Mortality and Risk

Introduction

In this post we provide information on retirement spending patterns when presented with both investment risk and mortality. To date we have considered these separately. This post builds on the work in previous posts:

In the Retirement Calculations post we  worked out the spend per year assuming we are on the age pension only at age 90 and also assuming we would like a constant spend to 90 where possible (or at least a constant spend subject to specified percentage drop at various ages).

In the More on Risk post we worked out how our retirement average spending will vary if we assume annual Super returns vary independently according to a normal distribution and  the spend per year during each year of retirement is worked out by solving for a constant annual spend for remaining years while being on the age pension only at age 90. As an aside, in the ALP Super Tax post we showed how the spending each year will vary (rather than just the average).

In the Mortality post we got rid of the assumption that we need to be on the aged pension only at 90, and instead assumed that in order to work out our spending for a given year, we would assess our likely longevity at the end of the year and spread our remaining funds from the present age to a longevity-dependent future age.

In this post we combine the concepts in the Mortality and More on Risk posts.

Because we are getting into some serious number crunching territory now, I will focus on the Single person.

Single Person – Mortality and Risk

In the Tweaks and Mathematical Diversions post we worked out the spend per year using us as an example, commencing in 2015 and using pre-January 2017 age pension rates. We also assumed a drop in spending at 70 of 10% and another drop at 80 of another 10%.

The below graph is an update, now showing for a single person rather than a couple, using post-January 2017 age pension rates rather than pre-January 2017 age pension rates, and also using a more realistic spending drop of 1% per year from 65 through to 85. You can see that there is very little aged pension!

Now, lets assume that Super returns are normally distributed, with a volatility of 6.21% (the same volatility we assumed in the More on Risk post). The graph below shows the variation in the spending per year for each age. The green band represents 60% of the outcomes and the blue + green band 80%. That is 60% of the time the spend per year will fall within the green band, and 80% of the time the spend per year will fall within the green + blue bands.

You can see that as time goes on, there is more uncertainty about the spend per year. Also, because we only have access to cash to 60, there is not much variation prior to 60.  Because we only have access to a limited amount of Super prior to the house sale, the variation prior to 64 is also less than after 64.

Now lets look at spending assuming we take in to account mortality. The graph below shows the spend per year assuming we moderate spending according to mortality information, and the spend per year is based on spreading funds from the present date to the whereby we will only be alive with a probability of 10% (for a male).

You can see that our drop in spending continues beyond 85 because of the reduction due to ageing and the spend per year falls below ASFA comfortable about 96.

Finally we can now show the mortality-based graph taking into account volatile super returns:

You can see that at around 89 90% of the time our spending will be above ASFA comfortable, while at 98 90% of the time our spending will be below ASFA.

Couple – Mortality and Risk

The below graph shows the spending for a couple, assuming we run out of funds at 90, and again we reduce spending by 1% from 65 to 85.

Here is the graph showing the variation in spending assuming variation in Super returns.

We can also show how spending for a couple varies when we plan to reduce our spending in accordance with our expected longevity. However, we are in some serious number crunching territory now, so this will need to wait until later!

Conclusion

We can combine the spending approach described in the mortality post with the approach used in the More on Risk post to show how mortality-based spending is likely to vary if we introduce super return volatility. This may be a useful graph to display on an interactive web site.

In the next post we will look at how spending varies with the riskiness of our investment portfolio.