You don't have to die to luck out

Financial Independence/Retire Early -- Learn How!
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JWR1945
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Joined: Tue Nov 26, 2002 3:59 am
Location: Crestview, Florida

You don't have to die to luck out

Post by JWR1945 »

You don't have to die to luck out

It has been pointed out elsewhere that your probability of financial planning success is higher than your calculated probability of portfolio success at a given duration and withdrawal rate. The way to luck out is to die early...before the end of the duration. I am less than enthusiastic about that.

I have not been able to reproduce the numbers that have been posted elsewhere. There can be a variety of reasons for that. It could be in the details such as using monthly data versus annual data. My guess is that the calculations themselves are flawed. It doesn't matter. I present my calculation details here. My calculations can all be verified.

The correct calculation starts with entering withdrawal rate assumptions into a calculator. I used the dory36 calculator. I set the initial retirement balance to $10000, the annual withdrawal to $457, the duration to 40 years, the stock allocation to 79%, the non-stock alternative to commercial paper, the inflation index to CPI and the expenses to 0.20%. These are supposed to produce a portfolio success rate of 90%. The dory36 calculator gives a different answer.

The next step consists of identifying when failures would have occurred. I use the notation 1902F39 to indicate that the 1902 sequence failed in year 39. The calculated failures were 1902F39, 1906F29, 1907F35, 1909F35, 1910F37, 1911F35, 1912F34, 1913F38, 1929F27, 1930F39, 1937F32, 1962F36, 1964F32, 1965F26, 1966F23, 1967F30, 1968F25 and 1969F24.

At some point you must choose how many sequences to include in your analysis. With a 40-year duration all of the sequences from 1871 to 1961 are complete...assuming that the data ranges from 1871 to the start of 2002. There are 91 complete sequences. There are 11 failures in these 91 years (i.e., 12%). However, it is misleading to ignore the partial sequences that started in the 1960s. Those that have already failed will certainly be among the failures ten years from now...when they become complete sequences. My preference is to use the 100 sequences that start from 1871 to 1970. There are 18 failures in these 100 sequences (i.e., 18%).

The next step is to determine the probability of being alive at the time for each failure. For purposes of illustration (and being consistent with the alternative calculations), I assume that these calculations are for a 51 year old man. From the 1902F39 failure, I see that it corresponds to a man's living to the age of 90.

Starting from www.FirstGov.gov, I eventually went to the National Center for Health Statistics and then to Tabulated Data and finally to Statistical table about death and life expectancy. The direct link to this table is http://www.cdc.gov/nchs/datawh/statab/u ... ortabs.htm. You can down load it.

The entries l(x) are the number of people who make it to the beginning of an indicated interval normalized to 100K. For the interval 51-52, the l(x) number is 89124. For the 90-91 interval the number is 3321. Dividing 3321 by 89124 produces 0.03726. A man who has just turned 51 years old has a 3.726% chance of making it to his 90th birthday.

To calculate the total number of failures inside a certain number of years, you identify all of the failures that occur during those years. Next, you calculate the probability of someone's being alive at that time. If someone has already died, his financial planning has been successful. His investments lasted longer than he did. If he is alive and his money runs out in a given year, his financial planning fails. At any given time the number of financial planning failures is the sum of the probabilities of being alive in each year that a failure occurs.

The overall probability of failure is calculated by dividing the total number of financial planning failures by the total number of sequences examined (i.e., 91 or 100).

If we limit ourselves to complete sequences (1871 to 1961), the sum is 1.4323863. Dividing by 91, the percentage of financial planning failures is 1.57405%. The financial planning probability of success has a calculated value of 98.43%.

If we include the period of 1871 to 1970, there are 100 sequences but some of them are not complete. The sum is 3.7325075. Dividing by 100, the percentage of financial planning failures is 3.732075%. The financial planning probability of success has a calculated value of 96.27%.

A casual observer may question the value of using highly precise numbers when ten years can make such a difference. He would be right. The logic behind including or excluding the 1960s is much more important than the other details.

I am happy to report that you don't have to die to luck out. If you convert entirely to cash as soon as your investment balance is large enough, you can eliminate all of the later financial planning failures. By converting to cash, I assume that you are able to match inflation via ibonds, TIPS or some other safe investment. In previous posts I have called such conversions using special thresholds. The number of failures becomes 7 instead of 18. The failures that remain are 1906F29, 1929F27, 1937F32, 1965F26, 1966F23, 1968F25 and 1969F24. The calculated values of financial planning success are 99.10% (versus 98.43%) using only the 91 completed sequences and 97.39% (versus 96.27%) by including the failures of the 1960s.

If you make it to that last decade, you can stay alive without harming your financial planning success rate.

Have fun.

John R.
hocus
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Joined: Mon Dec 02, 2002 12:56 am

Post by hocus »

I am happy to report that you don't have to die to luck out. If you convert entirely to cash as soon as your investment balance is large enough, you can eliminate all of the later financial planning failures.

Hey! Where's the rec button? (just joshin')
wanderer
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Posts: 363
Joined: Tue Nov 26, 2002 9:33 am
Location: anytown, usa

Post by wanderer »

jwr -

thank you for your dedication to detail and your devotion to accurate data interpretation. maybe i should pay you the tmf $30 fee.

wanderer
regards,

wanderer

The field has eyes / the wood has ears / I will see / be silent and hear
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