Confidence Limits

Research on Safe Withdrawal Rates

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JWR1945
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Confidence Limits

Post by JWR1945 »

I have misstated what our confidence limits mean. I have referred to Safe Withdrawal Rates plus and minus their statistical confidence limits.

The Safe Withdrawal Rate is the number at the lower confidence limit. The Unsafe Withdrawal Rate is the number at the upper confidence limit. I do not have a good term for the estimate itself. For the time being, I will refer to it as the Zero Balance Withdrawal Rate. I do not like that term since it excludes many approaches such as withdrawing a percentage of a portfolio's current balance.

Historical Database Rates are withdrawal rates that would have ended at a zero balance after a specified period of time, usually 30 years. We refer to those as actual outcomes. Based on information extracted from those outcomes, I make predictions of withdrawal rates that will end with a zero balance (after 30 years).

Those predictions contain an element of uncertainty, which I identify by using confidence limits. I have elected to use a 90% confidence level. There is a 10% chance that actual outcomes will be outside of the confidence limits. Each basic prediction has a 50% chance of being safe. At the lower confidence limit, at the calculated withdrawal rate a portfolio has a 95% chance of ending with a balance of zero or higher. At the upper confidence limit, at the calculated withdrawal rate a portfolio has no more than a 5% chance of ending with as much as a zero balance (and at least a 95% chance of running out of money before the 30 years are up).

Part of the uncertainty in my calculations is based upon our inability to extract information from the historical record. For example, if I had used Tobin's Q instead of P/E10, the uncertainty would be greater because my measure of valuation would not have been as good (for such calculations). We expect a degree of uncertainty to remain always because of such things as the sequence of returns. We expect the future to be similar to the past, but not identical to the past.

It is necessary to use a confidence level lower than 100% whenever there is an element of chance. If I am not mistaken, William Bernstein advocates using a level around 80% to 85% for a variety of practical reasons. In addition, whenever one looks at confidence levels greater than 90% to 95% (i.e., 1.64 sigma or 2 sigma), the statistical assumptions fall apart. (In practice, people start redefining terms, giving different names to various sources of randomness.) The bell curve (or the normal distribution or the Gaussian distribution) is an excellent approximation as long as you do not set the confidence levels too high. There are sound mathematical reasons for this. It is still useful around 3 sigma. It is meaningless when you try to extend it to 6 sigma. (As I mentioned previously, all sorts of special adjustments become necessary. When done right, something such as 6 sigma becomes meaningful again. But only after making the adjustments.)

If you talk to a professional statistician, he will tell you that using the bell curve is usually OK, but that the confidence levels of the actual distribution are almost certain to differ somewhat. When I calculate a 90% confidence level, the real number (in an idealized, theoretical sense and which I am unable to calculate) may be something like 82% or 93%. But my answer is likely to be good enough.

We can apply our estimates to the past. They tell us what would have been reasonable to expect under similar, but not identical, circumstances. We can compare these estimates to Historical Database Rates to determine how representative the past outcomes were. When we make our estimates, we are generally extracting information from the totality of the historical record, not just from one or two specific years.

Have fun.

John R.
Mike
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Post by Mike »

...bell curve...
Your post reminded me that in the June 23, 2003 edition of Forbes, Ken Fisher did a study showing that stock market returns do not follow a bell curve. Rather they are bimodal and skewed, with 70% of the annual S&P returns being either above 20% or negative. Most 10 year moves are more volatile than a bell curve would suggest. I don't know if this would have any effect upon confidence intervals.
JWR1945
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Post by JWR1945 »

We would expect it to widen the confidence interval or, equivalently, to lower the degree of confidence associated with a specified interval.

The worst case distribution statistically has only two values which are equally probable. In that case the Chebyshev inequality is actually an equality. In all other cases the level of confidence is greater.

Chebyshev's inequality states that at least 1 - 1/[n^2] of the distribution is within n standard deviations of the mean. If n = 2, the confidence level is at least 75% that a result will be within plus and minus 2 standard deviations. With a normal distribution, the confidence level is just above 95% at 2 standard deviations.

The confidence level for the distribution that you have identified would lie between these two levels. The bell curve would claim 95%. The actual confidence level would be lower, but it would be higher than 75%. I suspect that the actual number is closer to 95% than 75%. The bell curve is not great, but it is good enough.

Have fun.

John R.
Mike
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Post by Mike »

Ok, withdraw a little bit less.
JWR1945
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Post by JWR1945 »

I recommend that you visit www.crestmontresearch.com. Click on the stock section and see what Ed Easterling has put together. It presents statistical information in much greater depth than you have referenced here. You will find that many of today's widely held beliefs about the stock market are false. Demonstrably so.

The first thing that will attract your attention is a colorful chart that shows stock market gains and losses versus the start year and the finish year. Read it carefully because it has quite a bit of additional information.

You will find that multiple expansion and contraction have driven stock market returns much, much more than the economy. This explains why switching works. There are extended periods of time when it is good to be out of the market. It can take well over a decade to get back to where you started (in real dollars) even when you make no withdrawals, reinvest all dividends, pay no taxes (via a retirement account) and avoid all trading.

Other charts show things such as its being the percentage of days with advances that characterize a bull market or a bear market. It is NOT the amount that stocks advance or decline (on average) each day. In fact, the size of daily declines is larger than the size of daily advances during a BULL market.

Have fun.

John R.
Mike
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Post by Mike »

You will find that multiple expansion and contraction have driven stock market returns much, much more than the economy. This explains why switching works.
Have you devoloped any theories as to the cause(s) of multiple changes? I have been to Crestmont before, and it is indeed an interesting site.
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Post by JWR1945 »

Now to be more specific. This builds upon Ken Fisher's findings.

At the Crestmont Research site click Stock Market. Then click Significant Swings. www.crestmontresearch.com

The chart includes these findings for 1901-1999. In the 54 years of BULL markets, annual returns of the S&P500 never fell below -16%. Half of the annual returns fell between -16% and +16%. Half of the annual returns exceeded +16%. In contrast, in the 45 years of BEAR markets, 33% of the annual returns were below -16%. Almost half (49%) of the annual returns fell between -16% and +16%. And 18% of the annual returns exceeded +16%. In terms of the entire period, almost half of the returns (49%) fell between -16% and +16%.

BULL and BEAR markets have distinctive statistical characteristics. In addition, even when they are combined, over half of the annual returns fall outside of the central region. This is distinctly non-normal and, at first glance, it appears that you are stuck with a bimodal distribution. When you separate BULL and BEAR markets, the statistics are much better behaved.

Another chart to look at under Stock Market at Crestmont Research is Generation Returns. There have been two periods that produced a negative (real) total return after twenty years. The 1960s included several years with a (real) total return below 2% two decades later. This sends a strong message to people like me who strongly prefer to buy-and-hold.

The same chart also shows how valuations (as measured by P/E) varied. It is clear-cut from the chart that multiple expansion and contraction has an exceedingly strong relationship with returns. Another chart shows that the economy has a much weaker relationship with returns.

I do not have any distinctive theories as to why multiples change. IMHO, however, the latest change was caused by the combined effect of two arguments: 1) stocks are always the best investment in the long-term and 2) in the long-term, stocks have (almost) no risk, especially when you buy the entire market (via an index fund). In terms of the ratio of risk to rewards, most investors have increasingly perceived the risk to be zero and the rewards to be the maximum available from a passive investment. You could say that the stock market salesmen and other cheerleaders have succeeded. IMHO, several of them now realize that they have succeeded too well and they are advising caution.

Have fun.

John R.
Mike
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Post by Mike »

...the latest change was caused by the combined effect of two arguments...
These arguments draw much of their ability to move markets from the tax code (401k, IRA), which is different than it was before the 1980's. In 1929, only about 10% of the population owned equities, today the number is well over 50%. Company sponsored 401ks tend to offer only 2 broad categories of investments, equity and debt. Equity proponents can correctly show them that their low savings rate has little chance of growing their 401ks into something capable of providing them a secure retirement at paltry debt interest rates. Since they are generally unwilling to save more...

The sheer size of the baby boom cohort that is moving toward retirement age has magnified this effect.
JWR1945
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Post by JWR1945 »

In effect, individuals have always held a large amount of stock indirectly, but not directly until recently. In terms of retirement portfolios, professionally managed defined benefit plans had much higher stock allocations than individually managed IRAs and defined contribution plans when they first became available.

The prolonged bull market in stocks certainly has had its effects. Seemingly, it will go on forever. There are no risks and great rewards. There is only the occasional blip, hardly visible except in the very short-term.

One tax related argument in favor of higher multiples is that withholding dividends (to reinvest them into the company) is tax efficient, converting dividends into long-term capital gains with a lower tax rate.

I have been reading that taxes make the case for reducing dividends for many years now. It certainly is a common argument. I don't consider it to be compelling. I think back to the tax rates before the Reagan Tax Cuts.

Back then, the case in favor of long-term capital gains was far more compelling.

There was the $400 dividend exclusion. But dividend yields were high. You could expect $400 in dividends from a $10000 account. Marginal tax rates were exceedingly high. Half of long-term capital gains were excluded.

IMHO, tax issues are simply a topping on a salesman's pitch. They are a factor at the margin, but only at the margin.

Have fun.

John R.
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ataloss
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Post by ataloss »

asdf
Have fun.

Ataloss
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