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Why academics like lifetime annuities

It remains a mystery in academic circles why people do not purchase life annuities. Financial models suggest life annuities are beneficial to rational decision-making individuals, yet in Australia the number of life policies purchased remains small (albeit with some nascent signs of growth). This is a global phenomenon – whether in the US, Canada, the UK, Switzerland, Israel, Chile or Singapore (all countries with developed defined contribution accumulation systems like Australia’s), there is little take up of life annuities.

In this paper I explain the primary reasons why some researchers believe it makes sense for people to annuitise their wealth at retirement. In my next article I will discuss reasons why people do not annuitise.

In 1965 Menahem Yaari’s seminal paper on annuitisation was published. Titled “Uncertain Lifetime, Life Insurance, and the Theory of the Consumer”, this paper came at a time when optimal asset allocation was the talk of the day. Research by people such as Harry Markowitz and Bill Sharpe into the CAPM (capital asset pricing model) and mean-variance optimisation was attracting much research attention. However all this work on asset allocation didn’t consider uncertain lifetimes. Yaari not only introduced the concept, but he went on to model how a rational person would draw down their wealth in proportion to their self-assessed survival expectations (the amounts drawn down will decrease as one lives longer and experiences a lower balance). He introduced life annuities into the model and demonstrated that for rational people with no bequest motives, life annuities have great attraction because retirement income does not have to reduce as a person ages – income is guaranteed for life. Finally he noted that people who buy annuities will experience a valuable ‘mortality premium’ which will actually increase their retirement payout (I’ll explain this shortly). Yaari’s work creates the idea of product allocation as opposed to asset allocation and it could be argued that it has greater application to financial planning; in some circles Yaari is known as the ‘Markowitz of annuities’.

For academic researchers, there are three important benefits of life annuities (this article assumes zero default risk by the annuity provider).

1. Annuities eliminate longevity risk

Rational models suggest that the purchase of life annuities increases individual welfare by eliminating the financial risks associated with uncertain lifetimes (ie longevity risk). Specifically life annuities eliminate the possibility of exhausting the savings of those who live longer than expected.

2. Constant income for life enables consumption smoothing

Life annuities provide a constant income stream for life. This effectively guarantees consumption smoothing through a person’s retirement lifetime. There are many proponents of lifetime consumption smoothing – as far back as famous economists Franco Modigliani and Milton Friedman. It is held that a smoothed consumption profile yields more utility than the utility derived from any other spending pattern across time. A life annuity is the only financial instrument which can provide a constant payment for the duration of an uncertain lifetime.

3. Mortality premium delivers higher income

In theory, life annuities provide investors with a potential higher level of consumption, generated by what is known as the ‘mortality premium’. This important concept is a direct benefit of individuals pooling together, enabling the life company to pay a higher rate based on the expectation that not all policyholders will survive to subsequent periods.

Consider the example of an individual who has $1,000 to invest for a year. If they invest in an asset with 6% return, they will have $1,060 at the end of the year. Compare this with a one year life policy where the payment is dependent on the survival of the policyholder. Assume that based on life tables the policyholder has a 3% chance of not surviving the year. Then, assuming the life company has access to the same asset, it can afford to pay $1,093 (= $1,060 / (100% - 3%)) at the end of the year. If we expand this process to a second year and then a third and so on we can grasp the concept that because expected survival rates from one period to the next are less than 100%, a lifetime annuity provider can commit to paying higher rates compared to a direct investment in the same underlying asset. Each individual yearly calculation aggregates up into the pricing of a lifetime annuity contract.

How well educated are advisers on the benefits that life annuities provide? In the Australian marketplace, Challenger is the clear market leader in annuity sales and it has unofficially taken on the leadership role in terms of championing the benefits of annuities. This entails both retail and financial adviser education but also lobbying and education of policymakers and regulators. Looking through Challenger’s marketing and education materials, I find mention is clearly made of the first two benefits, namely a lifetime income that is consistent. But I could not find a single mention of the mortality premium. It may be a difficult concept for retail investors to understand but surely it is important that advisers have an appreciation of this concept.

In my next article I will explore some of the reasons for the low take-up of life annuities.

David Bell’s independent advisory business is St Davids Rd Advisory. David is working towards a PhD at University of NSW.

Stuart Barton
March 20, 2015

Hi David

Just thought I’d respond to your question concerning the absence of discussion of mortality premia/mortality credits in Challenger’s marketing materials for retail investors.

In a nutshell: after considerable consumer research, we've yet to devise a socially palatable way to pitch to retail investors the slightly ghoulish notion that you can thank the expected earlier death of your fellow investors for such an attractive upfront yield. It's all a bit Hunger Games, even among the 55+ demographic.

(Maybe we should try harder, and we would welcome any thoughts and suggestion on this topic, of course!).

While all investors generally appreciate a bit more yield, its often a secondary consideration when the risk management features of annuities have been explained. The Baby Boomers are alive to market and longevity risk, don’t want to make a miserable pact with themselves to be excessively frugal, and some are prepared to pay for a capital-backed, APRA-regulated life office guarantee that they’ll never have to fall back on the modest age pension.

Still on the topic of the mortality credit dilemma, I've watched with interest the product design and marketing approach to this issue taken by another company currently marketing a non-guaranteed, defined contribution-style "pooled survivor" fund.

Rather than build a portion of the expected mortality credits into a guaranteed yield payable to all members of the pool from commencement (as with a lifetime annuity), this product chooses to target lower expected returns just above cash for all members for the first decade or so, while fully back-ending mortality credits as an expected 'bonus' yield accruing only for the long-livers.

I'm not sure how it will be ultimately pitched to retail investors, but my sense is that the low but reliable expected returns and liquidity features (only 5% capital forfeiture on withdrawal) positions it less as longevity risk management tool and more as a new kind of cash-plus, estate-planning tool which ultimately rewards the estate of investors who don't use the liquidity features and survive long enough to collect bonus income they probably don’t need at that late stage of their lives. While the payment of a survivor's bonus is a certain event for the longer-livers, the fact that the quantum and timing of the income is unknown might allow it to be viewed as a 'nice to have' feature which is purchased with a view to benefitting your heirs rather than yourself.

In some ways it's a softer, gentler kind of bet against the longevity of your fellow pool members, but in other ways it isn't, because at the pointy end of the pool, there will be considerable spoils for the victor; the last man (but likely, the last woman) standing.

One thing’s for sure, and that’s that the payment and marketing of mortality credits in pooled retirement products present a unique and interesting design and communications challenge.


Stuart Barton
General Manager
Corporate & Consumer
Marketing & Communications
Challenger Limited

September 20, 2013

The market for lifetime annuities must develop and deepen in Australia. In the UK's deeper market, people with actuarially assessed lower life expectancies (e.g. thse with diabetes, even perhaps smokers and the obese) can get bonuses (better pricing) that improve the attractiveness of lifetime annuities

Bruce Gregor
September 20, 2013


Good article. It will take time but eventually I think we will see acceptance of lifetime annuities - particularly with low yields and low inflation people will see the "mortality premium" becoming relatively bigger - so long as life annuities start to pay out at advanced ages like 75 or 80. We have to find better ways of selling this both socially and politically. It's a bit like "preservation" rule for super. It wasn't popular but it's why we have $1.6 trillion in super assets rather than say $0.5 trillion. Providing it is compulsory, lifetime annuitisation means much higher incomes for all retirees (and less bequest to children!).

John Peters
September 19, 2013


I too am a fan of the lifetime annuities but prefer to see them as an inflation indexed style rather than a flat payment. I believe that there is a golden opportunity for such "government"backed instruments to be issued to fund our need for infrastructure development.

However, I think the poor take up of annuities lies more with the under-funding of superannuation assets and the fact that people do not like to face the reality of what their future income may be limited to.




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