Models and Their Applications

I use a variety of models. They have many applications.

Historical Sequence Method

The historical sequence method consists of running a portfolio against actual historical sequences of investment returns. This includes inflation. It includes fixed income investments, but not accurately.

This approach produces Historical Surviving Withdrawal Rates when you set the final balance at zero. You can also set the final balance at something other than zero.

If you assume that the lowest Historical Surviving Withdrawal Rate equals the Safe Withdrawal Rate, you will conclude that it is best to have a high stock allocation (close to 80%) and that the 30-year Safe Withdrawal Rate is 4% of the original balance (plus inflation).

This turns out to be a serious error.

When you bring measures of valuation into the model, you find that the true 30-year Safe Withdrawal Rate has varied between 2% and 9%+.

There are several good choices for the measure of valuation. My preference is Professor Robert Shiller’s P/E10. It is the current (real) price of the S&P500 divided by the average of the previous decade’s worth of (real) earnings. I actually use the reciprocal of this, the percentage earnings yield 100E10/P. I use Excel to generate the regression equation between Historical Surviving Withdrawal Rates and valuations (100E10/P). I determine confidence limits. I define the lower 5% confidence limit as the Safe Withdrawal Rate.

I make a similar calculation at a final balance equal to the initial balance (plus inflation). I invoke a theorem that allows me to interpolate accurately between the two final balances, zero and 100% of the initial balance (plus inflation).

The result is the Year 30 Retirement Risk Evaluator [Year 30 SWR button]. Using the Year 15 values, I have also produced the Year 15 SWR Retirement Risk Evaluator [Year 15 SWR button].

The historical sequence method also allows you to vary stock allocations in accordance with valuations. The critical issue is to avoid depending too much on the exact details of the historical record. If so, you run the risk of data mining and generating misleading results.

Still, it is clear that varying allocations with valuations (Valuation Informed Indexing, VII or Lucky 7) is superior to maintaining a fixed stock allocation through rebalancing. My Latch and Hold investigations showed that it has been a good idea to maintain a high stock allocation during the upward trend of a long lasting (secular) bull market.

Set the withdrawal amount equal to zero and you can determine stock returns relative to valuations. The result, complete with confidence limits, is the Stock Returns Predictor [Stock Returns button].

These are powerful findings generated by proper application of the historical sequence method.

Monte Carlo Simulations

Properly implemented, a Monte Carlo simulation can extend insights far beyond what is available from the historical record alone. It extracts information from the historical record to feed a random number generator. After that, it proceeds very much as with the historical sequence method.

The Monte Carlo method avoids the problem of data mining.

On the other hand, the Monte Carlo method is critically dependent on its inputs and their assumptions.

Valuations are important for determining returns. Mean reversion is important to avoid serious error.

The Investor’s Scenario Surfer [Scenario Surfer button] incorporates the Stock Returns Predictor (including a special version for long lasting (secular) Bear Markets) and two forms of mean reversion. It makes an outstanding retirement trainer. Users will find that they can trounce fixed allocation approaches easily by varying stock allocations according to valuations (P/E10 levels).

The Investment Strategy Tester [Strategy Tester button] automates the Scenario Surfer. It makes 1000 runs at a time and shows the range of outcomes. It does a great job of screening Valuation Informed Indexing approaches. It is limited to mechanically defined changes. It cannot be used with a Latch and Hold approach. For that, you must use the Scenario Surfer itself.

Both the Investor’s Scenario Surfer and the Investment Strategy Tester can be used by accumulators as well as retirees. You can, in fact, combine both.

The Scenario Surfer does a great job of estimating the odds of future market allocation sequences. For example, the bubble fell within its range even though it was unprecedented historically. It was, to be sure, an unusual outcome. But it was within the range of possibilities that investors should prepare for. Similarly, it provides realistic odds of future moves from today.

These Monte Carlo simulations do an outstanding job of preparing investors for unexpected outcomes. They help identify the risk that other approaches gloss over. Done right, they help to reveal hidden flaws.

SWR Translator

The SWR Translator is a historical sequence approach that mimics a Monte Carlo simulator. I determine the regression equation of a 30-year sequence relative to the total return of the market (without withdrawals) at a specified year in that sequence. It was useful for showing the effects of overlapping sequences.

The SWR Translator has not seen much application. It is hard to generate SWR Translator conditions. It is much easier to use a Monte Carlo model.

Dividend Models

In trying to characterize dividend approaches, I found that the nominal dividend of the S&P500 index has grown consistently at 5.5%. It is necessary to allow for a loss of buying power of 25%, mainly during times of high inflation.

General Findings

Identifying hidden flaws is one of the great values of any model. The historical sequence method revealed the vulnerability of approaches that include selling shares. It showed that retirees could end up selling too many shares when prices were depressed. Similarly, it shows that withdrawing a percentage of the existing balance is not the solution. It could lead to very low income levels.

All of this has led to support of changing allocations as valuations change (e.g. Valuation Informed Indexing and the Delayed Purchase approach). It has highlighted the advantages of steady income stream approaches (e.g., the Traditional Income approach and the Dividend Blend). It has also led me to write “The Safe Withdrawal Rate Solution.” You really can withdraw the long term return of the market (given its initial valuation) provided that you do it right.

Have fun.

John Walter Russell
May 31, 2009

The Safe Withdrawal Rate Solution