Extra Info from Moshe Milevsky about ER..........

[FinanceDude]

I'm just happy I brought some value to this discussion........

[bongo2]

Milevsky has a useful formula, but there is a very important caveat that I don't see in the short write-up linked above (the longer write-up does mention it). This is that Milevsky uses a constant force of mortality - that is, he assumes that the retiree is x% likely to die each year no matter how old. In fact, of course, people are very unlikely to die in their 40's and become much more likely to die as they age. For a standard retiree this won't be as big a problem, but for the early retiree in their 40's or even 50's this dramatically overstates the probability of dying early, and will overstate the "success" (success in this case is dying before running out of money) of the plan.

[FinanceDude]

Quote:

Originally Posted by bongo2 Milevsky has a useful formula, but there is a very important caveat that I don't see in the short write-up linked above (the longer write-up does mention it). This is that Milevsky uses a constant force of mortality - that is, he assumes that the retiree is x% likely to die each year no matter how old. In fact, of course, people are very unlikely to die in their 40's and become much more likely to die as they age. For a standard retiree this won't be as big a problem, but for the early retiree in their 40's or even 50's this dramatically overstates the probability of dying early, and will overstate the "success" (success in this case is dying before running out of money) of the plan.

Moshe uses actuarial data he gets from insurance companies for his longevity risk info.................

[Independent]

Quote:

Originally Posted by bongo2 Milevsky has a useful formula, but there is a very important caveat that I don't see in the short write-up linked above (the longer write-up does mention it). This is that Milevsky uses a constant force of mortality - that is, he assumes that the retiree is x% likely to die each year no matter how old. In fact, of course, people are very unlikely to die in their 40's and become much more likely to die as they age. For a standard retiree this won't be as big a problem, but for the early retiree in their 40's or even 50's this dramatically overstates the probability of dying early, and will overstate the "success" (success in this case is dying before running out of money) of the plan.

I agree with your observation - if Milevsky is using a constant force of mortality, then he is going to get bad numbers.

Looking at page 53 in the paper linked above, it certainly looks like the only thing he cares about is "average" mortality.

However, it you go to lengthier stuff that he's written, he really is doing this pretty well. He assumes that the force of mortality is an increasing function (my recollection is exponential, but I know he discussed a couple other possibilities). The lambda in the article is a parameter in the mortality function, not the result of the function.

[haha]

Quote:

Originally Posted by Independent He assumes that the force of mortality is an increasing function (my recollection is exponential...

Is that ever a depressing thought!

Ha

[bongo2]

Independent and FinanceDude: look at page 58 from ats5g's linked write-up (the "Caveats and Warnings for the Quants"). There he says he assumes ". . .the uncertain length of human life being exponentially distributed. This implies that the mortality rate is constant over time. . ." Milvesky does say "the results are remarkably accurate when compared against the true ruin probability under the complete mortality rates," but that was not what I found when I tested this.

One thing in this section that I've never noticed before in other write-ups is this comment: "equation 1 is an approximation based on moment matching techniques. . .errors are less than 5%." If you're trying to estimate a 5% failure rate this formula looks a lot less useful.

[Independent]

Quote:

Originally Posted by bongo2 Independent and FinanceDude: look at page 58 from ats5g's linked write-up (the "Caveats and Warnings for the Quants"). There he says he assumes ". . .the uncertain length of human life being exponentially distributed. This implies that the mortality rate is constant over time. . ." Milvesky does say "the results are remarkably accurate when compared against the true ruin probability under the complete mortality rates," but that was not what I found when I tested this. One thing in this section that I've never noticed before in other write-ups is this comment: "equation 1 is an approximation based on moment matching techniques. . .errors are less than 5%." If you're trying to estimate a 5% failure rate this formula looks a lot less useful.

It looks like I was wrong. I'm sure that actuaries will "recoil in horror". Intuitively, it seems that your earlier post is correct - the lower the age, the greater the error (even if you use a life expectancy that reflects the age).

I read Milvesky's book "The Calculus of Retirement Income" a little while ago. I "read" the book in the sense that I read most of the text but I didn't try to verify all the formulas.
I'm sure he discussed various models of mortality, and I thought he was settling in on an exponential force of mortality. I must have been too ready to skip the hard stuff.

[bongo2]

Quote:

Originally Posted by Independent I read most of the text but I didn't try to verify all the formulas.

Tell me about it! This is more than a little embarrassing for me since I'm supposed to know this stuff, and presumably even a quick check on the proof would have shown it to be an approximation.

[Nords]

Quote:

Originally Posted by haha Well, best to have a COLA pension! Ha

No need for snide comments-- you want a COLA annuity/pension then go buy your own through Vanguard or some other fine financial institution.

[haha]

Quote:

Originally Posted by Nords No need for snide comments-- you want a COLA annuity/pension then go buy your own through Vanguard or some other fine financial institution.

Nordsie, where you been? I've been missing your thin skin.

[Nords]

Quote:

Originally Posted by haha Well, best to have a COLA pension! Ha

Quote:

Originally Posted by haha Nordsie, where you been? I've been missing your thin skin.

You're right, Ha, we both have better things to do than slinging thinly-veiled attacks and pejorative diminutives at each other.

You have a nice life now.