# Longevity Risk

On Page 278 of Book 3 ( Asset Allocation ) they give a table for longevity risk of 65 year olds living to various ages.

Age Joint Individual Male Female

80 90.6% 74% 68.0% 80.6%

85 78.4% 56.8% 49.3 65.3

90 57.0 36.3 29.5 23.0

95 11.5 6.0 4.2 8.6

I have two questions:

1.The Joint probability of survival of at least 1 of the couple is not calculated the way we saw it in Book 2

(p1+p2-p1*p2) . It doesn’t appear to match this calculation

1. What is the meaning of “Individual” . Is it also calculated ?

Can someone pl. help explain the calculation?

No idea why column 1 doesn’t match the joint probability calculation you show; it should.

Not sure about “Individual”; because it lies between “Male” and “Female”, I was thinking that it’s some sort of average; i.e., if the joint survival probability is x, this (individual) would be the survival probability of each of two identical (hermaphroditic?) individuals. That doesn’t work, either.

I think that the table’s . . . well . . . amiss.

they mention - individual - shows the probability that an individual will survive to the various ages.

and the other one definitely is not p1 + p2 - p1 * p2. It is an actuary’s table … so god knows what they do to arrive at these numbers.

Yes, it is one of those actuarial things. There is a specific set of formulas for calculating multi-life mortality probabilities, but you need the mortality rates by person by year. The only thing for a CFA candidate to take away is that people can live a heck of a long time.

Some states don’t allow underwriting life insurance and annuities on the basis of gender, so the Individual rates reflect this.

This is bc the CFA’s way of calculating joint mortality is over simplified and wrong. Reality and the practice of finance is not always like they think it is or represent it to be. The actuaries have it right. A man living as an individual has a different mortality rate than a man living with a woman in a joint co-habitation. A man living with a woman lives longer than a single man. Women keep you all alive longer changing your mortality rate. They are using an underlying different rate in couples.

long live women