Implied inflation rate in an inflation adjusted SPIA

cashflo2u2

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If you have premium quotes for a single life immediate annuity one inflation adjusted and one without, is there any way to tell what the implied inflation rate the insurance company is using? Would you need the mortality table they are using along with other stuff?

I would calculate the yield-to-maturity for each, treating them as fully amortizing bonds with a maturity equal to your life expectancy. The difference in YTM's should be a pretty good estimate of the implied inflation, assuming the fees embedded in each are the same.

BTW, the company will probably tell you what expected inflation rate they are using if you ask. Vanguard told me when I asked them.

duh! I never thought of asking. Simple is better.

I would calculate the yield-to-maturity for each, treating them as fully amortizing bonds with a maturity equal to your life expectancy. The difference in YTM's should be a pretty good estimate of the implied inflation, assuming the fees embedded in each are the same.

BTW, the company will probably tell you what expected inflation rate they are using if you ask. Vanguard told me when I asked them.

I like your first method better than your second. It seems that the only plausible answer somebody inside could give you is the result of exactly the calculation you did in the first paragraph.

They don't need to assume an inflation rate for inflation-adjusted SPIAs, they simply need to hedge the risk with TIPS or something similar.
They don't need to assume an inflation rate for fixed SPIAs, because they are priced off fiixed bonds.

I like your first method better than your second. It seems that the only plausible answer somebody inside could give you is the result of exactly the calculation you did in the first paragraph.

They don't need to assume an inflation rate for inflation-adjusted SPIAs, they simply need to hedge the risk with TIPS or something similar.
They don't need to assume an inflation rate for fixed SPIAs, because they are priced off fiixed bonds.
I talked to a life underwriter today. If he is to be believed, this thread is based on an oversimplified premise. Since an individual's annuity purchase will always be small relative to the insurance company's reserves and surplus, annuities are not ordinarily individually hedged. The rate of return assumption for the entire portfolio- bonds, TIPS, forest lands, mortgages, office buildings, etc. is taken as one input. Life expectancy is also more complex than “18 years for a 70 year old man”. It is made up of a group of individual expectancies for living another year, which are then multiplied by the discounted payout for that year.

Likewise, pricing a COLA SPIA relative to a flat payout fixed immediate annuity is informed by a whole set of possible inflation rates, each of which is assigned a probability.

So we can sit here and decide what an insurance company can and can't do, but unless we are life underwriters we really aren't operating with an in-depth understanding.

Ha

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Likewise, pricing a COLA SPIA relative to a flat payout fixed immediate annuity is informed by a whole set of possible inflation rates, each of which is assigned a probability.

So we can sit here and decide what an insurance company can and can't do, but unless we are life underwriters we really aren't operating with an in-depth understanding.

Ha

I don't really need to understand it, I just want to know what it is. Their assumption for an inflation rate, either individually or in the aggregate.

I don't really need to understand it, I just want to know what it is. Their assumption for an inflation rate, either individually or in the aggregate.

O-K, I think I will turn that one over to someone else.

Ha