Saturday, March 17, 2012

Retirement Sustainability, Asset Allocation, and Retirement Length

On March 15, Joseph Tomlinson presented his  “A Utility-Based Approach to Evaluating Investment Strategies” article from the February Journal of Financial Planning in a research seminar at GRIPS here in Tokyo. I discussed his article in a past blog entry. It was a very interesting presentation, and I wish I could write a full report, but the presentation left so many interesting unanswered questions that I can't fully articulate my thoughts at this point.

Just one issue from the seminar that I would like to discuss now regards Joe's point that W. Van Harlow found an optimal stock allocation for retirees of only 5-25% because Van Harlow implicity assumed that retirees don't mind spending a few years of retirement without any remaining wealth but really don't like having to spend a longer period without wealth. Perhaps they don't mind being a small burden on their children but don't want to ask for too much.  Joe thinks that a more appropriate way to think about this is that retirees would really think quite negatively about spending any time in retirement without wealth.

An implication of this is that Van Harlow finds support for low stock allocations, while Joe has the interesting result that retirees are most satisfied either with 100% annuitization or 100% stocks depending on how important bequests are. More importance for bequests means stocks (see my description of William Bengen's original research for more on this).

But Joe is surprised about these stark results. Why doesn't a more balanced approach show up as an optimal strategy.

For now, I'd just like to show two figures to hopefully clarify a bit about this.

The first figure shows about traditional success rates for retirement withdrawals. For an inflation-adjusted 5% withdrawal rate with Monte Carlo simulations calibrated to large-cap stocks and intermediate-term government bonds from the SBBI data (1926-2010), we can see that more conservative strategies have higher success rates for short retirements but lower success rates for longer retirements. This makes sense, because the bond returns are not so volatile. For short retirements, there is little chance of running out. But once the return and withdrawal rate are combined for the simple annuity calculation for how long the money will last, the success rates plummet as fewer and fewer simulations would provide enough lucky returns to keep the strategy going.



The second figure I think is more interesting. This figure does away with the success rates idea about withdrawal rates and actually shows the magnitude of failure. That is something important. Retirees should care more about how long they spend without money rather than just knowing if the strategy succeeded or failed. This figure shows the probability of spending at least x years (the number of years on the x-axis) without any wealth. This is calibrated using mortality data for an opposite-sex couple who are both 65. What is interesting here is how there is a jump from 100% bonds to 100% stocks at about 12 years. 100% bonds is the "riskiest strategy" in terms of spending 1-12 years of retirement without any wealth. 100% stocks is the "riskiest strategy" in terms of spending at least 12 years without any wealth. I look forward to hearing Joe's comments, but I think this at least shows why Van Harlow may have found support for low stock allocations while Joe finds support for high stock allocations: it is that Van Harlow cares more about avoiding a very long time without wealth and Joe cares more about spending any amount of time without wealth. Regarding Joe's point though, that would lead to a more balanced asset allocation, but Joe is also incorporating bequests into the calculation, and bequests is something ignored in both of these figures. With enough interest in bequests, that would be a tradeoff that 100% stocks supports more bequests while having a higher probability of spending some time without wealth than a balanced allocation.





Update: Joseph Tomlinson provides the following comment, but as his comment includes a table which can't be formatted properly in the comments, I am including his comment here:

That's a very useful Figure 7 Wade came up with. I tried to guess numbers off the figure and extrapolate to come up with this chart that shows chances of spending at least "X" years in retirement with no wealth.



Stock/Bond
0 612
20%/80% (Harlow)24% 10%2.5%
100%/0% (Tomlinson)19% 13%6.5%
60/40 ("typical" mix)15% 8%2.5%
Annuity0% 0% 0%

The "zero column" shows the measure commonly used by financial planners. The other columns add important additional information about the potential magnitude of losses. I've used a 20/80 stock/bond split as a rough proxy for Harlow. One can see how an all-stock portfolio increases magnitude-of-loss risk even though 100% stock beats 20/80 on the "zero column" measure. It's interesting that 60/40 beats Harlow at 0 and 6 years, and ties at 12. As Wade has showed in other work, there are other aspects of Harlow's work, like his equity premium assumption, that may influence his results. It turns out that, for a 65-year-old couple, 5% is close to a hypothetical annuity payout rate based on SBBI historical returns—so I show the zero percent line at the bottom of my chart.

This shows why annuities become the allocation of choice in my article for those with high loss aversion ratios (that may also reflect a lack of bequest motivation). (Note that my loss aversion measure is really more a measure of the relationship between losses and bequests, rather than a pure loss measure.) What I need to study more is how my analysis jumps from 100% annuity to 100% stock when loss aversion goes down instead of making various stock/annuity mixes optimal. I can't seem to get all the way there from Figure 7, but perhaps I need to think about it more.