- This either is or will be or should be an important paper for some of the reasons they state: "Against the backdrop of declining defined benefit (DB) pension coverage and increasing reliance on defined contribution (DC) investment plans, there is a growing awareness that longevity risk pooling is being lost in transition." I agree with the authors that this awareness is a much bigger deal than people realize.
- In addition, this paper is a technical tour de force because it basically takes the lower half of Yaari's 1965 matrix (uncertain lifetime with insurance available) and: a) blows it out by extending the concept, and b) makes a (feeble?) attempt to make it accessible to a broader audience (see next point). This is one of those papers that actually does move the ball forward.
- One of the stated non-academic goals of the paper is to extend the dialogue on risk pooling beyond practicing actuaries and insurance and pension economists to general public, the media, advanced practitioners and regulators. My guess is that it will not find its way past a few research academics and some actuaries and maybe, as a very far stretch, some advanced practitioners. This is still pretty dense. I am not exactly a slouch in this area but even for me a lot of this was over my head...even though I could actually follow or at least recognize what they were doing with the math for a change. So, in my opinion, this does not have a broad audience yet.
- My bloggie-sense is that longevity risk pooling is a radically underutilized and sometimes mis-characterized tool that is more important today than it was yesterday and will be more important still tomorrow. This is basically the same as the first point but I thought I'd mention it again. My guess is also that folks like Milevsky will have an out sized impact on where we all go from here. I also think we have not gotten anywhere near a creative apex in the area of exploiting the value and goosing the efficiencies of longevity pooling (see my pseudo-tontine post)
- My advisor friend likes annuity products just enough to use them for the few clients for whom they make some sense but viscerally hates HATES the idea of annuitization (and proselytizes this discontent within a pretty wide radius) by which I assume she means irretrievably handing personal (and potentially bequest) capital over to the pool. I have been verbally beaten down on this issue many times. This bias is for a variety of reasons that are not all hers alone nor completely irrational in the context in which they are being viewed. Many people share this same bias. This paper, though densely obscure in its own aggravating way, goes a long way towards explaining why she and we might be wrong.
I had a hell of a time going back through the paper to find any excerpts near my underlines or annotations that would encapsulate or illuminate their important points in ways that would be understandable to a broad audience. First of all, there were really none that would work for that purpose. Second, this gap or lack illustrates my sense that they are working at cross-purposes with themselves if one of their goals is to truly broaden the base of people that should know or care about these issues. Let's give it a shot though. In no particular order here are a few items that I could extract:
- The algorithmic process for computing AEW value has been used by economists in the literature, going back to the work by Kotlikoff and Spivak (1981), Brown et al. (2001), or the reference on annuity markets by Cannon and Tonks (2008). What is less known – and we believe one of the contributions of this paper – is that by assuming some analytic representations for the remaining lifetime random variable, one can obtain closed form expressions for the value of longevity pooling. These formulae are simply unavailable or highly obscured when the mortality basis is a discrete mortality table and the optimization is done via backward induction or numerical dynamic programming.
- Under logarithmic utility preferences and the assumption that remaining lifetime is exponentially distributed with a mean value of: 1/λ (for example 20 years) and assuming the risk-free interest rate is coincidentally equal to the instantaneous mortality rate (for example 2.5%), then the value of longevity risk pooling is: √ e − 1, which is approximately 65%.
- More generally when the life expectancy is not equal to the interest rate, the value of longevity pooling can be expressed in an equally simplified manner as a power function of the ratio of two annuity factors.
- In contrast to what someone might expect, the value of pooling one more dollar (v using our notation) is worth more than the value of pooling the entire wealth (δ, using our notation), even in the presence of pre-existing annuities
- It’s evident from the numerical results that if one already has ψ = 75% of retirement wealth pre-annuitized, and one has to pay a loading of 30% to acquire additional annuity income, possibly due to stochastic mortality, the value of pooling can be negative. The rational consumer would be better off spending-down assets and living-off pension annuity income at the wealth depletion time. We leave these frictions as an avenue for future research. [emphasis added]
- On a separate path, Feigenbaum et al. (2013) use an overlapping generation model to argue that full annuitization is not welfare maximizing even with a deterministic mortality rate. In other words, the annuity debate (in academia) continues.
- In sum, we believe that building a strong case or consensus for annuitization in the future will crucially depend on a strategy of being able to explain the value to individual retirees who are limited by behavioral and cognitive obstacles. This is in contrast to a research strategy of extending the economic lifecycle model to include more general behavioral preferences, longevity insurance products and asset dynamics. In some sense this group is preaching to the (very small) choir of economists within the existing literature. We hope that some of the simple, analytic and digestible expressions we presented in this paper might be lead to contributions beyond the academic literature. At the very least √e now has an actuarial economic interpretation. [emphasis added; goal of strategy: not achieved]
- It might seem odd to split up the objective function in this manner, but in fact when π > 0, there is a qualitative change in optimal consumption at some point during the horizon t ∈ [0,∞). That is, liquid wealth is actually depleted and the optimal consumption rate c ∗ t = π from that point onward. That is the τ value we select. Until that wealth depletion time consumption is sourced from from both pension income and wealth. But after t ≥ τ consumption is exactly equal to the pension, the individual has run out of liquid (non-annuitized) funds and Wt = 0, for t ≥ τ . [this is an obscure but important point that I have not completely digested yet]
- We simply note that the integral in the denominator of equation (12) is an annuity factor (of sorts) assuming that the survival probability (tpx) is shifted or distorted by 1/γ. For example, when γ = 1 and utility is logarithmic, the optimal consumption function c ∗ t in equation (12) collapses to the hypothetical annuity consumption w/ax times the survival probability (tpx), which is clearly less than what a true annuity would have provided. The individual who converts all liquid wealth w into the annuity would consume c ∗ t = w/ax forever, but the non-annuitizer must continue to reduce consumption in proportion to their survival probability as a precautionary measure. Although it might seem as if equation (11) or equation (12) is plucked-out of thin air, neither of these are new or novel. [emphasis added]
- Perhaps this is a stretch, but [this is] an interesting expression nevertheless which provides an actuarial economic interpretation to √ e.
Ok. That's enough. Maybe you can see my point that the authors will defeat themselves if they think that this is going to explain anything at all to average individual retirees anytime soon (see bullet 7) and we haven't even integrated anything yet. On the other hand there really is some good stuff hiding behind the academic-ese. For example, in the 2nd to last bullet, there is something there on which an entire book could be written. Note the italics. In the absence of an annuity one must reduce consumption as a precaution...or maybe have a pool of "dead" capital allocated for the purpose of covering superannuation risk...which is really the same thing. The paper shows exactly how this works mathematically. That is good stuff. I made a weak attempt at this same point as clearly as I could in one of my last posts. The point in the fuzziest of terms was that the pool creates value that cannot be achieved anywhere else. It's a big deal and people that ignore it past a certain age, including my advisor friend, may do so willingly but they also do so to their own detriment. I look forward to the creativity of the financial services industry on this kind of thing in the future. Maybe I shouldn't hold my breath though.
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