why the payout amount is reduced by mortality credits?

(2020 ,level 3,Notes,book4,page 228.)

mortality credits you get back. So reduces your debit.

The wording here really bugs me. The higher the probability of survival, the lower the annual payout.

Mortality credit is not probability of survival of an individual. Mortality credit is what you reap ( assuming you are an old hag of 70 yrs.) owing to other oldies who die leaving behind their surredered annuity. So no, it cannot reduce the payout if the vesting happens late on life. One of those things, I could never get my head around.

Maybe Magician can help.

Apparently this isn’t a quote from the curriculum.

@ Magician , I may stand corrected but so far my memory serves me it is from the he curriculum .

I just looked through the curriculum. I didn’t notice that example.

Also, in the curriculum, this is in volume 2, not 4.

Mortality credits are gained when your assets are pooled (when you have already annuitized your lump sum). The example is talking about waiting some years to annuitize in order to get a bigger lump sum and therefore get 6k annuity instead of 5k, however you forgive mortality credits (dead annuitants’ surrendered funds used to pay living annuitants). It is like a trade-off decision.

I think, I may have an explanation, I could be wrong. Suppose at 60, there are 100 beneficiaries in the pool who have purchased annuity. Obviously, the ones having low ( lower) probability of survival will contribute to the mortality credit of the ones that have high(higher) probability of survival. What happens at 65 ?

Regardless of one purchasing the annuity at 60 or 65, definitely the pool would have shrunk (there will be less than 100 in the pool) i.e. the no. of people contributing to the annuity pool would reduce drastically thereby contributing less to the mortality credit. This, of course is in absolute terms.

Hence the incremental mortality credit reduces while the ones surviving would definitely reap higher payout owing to lesser no. of surviving individuals enjoying the increased payout.

The above, to my mind is very much similar to the pass through securities in the mortgage market. Owing to prepayment, you receive a lump sum CF (one time). But you also buy in the prepayment risk, reinvestment risk and contraction risk, not to mention that your interest payout reduces drastically (in absolute terms) even if the market conditions (interest rate) remains unchanged.

Suggestions, Criticism, welcome.

i think it’s easier to understand if we think about total PV of payouts (instead of annual payout).

let’s say that we buy an annuity at age 60 that has a total PV of X. in comparison, if we buy that annuity at age 65, then the total PV would be less than X, because we no longer receive mortality credits accumulated from folks who died early (relative to their expected longevity) in those 5 years that transpired (i.e., from 60 to 65).