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.

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.   


  1. The trip to Tokyo provided a terrific opportunity to meet with Wade and students at GRIPS. There are a lot of interesting questions worth exploring.
    I generally agree with Wade's description of the key differences between my approach and W. Van Harlow's, but I might characterize my approach somewhat differently. Rather than saying "retirees would think quite negatively about spending any time in retirement without wealth," I would say that the level of negative feeling varies by what I characterize in my article as "loss aversion." Both Harlow and I use similar concepts of financial gain (leaving a bequest) and loss (living the end of life without wealth). However, we use different shaped functions in the loss region to turn financial outcomes into "utility" or "value." For example, under Harlow's measure, the prospect of 2 years living without wealth is more than 2 times worse than 1 year without wealth. My view is that such a prospect would be viewed as 2 times as bad or slightly less. (The "slightly less" view is based on Kahneman's concept of diminishing sensitivity as one moves away from a zero gain or loss reference point. See chapter 26 in Kahneman's new book for a good description.)
    A key point, in my view, is that concave utility functions that may be entirely appropriate when applied to levels of wealth or consumption may turn out to be inappropriate when applied to the financial losses (again see Kahneman). For example, let's say an individual faces two alternative prospects for retirement. "Living with wealth" means continuing to live in the family home, and "living without wealth" means living in a small apartment. How would we expect this individual to view the prospect of 2 years living without wealth versus 1 year—twice as bad, more than twice, less than twice? I would argue that "more than twice as bad" doesn't make sense unless one complicates the example.
    For instance, one of the individuals at the seminar made an excellent point about the availability of family money changing the picture. I agree, but when you think about this, it could mean that the individual isn't truly "living without wealth" or alternatively that instead of the individual's "loss function" we have substituted the utility function that applies to wealth or consumption of other family members. This may be entirely appropriate in certain cases, but I don't see it as the general case.
    All of this does point out the importance of taking individual and family circumstances into account when doing real-world retirement planning. But perhaps there are still things we can learn from general examples that can help improve the planning process.

  2. Wade and Joe --

    What you are both doing is marvelous -- major value to people and national economies as so many face bleak outlooks for retirement-years finances.

    There may be some difference between what you two are considering as the non-stocks parts of portfolios. I don't remember the mean return rate Joe assumed for the "fixed income" part of his portfolio, but I do remember he assumed its standard deviation to be zero, which I suspect makes the non-stocks part of Joe's portfolio more conservative than Wade's. That could also be part of the reason that for Joe all-stocks appeared the best portfolio.

    Joe, I can think of a couple of reasons why as years short of funds are added, each year added (which is closer to now) is worse than the prior one. With likelihood of gradual mental decline, I value earlier old-age years more because I am more likely to be more completely me. And there's sort-of a "present value" aspect in which years just ahead are of more immediate importance than those further in the distance.

    Maybe this just further underlines the importance of your concluding thought above: "the importance of taking individual and family circumstances into account when doing real-world retirement planning." Individual values and priorities too.

    Dick Purcell

  3. Joe and Dick,

    Thank you for the comments and clarifications.

    Joe, I've added your second comment up into the blog post so that the table can be formatted better.

    I agree with what you are saying about the utility functions. In trying to translate the equations into words, I didn't say your position properly.

    Dick, that is a good point about the bond assumptions. Joe has a 1% real return with 0 standard deviation. That will allow for a 100% success rate until money is gone and then a 0% success rate. My assumption above is back to the historical data for a constant-maturity bond fund, with a real arithmetic return of 2.52% and a SD of 6.84%. I think Joe has the right way to think about the bond return, but I do think it is nice to include some SD for it. The question is: what should that be when bond yields are lower than historical averages?

  4. To change the subject ... just to follow up on a topic Wade started to look at recently --- the pricing of annuities vs interest rates.
    Look at a recent paper

  5. Dick,

    I very much appreciate your comments. I find it quite a challenge dealing with this subject area, but it's very interesting work. I guess if it were easy, someone would have solved all these issues already.

    Re: the bond interest rate, I think the zero std dev may be appropriate if one is using a bond ladder to match retirement spending, but, if not, it's probably best to include some deviation. For some reason, people like Sharpe use a riskless asset in their modeling with zero std dev, but I don't know their rationale.

    Wade raises a question about what to do when bonds are below their historical average. Perhaps, if you're trying to develop general planning principles that can be applied for many years (like Bengen's work) it makes sense to use historical averages rather than current rates, unless you think the world has changed and future rates will be different (for instance, I think future stock returns will be lower).

    Re: my all-stocks conclusion, I can see why, in my modeling, annuities beat bonds--an annuity is like a bond with longevity protection. I don't include a downside for the illiquidity of the annuity. Also, I assume minimal profit margins in the annuity compared to a bond. So at this stage the question I hope to look at more closely in the next few days is why I tend to get all-stock or all-annuity mixes rather than stock/annuity mixes, which I would intuitively expect.

    That's a good idea you have about the importance of earlier years re: the utility of number of years-without-money. What I'd like to do at some point is to get a survey funded where we could learn more about how people value these prospects--and get a better understanding of variations and underlying reasoning. It would give a better idea of which parameters to base on average assumptions and which need individual input.

    1. Joe --

      On the non-stocks part of your portfolios, that was my misinterpretation. I did not understand you were laddering, and thought that by zero standard deviation you were specifying most-conservative T-bills.

      In Sharpe's Investments textbook he devotes a whole page, plus a footnote elsewhere in the textbook, to specifying the "risk-free" or zero standard deviation can exist only for a single period that matches the life of the bond to maturity. Seems to me that means on this one Sharpe agrees with you, which means on this one he's right.

      Dick Purcell

    2. Thanks guys.

      Joe, I think you are not assuming a bond ladder, right? It does seem that current interest rates are the best choice anyway, though, because they are the best predictor of the subsequent bond returns. But the issue of the standard deviation may not make much difference in the end. Probably the key is to make sure the interest rate for the annuity calculation matches the interest rate for the bond returns.

  6. Wade --

    Seems to me your message just above suggests that the bonds asset class has no reversion toward mean. But at least in U.S. history, the stocks asset class does -- so strong a reversion that for 30-year results, the reversion is equivalent to reducing return-rate standard deviation by half.

    If the stocks asset class has powerful reversion toward a mean, and the bonds asset class has none, what does that do to the notion of the two being related by a risk premium"?

    I don't mean to be straying off topic. These assumptions are the foundations of our outputs and conclusions!

    Dick Purcell

  7. Wade and Joe –

    I just wanna refine my raising of questions re stocks v. bonds v. SPIA, on the matter of assumptions.

    Wade, I think you’re using Monte without reversion-toward-mean for stocks, so handling bonds without such reversion would be consistent. But for assumptions for means, I think that for stocks you’re using long-term average, in which case it may be unfair to bonds to use current lower-than average?? I’m not arguing against conservative assumptions, not at all, just raising a question of fairness to bonds. Is this point relevant? I dunno, just asking. ???

    Joe, using current lower-than-average conditions for both SPIA and bonds may be unfair to bonds, because low interest rates hurt SPIA less, since the effect of low interest on SPIA pricing is damped by their pricing being partly determined by mortality. Is this point relevant? I dunno, just asking. ???

    Regarding the role of equity risk premium in the stocks-bonds competition: There is an interesting thread on historical risk premia wouldwide at Bogleheads, here:

    Dick Purcell

    1. Thanks Dick.

      Maybe there is some mean reversion for bonds, I don't know, and the case seems to be less strong than for stocks. Lack of bond mean reversion could be something which slows down mean reversion for stocks.

      But at any rate, during retirement drawdown, what happens in the first years of retirement matter the most. If bond yields are low, then with no mean reversion returns will be low, and with mean reversion returns will be even lower as interest rates move up.

      I think neither Joe or I have used bond ladders, but with bond ladders you certainly would just use the current yield curve as a starting point.

      I do agree that something like Joe is also doing needs to be done: he uses a bond yield assumption and an equity premium assumption. I would agree that you should not mix current bond yields with historical stock averages, as that would benefit stocks a lot.

      Ultimately, it may just be a matter of presenting results with two sets of assumptions: historical US data really provides an upper bound of possibilities and something with a lower starting bond yield and lower equity premium could provide a lower bound.

      What do you think about that?