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Your money or your life: what’s more certain?

Death and taxes are the proverbial certainties in life. Life, however, is full of uncertainties, like just how long a recently retired 65-year old will actually live and what the share market is going to do for the first ten years of their retirement.

Using a concept first explored by Moshe Milevsky, it is possible to compare the relative uncertainty around retiree lifespans and equity market returns using Australian data.

Market uncertainty

Investors are, of course, aware that equity markets are volatile. If a capital sum is invested for a period of time, the amount of capital available at the end of the period will be uncertain. The question is: how uncertain?

This question depends on the investment timeframe. As a rule of thumb, equity markets are volatile in the short term, but over the long run there is some reversion to the mean that partially reduces this volatility. For a retiree, the impact of returns in the first 5–10 years after retirement has a big impact on their capital base. So a 10-year period is an appropriate term to consider in a retirement context.

Data on equity markets from Credit Suisse, based on work by Dimson, Marsh and Staunton, provide the real returns on equities in Australia since 1900, split into 10-year periods. The returns for each decade can be seen in figure 1. These returns include all dividends and are before tax.

Figure 1. Real returns on Australian equities in 10-year periods.

Source: Credit Suisse using data from Dimson, Marsh and Staunton

One way to consider volatility is to look at the variation (standard deviation) from the average outcome (mean). Using Australian equity market returns, the mean real growth can be measured by the 10-year effective compound annual growth rate (CAGR): 8.7%. The volatility in this example is the measure of plus and minus one standard deviation from the mean, which is 13% and 1.9%, respectively.

Another way to look at volatility is to use a co-efficient of variation (the ratio of the standard deviation to the mean). Using the same average 10-year Australian example, the co-efficient of variation is 47%.

Life expectancy vs actual lifespans

What about the variation of actual retiree lifespans from average life expectancies? How much certainty can a retiree have about the length of their own life from retirement onwards? The answer to this question might be a surprise for most retirees and their advisers.

In 2012, the most common age at death for someone who was 65 years-of-age or over was 87 (the mode). Despite this, taking the probability of survival from age 65, the mean ‘expected’ length of life for a 65-year-old was 18.1 years or to age 83. In reality though, very few people live exactly that long. Some live longer and some not as long. The range of actual lifespans around this mean point is represented by a standard deviation of 8.4 years either side of 83, figure 2.

Figure 2. Number of deaths (males and females) by age at death, Australia 2012.
Source: ABS

For a 65-year-old, it is also possible to measure the volatility as a ratio between the variation of actual lifespans to the average life expectancy. Remarkably, the co-efficient of variation, the range of actual lifespans proportional to the mean, is also 47%. So it turns out that a 65-year-old has to cope with a lot of uncertainty around how long they are actually going to live.

Relative uncertainty

Both equity market returns over 10 years and actual lifespans (versus average life expectancies) for 65-year olds have the same relative level of uncertainty: 47%. While this result is generated through some selective data use, it does highlight that both the equity markets and actual lifespans at retirement are similarly uncertain.


Longevity risk is not just the risk of living longer and outliving retirement savings. Uncertainty around a retiree’s actual lifespan is another, more complex, aspect of longevity risk. Financial models and retirement plans generally revolve around average or expected life expectancies, done so for the sake of convenience. This is a serious industry shortcoming.

Two known retirement uncertainties – a retiree’s actual lifespan and the money earned on equity investments (pre-tax investment returns) – have a surprisingly similar dimension. Both forms of uncertainty need to be managed in retirement at the same time. The first step in doing this is to move away from planning for averages. Retirees know that they won’t achieve average share market returns and will build a portfolio to adjust for this.

What far fewer retirees will have realised is that they will almost certainly not live to their average life expectancy either.


Jeremy Cooper is Chairman, Retirement Income at Challenger Limited.


Peter Vann
May 31, 2014

The BBQ conversation in the link below illustrates the misleading results from using averages for investment returns

We believe that the inclusion of investment volatility and mortality uncertainty in estimating retirement outcomes should be handled differently. Investment volatility affects most retirees according to their specific investment strategy. However, whilst we all are subject to mortality, it is much more idiosyncratic (as mentioned by Ramani in comment #2).

But assessing retirement income within mortality considerations is much easier than investment volatility. It involves providing the relevant information to a retiree (or their planner) which illustrates the trade-off between the level of a sustainable retirement income* and how long it will last. The chart in the above link shows this trade-off for one member using their investment strategy.

Then a retiree can then make informed decisions regarding the likelihood of retirement income levels** against financial longevity incorporating their own “mortality” situation and investment volatility.

* including the impact of investment volatility
** optionally incorporating a different relative income level through each retirement phase

May 31, 2014

Navigating life based on averages is not dissimilar to crossing a river: on an average you are unlikely to drown.

Taking Steve Schubert's comments into greater granularity, individual retirees should have a better basis to calibrate their own mortality by considering personal health, heredity, past occupation and current life style factors. More difficult to do this with exogenous investments especially in our DC model (as argued in my joint paper 'Actuarial Challenges in DC Schemes', Diversification across assets, industries and locations and life-cycle transformation have been suggested as plausible ways of dampening undue variances around the average.

We should also reduce the system's load by discouraging super being used as an inheritance tool as it now blatantly is.

A less travelled route worth exploring is to minimise retirement expectations by considering the controllable components on the contra side: after all, in the twilight years some of the more pleasurable and expensive pursuits are medically or physically contra-indicated. The flesh is less willing to pursue expensive escapades. If we could add to this a modicum of family support (replicating what we do to our kids in their vulnerable ages and Confucius-led Singapore has illustrated), we might about get it right. Finance alone will never cut it.

If all this fails, resort to Omar Khayyam:

Ah, Love! could thou and I with Fate conspire
To grasp this sorry Scheme of Things entire,
Would not we shatter it to bits — and then
Re-mould it nearer to the Heart’s Desire!

Steve Schubert
May 30, 2014

Good article Jeremy. A former colleague of mine, Don Ezra, also reached this conclusion about the relative uncertainties of equity markets and lifespan. Another longevity issue impacting retirement planning is what "population" the average is drawn from. The most obvious and common population refinement is to separate male and female life expectancies. However, taking into account socio-economic status, smoking habits and other characteristics if data is available can help futher refine the relevant average (though not necessarily the variation around the mean).


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