In last month’s blog item, I wrote about the importance of ascertaining the right investment horizon in retirement planning. This post can be found here.
In this blog item, we consider that there are two levers available to retirees, asset allocation and consumption. Again we consider the comparison of the differences that arise when someone focuses on the incorrect Terminal Wealth (TW) objective rather than the correct Retirement Income (RI) objective.
Setting the scene
Consider an individual aged 25 just entering the workforce. Their superannuation balance is 0. Let us assume they will work till age 65 and retire immediately after that. In our simple example we allow for no tax and social security benefits (one of the simplifications that will be relaxed in future research). We assume that the individual earns an annual salary of $72,800 inclusive of superannuation in real terms and there are no promotional increases in the future.
In order to model this scenario, we use a utility function approach. The utility function chosen is Constant Relative Risk Aversion with a risk aversion parameter of 5. (Another future research topic is to allow for different utility functions). Under the RI objective, the aim is to maximize income in retirement and under TW is to maximize the balance at retirement. Both these objectives are translated to essentially maximizing lifetime utility.
We now have two levers available to us – asset allocation and consumption. Both these combine together to determine the superannuation balance. For example, higher allocation to risky assets lead to (on average) higher investment returns which increases superannuation balance. On the other hand, higher consumption leads to lower savings (from a fixed income of $72,800), which leads to lower balance. Moreover, the interplay between investment horizon and asset allocation mentioned in the previous post is still applicable here.
A further added complexity is that in the pre-retirement phase, the risky asset allocation is also dependent on superannuation balance, especially between ages 40 and 60. A higher balance leads to risk averse behaviour (lower risky asset allocation) while a lower balance leads to risk seeking behaviour to maximize balance.
Outcomes under the two objectives
The figure below provides a graphical representation of the asset allocation and consumption decisions and their impact on the balance under the two scenarios. (Solid lines refer to RI and dotted lines to TW; Black represents allocation to risky assets, Blue is for consumption and Magenta represents Superannuation Balance).
(Please note that this figure is directly sourced from my publication. If you would like to reproduce this figure please cite it as: Butt, A., & Khemka, G. 2015. The effect of objective formulation on retirement decision making. Insurance: Mathematics and Economics, 64: 385-395.)
In the pre-retirement phase, we find that under RI, consumption is lower than under TW. This difference arises in order to safeguard against the longevity risk for the individual. A lower consumption translates to higher contribution to superannuation. This higher contribution leads to higher balances under RI as represented above. Note, as balance increases with age, the amount consumed increases.
Asset allocation shows that the individual is fully invested in risky assets to about age 45 and then gradually decreases to be at about 35% at age 65. Interestingly, risky asset allocation is higher under TW than under RI and is a reflection of the lower superannuation balance under TW. The sudden drop in risky asset allocation at age 64, under TW, is to safeguard against adverse market movements (and hence maintain superannuation balance at retirement).
At retirement, the first question someone following TW should ask is: What do I do now with this large sum of money? Unfortunately, they realise that they still have to provide for themselves. Hence, at retirement, they switch to the more sensible RI strategy. At this point, the lower superannuation balance, essentially determine their choices (which are identical to the RI choices).
Post-retirement, as we saw in the previous blog, asset allocation is independent of age and balance and is almost constant at about 35% in the retired ages.
Consumption increases with age, till about age 85 and then falls until death. Interestingly, we find that under this model, consumption actually increases till the average life expectancy. (The expected age at death of a male aged 65 is 84.2). This an interesting glide path which was an unintended outcome of this research.
Post-retirement consumption, we find, is actually a fixed proportion of balance at each age. According to our research, the optimal consumption amounts were 4.5% of balance at age 65, increasing to 5.6% at 75, 7.7% at 85 and 11.4% at 95. This was another unintended outcome of this research. Given the government withdrawal requirements from account based pensions, this particular insight combined with the social security and tax implications would be an interesting policy paper in the near future.
Again, we find that the incorrect TW objective fails to maximize balance at retirement and provides worse outcomes in retirement compared to the RI objective. This simple model highlights the importance of understanding the wider context of retirement issues, particularly the need of getting the right investment retirement horizon.
Garry Khemka is an Assistant Professor of Actuarial Science at Bond University. His main area of research is optimizing the retirement outcomes for Australians. This blog entry is based on his publication “The effect of objective formulation on retirement decision making”.