SWR Calculators
Updated: August 29, 2006
You may download several of my Safe Withdrawal Rate calculators from my Yahoo Briefcase. You must register with Yahoo, but there is no charge.
I have updated the data in my main calculator. I call it Deluxe Calculator V1.1A08a. I have placed it in the Deluxe V1.1A08a folder.
Briefcase of SWR Calculators
All of my calculators are modifications of the Retire Early Safe Withdrawal Calculator, Version 1.61, dated November 7, 2002. John Greaney built the Retire Early Safe Withdrawal Calculator and he has made it available to the public from his website.
Retire Early Home Page
This is an outline of the changes that I made to my Deluxe Calculator V1dot1A08 so that I could investigate TIPS Ladders.
TIPS Ladder Calculators
These calculators use the historical sequence method to determine Historical Surviving Withdrawal Rates. The historical sequence method uses actual, historical returns in their actual sequences to determine what would have happened to a hypothetical portfolio.
The other major approach for estimating portfolio safety is to use a Monte Carlo model. With a Monte Carlo model, annual returns are picked at random from a probability distribution that has been determined from analyzing historical data.
Monte Carlo models have great statistics but uncertain accuracy. That is, they generate a large number of sequences, typically 1000 or 10000, but their realism is uncertain.
The historical sequence approach has great realism since all of the sequences have actually occurred, but limited statistics. The longest history is from 1871 through the present. This corresponds to 103 complete 30-year sequences and there is considerable data overlap.
Detailed mathematical analysis of Historical Surviving Withdrawal Rates show that there is the equivalant of one completely independent data point (or degree of freedom) roughly once every seven years.
When we isolate the effects of valuations, however, we pick up one degree of freedom in less than two years. By far, the greatest source of randomness in Historical Surviving Withdrawal Rates is associated with valuations at the start of retirement. Most of this randomness is found in the year-to-year price changes. The effect of data overlap is muted in comparison.
Calculator Description
This article will help you understand my Deluxe Calculator V1.1A08a.
Calculator Description
Problem Downloading Calculators?
I have written a NOTE for those of you who have had problems downloading calculators from my Yahoo Briefcase.
Problem Downloading Calculators? NOTE
Using P/E10
This tells you how to use P/E10 with my calculators.
I use P/E10 to vary allocations. This is known as Switching (allocations). I also use P/E10 extensively in data analysis.
Using P/E10
Unclemick 01 Calculator
I have put a new calculator into my Yahoo Briefcase. It is the Deluxe Calculator V1.1A08aUM01. I call it the Unclemick 01 Calculator for short.
Yahoo Briefcase
[See my NOTE about downloading calculators. It may be necessary for you to use the FIREFOX browser. It is free.]
Unclemick wrote a Letter to the Editor suggesting that I use the Dow Jones Utilities Average in my research.
I started with a copy of the Deluxe Calculator V1.1A08a. I replaced the January S&P500 prices from 1929-2005 in row 149 with the January prices of the Dow Jones Utilities Average.
I scaled the January S&P500 prices from 1871-1929 by multiplying them by the Dow Jones Utilities price in 1929 (97.92) divided by the S&P500 price in 1929 (24.86). The price scale factor is 3.9389.
I replaced the January S&P500 dividend amounts from 1929-2005 in row 163 with the January dividend amounts of the Dow Jones Utilities Average.
I scaled the January S&P500 dividend amounts from 1871-1920 by multiplying them by the Dow Jones Utilities Average dividend amounts in 1929 (3.04) divided by the S&P500 dividend amount in 1929 (0.86). The dividend scale factor is 3.5297.
I changed some words in columns D through H, rows 1-3.
Otherwise, the Unclemick 01 Calculator is identical to the Deluxe Calculator V1.1A08a.
Keep in mind that the dividend amounts are only approximate. I determined them by working with a downloaded chart of yields and then multiplying by prices.
Valuation-Informed Indexing (Lucky 7) Calculators
I am placing a series of simple calculators into my Yahoo Briefcase. I call them Valuation-Informed Indexing (Lucky 7) Calculators. Or Lucky 7 Calculators for short.
Unlike my research calculators, these will be simple to use. In essence, they present the formulas that I have already generated in a more convenient form.
These calculators are small, typically using 20 to 30 KBytes.
I believe that it would be easy to host these calculators at a more convenient location. Unfortunately, doing so is beyond my software capabilities.
These are the titles of the calculators that I have placed into my Lucky 7 Calculators folder:
1) Balances with 0% TIPS
2) Balances with 1% TIPS
3) Balances with 2% TIPS
4) Dollar Cost Averaging
5) Gummy Slices Stocks
6) Safe Withdrawal Rates
7) Stock Returns
8) TIPS
9) Time to Catch Up
10) Growth with Switching
Yahoo Briefcase
[See my NOTE about downloading calculators. It may be necessary for you to use the FIREFOX browser. It is free.]
I developed new formulas for the following calculators:
1) Balances with 0% TIPS
2) Balances with 1% TIPS
3) Balances with 2% TIPS
I have summarized the conditions and equations in Balances with TIPS Calculators.
Balances with TIPS Calculators
I have added some pictures to my Lucky 7 Calculators folder. They show how real, annualized stock returns vary with P/E10. They are Microsoft Word documents.
P/Ex Data
I have calculated values of Professor Shiller’s P/Ex for 1, 5, 15, 20, 25 and 30 years to go along with P/E10. I have put annual data (that is, thinned from monthly data) into my Yahoo Briefcase. Download the file in the PEx versus Dates Folder. It is a Microsoft Word document. It includes several graphs.
Yahoo Briefcase
UPDATE: I intended to create a calculator that would allow switching in accordance with P/Ex, where x is no longer limited to 10 years.
I will not build the new calculator after all. P/E10 turned out to be the best choice among all of the timeframes.
Long-Term Stock Returns
I have added a spreadsheet with S&P500 real, annualized, total returns to my Lucky 7 Calculators folder.
When asked for a single number, I report the long-term real, annualized, total return of the S&P500 as 6.8%.
If you go back before the modern era, this number drops to 6.3% to 6.6%.
I have added a Growth with Switching calculator to the Lucky 7 Calculators folder as well. It shows what happens after 30 years if you switch among 100% stocks, 50% stocks-50% TIPS and 100% TIPS according with P/E10 at the beginning of each decade.
Yahoo Briefcase
The Big Project
I have set aside Current Research H for the Big Project. I am building a slew of calculators to display our results. I am placing them into my Yahoo Briefcase for downloading.
This includes an SWR Calculator where you enter P/E10 and TIPS interest rates. You can see what happens to your odds for all S&P500/TIPS allocations in increments of 10%. If you don't know P/E10, just look at the display. It includes the S&P index value.
Just be sure to read the note about the TIMING MISMATCH. Otherwise, the results can be misleading when the stock allocation is lower than 20%.
I have just added Dividend Calculators A and B. I based them on Dividend-Based Design Example. They allow you to estimate dividend growth. The estimates are in terms of the income stream, dividend amounts, not dividend yields, which vary with price.
All of the numbers include inflation adjustments (i.e., real dollars).
You can read all of the details in Current Research H, the Big Project. All of these new calculators are in the Big Project folder in my Yahoo Briefcase. I have listed the newest as Dividend Calc A and Dividend Calc B.
Current Research H: The Big Project
Dividend-Based Design Example
Yahoo Briefcase
UPDATE: I have continued adding calculators to Current Research H. These include Constant Terminal Value Rate Calculator A (CTVR Calc A) and Half Constant Terminal Value Rate Calculator A (HCTVR Calc A). Constant Terminal Value Rates (CTVR) are withdrawal rates that leave the balance at the end of a period identical to the initial balance (plus inflation). Half Constant Terminal Value Rates (HCTVR) leave a final balance of one-half of the initial balance (plus inflation).
Half Constant Terminal Value Rates are useful for retirees who have a reasonable chance of living longer than the 30-year planning period. They can look upon long life as a blessing even if their retirement portfolio disappoints.
For young retirees, this defines an intermediate level of risk. It is not as restrictive as a Safe Withdrawal Rate. They can relax their safety demands at the Constant Terminal Value Rate, while maintaining a high level of safety at the Half Constant Terminal Value Rate.
UPDATE: I have added several more calculators with Terminal Value Rates TVR other than zero, Variable Terminal Value Rates VTVR and Compact Variable Terminal Value Rates CVTVR. Keep scrolling down to read about them.
Variable Terminal Value Rate Calculator A
I have added the Variable Terminal Value Rate Calculator A to my Yahoo Briefcase. It interpolates withdrawal rates for balances between 0% and 100%.
Constant Terminal Value Rates (CTVR) are withdrawal rates that leave the balance at the end of a period identical to the initial balance plus inflation. Half Constant Terminal Value Rates (HCTVR) leave a final balance of one-half of the initial balance (plus inflation). I use my 30-year Safe Withdrawal Rate calculator for balances of zero at Year 30.
This adds flexibility for traditional retirees who have a reasonable chance of living longer than the 30-year planning period. This allows younger retirees to look at intermediate levels of risk.
This is another product of Current Research H: The Big Project.
Current Research H: The Big Project
Yahoo Briefcase
Variable Terminal Value Rate Calculator B
My latest Variable Terminal Value Rate Calculator B identifies optimal stock allocations (subject to constraint B).
Constraint B is that stock and TIPS allocations are both between 20% and 80%. This is similar to Benjamin Graham’s constraint (Constraint A) that both stock and bond allocations remain between 25% and 75%.
I find it very interesting to see the strong influence of high valuations. When valuations are in the reasonable range (i.e., whenever P/E10 is less than 20), the optimal stock allocation is almost always 80%, the largest percentage that I allow. Low TIPS interest rates and high terminal value percentages also favor high stock allocations.
Today’s story is new. Today’s valuations are unusually high. Today’s P/E10 is 26.8. Requiring high levels of safety has a great influence at today’s valuations. It had minimal influence in the past.
I have included some computational details in Current Research H.
The calculator is in the Big Project folder in my Yahoo Briefcase.
I have just added Variable Terminal Value Rate Calculator C to my Yahoo Briefcase. It too is in the Big Project folder. I placed an extra copy of the optimal allocations and withdrawal rates in a more convenient location (columns M through Q, rows 1 through 9). Otherwise, it is identical to Variable TVR Calc B.
Current Research H: The Big Project
Yahoo Briefcase
Latch and Hold Calculators
I am building calculators that latch onto a high and/or low P/E10 threshold for a specified number of years. I have put my Latch and Hold LH01 and LH02 calculators dated June 8, 2006 into my Yahoo Briefcase. These calculators will give us better insight as to what happens if you stick with an allocation for several years after P/E10 passes an extreme level.
LH01 and LH02 are very large even though I have placed them into self extracting zip files. The new software starts in row 8000. It calculates an alternative for P/E10, which is found in row 186.
I have added LH Spreadsheet A, which calculates the withdrawal rates of the Latch and Hold portfolios in Current Research I: Latch and Hold. You enter P/E10 and the percentage balance of your portfolio at year 30.
[For ease of use, the spreadsheet also converts P/E10 into current S&P500 values and displays the result.]
Look in the Latching Calculators folder in my Yahoo Briefcase.
UPDATE: I have set aside Current Research I for Latch and Hold.
Current Reseach I: Latch and Hold
Yahoo Briefcase
Compact VTVR Calculators
I have made some compact versions of my Variable Terminal Value Rate (Compact VTVR or CVTVR) Calculators. They are part of Current Research H: The Big Project. I have placed them into the Big Project folder in my Yahoo Briefcase. My latest version, CVTVR D adds a graphical display. It also has TIPS baselines at year 30 in row 56.
These calculators show the range of withdrawal rates that will leave you (at year 30) with a final balance of zero (that's right, completely depleted), 50% of your initial balance (plus inflation) and 100% of your initial balance (plus inflation). Portfolios consist of the S&P500 and TIPS. You can vary allocations between 20% and 80%.
The probabilities that separate each range of results are (roughly) 5%, 20%, 50%, 80% and 95%. Keep in mind that you still have a 10% chance of being blindsided, possibly to your benefit and possibly to your detriment.
When you look at the graph, think about what you could do with a dividend-based strategy or even a TIPS-only approach. Many people, especially younger retirees, would like to have their portfolios maintain at least one-half of the buying power at year 30 even if lightening strikes. Most dividend-based strategies do much better. They retain full value. They even grow.
Withdrawal rates are percentages of the initial balance. I have adjusted all withdrawals to match inflation.
JULY 25, 2006 UPDATE:
I have replaced CVTVR D with CVTVR Da. This removes an error when I tried to constrain the maximum display to 10%. I have added CVTVR Ea and CVTVR F. These replace the column display with bar displays. CVTVR Ea is similar to CVTVR D. It shows what happens with year 30 balances of 0%, 50% and 100% of the initial balance. CVTVR F has you specify the year 30 percentage balance. It shows you what happens to portfolios with 20%, 50% and 80% stock allocations. It also calculates the optimal stock allocations to reach the final percentage that you specify.
JULY 27, 2006 UPDATE:
I added CVTVR G, CVTVR H, CVTVR I, CVTVR J and CVTVR K this morning.
CVTVR K is my first two step calculator. In the first section, I assume that you invest entirely in TIPS for N years because of today's valuations. In the second section, you see what happens to withdrawal rates for the next 30 years. You can enter your guesses as to future P/E10 levels, such as 14 to represent typical valuations, 8 for bargain valuations and 18 for higher than normal valuations. The calculator displays percentages in terms of your initial balance.
Typical choices for N are 10 years, a conservative estimate of how long it takes to reach reasonable valuations, 15 years, a conservative extreme to reach bargain valuations, and 20 years, a pessimistic extreme.
For younger retirees, a good place to start is N = 10 years with a 50% terminal value percentage, which is 50% of the buying power of the initial balance at year 40. If you can get 2.3% interest from TIPS throughout the first decade (you can get 2.5% today), and if P/E10 falls to 14, which is historically typical, well above bargain levels: the calculator tells us that you can withdraw 4.0% (plus inflation) for the full 40 years and still end up with 50% of your initial balance (after adjusting for inflation).
July 28, 2006 UPDATE:
I have added CVTVR L. It is similar to CVTVR K, but I have added results for 100% stocks during the second period.
July 30, 2006 UPDATE:
I added CVTVR M last night. It adds switching portfolios SwAT and SwOptT to CVTVR L. These switching algorithms are optimized for starting at times of high valuations. Refer to Current Research A, B and C for details. They differ from Latch and Hold. They have no memory. They vary allocations strictly on the basis of the current level of P/E10.
August 2, 2006 UPDATE:
I have added CVTVR Ma and CVTVR N. CVTVR Ma corrects the portfolio labels in the graph. The lowest bar, which is very short, should be for TIPS. What I previously identified as TIPS is really a 100% stock portfolio.
CVTVR N adds another TIPS section. You can invest entirely in TIPS before and/or after investing for 30 years in portfolio that includes stocks. I report all withdrawal rates in terms of the initial balance. If you wish to bypass a TIPS-only section, simply enter 0 for the number of years (N or M).
I report quite a bit of information. Just remember that I include boxes for all calculator entries. For example, you need to enter P/E10 only once. [To make this easier, I translate P/E10 to the equivalent current value of the S&P500 index.]
Current Research H: The Big Project
Yahoo Briefcase
A Tip about my Yahoo Briefcase
Often, I have to press refresh several times to get my Yahoo Briefcase to display a page.
Super Variable Terminal Value Rate SVTVR Calculators
I have now developed two Super Variable Terminal Value Rate SVTVR calculators. Each consists of four Compact Variable Terminal Value Rate (Compact VTVR or CVTVR) Calculators side by side, in a single spreadsheet. Each has its own set of inputs at the top.
Making comparisons is easy.
I have placed these calculators into the Big Project folder in my Yahoo Briefcase. They are SVTVR A and B.
AUGUST 9, 2006 UPDATE:
I am continuing to make improvements. My latest is Super Variable Terminal Value Rate Calculator SVTVR I1. It is very easy to use.
AUGUST 12, 2006 UPDATE:
I have placed Super Variable Terminal Value Rate Calculator SVTVR J into the Big Project folder in my Yahoo Briefcase. It is very easy to use.
AUGUST 19, 2006 UPDATE:
I have added Super Variable Terminal Value Rate Calculator SVTVR K and L. They are easy to use.
Yahoo Briefcase
Current Research H: The Big Project
A Helpful Theorem
To calculate withdrawal rates for various final balances, it is sufficient to know the withdrawal rates for final balances of zero and 100% of the initial balance. Rates for intermediate balances maintain the same proportions.
I have incorporated these findings into Super Variable Terminal Value Rate SVTVR calculator L. It is a simplified version of SVTVR K.
A Helpful Theorem
Year 15 Calculator A
I have placed Year 15 Calculator A into my Yahoo Briefcase. It is the same as Super SVTVR Calculator L except for its 15-year timeframe.
Enter P/E10, your stock allocation, TIPS interest rate and final balance percentage for four portfolios. See how likely you will be of reaching your final balance percentage as a function of your withdrawal rate.
You can combine the results of SVTVR Calculator L and Year 15 Calculator A to see what happens at Year 45. When doing so, it is best to use the longer time period first. That is, look at a 30 year segment followed by 15. You can see what happens at the midpoint with a 30-year retirement portfolio.
Year 15 Calculator Equations
Yahoo Briefcase
Deluxe Calculator V1.1A08b
I have added Year 15 data analysis software to Deluxe Calculator V1.1A08a. The new software is in columns H and I, rows 1 through 4 and in columns N through R. I built special summaries for years 1921-1980.
I call it Deluxe Calculator V1.1A08b. I have placed it in the Deluxe V1.1A08a folder.
Yahoo Briefcase
Retirement Trainer
I have built a Retirement Trainer. It automatically adjusts stock market returns in accordance with valuations. I have placed a copy (Retirement Trainer B) into my Yahoo Briefcase. It is in a new Retirement Trainer folder.
Play with this Retirement Trainer. Have fun. Enjoy yourself. Discover how well you react to the numbers.
AUGUST 29, 2006 UPDATE:
I have placed Retirement Trainer C into my Yahoo Briefcase. It is easier to use. The directions are easier to understand.
I have placed Bull Bear Retirement Trainer B into my Yahoo Briefcase. It allows you to specify a long lasting (secular) market trend: Bear Market, Neutral Market, Bull Market. It can be more realistic, but you must identify the market trend correctly.
Retirement Trainer Overview
Yahoo Briefcase
P/E10 Predictions Revisited
New Search Feature
I have added this new search feature. It includes an index and a site map.