Why would males' shorter pension's savings produce more, and not less, income?

Question

_{Source: The European Union: A Beginner's Guide (1 ed. 2012) by Alasdair Blair.}

[p 139:]  Gender has traditionally played a key role in the pricing of insurance policies.
  In 2004 an EU Directive prohibited all discrimination based on sex in the access to a supply of goods or services. In principle the Directive therefore prohibited the use of gender as a method of determining insurance premiums and benefits with regard to contracts that were entered into after 21 December 2007. However, the Directive also stated differential pricing could be maintained where statistical evidence supported such an approach. Insurance companies regarded this as crucial because as women drivers are statistically proven to have fewer accidents than male drivers, premiums for female insurance policies have generally been lower. In a similar way, because women live longer, men have traditionally

[p 140:]

received a higher rate from their pension annuities because their life expectancy is lower and as such their pension savings are able [1.] to produce more income over a shorter time [End of 1.].

What have I misunderstood about 1? If male pensioners die earlier, then their pensions would be shorter, and the principal would generate less interest and fewer payments. So why more income?

Answer 1

I suspect your confusion is merely because you don't know what an annuity is. An annuity pays you a regular stream of income until your death (e.g. $10,000 every year until you die).

So say there's a man and a woman. Each is aged 65 and each has \$100,000 in pension savings. Each person uses their pension savings to buy an annuity.

Suppose the financial institution (usually an insurance company) selling them the annuity estimates that the man's life expectancy is 20 years, while the woman's is 40 years. Then the actuarially-fair payout would be \$5,000 per year for the man and \$2,500 per year for the woman (if we ignore interest rates, discount rates, and similar complications).

Hence, for the same amount spent on the annuity (\$100,000), the man gets a highly yearly income (\$5,000 per year) than the woman (\$2,500 per year). This is what your quoted passage means.

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(More on how the annuity works: If the man/woman lives longer than the expected 20/40 years, then good for him/her. He/she keeps receiving the agreed-upon yearly payout even past those 20/40 years.

Conversely, if the man/woman lives shorter than the expected 20/40 years, then too bad for him/her. He/she gets the agreed-upon yearly payout only until he/she dies.)

Answer 2

By more income here is meant a higher annual income for a pensioner from an annuity purchased at a given cost.

Suppose an annuity will provide the purchaser with a stream of $X$ per year until death. In deciding how much to charge for such an annuity, a company will want to consider the stream of liabilities it is committing itself to. If a male pensioner has a life expectancy of $m$ years, and a female pensioner a life expectancy of $f$ years with $f > m$, then the respective expected commitments, as a first approximation, are $mX$ and $fX$, with $fX > mX$. Obviously there are a whole lot of other factors the company will consider, eg inflation, interest rates, age of pensioner on date of purchase, variance of life expectancy. But broadly, the company will want to charge a male pensioner less because its expected liabilities will be less.

Suppose that for the above annuity the company would charge the male $M$ and the female $F$, with $F < M$. Now look at this from the standpoint of a pensioner who has savings of $S$ with which to purchase an annuity. The male can obtain an annual income of $SX/M$, while the female can obtain $SX/F$. Since $M<F$, the male will have a higher annual income.