Mortality and the perfect retirement calculator

[Independent]

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Originally Posted by ERD50 Thanks, now I have a better idea of what you are talking about, and I can see the logic of it. Like others, I'm interested in the worst case. But to get at what you are looking for, I guess what I do is either eyeball the failures for the year they fail, or do multiple runs, extending the time period to see where the failures occur. I'm not sure that trying to merge that into one number would be that helpful. It starts to sound too much like that old saw of the 6 foot tall statistician drowning in a pool of average 4 foot depth. JMO. -ERD50

Maybe we're imagining different things. With a traditional SWR, we say:

"Given this distribution of investment returns, and a real annual withdrawal of ___, I have a 5% chance of running out of money before 30 years have elapsed."

Instead of saying that, adding mortality probabilities means that we would say:

"Given this distribution of investment returns, and this distribution of possible dates of death, and a real annual withdrawal of ___, I have a 5% chance of running out of money before I die."

The second statement is more meaningful to me.

[Fred123]

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Originally Posted by Independent Maybe we're imagining different things. With a traditional SWR, we say: "Given this distribution of investment returns, and a real annual withdrawal of ___, I have a 5% chance of running out of money before 30 years have elapsed." Instead of saying that, adding mortality probabilities means that we would say: "Given this distribution of investment returns, and this distribution of possible dates of death, and a real annual withdrawal of ___, I have a 5% chance of running out of money before I die." The second statement is more meaningful to me.

Thank you for phrasing it so much better than I did! That's exactly what I was trying to say. I think most people on this board are trying to figure out the solution to the second statement, not the first.

[NW-Bound]

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Originally Posted by Fred123 I think most people on this board are trying to figure out the solution to the second statement, not the first.

I am not so sure.

Most people seem to say "Of course I will live for another 30 years, or even 50 years". So the two problem statements are synonymous in their mind.

Of course I am talking about geezers who are already in the mid-50s or 60s and above, not the youngun's who can afford to retire in their 30s and 40s.

[bmcgonig]

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Originally Posted by NW-Bound I am not so sure. Most people seem to say "Of course I will live for another 30 years, or even 50 years". So the two problem statements are synonymous in their mind. Of course I am talking about geezers who are already in the mid-50s or 60s and above, not the youngun's who can afford to retire in their 30s and 40s.

I'm not so sure either. The reason we all bandy 4% or less about is because that is almost the worst case scenario. I apply the same to my life expectancy. The worst case is I live to 100 or so. My mother is 96 alive and kicking. Life expectancy is increasing every decade. The failure case is so dire that probabilities of dying are unimportant to me. I really want to plan for the <1%

[harley]

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Originally Posted by Chuckanut My worst case scenario would be passing at a ripe old age, with a ton of money and having skipped and avoided enjoying my ER, full of regrets for what I didn't do, for not helping others I could have helped, and generally living in fear. Very close behind is the next worse case which would be to run out of money many years before I run out of time. Figuring out when and how much to spend is the issue for most of us. Are we having fun yet?

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Originally Posted by comicbookgujy Same here. My worse fear is dying with too much money...followed by dying without enough. I save about $40k a year, but I don't go overboard. I spend about $20k to $30k for crap and experience I don't need, but want to because I don't want to die without enjoying my hard work

Seriously? You would prefer living your last few years in a crappy Medicaid-paid nursing home cared for by minimum wage or below caregivers, suffering bedsores and neglect, just so you can say "damn! Sure glad I spent all my money before I died."?

Not me. I want top quality pain meds, a beautiful and well trained and well paid young nurse, and a golden bedpan (or at least a Teflon catheter). If I end up leaving some money to my daughter, grandkids, or even a charity, so it goes. I'm having enough fun in retirement already without worrying about whether I'm going to bounce my last check.

[Khufu]

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Originally Posted by Fred123 OK, based on some of the comments I should elaborate a bit. There really are two big considerations in a retirement calculator: how long you will live, and how your portfolio will evolve over time. All of the retirement calculators that I'm aware of focus on the probability distribution of the second consideration and ignore the probability distribution of the first. This seems like a mistake to me. Here's an example (a bit contrived but illustrative): suppose you are 60 years, and you withdraw 4% of the initial value of your portfolio per year, and, to keep things simple, the returns on your portfolio are exactly the same as inflation. After 25 years, you will be out of money. If you run this through a calculator, and you use 25 years as the time period for the calculator, it will come up with a 100% chance of failing. But say the mortality tables tell you that have a 40% chance of living to be 85 years or older. Then a better guess at the chance of running out of money is 40%, not 100%, since you have a 60% chance of dying before your portfolio is exhausted. I believe that you would calculate this by running your retirement calculator for the maximum number of years from your age to the end of the mortality table (about 100 years old) and instead of counting up all of the failures and dividing by the number of simulations to get the failure rate, you would weight each failure by the probability of surviving to the age of the failure and then divide by the number of simulations. Does that sound correct?

It sounds like a reasonable approach to a problem that is different from the one we retirees are trying to solve. The weighting you are talking about is going to be influenced more by averages since they are very much more likely. But that's not my problem. I am an "n" of one. My problem is how to fund my living if I hit the long odds and still have expenses to pay at age 95. So only the worst case, or let's say the likely worst case, is of interest to me. If I do find myself surprised to be above ground at age 95 and, by the way, broke, it will not be of much consolation to me how unlikely that outcome was.

Similarly, using my previous example of fire insurance on the home, the likelihood of a fire is known to be quite low. No one in my acquaintance has ever experienced his house burning down. Yet, most homeowners buy first insurance because they would face ruin otherwise if the very low probability event did occur. So, homeowner's provide for the worst case scenario. If they used a weighting by average outcomes they could just forget about fire insurance altogether.

So, the problem we face is how to provide for the worst case, not what my portfolio is likely to be worth the day I die.

[clifp]

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Originally Posted by RunningBum OK, I get you. If there is a small chance you will live to be 95, and a small chance that your portfolio will not last if you make it to be 95, there would be a very small chance of both events actually happening to you. Suppose each is a 5% chance, that means your plan actually has a 1/4 of 1% chance of failing--or 99.75% chance of succeeding, rather than 95% as many look at it. .

The data is a decade out of date but still worth looking at. Intrcast, a pioneer in early retirement finances, did some work on joint probabilities of running out of both money and living a long time.

[NW-Bound]

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Originally Posted by harley I want top quality pain meds, a beautiful and well trained and well paid young nurse, and a golden bedpan (or at least a Teflon catheter). If I end up leaving some money to my daughter, grandkids, or even a charity, so it goes. I'm having enough fun in retirement already without worrying about whether I'm going to bounce my last check.

If one has top quality pain meds (which do not cost much by the way, if it is not purchased on the black market), one does not even recognize the cute nurse, or care about the gold bed pan, nor feel the sand-coated catherer. It's really that sad!

But the above said, I still prefer to die a millionaire. I love money and do not want to part with too much of it. Here drawing 3.5% and not expecting to live till 80.

[Fred123]

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Originally Posted by Khufu My problem is how to fund my living if I hit the long odds and still have expenses to pay at age 95. So only the worst case, or let's say the likely worst case, is of interest to me. If I do find myself surprised to be above ground at age 95 and, by the way, broke, it will not be of much consolation to me how unlikely that outcome was.

So, how exactly do you calculate the odds of your worst case happening? You calculate it by calculating the probability of your investments lasting for the lifetime of you or you and your life partner. And to do that you have to sum the combination of the probability of your investments lasting for n years and the probability of living for n more years for different values of n up to the maximum possible lifespan. If you want to be as safe as possible, you would set your acceptable failure rate to zero (or very close to zero), not choose a fixed lifespan.

Another way of looking at it is that by choosing only one life span you already are implicitly using a mortality probability table: it's a table that has a probability of living from, say, 65 to 95 of 100% and a probability of living beyond 95 to 0% (a step function). But what if you live to 100? Or 110? And this table is much less accurate than a "real" mortality table that might have a probability of living from 65 to 70 of 95%, from 65 to 75 of 90%, etc. In fact, by setting your maximum lifespan to 95, you are discounting the risk that you will live beyond 95.

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Originally Posted by Khufu Similarly, using my previous example of fire insurance on the home, the likelihood of a fire is known to be quite low. No one in my acquaintance has ever experienced his house burning down. Yet, most homeowners buy first insurance because they would face ruin otherwise if the very low probability event did occur. So, homeowner's provide for the worst case scenario. If they used a weighting by average outcomes they could just forget about fire insurance altogether. So, the problem we face is how to provide for the worst case, not what my portfolio is likely to be worth the day I die.

No, you just would replace the probability of you investment lasting n years with the probability of a fire in n years, and the probability of dying in n years with the probability of staying in a home for n years and combine the probabilities in the same way. Since this would result in a non-zero probability, you still would want to buy insurance. Just as you might want to consider purchasing a longevity annuity if you are worried about running out of money at the end of your life.

[Khufu]

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Originally Posted by Fred123 So, how exactly do you calculate the odds of your worst case happening? You calculate it by calculating the probability of your investments lasting for the lifetime of you or you and your life partner. And to do that you have to sum the combination of the probability of your investments lasting for n years and the probability of living for n more years for different values of n up to the maximum possible lifespan. If you want to be as safe as possible, you would set your acceptable failure rate to zero (or very close to zero), not choose a fixed lifespan. Another way of looking at it is that by choosing only one life span you already are implicitly using a mortality probability table: it's a table that has a probability of living from, say, 65 to 95 of 100% and a probability of living beyond 95 to 0% (a step function). But what if you live to 100? Or 110? And this table is much less accurate than a "real" mortality table that might have a probability of living from 65 to 70 of 95%, from 65 to 75 of 90%, etc. In fact, by setting your maximum lifespan to 95, you are discounting the risk that you will live beyond 95. No, you just would replace the probability of you investment lasting n years with the probability of a fire in n years, and the probability of dying in n years with the probability of staying in a home for n years and combine the probabilities in the same way. Since this would result in a non-zero probability, you still would want to buy insurance. Just as you might want to consider purchasing a longevity annuity if you are worried about running out of money at the end of your life.

I don't attempt to calculate the odds of the worst case, because to do so would be meaningless. I am not a population with a normal distribution. I am a single person for whom the outcome function is binary. Under that circumstance the only interest in such a calculation would be if I regarded spending money as the very purpose of living and leaving a legacy as a kind of failure to be avoided. But I don't look at it that way. My only goal is to fund my life while I am alive.

Since calculating probabilities in the way you suggest, will not alter the binariness of my individual outcome function, it is irrelevant. Your example reduces your own probability function to the same binary outcomes when you recommend insuring against fire if your weighted summation of probabilities turns out to be non-zero. It will always turn out to be non-zero. Ergo, buying the insurance is always the right choice. Each year that my house does not burn down my lifetime risk of catastrophic fire loss goes down. Yet, each year the right choice is to pay the premium yet again, because the risk of ruin remains unbearable at any age.

Fire insurance is cheap however, making the decision to purchase it easy. With the provision for funding extreme old age, cost is significant and has to constrain the decision for most of us. So, recourse must be made to rules of thumb and other approximations: reduce consumption now to extend portfolio life, but not to the point of deprivation, delay SS, move to a location that offers a lower cost of living, invest for a modest, rather than aspirational standard of living, etc.

If I were an insurance company or an advisor to a room full of retirees, I might use the probabilities you suggest because they could improve the aggregate outcome. But I am not a pool and the aggregate outcome is not my problem. My decision is to make choices to reduce the worst case possibility at the maximum cost (in current consumption, risk, etc.) that I think I can bear. I am willing to dismiss the risk of living to 110 just as I am willing to dismiss the risk of shark attack in the ocean, even though neither risk is zero. Theoretically, that is an arbitrary choice, but seems practical enough. At some point I have to eat some non-zero risk whose cost to me is subjective and uncertain, but that unsatisfactory result does would not appear to be mitigated by a refined appreciation of the probabilities.

[donheff]

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Originally Posted by photoguy Maybe to make the assumption explicit for the users of the program?

In Firecalc you plug in the length of time you want to model - 30 years, 40 years. It calculates how a given portfolio and expense level would have done historically. Everything is explicit. Seems pretty transparent to me. If mortality tables were incorporated to provide some sort of likelihood of success adjusted for average life expectancy it would seem to be less transparent. Toss in joint average life expectancies or life expectancies adjusted for health factors and and it gets worse. Seems much better to use years in retirement and run a few scenarios.

[Tekward]

This sounds like a Monte Carlo simulation problem. Here is a simplified discussion of combining distributions by just using probabilities:

We can assume that the age of passing is roughly a normal distribution - let's use a mean of 85 for discussion. We could calculate the standard deviation but then we're in the weeds. Let's make it easy and say there is only a 10 % chance that an average person will live past age 100. (From the ssa tables the average is closer to 5%, but we are all above average here so let's be conservative and assume higher survivability)

FireCalc calculates a historic distribution based on your situation and let's say for simplicity that at age 100 you have a 90% chance of still being wealthy. Now the product of the assumptions is:
~81% chance that you pass <=100 with money (.9*.9)
~9% chance you pass <=100 without money (.9*.1)
~9% chance you live >100 with money (.9*.1)
~1% chance you live >100 without money (.1*.1)

So the bottom line is that if you pick a number of years based upon 90% survivability you can use the FireCalc success % to look at the combined probabilities. Of course this is still using point probabilities where a Monte Carlo simulation would run thousands of trials and deliver a combined distribution but hopefully this adds to the discussion.

Note that you can not assume a survivability of 100%

[Tekward]

For inquiring minds, Figure 5 is the survivability curve.

Life Tables

[Independent]

Quote:

Originally Posted by Khufu I don't attempt to calculate the odds of the worst case, because to do so would be meaningless. I am not a population with a normal distribution. I am a single person for whom the outcome function is binary.

This is true. Similarly, the economic conditions that you will experience in retirement are not a normal distribution, they are one and only one sequence of events.

We need to decide whether we can afford to retire, or how much to spend this year, or when to start SS. I believe that you are saying that you write down the worst investment/inflation scenario you can imagine and the longest lifespan, then you do a deterministic calculation with those assumptions.

That's one of the approaches I've taken. When I do that, I discover that I should defer SS as long as possible, and consider a private SPIA besides.

[Independent]

Quote:

Originally Posted by Tekward This sounds like a Monte Carlo simulation problem. Here is a simplified discussion of combining distributions by just using probabilities: We can assume that the age of passing is roughly a normal distribution - let's use a mean of 85 for discussion. We could calculate the standard deviation but then we're in the weeds. Let's make it easy and say there is only a 10 % chance that an average person will live past age 100. (From the ssa tables the average is closer to 5%, but we are all above average here so let's be conservative and assume higher survivability) FireCalc calculates a historic distribution based on your situation and let's say for simplicity that at age 100 you have a 90% chance of still being wealthy. Now the product of the assumptions is: ~81% chance that you pass <=100 with money (.9*.9) ~9% chance you pass <=100 without money (.9*.1) ~9% chance you live >100 with money (.9*.1) ~1% chance you live >100 without money (.1*.1) So the bottom line is that if you pick a number of years based upon 90% survivability you can use the FireCalc success % to look at the combined probabilities. Of course this is still using point probabilities where a Monte Carlo simulation would run thousands of trials and deliver a combined distribution but hopefully this adds to the discussion. Note that you can not assume a survivability of 100%

You've going in the right direction. But note, as I mentioned above, you don't need Monte Carlo for mortality, the table itself implies a probability distribution of ages at death. (Again, assuming that you don't plan to get fancy with income/spending changes after the first death for couples.)

[RunningBum]

Quote:

Originally Posted by Tekward This sounds like a Monte Carlo simulation problem. Here is a simplified discussion of combining distributions by just using probabilities: We can assume that the age of passing is roughly a normal distribution - let's use a mean of 85 for discussion. We could calculate the standard deviation but then we're in the weeds. Let's make it easy and say there is only a 10 % chance that an average person will live past age 100. (From the ssa tables the average is closer to 5%, but we are all above average here so let's be conservative and assume higher survivability) FireCalc calculates a historic distribution based on your situation and let's say for simplicity that at age 100 you have a 90% chance of still being wealthy. Now the product of the assumptions is: ~81% chance that you pass <=100 with money (.9*.9) ~9% chance you pass <=100 without money (.9*.1) ~9% chance you live >100 with money (.9*.1) ~1% chance you live >100 without money (.1*.1) So the bottom line is that if you pick a number of years based upon 90% survivability you can use the FireCalc success % to look at the combined probabilities. Of course this is still using point probabilities where a Monte Carlo simulation would run thousands of trials and deliver a combined distribution but hopefully this adds to the discussion. Note that you can not assume a survivability of 100%

In my calculation I had only considered the possibility of living > 100 and running out of money. I didn't consider the failure scenario of running out of money before age 100, which you have. Thanks for pointing that out.

The one flaw I see in your calculations, and maybe you just did this for simplicity, is that you have the same 10% rate of failure <=100 as >100. It's a lot more likely that if you die early you won't run out of money.

You could divide this into 10 year blocks and figure the odds of you dying in that 10 year range, and the odds of you having money at death, and adding together the results of each range. So it might be:

50s - 5% chance of dying * 99.9% success rate = 4.995
60s - 10% chance of dying * 99.5% success rate = 9.95
70s - 30% chance of dying * 99% success rate = 29.7
80s - 40% chance of dying * 98% success rate = 39.2
90s - 10% chance of dying * 95% success rate = 9.5
100s - 5% chance of dying * 90% success rate = 4.5
Total success rate of plan = 97.845% (sum of last column)

These aren't real numbers, just some quick and dirty guesses. I'd guess my success rate is a lot higher in my 50s, maybe 99.9999 but since my chance of dying in my 50s is small, it barely moves the bottom line anyway.

Plug in your own mortality numbers from actuarial tables and success rates from FIRECALC or whatever tools or guesses you want to use. You can do it in 1 year or 5 year increments or whatever you prefer.

Or just use the 4% or 3.5% rule and don't fret about it.

I think this exercise can help people who have been taking more extreme mindsets on either end of mortality:

- Those who fret about living to 100+ and being uncomfortable with the success rate there, to show that the overall chance of both events isn't a very high factor in the plan success rate

- Those who figure from family history that they probably won't make it into their 70s or 80s, to factor in the impact of if they actually do make it that long

[ERD50]

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Originally Posted by Khufu I am an "n" of one.

That, IMO, is the concise and correct way to look at it. Averages be damned! This is my life I'm talking about, not a group being pooled together for me to bet on.

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Originally Posted by Fred123 So, how exactly do you calculate the odds of your worst case happening?

One of the problems with your view is, the number changes over time:

A 55 YO has an 18% chance of reaching 90, and a 38% chance of reaching 85.

But an 85 YO has a 48% chance of reaching 90.

Here's the conundrum - if you are the 55 YO, and you become one of the 38/100 that reach 85, you now have a 48% chance of reaching 90. So what are your chances of reaching 90 - 18% or 48%? Sure, you can do it based on averages, but then why would I use my seat belt, on average it is extremely rare for me to have a life threatening accident. I do it on the outside chance that it happens, I want to be prepared.

The 'nice' thing about this, is as you adjust your WR to prepare for a very long life, it approaches a 'forever' portfolio, where it starts to look like that WR could be sustained indefinitely. IOW, planning for 100 or 105 joint, isn't that much harder than planning for 90-95. Historically.

-ERD50

[ERD50]

An analogy:

Imagine you have a very important appointment that will provide a fantastic gain for you just for showing up. But if you are one second late, the doors are locked and you are out of luck. It's binary.


Let's say that you don't have a full tank of gas, and you have ~ 95% chance of getting there w/o running out, and you have no money for gas.

An extra gallon or two of gas is very valuable to you, as there is a lot at stake. You either get that gain at the appointment or you do not. You don't get some fraction of it. You will go to great lengths to get that extra gas.

That's how many of us feel about running out of money on the relatively small chance that we live to an outlier-range old age. We don't want that to happen, so we will go to great lengths to avoid it. So we run the scenarios to get an idea of the cost of preparing for old age (historically), and the cost seems fairly reasonable to many of us.

-ERD50

[ERD50]

One more analogy ( then I can rest - I just have to get this out of my head! ):

Let's say your nest egg is $1M, and you have no pension and no SS and no chance of going back to work.

I offer you a crazy bet - You put up all $1M, and we flip a coin. If I win, I get your $1M. If you win, I give you $10M.

Hey, the math says that is a fantastic bet! 10:1 payback on a 50:50 bet! Wowsers!

But you won't take it, because you can't afford to lose your only $1M, right? Hey, what happened to the math?

-ERD50

[MichaelB]

Very interesting discussion.

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Originally Posted by ERD50 One more analogy ( then I can rest - I just have to get this out of my head! ): Let's say your nest egg is $1M, and you have no pension and no SS and no chance of going back to work. I offer you a crazy bet - You put up all $1M, and we flip a coin. If I win, I get your $1M. If you win, I give you $10M. Hey, the math says that is a fantastic bet! 10:1 payback on a 50:50 bet! Wowsers! But you won't take it, because you can't afford to lose your only $1M, right? Hey, what happened to the math? -ERD50

The math is still there. Just that odds are only meaningful (and actionable) when they can be applied to a statistically relevant universe.

That is one of the things being discussed - how do we apply this to individual situations?