    125770
1916   147215    133032
1917   115896    108624
1918   152036    136979
1919   167372    151336
1920   196832    177361
1921-1980

Code: Select all


1921   268716    226803
1922   251513    209531
1923   222192    188484
1924   221472    188460
1925   256490    213990
1926   271522    225410
1927   247777    207480
1928   167167    148357
1929   155502    138912
1930   179563    156071
1931   217488    179124
1932   371305    265945
1933   348546    247376
1934   277357    203772
1935   351931    248018
1936   257307    190141
1937   181764    142378
1938   284359    202098
1939   258653    185407
1940   215513    158437
1941   240349    172036
1942   317076    217711
1943   325004    223346
1944   212279    156803
1945   132742    105942
1946   127217    101654
1947   177304    135298
1948   163706    127469
1949   159715    123622
1950   136971    106621
1951   124502     97922
1952    94364     77503
1953   102453     82767
1954   115143     90852
1955    82910     68361
1956    78501     64980
1957    96712     77639
1958    99688     79520
1959    82220     67204
1960    89602     71866
1961    80943     65755
1962    87389     70031
1963    94348     74369
1964    86572     69116
1965    74692     60996
1966    89057     70744
1967   119947     90531
1968   134605     99994
1969   163630    118150
1970   211505    146213
1971   191974    135642
1972   149390    111048
1973   104941     83586
1974   107126     85827
1975   117500     93547
1976    73116     63515
1977    55340     50696
1978    50956     47675
1979    38802     38205
1980    30812     31691

Only 20% of Interest Reinvested

Conditions

Code: Select all


Final Balances: 30 Years
50% stocks / 50% commercial paper
4.2% expenses
20% Reinvested Interest
1871-1920

Code: Select all


Year   CTVR50N   CTVR50
1871   193570    151031
1872   197119    151929
1873   179544    139349
1874   157601    129116
1875   171841    131817
1876   182315    133562
1877   199213    138179
1878   141584    107547
1879   142610    102615
1880   126599     97901
1881   103303     86491
1882   115053     95537
1883   108129     88887
1884    98011     80463
1885    91829     73656
1886    87348     69703
1887    75986     61046
1888    58177     49488
1889    51961     42678
1890    46171     36769
1891    45155     36996
1892    44714     37502
1893    56489     44745
1894    58555     42363
1895    66469     44965
1896    75959     48190
1897    80832     49809
1898    94438     55663
1899   109114     61594
1900   113707     67718
1901    82135     57926
1902    53385     48706
1903    57172     54523
1904    87494     69672
1905    65198     57825
1906    78069     64871
1907   100673     76128
1908    90238     70827
1909    81028     67111
1910    81985     70257
1911    72086     62778
1912    58249     52587
1913    63215     55111
1914    77466     61887
1915    93061     68293
1916    98748     70941
1917    78764     61078
1918   101857     72536
1919   112582     81640
1920   132533     96215
1921-1980

Code: Select all


1921   176419    108005
1922   164333     96652
1923   145886     89636
1924   145524     90047
1925   167426     98234
1926   177038    102709
1927   161786     95440
1928   111020     75313
1929   103509     71239
1930   118478     76284
1931   141632     80043
1932   237145     96686
1933   222374     88522
1934   177955     77946
1935   224717     89267
1936   165618     74830
1937   118402     62077
1938   182446     76274
1939   166190     71096
1940   139012     63307
1941   154423     65985
1942   202789     79178
1943   208036     82189
1944   137403     64910
1945    87336     49396
1946    83742     47526
1947   115670     59806
1948   107427     58755
1949   104650     56450
1950    89821     48897
1951    82048     46254
1952    63176     39758
1953    68162     41271
1954    76063     43699
1955    55805     35842
1956    52947     34352
1957    64417     38891
1958    66313     39607
1959    55319     35171
1960    59808     36318
1961    54283     33963
1962    58242     35192
1963    62519     36272
1964    57629     34480
1965    50155     31678
1966    59106     34845
1967    78430     40869
1968    87660     43932
1969   105874     49369
1970   135900     57034
1971   123759     54780
1972    97174     48505
1973    69356     40528
1974    70876     41849
1975    77659     45374
1976    50037     35832
1977    38986     31352
1978    36349     30507
1979    28933     27009
1980    24343     24828
Only 20% of Interest Reinvested

Conditions

Code: Select all


Final Balances: 30 Years
50% stocks / 50% commercial paper
2.8% conventional withdrawals
20% Reinvested Interest
1871-1920

Code: Select all


Year   CTVR50N   CTVR50
1871   416675    318463
1872   423730    321322
1873   375078    286634
1874   328958    263864
1875   352229    264026
1876   382264    273771
1877   412785    273648
1878   287749    205856
1879   315084    218079
1880   237303    178133
1881   191013    156794
1882   216120    175424
1883   193711    154902
1884   169354    133245
1885   170179    128460
1886   145293    109979
1887   127733     97907
1888    96055     77083
1889    81460     62364
1890    72171     53479
1891    69923     51756
1892    67784     52332
1893    67085     46714
1894    82664     49692
1895    95913     53733
1896   104130     53154
1897   116523     58112
1898   120053     57241
1899   141205     69490
1900   143013     73033
1901    90199     55367
1902    58495     48617
1903    52319     45179
1904   111893     78036
1905    61075     48236
1906    62209     47706
1907    78552     53902
1908   117057     79127
1909    90880     67902
1910    64896     49099
1911    62561     47464
1912    59871     48627
1913    64093     50797
1914    89345     64170
1915   125421     82336
1916   128057     85977
1917   125529     93341
1918   210646    142376
1919   247419    173047
1920   279679    196890
1921-1980

Code: Select all


1921   380242    220048
1922   353048    196429
1923   297274    175237
1924   300473    178215
1925   330458    188799
1926   318634    182685
1927   282559    165637
1928   161920    112131
1929   110027     79755
1930   127292     84128
1931   172599     93167
1932   409398    140334
1933   429999    143973
1934   278541    101416
1935   396486    130908
1936   224845     81771
1937   125652     50159
1938   286329     91191
1939   242944     76864
1940   211590     71446
1941   288926     97797
1942   431527    137402
1943   433346    139446
1944   273447    104419
1945   167067     75745
1946   157570     74168
1947   252979    111130
1948   241185    111739
1949   231177    104117
1950   199659     91790
1951   169828     80577
1952   122726     64252
1953   127344     63620
1954   142997     66799
1955    81926     41478
1956    63837     32115
1957    79017     37122
1958    92002     42368
1959    51967     23689
1960    53724     22780
1961    46396     19439
1962    36198     12753
1963    47460     16630
1964    27537      6938
1965    14230       668
1966    12202    (1779)
1967    38215      7225
1968    33569      3910
1969    44750      6689
1970   105379     24944
1971   100240     25555
1972    72757     20062
1973    52613     18165
1974    93178     40008
1975   137248     61014
1976    75253     39692
1977    59098     35717
1978    64900     42734
1979    52788     40258
1980    44113     37941
More follows.
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Post by JWR1945 »

Only 20% of Interest Reinvested

Conditions

Code: Select all


Final Balances: 30 Years
50% stocks / 50% commercial paper
3.3% conventional withdrawals
20% Reinvested Interest
1871-1920

Code: Select all


Year   CTVR50N   CTVR50
1871   374771    284582
1872   380953    287412
1873   334174    254087
1874   293003    233401
1875   311873    231969
1876   340978    242405
1877   366796    239486
1878   254059    177994
1879   285659    195363
1880   203610    151116
1881   163051    132823
1882   185581    149344
1883   163331    129154
1884   140705    108691
1885   145391    107142
1886   118754     87735
1887   104885     78710
1888    78251     61111
1889    64785     47857
1890    57316     40936
1891    55277     38768
1892    53021     39143
1893    45122     28170
1894    62241     33110
1895    73101     36310
1896    77084     33690
1897    88761     38560
1898    84746     34017
1899   100857     44889
1900   100228     45385
1901    56954     30448
1902    36863     28032
1903    27309     20485
1904    79302     50107
1905    32806     22105
1906    26408     17246
1907    32088     17784
1908    83739     50699
1909    58422     39703
1910    27222     15652
1911    30418     18218
1912    35562     25713
1913    37555     26753
1914    58753     38442
1915    91900     56003
1916    91590     58704
1917   100618     73310
1918   187058    124216
1919   223954    154893
1920   249986    174236
1921-1980

Code: Select all


1921   342138    194446
1922   317350    173431
1923   262700    152670
1924   266688    155933
1925   288867    163488
1926   269156    153593
1927   235804    137868
1928   124126     86902
1929    67480     51191
1930    78833     53314
1931   118318     61709
1932   340012    107298
1933   373166    116493
1934   221353     72691
1935   332262    100646
1936   165481     51409
1937    76946     21816
1938   227833     61644
1939   186468     47870
1940   165846     46165
1941   247732     75613
1942   386736    114362
1943   385727    114962
1944   239715     84063
1945   144423     59591
1946   135390     58856
1947   228651     95039
1948   219705     96389
1949   209578     88790
1950   181342     78800
1951   150854     67173
1952   106681     51836
1953   109128     50182
1954   122828     52470
1955    63024     27349
1956    43423     17209
1957    54422     20382
1958    68585     26136
1959    28007      6787
1960    27381      5025
1961    22064      2503
1962     7666    (6124)
1963    18369    (2196)
1964   (2174)   (12581)
1965   (13412)   (18338)
1966   (21235)   (23167)
1967   (2087)   (16104)
1968   (13145)   (21902)
1969   (10901)   (21891)
1970    42539    (4877)
1971    43777    (2798)
1972    27361    (5507)
1973    20334    (2945)
1974    67230     22007
1975   115094     44646
1976    58625     25249
1977    46226     23256
1978    54648     32034
1979    44830     31218
1980    37363     29798

Only 20% of Interest Reinvested

Conditions

Code: Select all


Final Balances: 30 Years
50% stocks / 50% ibonds (2.5%)
4.2% expenses
20% Reinvested Interest
1871-1920

Code: Select all


Year   CTVR50N   CTVR50
1871   190780    143813
1872   194593    145211
1873   177734    134511
1874   155930    124907
1875   170593    128214
1876   181245    130238
1877   198288    135090
1878   140781    105071
1879   142128    100838
1880   125707     95494
1881   102431     84381
1882   113776     92436
1883   107284     86763
1884    97431     78991
1885    91436     72621
1886    87151     69096
1887    76176     61362
1888    58659     50517
1889    52725     44380
1890    47082     38876
1891    46010     38882
1892    45607     39384
1893    57355     46775
1894    59359     44499
1895    67268     47318
1896    76794     50878
1897    81654     52565
1898    95212     58473
1899   109827     64423
1900   114232     69675
1901    82719     59670
1902    53969     49949
1903    57662     55466
1904    88146     71429
1905    65941     59546
1906    78941     67155
1907   101628     79001
1908    91330     74116
1909    82123     70129
1910    83011     72955
1911    73206     65688
1912    59598     55955
1913    64665     58913
1914    79000     66446
1915    94660     73608
1916   100397     76596
1917    80512     66640
1918   103628     78638
1919   114296     87467
1920   134159    101826
1921-1980

Code: Select all


1921   178293    115954
1922   166138    104650
1923   147744     97342
1924   147422     97852
1925   169362    106873
1926   178978    111533
1927   163761    104208
1928   113053     82773
1929   105590     78608
1930   120560     84261
1931   143613     88767
1932   238973    107650
1933   224038     98746
1934   179578     86691
1935   226287     98697
1936   167125     82446
1937   119848     68204
1938   183829     83579
1939   167492     77793
1940   140228     69168
1941   155590     71992
1942   203871     85291
1943   208998     87626
1944   138272     68986
1945    88184     52724
1946    84558     50712
1947   116338     62642
1948   107976     60953
1949   105152     58500
1950    90339     50967
1951    82422     47730
1952    63449     40713
1953    68390     42137
1954    76220     44362
1955    55934     36310
1956    53068     34785
1957    64497     39240
1958    66344     39774
1959    55326     35249
1960    59816     36405
1961    54292     34046
1962    58265     35323
1963    62561     36477
1964    57676     34696
1965    50200     31872
1966    59157     35078
1967    78474     41116
1968    87692     44142
1969   105908     49613
1970   135927     57281
1971   123782     54997
1972    97211     48774
1973    69449     40988
1974    71002     42451
1975    77755     45849
1976    50137     36248
1977    39102     31772
1978    36495     30990
1979    29119     27523
1980    24525     25282
No more results follow.

Have fun.

John R.
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Post by JWR1945 »

I wish to add some more comments relating to this question.
hocus2004 wrote::
Is it mathematically correct to determine the take-out number that insures against portfolio loss at the end of 30 years by subtracting 3.3 percent from the SWR? I don't know how the numbers work well enough to say. But if that is so, it means that those with 80 percent stock portfolios who retire today cannot be sure that taking 0 percent out per year will leave them at the end of 30 years with the same level of financial independence as they possess today.
The answer is no, but a better explanation is in order.

If a person withdraws nothing from an 80% stock portfolio, his portfolio balance can decrease for several years even though all of his interest and dividends are reinvested. Historically, however, his portfolio has recovered fully by thirty years and it has grown.

The same is not true when there are withdrawals. Withdrawing from the portfolio has the effect of emphasizing shorter-term losses. With zero withdrawals, no shares of stock ever have to be sold. When there are withdrawals, stock shares have to be sold and/or new shares are not purchased. This has a long-term effect. There is much less of an ability to recover in later years when stock market returns are better.

Without withdrawals, only the cumulative returns of thirty years come into play. With withdrawals, the sequence of returns is important. The first decade's investment results are the most important. Along the same lines, if an investor is still in the accumulation stage and making deposits, the last decade's investment results are the most important.

Have fun.

John R.
JWR1945
***** Legend
Posts: 1697
Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

Post by JWR1945 »

This may be the best way to characterize rebalancing versus not rebalancing.
1) Rebalancing reduces the amount of variation in the final balances.
2) When both investments produce similar returns, there is a slight advantage for rebalancing when focusing on worst case results.
3) When the two investments produce substantially different returns, there is a substantial disadvantage with rebalancing.
4) When graphed versus earnings yield, both rebalancing and not rebalancing have similar minimum values. Maximum values are much greater when there is no rebalancing.

As an additional note regarding Safe Withdrawal Rates:

Although we emphasize high degrees of safety, we do not limit our investigations to the point of excluding other factors entirely. We are still normalizing our comparisons to high degrees of safety. We found first that a decision to rebalance has only a minimal effect on safety. Then we looked at the implications. There can be large differences in final balances depending upon whether we rebalance.

Have fun.

John R.
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