Retirement

[drkitten]

I'm not sure of the purpose of the above analysis, but it is quite flawed.

It is, but the flaws are instructive, precisely because of the types of flaws.

Basically, you're doing the math using "acceptable" risk levels; he's specifically aiming at zero risk. You're also assuming that the population is renewing "fast enough," an assumption that has already bitten the Japanese in the ass -- but he's assuming that there's no population renewal at all.

What's a "reasonable" assumption for the rate of population growth?

 

[Perpetual Student]

It is, but the flaws are instructive, precisely because of the types of flaws.

Basically, you're doing the math using "acceptable" risk levels; he's specifically aiming at zero risk. You're also assuming that the population is renewing "fast enough," an assumption that has already bitten the Japanese in the ass -- but he's assuming that there's no population renewal at all.

What's a "reasonable" assumption for the rate of population growth?

Actually the flaws are fundamental which renders the "analysis" useless! What does zero risk mean? Zero population renewal? What are you talking about?

 

[Dunstan]

Getting back to the original question, Fidelity's web site has a retirement calculator. I don't think you need an account with them to use it. Yes, I'm sure they will encourage you to sign up for one, but the calculator is probably still useful as a crude measure of whether you're on track or not. I expect other investment firm web sites offer something similar; that's just the one I know about. You can adjust various assumptions about Social Security, your retirement age, living expenses in retirement, etc.

 

[drkitten]

Actually the flaws are fundamental which renders the "analysis" useless!

"Fundamentally flawed" can still be instructive and therefore useful.

What does zero risk mean? Zero population renewal?

Exactly. Daeku32 is asking the question "how would we pay for today's retirees if everyone under the age of 65 died tomorrow?" (no population renewal), and he correctly points out that we probably can't.

It's instructive to point out the role that population renewal plays in this, and how unlikely a zero renewal rate is....

 

[Perpetual Student]

Yes, how illuminating: if everyone under the age of 65 dies, we will need some trillions of dollars in a savings account to fund the pensions for all retirees. Well, then -- we had better plan for that contingency ASAP!
Hmm, who will do all the farming, storage and distribution for all the food we old folks will need?

 

[Francesca R]

I'm not sure of the purpose of the above analysis, but it is quite flawed. First, the present value of a $25,000 annual annuity, using very conservative actuarial assumptions, is under $300,000.

For assumptions like [number of years]=15 and [real discount rate]= 3% you're correct. But I wouldn't call those conservative. Currently the real interest rate is much lower than that, and post-65 longevity is already higher than 15 years. (However that seems to be a generous entitlement for a government scheme--more than anyone would get in the UK)

Second, when one considers all 39 million current retirees, a huge number have only a few years or even months left to live.

The average residual longevity tends to increase over time.

Third, for such a huge renewing population

Fertility is below or falling below replacement rate in many countries (though it is yet to do so in the US)

there is no need for a "savings account." A "pay as you go" system with a reserve for a few years (perhaps two or three) of payments works quite well.

Works quite well if two of your premises were solid, but they're not, and if your assumptions really were conservative, which they're not. Hence the growing problem with PAYG state retirement systems

 

[Perpetual Student]

For assumptions like [number of years]=15 and [real discount rate]= 3% you're correct. But I wouldn't call those conservative. Currently the real interest rate is much lower than that, and post-65 longevity is already higher than 15 years. (However that seems to be a generous entitlement for a government scheme--more than anyone would get in the UK)

The average residual longevity tends to increase over time.

Fertility is below or falling below replacement rate in many countries (though it is yet to do so in the US)

Works quite well if two of your premises were solid, but they're not, and if your assumptions really were conservative, which they're not. Hence the growing problem with PAYG state retirement systems

You really do need to study a bit of actuarial science and demography to participate in this discussion. One does not use 15 years of life expectancy as a basis for such calculations; one uses a mortality table. The assumptions I used are quite conservative -- try to buy a $25,000 annual annuity for someone age 65 from a solid insurance company and see what you'll have to pay (remember insurance companies make lots of money selling annuities).
Fertility rates effect only very long term planning, which is what responsible governments should do. Today's fertility rate has no bearing on today's retirees. If fertility rates were to suddenly decline, they would only begin to effect retirement funding levels in well over twenty years.

 

[I Ratant]

Yes, how illuminating: if everyone under the age of 65 dies, we will need some trillions of dollars in a savings account to fund the pensions for all retirees. Well, then -- we had better plan for that contingency ASAP!
Hmm, who will do all the farming, storage and distribution for all the food we old folks will need?

.
When I mention how important it is to me to have all those young folks working to keep my SS fund solvent, they look at me funny!

 

[Francesca R]

One does not use 15 years of life expectancy as a basis for such calculations; one uses a mortality table.

And your mortality tables are (already) out of date, and will get more so.

The assumptions I used are quite conservative

They are equivalent to approx 15 years of residual life expectancy, which is not conservative.

Fertility rates effect only very long term planning, which is what
responsible governments should do.

Except that they haven't, which is why social security systems are non-viable without reduction in benefits or increase in retirement age.

 

[Perpetual Student]

And your mortality tables are (already) out of date, and will get more so.

That's just silly. Actuaries always update and project mortality rates in developing annuity rates. Have you ever heard of an insurance company losing money on annuities?

They are equivalent to approx 15 years of residual life expectancy, which is not conservative.

No, it is not equivalent. You do not understand how present values are calculated.

Except that they haven't, which is why social security systems are non-viable without reduction in benefits or increase in retirement age.

Political pressure too often results in overly aggressive government retirement plans. The US social security system is currently projected to be solvent until 2037. It would take relatively minor adjustments in taxes, benefits and/or eligibility age to extend it far into the future. In any case, the major problem with such long term projections is that inflation, immigration, fertility are quite unpredictable. Mortality rates have been basically the same for the last couple of decades, with only very slow and minor improvements. Over the last 60 years, life expectancy has increased by about 6 years and seems to be approaching a plateau. It would require a huge breakthrough of some kind to change that. At the current rate of our growing national debt, the US may not survive as a nation to see that day.

LINK: SS Proposals

 

[Francesca R]

That's just silly. Actuaries always update and project mortality rates in developing annuity rates. Have you ever heard of an insurance company losing money on annuities?

I am not talking about actuaries--but about you and your errors.

No, it is not equivalent. You do not understand how present values are calculated.

$300,000 is the approximate PV of a $25,000 (real) annuity for 15 years with a 3% real rate. Do the maths. I think you don't understand annuity calculations. So maybe remain a student a bit longer.

 

[Perpetual Student]

I am not talking about actuaries--but about you and your errors.

I am an actuary; pay attention to someone who knows a lot more than you do about this subject. Your opinions here are uninformed and childlike.

$300,000 is the approximate PV of a $25,000 (real) annuity for 15 years with a 3% real rate. Do the maths. I think you don't understand annuity calculations. So maybe remain a student a bit longer.

First, life annuities are discounted for interest and mortality, which operates mathematically just like an interest rate; life expectancy is irrelevant. Second, historically, 3% is quite conservative; do a little research! Since you demonstrate no attempt to learn anything but prefer to cling to your uninformed preconceived notions, this is the end of this discussion.

 

[Francesca R]

life expectancy is irrelevant

False.

Second, historically, 3% is quite conservative

Yes historically . . . wake up.

 

[Perpetual Student]

I'll try one last time to educate you.

The present value of a life annuity is determined by:

[latex]a_x = \sum_{t=1}^{\infty}(v^t)_tp_x[/latex]


Life Expectancy is calculated by:

[latex]e_x = \sum_{t=1}^{\infty}_tp_x[/latex]


The naive public believes life annuities are calculated using life expectancy, which is erroneous and quite misleading, and is the basis of your confusion. The present value of a fixed term annuity is:

[latex]a_n/_i = \dfrac{1-v^n}{i}[/latex]

You are confusing the result obtained when n = e_x in the above formula, which yields a very different (and wrong!) result. As I said, the present value of a life annuity is not based on life expectancy. If you were to use the formula for a_x above you would see that the present value I originally estimated is very conservative. If you would like to confirm the above in a very simple way, just obtain a quote form any reputable insurance company for a $25,000 annual annuity. Insurance companies do not lose money on annuities, which are currently based on historically low interest rates. If we do experience inflation in the future (which is quite likely), interest rates will rise and annuities will be even cheaper.
I hope you learned something here.

 

[Francesca R]

Your formula confirms that life expectancy is a determinant of the present value (cost) of a life annuity. No idea why you continue to maintain that this is not the case. Would you similarly argue that life expectancy is irrelevant to mortality?

And government retirement benefits are indexed to inflation, almost everywhere, so unless real interest rates rise, the solvency of PAYG state retirement systems is not improved.

 

[Perpetual Student]

Your formula confirms that life expectancy is a determinant of the present value (cost) of a life annuity. No idea why you continue to maintain that this is not the case. Would you similarly argue that life expectancy is irrelevant to mortality?

And government retirement benefits are indexed to inflation, almost everywhere, so unless real interest rates rise, the solvency of PAYG state retirement systems is not improved.

I guess your not very good at mathematics!

 

[Francesca R]

Recognised (again) for the retreat that it is.

PS: you're