This is a general context for those new to this board. We have stopped mentioning many of these points because we have mentioned them so many times before. They still apply and they are still important. For those who have been following this board all along, I will begin with some new content.Because investor newbies who chance upon the board may misinterpret what they are reading, I wonder if a sticky post at the top carefully worded to explain things to newbies might help to avoid actions by them based upon incomplete understanding. Most of the regulars who post on NFB are seasoned investors who think before they act, but I have no idea how many newbies might be lurking on the boards.

Using all of the Data

We take great care to use as much of the historical record as we can when we analyze Safe Withdrawal Rates. One of the critical failings of the conventional methodology is that it focuses on only a handful of historical sequences. Conclusions are based upon only one or two worst case conditions. This is not enough to merit a high degree of confidence.

Our approach exposes and quantifies the uncertainty of our conclusions. This makes our conclusions much stronger and much more reliable than the alternatives. Unfortunately, it can give the impression of being weaker. The alternatives seem strong only because their weaknesses are hidden.

The strongest conclusions are based directly upon mathematical fact. But there are only a few of them.

Almost as strong are those conclusions extracted from data analysis and which have a strong foundation in logic and common sense. For example, the fact that dividends provide a floor to Safe Withdrawal Rates needs only a simple observation to make it useful. Historically, dividend amounts have grown at least as fast as inflation with only a few exceptions. This means that the initial dividend yield is likely to provide a floor to the Safe Withdrawal Rate. It is not certain, but we know what to look for. We can know right away if we have made a mistake.

Weaker are those quantitative estimates that we draw from Historical Database Rates. They tell us about what has happened in the past and we can handle them statistically. The result is a blend of mathematical certainty and mathematical estimates of the remaining uncertainty. A good example is the relationship between a portfolio's total return and the sequence of returns. [Note: You will see more about this shortly when I introduce the New Tool.] With mathematical certainty, we can identify the sequence of returns as a source of randomness in Historical Database Rates. The sequence does not have any effect on a portfolio's total return (in the absence of withdrawals). The magnitude of those returns influences both the Historical Database Rate and the total return. We can relate the randomness of the sequence of returns and the magnitude of returns (as reflected by the total return) to characterize Historical Database Rates statistically. By using Historical Database Rates in these calculations, we acknowledge that some sequences might be more likely than others. We do, in fact, have a strong reason to believe that this is so. We have evidence in the auto-correlation functions of historical sequences (i.e., mean reversion).

We frequently make use of such a blend of certain and uncertain information. To the extent that we can use a large fraction of the Historical Database Rates, our confidence is increased.

Our positions become progressively weaker as we force ourselves into looking at less and less of the historical record. History can tell us what can happen by providing us examples of what has happened. It does a great job in this regard. It does a poor job of telling us what is highly unlikely to happen (or what will not happen) simply from the observation that something has not happened in the past. We want to know what is unlikely to happen when we look at Safe Withdrawal Rates. The conventional methodology is especially weak in this regard.

Historical Database Rates are helpful because they are very closely related to Safe Withdrawal Rates. They are not the only source of useful information that can be extracted from the past. History contains much information that can be used as statistical inputs to Monte Carlo models. And there is much more that can be done to improve Monte Carlo models as well. Most Monte Carlo models are very crude. History undoubtedly contains undiscovered information that can be used with direct mathematical calculations. Using Historical Database Rates has the advantage that some powerful tools already exist to calculate them.

Our hierarchy remains. The best information is mathematical fact. The second best information is based solidly on logic and common sense. As we move to lower levels of confidence, we prefer to use as much of the historical data as possible. Our strongest conclusions include estimates of our degree of uncertainty. The weakest conclusions extracted from the historical record are those that use the smallest number of unique inputs. They often appear stronger than they are because the degree of uncertainty remains hidden.

Have fun.

John R.