Surviving Rates versus Half Failure Rates
Moderator: hocus2004
Surviving Rates versus Half Failure Rates
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.
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.
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.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.
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.
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.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.
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.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.
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.
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?
Yes. I have just posted a complete set of results for 80% stocks: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?
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.]
CVTR80 versus Earnings Yield dated Sat Aug 07, 2004.
http://nofeeboards.com/boards/viewtopic ... 059#p23059
I responded on the new thread.
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.
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.
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.
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.
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.
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.
Conditions
Code: Select all
Final Balances: 30 Years
80% Stocks / 20% commercial paper
3.3% withdrawal rates
100% Reinvested Interest
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
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
Conditions
Code: Select all
Final Balances: 30 Years
80% Stocks / 20% commercial paper
3.8% withdrawal rates
100% Reinvested Interest
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
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
Conditions
Code: Select all
Final Balances: 30 Years
80% Stocks / 20% commercial paper
4.2% expenses only
100% Reinvested Interest
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
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
Conditions
Code: Select all
Final Balances: 30 Years
80% Stocks / 20% commercial paper
5.2% expenses only
100% Reinvested Interest
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
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
Conditions
Code: Select all
Final Balances: 30 Years
50% Stocks / 50% commercial paper
3.8% withdrawal rates
100% Reinvested Interest
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
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
Conditions
Code: Select all
Final Balances: 30 Years
50% Stocks / 50% commercial paper
5.2% expenses
100% Reinvested Interest
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
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
Conditions
Code: Select all
Final Balances: 30 Years
80% stocks / 20% commercial paper
4.2% expenses
20% Reinvested Interest
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
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
Conditions
Code: Select all
Final Balances: 30 Years
80% stocks / 20% commercial paper
2.8% conventional withdrawals
20% Reinvested Interest
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
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
Conditions
Code: Select all
Final Balances: 30 Years
80% stocks / 20% ibonds (2.5%)
4.2% expenses
20% Reinvested Interest
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
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
Conditions
Code: Select all
Final Balances: 30 Years
50% stocks / 50% commercial paper
4.2% expenses
20% Reinvested Interest
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
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
Conditions
Code: Select all
Final Balances: 30 Years
50% stocks / 50% commercial paper
2.8% conventional withdrawals
20% Reinvested Interest
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
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
Conditions
Code: Select all
Final Balances: 30 Years
50% stocks / 50% commercial paper
3.3% conventional withdrawals
20% Reinvested Interest
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
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
Conditions
Code: Select all
Final Balances: 30 Years
50% stocks / 50% ibonds (2.5%)
4.2% expenses
20% Reinvested Interest
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
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
Have fun.
John R.
The answer is no, but a better explanation is in order.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.
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.
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.