If my assumption above is correct then it should be relatively straight-forward to look at this even though this has probably been done a million times before. I've often been accused, in an unfortunate expression, of overthinking things, especially by my romantic partners, and perhaps I am doing that very thing here but me? I'd look at the discounted cash flow weighted by the conditional survival probabilities. It's basically an annuity pricing calc. The weighting is a challenge, though, because I'm not sure if I should weight based on my current age or the conditionally-attained age at the claim state. My assumption is that I'd use the probability vector based on my age now since I am making a policy choice now (to be updated again later) based on my probabilities of survival as I know them now. I'll go with that but maybe I'm wrong.
The weighting issue also begs the question: "which weighting?" by which I mean what table or what assumptions about longevity? One could use the Social security tables which represent a broad average type of population. One could also use the Society of Actuaries Annuitant table which represents a healthier longer lived cohort due to possible selection bias. But one could also go ad-hoc in either direction. I'll do all of the above.
First, here are the longevity scenario assumptions I'll use. These four scenarios should represent the conditional survival probabilities for a 60yo male (me).
A. Average. The social security period life table from 2016. This represents a broad average-type population.
B. Healthy. The SOA IAM table from 2012 with longevity expectations extended to 2018. This is a longer lived cohort and approximates a healthy person with longer mortality expectations. There's probably a socioeconomic overlay kind of thing here but I have not done the research.
C. Ill. Gompertz Equation - Low. This uses an equation that can mimic longevity expectations in a human population. The math can be more or less fit to A or B but here it is tweaked to represent an expectation that is shorter than "A." This might be relevant if there is inside info on ill health. The mode and dispersion parameters are 80 and 12 respectively where A might have 85.5 and 10.5 and B might have 90 and 8.5.
D. Extreme Longevity. Gompertz Equation - High. This is the same as C except that the mode and dispersion are set to 95 and 7. This would represent a very very long expectation for mortality for someone who is still also constrained by the known-to-be-longest-lived humans at ~120 years.
Then it's just a matter of discounting and weighting the cash flows. The math is basically X*Y/Z where X is the cash flow Y is the conditional survival probability and Z is the discount. Some other extremely convenient and unrealistic assumptions are as follows
- 60 yo male
- cash flows at each age as follows. This is not really me but is close in proportionality. Otherwise arbitrary. If I have not translated the income proportions correctly all of the following might be wrong:
o 62 = 1100/mo
o 66+8months (specific to me) = 1500
o 70 = 1900
- inflation and the discount rate happen to be the same for all years
- there will be no SS policy changes, lol
- No other "frictions"
- Gompertz math is set-up like this with x being age(60), m = mode, b = dispersion, and t = year:
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| Gompertz Eq |
When we run the numbers, assuming I have gotten this right, we get the following weighted NPVs:
It would be interesting to run same analysis on a couple.
ReplyDeleteYes. I admit I get a little solipsistic on my own situation. Others have done something like this for couples. Not sure how I'd approach it. I've heard that modeling it like 1 person with some kind of adjustment for longevity like a 1.4 or 1.6x factor works like two people. I'd have to read up. Personally I'm not getting married again so would never apply to me. I'll tune into this more as I continue my reading.
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