(snip)...In addition, portfolio returns usually suffer from kurtosis or negative skew, so the effects of volatility would likely be even worse than a simulator shows.

Jim

This caught my attention. What do you mean?

Attached is a histogram of annual S&P 500 returns, which doesn't appear to have any negative skew. Maybe a little skewed to the positive side, if anything.I retract that statement

There's a strong positive bias, that's for sure! That's why we invest!

Does the negative skew in portfolio returns come from the inclusion of constant withdrawals?

BTW, I pilfered the data from the REHP retire-early spreadsheet, which in turn comes from Schiller. I picked the month of January.

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I think she is right. It is only if the gap drops that she might be wrong.

The key error here is that an inflation of below 10% will mean you are improving your net worth every year. For every $1 million of starting assets, you will have $8.4 million after 30 years, and $19.7 million after 40 years:

Such is the power of compounding! Plenty left for the kids...

Quote:

Quote:

Quote from: kcowan on January 09, 2007, 11:45:22 AM
The reason I did the simple spreadsheet is to avoid the mistake in this thinking. Inflation only applies to your spending. So SWR of 4% will decline as the portfolio returns more than 3.5%. Plus the easiest thing to focus on is spending because investment returns are influenced by many things outside our control.

kcowan,

I still stand by my logic, although reasonable people can differ as to how to best visualize this problem.

My point was that you can remove the inflation variable from the equation by subtracting it out of the portfolio growth rate up front. Maybe you don't find this intuitive and would rather focus on the spending side, but calculation wise, it's six for one and half-a-dozen for the other (except for taxation differences).

The engine that powers spending in retirement is the portfolio balance. The horsepower of that engine is affected by the portfolio's real rate of growth. As a portfolio's real rate of growth diminishes (especially below zero), the likelihood of retirement ruin increases, especially for longer retirements.

One reason we might see this problem differently is that I retired in my early 40s, so my time horizon is very long. I need to stay focused on keeping our portfolio's real value from declining or else my odds for success aren't good.
Jim

OK Jim I have no problem with your being exceptionally cautious in order to preserve your portfolio. However it is really important to get the numbers right. I have adjusted my planning spreadsheet with your simplifying assumptions:
Portfolio growth = 10% minus inflation at 3.5%
SWR at 4% of previous year-end portfolio

Here are the comparisons:

The differences are dramatic and speak for themselves. Most importantly, you think you need to average 10% returns over the years, and I can match your portfolio with only 7.25% average returns so I can take much less risk. In fact, I use 7%.

Turning the comparison around, your math would require you to achieve 15.3% annual returns to match my math at 10%.

My point is that you need to be realistic about the numbers. Most seniors die with plenty of money left while depriving themselves of many pleasures. Usually it is because they don't understand the math and so live overly cautious lives. You can adopt any strategy you want. But you can't change the math.

I intend to share my wealth while I am around to enjoy it rather than have my heirs be amazed at how much I was worth and still so frugal!

On the "Jim's Math", the withdrawal should be $40,000 for all the years. It shouldn't creep up. That's what Jim intended. He wants you to factor out inflation off the top.

Does the negative skew in portfolio returns come from the inclusion of constant withdrawals?

Actually, I misspoke earlier when I said kurtosis was the same as skew. (use-it-or-lose-it I guess). I did some googling to refresh my memory.

Kurtosis and skew are usually mentioned together and refer to that fact that portfolio returns don't exactly model the "normal distribution" that's used in Monte Carlo portfolio models. Skewness refers to a distribution having more weight on one side vs the other side, (ie. more likelihood of negative returns than positive). Kurtosis refers to a flatness in the return distribution, where the tails (extremes) in the distribution are fatter than they would be if they were truly normal. The "fat tails" theory says that most models are overly optimistic because they don't account well enough for really bad outcomes.

The whole normal distribution debate is highly academic and probably not of much use in practical applications at this point. To me the most important point is to keep from thinking that all these mathematical models are foolproof. For a very controversial read around this subject, you might try this book from the inventor of fractals.

On the "Jim's Math", the withdrawal should be $40,000 for all the years. It shouldn't creep up. That's what Jim intended. He wants you to factor out inflation off the top.

Exactly. Thanks Mike.

Kieth, I'm starting to think that I'm not quite following you on this stuff. I'm not being all that conservative really. In rough numbers, I've chosen a 3% SWR instead of 4% in order to account for the long retirement timeframe. If I had to, I could probably use 3.5% and still feel ok about it, but don't worry, we're not starving ourselves.

Thanks for the link. I'm putting that one on my reading list.

Just don't tell anyone it was me that recommended it. Some people think he's a bit nuts. Personally, I thought he came off in the book as somewhat arrogant, but the message from the book was important. His credentials in mathematics are pretty darn impressive.

If you read the amazon reviews, the biggest complaint (other than arrogance) is that the model he proposes to "replace" modern portfolio theory isn't developed enough to be seriously considered.

For my money, I was more interested in his critique of MPT, rather than his suggestions for a replacement. The whole idea that results from the recent past can be predictive in the distant future is very unsettling to me, yet it's the basis of most retirement and portfolio planning (and it's how I do it myself!).

Reading this book should be a must for all the quants that have unyielding faith in their massively complex models (ala Long-term capital, etc). Not that we should throw out the MPT toolkit, only that we should use it with the respect/trepidation that it deserves.

Something like -- MPT is the worst model except for all the others that have been tried from time to time...

Actually, I misspoke earlier when I said kurtosis was the same as skew. (use-it-or-lose-it I guess). I did some googling to refresh my memory.

Kurtosis and skew are usually mentioned together and refer to that fact that portfolio returns don't exactly model the "normal distribution" that's used in Monte Carlo portfolio models. Skewness refers to a distribution having more weight on one side vs the other side, (ie. more likelihood of negative returns than positive). Kurtosis refers to a flatness in the return distribution, where the tails (extremes) in the distribution are fatter than they would be if they were truly normal. The "fat tails" theory says that most models are overly optimistic because they don't account well enough for really bad outcomes.

The whole normal distribution debate is highly academic and probably not of much use in practical applications at this point. To me the most important point is to keep from thinking that all these mathematical models are foolproof. For a very controversial read around this subject, you might try this book from the inventor of fractals.

Jim

Well you sort of got skewness and kurtosis...

just for fun i want you to know that skewness and kurtosis are the 3rd and 4th order statistics of a measured distribution (the mean and standard deviation are the first and 2nd moments). The skewness measures how a distribution leans to either side (positive or negitive skewness). Kurtosis is usually described as the distribution peakedness or in other words does the distribution peak more (or less) than a normal - gaussian distribution.

People often use the kurtosis value as a measure of how normally-distributed gaussian a distribution is. If the kurtosis is close to zero then one could say that a distribution is normally (gaussian) distributed.

All that being said, the underlying skewwness and kutosis measurements are tough to measure on a distribution. You need ever increasing amounts of data to accurately measure skewness and kurtosis (compared to the mean and standard deviation stats). So, the variance of the skewness and kurtosis calculations of a given distribution are often (usually) much larger than the separation of different data populations. This leads to people making sweeping conclusions based on small data populations when all they are actually seeing is a noisy and hard to measure skewness or kurtosis calculation.

So there you have it. Now go impress your friends !

Well you sort of got skewness and kurtosis...
.
.
.
So there you have it. Now go impress your friends !

That's was all very informative, but you didn't weigh in on the most important question - Do you think any of it matters in estimating portfolio returns?

That's was all very informative, but you didn't weigh in on the most important question - Do you think any of it matters in estimating portfolio returns?

Jim

I haven't given it much thought. My experience tells me that these measures often bounce around quite a bit depending on the samples used. So my first reaction would be to be skeptical of people making claims based on such statistics.

So maybe it will work, and then maybe you have some people who are just fooling themselves (and perhaps you).

If someone tells you... see here the kurtosis of the S&P500 is X that means we should buy now...

Your question should then be... How did they measure kurtosis ? How many (independent) samples were used and over what time frame ? What is the variance of the measurement ? Is that variance larger than the shift that you suggest indicates a buy ?

Like I said... be skeptical. Maybe you are just looking at noise effects.

Actually, they're not fooling me since I'm on the sidelines watching.

Anyhow, There's nothing actionable coming out of any of the "returns aren't normally distributed" research that I know of. It seems to be mostly fodder for PhD candidates to occupy themselves for a couple of years while waiting for their upgraded credential.

On the "Jim's Math", the withdrawal should be $40,000 for all the years. It shouldn't creep up. That's what Jim intended. He wants you to factor out inflation off the top.

-Mike Miller

Well maybe we need to speak to Jim. I kept SWR at 4% of previous year portfolio. Making it flat at $40,000 brings the difference down to $14.2 million instead of $17.2 million, hardly material. Not that I would sneeze at $3 million but he is still understating his portfolio seriously after 40 years. That was the point I was making. The simplification just does not work.

Kieth, I'm starting to think that I'm not quite following you on this stuff. I'm not being all that conservative really. In rough numbers, I've chosen a 3% SWR instead of 4% in order to account for the long retirement timeframe. If I had to, I could probably use 3.5% and still feel ok about it, but don't worry, we're not starving ourselves.

Jim

Just don't get on your DWs case (because she is more correct than you are), especially because you are really early retirees, i.e. the effects show up more dramatically in 40 years.

(Hey I was in charge of planning for a big multinational technology company for a few years so I got indoctrinated by the importance of correct numbers. I can send you the spreadsheet if you want to play with it yourself. The power of compounding is dramatic!)

Well maybe we need to speak to Jim. I kept SWR at 4% of previous year portfolio. Making it flat at $40,000 brings the difference down to $14.2 million instead of $17.2 million, hardly material. Not that I would sneeze at $3 million but he is still understating his portfolio seriously after 40 years. That was the point I was making. The simplification just does not work.

Dude, the other factor, which I forgot to mention, is that Jim's method gives you the ending balance in present dollars. Your method shows the ending balance in inflated dollars.

So to compare Jim's ending balance to yours, the equation should be:

My point is that you need to be realistic about the numbers. Most seniors die with plenty of money left while depriving themselves of many pleasures.

I hear this all the time but I'm not sure that the quality of the "data" is any better than anecdotal. It certainly doesn't jibe with the threads about financially supporting your parents.

So... how do we know that seniors are dying with "plenty" of money left?

More importantly, how do we determine whether or not the people in the surveys or other "gathered data" are telling the truth about their wealth?

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Well Nords I cannot argue about the data. I guess I assumed that the motivation for Dubya to reduce estate taxes was because there were a lot of estates.

My problem with Jim trying to do everything in current dollars is that it will probably understate future tax liabilities such as AMT or even revived estate taxes.