A Survey using Minimum Balances

Research on Safe Withdrawal Rates

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JWR1945
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A Survey using Minimum Balances

Post by JWR1945 »

I have taken a break from my latest calculator update, which will be named the Deluxe Calculator V1.1.

I am in the process of adding numerous data summaries similar what is already in rows 1 through 9 and columns L through P. I have completed my first new area. It tells us how many times the PORTFOLIO BALANCE would have fallen below a minimal balance that we specify. We can choose whether the threshold is in real dollars or nominal dollars. The range of years summarized remains as specified by cells M1 and M2.

I set the initial balance equal to $100000. I set the minimum balance threshold at $50000. I chose to use inflation adjusted (real) dollars. I selected start years 1921 through 1980. I set expenses equal to 0.20%.

I looked at a variety of portfolios.

I varied withdrawal rates as a percentage of the initial balance with adjustments to match inflation. I have focused on 30-year portfolio lifetimes.

I determined withdrawal rates in increments of 0.1%. I determined the minimum rates with 1 failure, 7 failures, 13 failures and 31 failures and then subtracted 0.1%. There are 60 historical sequences that begin from 1921 to 1980.

Data collection was very simple. I set up a portfolio in the traditional manner. I varied withdrawal rates in cell B9. I read the number of 30-year failures from cell W6, which is in a new summary table, instead of M6, which shows the number of portfolios that would have been depleted entirely (i.e., with a threshold of zero dollars).

In the results that follow, failure means that a portfolio's balance fell below its threshold (of 50% of its initial balance in real dollars) within 30 years.

Conventional Portfolios

I looked at HDBR50 first. It consists of 50% stocks and 50% commercial paper. Its traditional Historical Surviving Withdrawal Rate (HSWR or Historical Database Rate) is 3.9% (or, more precisely, 3.91%). The portfolio would have fallen below 50% of its initial balance (in real dollars) at the levels indicated. It would have fallen below threshold in at least one more sequence at a withdrawal rate 0.1% higher than what is listed.

No failures: 2.8%.
Six failures (10%): 3.5%.
Twelve failures (20%): 3.7%.
Thirty failures (50%): 4.6%.

The first failure was with start year 1937. At a withdrawal rate of 3.6%, the (six) failures occurred with start years 1936, 1937, 1965, 1966, 1968 and 1969.

I looked at HDBR80. It consists of 80% stocks and 20% commercial paper. Its traditional Historical Surviving Withdrawal Rate (HSWR or Historical Database Rate) is 3.9% (or, more precisely, 3.95%). The portfolio would have fallen to below 50% of its initial balance (in real dollars) at the levels indicated. It would have fallen below threshold in at least one more sequence at a withdrawal rate 0.1% higher than what is listed.

No failures: 2.4%.
Six failures (10%): 3.1%.
Twelve failures (20%): 3.6%.
Thirty failures (50%): 5.5%.

The first failure was with start year 1966. At a withdrawal rate of 3.2%, the (six) failures occurred with start years 1965-1969 and 1973.

I looked at HDBR50T2. It consists of 50% stocks and 50% TIPS at a 2% (real) interest rate. Its traditional Historical Surviving Withdrawal Rate (HSWR or Historical Database Rate) is 3.9%. The portfolio would have fallen to below 50% of its initial balance (in real dollars) at the levels indicated. It would have fallen below threshold in at least one more sequence at a withdrawal rate 0.1% higher than what is listed.

No failures: 3.3%.
Six failures (10%): 3.6%.
Twelve failures (20%): 3.9%.
Thirty failures (50%): 5.0%.

The first failure was with start year 1966. At a withdrawal rate of 3.7%, the failures occurred with start years 1962, 1964, 1965, 1966, 1968 and 1969.

I looked at HDBR80T2. It consists of 80% stocks and 20% TIPS at a 2% (real) interest rate. Its traditional Historical Surviving Withdrawal Rate (HSWR or Historical Database Rate) is 3.9%. The portfolio would have fallen to below 50% of its initial balance (in real dollars) at the levels indicated. It would have fallen below threshold in at least one more sequence at a withdrawal rate 0.1% higher than what is listed.

No failures: 2.5%.
Six failures (10%): 3.2%.
Twelve failures (20%): 3.8%.
Thirty failures (50%): 5.6%.

The first failure was with start year 1966. At a withdrawal rate of 3.3%, the (seven) failures occurred with start years 1964-1969 and 1973.

Switching Portfolios

All portfolios consisted of stocks as represented by the S&P500 index (with all dividends reinvested) and 2% TIPS.

With two thresholds:

The simplest approach uses two thresholds and three stock allocations. The best choices are P/E10 thresholds of 11 and 24 and stock allocations of 100%-30%-0%, respectively.

Its traditional Historical Surviving Withdrawal Rate (HSWR or Historical Database Rate) is 5.2%. The portfolio would have fallen to below 50% of its initial balance (in real dollars) at the levels indicated. It would have fallen below threshold in at least one more sequence at a withdrawal rate 0.1% higher than what is listed.

No failures: 0.7%.
Six failures (10%): 4.3%.
Twelve failures (20%): 4.5%.
Thirty failures (50%): 5.6%.

This is a very strange result. It can be traced to the dummy data after 2002. The dummy data introduce heavy losses into hypothetical portfolios. Examining the real portfolio balances, it was these late declines that brought the portfolios down for start years 1976-1980.

The first failure occurred with the 1980 sequence. The second was in 1979. The third was in 1978. The fourth was in 1977. The fifth was in 1976. The sixth and seventh occurred at a withdrawal rate of 4.4%. They were in 1956 and 1959.

Without the effects caused by the dummy data, the first failure occurred at a withdrawal rate of 4.3%.

[It was this anomaly that caused me to reexamine the data and to report the start years associated with first few failures.]

With four thresholds:

The best choice with four thresholds and five stock allocations are 9-12-21-24 or 9-13-21-24 (with no preference) with 100%-50%-30%-20%-0%, respectively. There is relatively little sensitivity to changing the lowest adjustable allocation or the lower middle P/E10 threshold.

My choice was to us 9-12-21-24 and 100%-50%-30%-20%-0%.

Its traditional Historical Surviving Withdrawal Rate (HSWR or Historical Database Rate) is 5.2%. The portfolio would have fallen to below 50% of its initial balance (in real dollars) at the levels indicated. It would have fallen below threshold in at least one more sequence at a withdrawal rate 0.1% higher than what is listed.

No failures: 1.0%.
Six failures (10%): 4.4%.
Twelve failures (20%): 4.5%.
Thirty failures (50%): 5.2%.

This strange result follows the earlier pattern (with two thresholds and three allocations). The first failure occurred in 1980. The failures at 4.3% were for start years 1976-1980. At 4.4%, the new failures were with start years of 1956 and 1959.

Without the effects caused by the dummy data, the first failure occurred at a withdrawal rate of 4.4%.

Comments

This is a peek at the kind of information that we will be able to collect easily with the new Deluxe Calculator V1.1A.

This report makes use of only the first of the new data summaries. There will be more.

It took about three hours total to put this together, including this write up.

Have fun.

John R.
JWR1945
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Location: Crestview, Florida

Post by JWR1945 »

Whenever switching is selected, the dummy data causes the portfolio to lose 18.64% per year from 2004 through 2010.

Here are the details.

The dummy data prices and dividend amounts decline 20% per year starting in 2003. The last real data are in column EC for 2002. Dummy prices are in ED184 through EK184. Dummy dividend amounts are in ED185 through EK185. The last value of P/E10 is in cell EC186. Cells ED186 through EK186 are all blanks. Blank cells are treated as if they were set to zero.

Whenever switching is used, the switching logic (in row 182) typically selects 100% fixed income for 2003 and 100% stocks from 2004 through 2010. For 2003, the switching logic (in cell ED182) depends upon the contents of cell EC186 (which is P/E10 for 2002). Typically, that causes the fixed income allocation to be 100% (and the stock allocation to be 0%) because P/E10 was still at bubble levels in 2002 (P/E10 = 30.3). For 2004 through 2010, the switching logic (in cells EE182 through EK182) selects 100% stocks because the switching logic depends upon the contents of cells ED186 through EJ186, which are all blanks (and all are assigned a value of zero).

There is a small, positive dividend that reduces the annual stock losses (in the dummy data) in years 2004 through 2010 from 20.00% to 18.62%.

Have fun.

John R.
hocus2004
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Post by hocus2004 »

Big Scary Numbers do me in every time, as you know. It is always a help for me when you include at the bottom of one of these data-rich posts a statement as to the significance of the findings. I'll set forth my thought as to one of the uses to which the findings above might be put. But please understand that I am just guessing, and am happy to be corrected in what I say below.

The failure to take into account the effect of valuation changes is not the only serious flaw of the conventional methodology studies. Another big problem is that they employ an extremely artificial assumption that the investors who rely on their safety assessments will be able to "qualify" for the results reported. The conventional studies assume that investors using them will stick with their stock allocations regardless of the extent of the portfolio declines they experience in the early years of their retirements. The REHP study says that a 4 percent withdrawal "worked" for a hypothetical retiree who handed in his resignation in 1929, but the calculations backing this finding assume that the hypothetical retiree never lowered his 74 percent allocation to stocks even a tiny bit despite a price drop of 90 percent. Had he lowered the stock allocation sometime during the 90 percent drop, his retirement would have gone bust prior to the end of the 30-year time-period examined.

This analytical framework is an exercise in pure silliness, of course. It may well be that there has never been a single retiree in the history of Planet Earth who behaved in the way that all readers of the conventional studies must behave if they hope to have the hypothetical reported on in these studies apply to them. I believe that realistic SWR analyses need to be rooted in more reasonable assumptions.

It seems to me that the findings you have put forward above could be used to develop more realistic analytical approaches. Instead of showing what withdrawal rate survives in a hypothetical circumstance that is unlikely ever to occur in the real world, you are providing aspiring retirees insights as to what are the probabilities in various circumstances of a portfolio value drop of 50 percent (and at what stage in the retirement this sort of portfolio value drop is most likely to take place). Those who believe that a 50 percent drop is the greatest loss that they could sustain without reducing their stock allocation below 74 percent could use this information to assess whether that allocation is a good one for them or not.

Is that one of the purposes for which you foresee investors making use of this type of analysis?
JWR1945
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Post by JWR1945 »

Is that one of the purposes for which you foresee investors making use of this type of analysis?
It could be. I am trying to find out what people are interested in.

Sometimes it helps people to have an example in front of them, something tangible. That way, they can say, "I want something like that, but a little bit different." Then they can describe the differences.

I will shortly be able to introduce similar thresholds on the amount withdrawn (as a total and/or as dividends and/or as interest). That is something that we have not been able to look at before. Many people like to think in terms of making a basic, minimal withdrawal plus a fraction of their dividends and/or a fraction of their interest plus dividends and/or a fraction of the amount that their portfolio has grown from the previous year. The latter is what Gummy called Sensible Withdrawals, except that Gummy added an upper limit on how much he would remove.

When we start looking at amounts withdrawn, we will learn quite a bit about the stability of the income streams from complex withdrawal strategies. Is it always boom or bust? Does it change abruptly or gradually? What are the long-term effects of earlier actions?

I don't know what the best questions to answer are. I have remembered that some people are interested in having a floor on their portfolio's decline. I used that as a starting point. What I am really after is having a lot of good questions to look into.

As a side comment, there are a couple of interesting facts that came out during this investigation. The first is a repeat, but it is worth remembering. When using the conventional methodology, the difference in between a 50% stock portfolio and an 80% stock portfolio is very small, less than 0.1%. This difference is smaller than originally reported because withdrawals are now broken into two parts, one at the beginning of the year and the other at the end of the year. The other is that the high volatility of an 80% stock holding causes substantial declines even when a portfolio eventually recovers. Such portfolios get saved by high growth, but only at the cost of a roller coaster ride that many people would find unpleasant.

Another observation is that switching stock allocations still offers a substantial advantage even when the criteria is changed from avoiding bankruptcy to staying above a minimal threshold. [It didn't look that way at first. That is why I started looking into when failures occurred and why.]

Have fun.

John R.
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