Advancing the Retirement Finance Ball a Couple Yards Down the Field

There is no plausible scenario, at my current stage in life, where it would be believable that I would want to or need to know more about partial differential equations, and yet...  And yet my PDE innumeracy intrudes on my ability to appreciate a paper like Approximate Solutions to Retirement Spending Problems and the Optimality of Ruin (Habib, Huang, Milevsky 2017).  For while there has been tremendous forward movement in retirement and life-cycle finance over the last 20 or 30 years, there are still those that continue to move the ball forward a few yards at a time, which this paper does. It seems unfortunate, then, that the paper is so opaque and/or my skills are not up to it because it looks like it confirms several of my retirement finance intuitions and biases.  And though it's lovely to have one's biases confirmed vaguely and in general -- that's the engine that makes modern far-bi-polar media institutions thrive so well these days, not to mention my Facebook timeline -- it's better (when it comes to the ret-fin math anyway) to "see," to use and to know if not to replicate. That last is my typical goal if I think I either have or can get the skills.

The unfortunateness of the opacity is also that it obscures some key points that I think either are or will or should become important. ...And important, especially in this current era, because longevity continues to extend (or at least ex-US because we here are having a middle-america drinking and opioid binge that for the first time is causing longevity to contract for some cohorts, something others have called an epidemic of despair), retirements seem to start ever earlier, and the one really great finance invention we had going for us (defined benefit pooled-risk pensions) is in full retreat.  Papers like these and math like they deploy are sometimes all that is left between us and late retirement hardship. It's not just nice to kinda know this stuff then, it's essential , in my opinion, that we try to understand them fully.

This is not comprehensive or exhaustive but here, at the risk of copy-pasting the whole paper, are some excerpted points that resonated with me -- after a half morning with a pen and a coffee -- while ignoring or subtracting out the equations

• In particular, Bayraktar and Young (2007) show that when utility is a power function and the consumption rate is proportional to wealth, the individual who minimizes lifetime ruin probability behaves like an individual who maximizes the expected discounted utility of consumption.
• In other words, from a life-cycle perspective, ruin is not a scenario or outcome that should be avoided at all costs. Rather, the rational objective should be to slowly and smoothly deplete financial resources accounting for the declining probabilities of living to very old ages.
• Rather, if indeed the retiree reaches that age they should plan to live off their pension annuity income (if it is available). Stated bluntly, if there is only a 5% chance of reaching the age of 100, it is quite rational to (i.) assume that you won’t and (ii.) reduce your consumption to the minimal pension level, if you do.
• We demonstrate that the resulting procedure is reasonably well-approximated by a deterministic algorithm originally presented in Milevsky and Huang (2011) – so long as the calculations are repeated on a frequent basis. [that's a little obscure but the repetition thing is key]
• According to the authors, there is no fixed withdrawal policy – the forward-looking spending rate is proportional to survival probabilities that is adjusted upwards for pension income and downward for longevity risk aversion.
• The initial spending rate critically depends upon a retiree’s risk aversion and pre-existing pensions.
• The optimal consumption (i.e. sum of all pensions and withdrawals from the account) is a declining function of age. Retirees should consume more today than what they consume in the future.
• Wealth trajectory declines with age and retirees with sufficient pensions spend down their wealth well ahead of reaching an advanced age.
• Converting some of the initial investible wealth into a stream of lifetime income increases consumption at all ages even when interest rates are low
• On the other hand, the general conclusion of a declining wealth and spending rate over time remains valid. Furthermore, the approximate solution based on the deterministic approach, whereby the rate is adjusted to the return of the portfolio and solved annually with an updated wealth level, agrees well with that of the full optimal control solution.
• Our approximate solution is obtained by computing the withdrawal rate using the solution under deterministic return on a yearly basis, while allowing the wealth process to be stochastic, thus adapting to current market conditions, when the model is parameterized to realistic (historical) equity and bond return coefficients. In other words, the simplistic approximation [e.g. Milevsky and Huang 2011]  – when calibrated properly and frequently – can indeed be used as an accurate guide for retirement spending policy.

I guess all this means is I need to go back and review the 2011 paper...