Mar 17, 2018

Some thoughts on bequests and fairness: a mini moral-theory story about me vitiating my optimal path - draft 1

I thought I was going to jot down some thoughts on bequest and annuity pricing for around 20 minutes. Five days later and this is one of the longer pieces I've done and probably the second hardest.  There are a ton of mistakes and wrong paths followed but one of the themes of the blog is to use writing to consolidate my memory so let's soldier on if for no other reason than that...

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The Problem of locking up assets and "cheating" bequestees

I've been told, quite assertively and quite often by an advisor friend of mine, despite my (formerly) shallow, naïve, amateur insights on the value of longevity pooling, to never ever annuitize…ever. Ever!!!  Trying to press on this issue, even for some perspective or to get more info, is a little like a wall-head-banging excercise. So I don't. Or at least not anymore.  My presumption is that, in the absence of a reasoned and calm discussion, the rationale for her position is that: A) there are products and strategies that can provide longevity risk hedging and income flooring similar to a traditional annuity but without the irreversibility of giving your capital to an insurance company "forever" -- and here she used a particular company's GLWB rider with step-ups and minimum withdrawals as an exemplar, and B) not so unrelatedly, the idea is that irreversibly giving your capital away to the evil insurance company is both "unfair" to potential bequestees if you die the day after signing the contract as well as risky if you happen to have spend shocks in the future (the latter part of "B" I will mostly ignore). This is part of the fabric of the annuity paradox, by the way. This is also something I want to understand. Let's hit both A and B and see what happens.



On "A" - that there are products or strategies that can somehow square the circle of longevity-pooling-value vs. allowing for a bequest

To my mild chagrin, she is probably more right than I gave her credit for on this point. Some of the new products out there are in fact worthy of attention if one is careful about the analysis.  On the other hand it is still not a simple problem and I am still not all that sanguine on things like GLWB riders. It is a much more complex problem than I expected and I still think that it (GLWB) does not unlock the true power of "the pool" for fully supporting lifestyle in real terms at later ages like "real" annuitization can [1]. Joe Tomlinson, a quantish advanced advisor that I totally trust, did a good cover on the GLWB vs Annuity question back in 2013 at Advisor Perspectives here (Do Annuities ReduceBequest Values? ).  I am not yet an expert on GLWB features so let's at least start this discussion by using a wise average-joe version of a thought on GLWB (random internet quote on a bogleheads bulletin board): 
It's not like the insurance co rubs their hands together and creates money you're otherwise not entitled to. Monte Carol analysis shows that these annuities turn out better than a conventional portfolio something like 6% of the time. --see appendix A
Now let's also quote Moshe Milevsky (Life Annuities: An Optimal Product for Retirement Income, Moshe Milevsky CFA institute 2013) because, well because he is ubiquitous in ret-fin, unconscionably prolific, blindingly bright, and has written on this a number of times with continuous math in hand:

Whether the GLWB is better than the life annuity from the consumer’s perspective depends on a complex relationship between the pricing of the guarantee, the retiree’s optimal consumption strategy, and the existence of bequest motives.

The common denominator of all these insurance riders is that they contain an implicit put option on financial markets plus some form of longevity insurance, akin to a pure life annuity. Of course, using the concept of put–call parity, they can also be viewed as call options to annuitize at some variable strike price. The (anecdotal) “sales pitch” for these products revolves around the idea that the guarantees permit investors to take on more investment risk than they would without the guarantees.1 

Here is the bottom line: To the naked eye, the VAs with GLWB might appear to have all the benefits of a life annuity—guaranteed income, risk pooling—but without the costs associated with illiquidity and irreversibility. However, although the GLWB product has merits, especially considering the research evidence that it was initially underpriced, it is not a substitute for pure life annuities because of its lower yields. For example, whereas a life annuity might pay 6% to a 65-year-old, the GLWB rate under the same market conditions would be in the vicinity of 4%
   
So, is GLWB a magic bean that allows one to displace a traditional annuity so that one can both hedge out longevity risk AND keep access to capital for some reason (bequest, spend shocks, etc.)? A little bit yes and a little bit no.  They do what they say they will do (and keep in mind, it appears as if fewer and fewer offerings are on the table these days) but they sag a bit when trying to deliver real (vs. nominal) returns in the very late game, there is a distinctly lower payout (vs annuities) due to whatever the insurer thinks it needs to keep to be able to make the promise (those fees that help compensate for longevity risks, admin costs, maybe market volatility risk, etc etc), and there are maybe more problems in the details if one were to dig into the contract terms[2].  There is probably a default risk factor in there too. I'd say the jury is out but getting more biased by the minute. 

For some additional links and excerpts and thoughts see Appendix A below.

On "B" - that it is somehow unfair to "someone other than me" to irreversibly throw my capital away into an insurer annuity hole…because I might die tomorrow and all that money will go to the pool (incorrectly described as the insurance company) rather than someone in my circle.

We can talk about the technical pros and cons of products and strategies all day long but I think this "B" thing is quite a bit more interesting than "A." We'll use me as part of a case study. But first, let's start with a baseline set of assumptions that includes the idea that I think I am already in some optimal equilibrium and that I have a no-big-bequest strategy.  That means that [Wealth - PV(LS+SS+SA+SR+MC+O) = 0] [3]  which also means I am in perfect equilibrium and that that equilibrium might just include a big future allocation to tradition SPIAs[4] if I decide that that allocation will optimize my lifetime utility of consumption. So who is this then, exactly, that insists that I not seek my optimal welfare the way I think it should be sought? A third party? They have no stake! A child? Perhaps but I have stated "no bequest." This is not their call to make, it is mine and I have already factored their future welfare into my equation.  If there is to be a disequilibrating event, like switching strategies to suit someone's interests other than mine, then there should also be fairness. That question of fairness brings me to the beginning of what we might call my "mini moral theory of bequest."

B.1 - A question of symmetry

This, by the way, is my (possibly over-wrought) purpose for the post. I think that if I am going be induced by a third party to change from one optimal strategy to another less optimal one (my unexamined strawman here was that a SPIA might be part of the optimal thing and anything else will be less so) that there should be some symmetry: the negative cost I have to incur to revise my strategy to "their" liking (benefit?) should have some symmetry with some positive thing that I receive from them in exchange.  So, let's define my switching costs as maybe framed in these terms: a) a general loss of optimality, b) probably a substantial increase in unfunded superannuation risk if I were to seek "no longevity hedge at all" (call that "no hedge" a systematic withdrawl plan or SWP) in order to favor bequests, and c) there will be a presumed smaller cost, given my various biases, to swapping a traditional longevity pool strategy for a GLWB longevity rider strategy, two strategies that some people put in the same bucket even if I don't.

My big question then is "where is the other side of the deal?" A third party of any kind, child or otherwise -- if they want to make a claim on the bequest-value of my estate if I die tomorrow after I would have handed a check to New York Life or Ohio National, a proposition they do not seem to like -- should at least be willing to pay for some of the value of that incremental benefit (their benefit, my new risk) that they would propose to receive (that is, if I am willing to sell it (and I wasn't before) and if I am convinced of my current plan's optimality). Really? They get a benefit if I croak early but aren't there for me if I don't and I run out of money because they talked me out of annuitizing!?  That is a terrible deal that I call "not fair." I wan't to be compensated for my new risk. Overthinking? Of course it is and yes I realize I am exaggerating everything here but let's take a look at this anyway because it's fun.  This is fun, right? The question, I suppose, is now about how to value the symmetry.

B.2 - Valuing the fairness and symmetry - a map

Let's say for the sake of argument that there are two types of switch: 1) from a full immediate annuitization strategy to an uninsured systematic withdrawal plan SWP, and 2) from a full immediate annuitization strategy to a GLWB strategy. There are others, perhaps. In any case, I should try to evaluate the fairness (impossible?)[5] and cost (possible) of these switches. First a map:  
For what it's worth, if one were to want to have a more formal and less amateur evaluation of GLWBs one might look at Wade Pfau's piece at Advisor Perspectives on this… GLWBs: Retiree Protection or Money Illusion? 

  
B.2.1 - Swap 1: Swapping out SPIA for a systematic withdrawal plan

First the hard part. What is fair?  I have no idea but what I hear from others is that if one dies the day after contract signing and all the money is gone and (importantly) one does not understand the theory of longevity pooling, that that's not "fair." If one understands longevity pooling it is another story entirely. On the other hand, if one were to die at age 253, well then, it was fair or you at least beat the insurance company (forgetting about the theory of risk pooling again).  The point where it flips from unfair to fair is somewhere in between tomorrow and age 253 and is 100% opinion, especially if risk pooling is not understood. We'll run some numbers though. The way I have seen this done in the past by someone somewhere is to look at something like:

a. fair = when the cumulative PV of payments is at least = the original annuity price
b. fair = when the IRR passes the discount rate
c. fair = when payments continue past when a SWP would have run out

Some bad assumptions first. There is no: inflation; company defaults; insurance loads; fees; worries about rate reversion and low current rates; taxes; knowledge of advanced topics like Annuity Equivalent Wealth, wealth depletion time, real option value of not annuitizing; or free boundary of annuitization, etc.  Human capital is depleted. There may be more...

Let's say we are 59, male, have liquid wealth = W = $1,798,528, mean annuitant longevity is ~86 depending on how you do it, and we and want to lock in C=100k in lifetime cashflow for our optimal plan.  We kinda backed into W by way of the 100k by using this formula: 
where "l" (load) is zero and the tPx comes from a SOA table using G2 extensions to 2018 for a 59yo male and where the annuity discount rate is ~3.01% for now. [6] If we double check this idea on AAcalc.com with the proper assumptions we get an annuity price est. of 1,807,806 (3/15/2018). Close enough for a reality check. I could try harder but why?  With respect to our a b c:

a. The cumulative PV (npv) of the 100k cash flow discounted at the same discount (this analysis is not shown) hits W at ~84.

b. the IRR of the annuity cash flow passes the discount rate at around age 85 if I did it right. 

c. If I run a net wealth process with the same W and C and return = discount, it runs dry, not surprisingly, at ~84. This would be a stochastic process in real life so the distribution of "run dry" would be relatively wide depending on volatility and the sequence of returns in individual paths of the random return generating process. 

Let’s say that a reasonable person, unaware of longevity pooling theory, would conclude that the annuity would be "morally fair" if death occurs at around 84-85. Let's give that some more room for the unmodeled variability and risk of "c" (the SWP) and say that 75-80 might be fair too.  We're 59 so let’s call it 79, so 20 years.  This is debatable but not totally insane.  Many people might lean a little later than that to try to get a bigger "fair" share of the pie…recalling that they might not know about how risk pooling works. Have I mentioned risk pooling yet?

B.2.1.1 - Swap 1: Fairness valuation - a minimum price

Given the above, if someone wants to call an SPIA "unfair" (or suboptimal) and wants me to switch to a SWP so they can have access to my estate if I die the day after the contract, they would have to at least offer to pick up the tab for the age 79 ->risk if it unfolds, because I just threw my longevity risk "hedge" to the wind...for their benefit. That would be fair, right?  Using the following: 

the price would be 385,389 and is in practice -- and unsurprisingly -- no more no less than a DIA price for a 59 year old looking for 100k cash flow in 20 years. A quick check at AA calc shows a 391,620 price for a DIA price for a given set of assumptions.  Close enough. So if they want me to ditch my optimal consumption plan and longevity security blanket, they'd have to at least cover my superannuation risk for ~390k. Plus given the stochasticity of both returns and spending and the possibility I might run out of $ before 79, it might be more more than that.  This is a minimum price.

B.2.1.2 - Swap 1: Fairness valuation - a max "threshold" price

The max price we might consider is another matter altogether.  I suspect it involves some kind of real option valuation thing. I can't do that (yet). But! We have been given a new tool by a ret-fin god.  Moshe Milevsky just wrote a paper on the utility and valuation of longevity pooling.  In that paper (you can read it yourself here) he gives a specific way to value the exact price of the longevity pooling we are being asked to give up for someone else's benefit. Using the principles and math in that paper we can uncertainly say that the price could range anywhere from:

on the high side, with unrealistic assumptions for returns and longevity, to maybe


on the lower side (and if we were to use more realistic assumptions for the mortality curve, the presence of income like Social Security or pensions, and risk aversion).   The delta value, as I mentioned in a past post, is defined as:  
"Basically, its DELTA percent of the money you have available to annuitize at retirement. So, if you have $100,000 and decide not to purchase the longevity insurance -- and take the chance of living longer than life expectancy -- you would need to be compensated with $100,000 times DELTA." -- Prof. Milevsky
Given some amateur hack assumptions that you can play with in his paper on your own, we can say that the "delta" can range from something like .279 (see where I came up with that in something I did below) to .649 of W per equation 25.  That would mean that the delta -- or the true "price" for the value of my involuntarily forgoing the pool (as always, my disclaimer is: "if I have that right") -- might range from 500,963 (eq 33) to 1,167,245 (eq 25).  In other words, if someone wants me to forgo my own rationalized, longevity hedged, and possibly optimal strategy for something that I know is not to my benefit but might plausibly be to their benefit…then they better bring a checkbook.

B.2.2.1 -- Swap 2: Swapping a SPIA for GLWB product - using annuity pricing first

I am going to assert by way of what a former boss called "proof by intimidation" that GLWB products are inferior over the long run for a retiree when compared to full SPIA products (or I can at least lean on the Milevsky quote above for now). That means I assert there is a real cost to ditching annuities for a GLWB. If you disagree, write it up and send it here.  Otherwise we have to come up with a price for swap number 2.  To do that in this section I'll see if I can come at it in a way similar to what I did above.

For fun, and for the sake of argument, let's say my advisor friend is precisely correct (GLWB is always >= annuity especially in the presence of a bequest motive) and that Milevsky is also correct (ignoring bequest, GLWB is always <= annuity and produces, on average, a payout on the order of something like 1/3 less than the annuity; that average thing is important, btw, but ignored for now).  That gives us an idea that maybe we can look at a net negative 1/3 payout as a fairness factor, all else being equal which of course isn’t really the case. This kind of thing is highly debatable of course but let's roll with it.  One problem though is that I do not know when GLWB income can start for a 59 year old.  I'll assume it can be somewhere between 59 and 79, 79 being the arbitrary "fair" age we chose above.  In practice I don't think it can start right away because of blackout periods, but I might be wrong and in any case it does not really matter here in this post. Then we can say that the price of swap 2 might be the following after admitting that the notation is totally "amateur" (it's a good thing these posts can't get red pen marks):


where fg(a) is basically, for today anyway, something like the 1/3 reduction in payout from going from annuity to GLWB or we'll say the incremental fair value price for switching is the sum of 1/3 of my planned, probability weighted, discounted, 100k payout over some interval of remaining age, whether 59+ or 79+ or whatever. If you want something more complex, you are on your own.  If you buy in, then we are in business.   In that case we can say that if the diminution or vitiation of my preferred optimal annuity cash flow is run from a start age of 59 then the cost/price is 598,910. If it is run from age 79 it is 128,334. The point here is that if one believes, like I do, that the net GLWB benefit ex bequest is <= annuity, then the cost of asking me to switch is not zero, it is something.  As above, if you want me to bequest something to you, bring a checkbook. Or convince me that my bequest plan in morally flawed…but that is not a math problem. That is a moral debate.

 B.2.2.2 -- Swap 2: Swapping a SPIA for GLWB product - using the pooling-delta method

[ I had some conceptual errors in this section in the 2nd paragraph that I tried to fix in a later post here in this later post: Correction - My post on bequests and fairness...esp wrt the delta concept . Even without the correction, recall that one has to take what an amateur blogger says with a grain of salt in the first place.]

In effect the question at hand is really one of the tradeoffs on the margin between risk aversion and bequest motive. Milevsky's choice of mathematical object for "delta" is


which shows that the value of longevity pooling is a strictly a function of risk aversion and the shape of the mortality curve (from page 23 of the link I provided: "Note that the results are not as sensitive to interest rates. The δ benefits really are driven by risk aversion γ and by the assumed mortality rates.") to which I would add the bequest consideration too.  So, I'd say: if bequest motive is zero and no one is pestering you about getting a piece of the estate then maybe stick with the annuity if it optimizes your lifetime utility of wealth and consumption (that's a different topic).  If the bequest motive is > 0 then maybe we can view the GLWB as a class of partially defective but liquid annuity that leaves at least some longevity risk and/or consumption disutility on the table. That means we still have to evaluate the nudge from annuity to "slightly-less-than" annuity.  

In Milevsky's table 1, case B in the link I mentioned (before he gets to eq 33; this is the sub-table with exponential but moderate mortality, moderate risk aversion, and a row with the presence of 99% prior annuitization; this is my proxy for the defective annuity idea, btw), delta is still .078 which would make the delta against the ~1.8M grubstake we mentioned = $140,285.  So maybe that is a lower bound for a price for our bequestee, on the margin, when moving from 100% annuity (SPIA) to 99% annuity (again: proxy for GLWB).  

For an approximate "upper bound"[7] we can try to use Milevskys's equation 33.  In eq 33, a(x) = a normal annuity factor for the annuitant and a(x*) is an annuity factor with an economic age substituted in for a real age where the economic age is one that is adjusted for risk aversion or in the paper adjusted like this: x* = x - b* ln(gamma). b in this case is the mortality dispersion and gamma is the risk aversion coefficient.  Here is an example.  In this chart below I first fit a curve using Gompertz-Makeham math to the SOA data I used above; actually I set the dispersion to 8.4 to partially fit the curve and then I solved for the mode that gave me the same annuity factor (1.7985) that I used before and that I validated against AAcalc.com. The PDF plotted with the newly fit GM math is the red line where the dotted line is the curve based on the original SOA table.  Then, adjusting the economic age to 53.2 using the x* method I mentioned, the blue line is the adjusted mortality PDF.  That means that the new annuity factor a(x*) is 18.629.  For an illustrative and arbitrary risk aversion coefficient of "2," plugged into eq 33, that gives us a delta of .279.  That delta, if thrown against W, would be a price of 501k for our would be bequestee.
   




This range that we got in this section of 140k to 501k, using delta, is not radically different from 128-599k in the previous section using annuity pricing.  I might be wrong but I want to call this more or less a validation of the idea that there is probably a price of some kind for being nudged towards a bequest motive by "unlocking" the annuity strategy even in the presence of a "full but defective annuity" like a GLWB (or maybe call it unfilled residual hedging). That's only if we consider a GLWB to be a type of defective annuity.  But recall that this concept of defective annuity hinges on the quote from Milevsky in the "A" section above. If you don't believe that then it is this post that is defective rather than the GLWB.

Conclusion …and a question on their value proposition….

All this above was fun (or it is if one has an odd sense of fun like RH). And, if it were to be real, it would go a long way towards immunizing me from the risk you were asking me to take in a fair, symmetrical way. That's only for me, though. This is only my side of the table.  While I now feel fairly dealt with, the new question might be whether you think this is a fair deal for you.  That is not my problem, though and this is starting to feel like a game theory kind of thing…a second move in a two player game.  It would be interesting to see what the math is on the other side. By that I mean: is the price (or one of the prices) that you paid above worth the probability that my estate will not be decimated by my spending and that you will get some "fair" value for what you spent in order to get access to an option on my estate by asking me to ditch my SPIA.  Option pricing is hard enough but there is also now some kind of odd moral hazard because I am going to spend like crazy to blow out your option value if I can… unless, of course, you are my children, in which case I will spend like a miser -- my "policy" notwithstanding --so that not only do you get every last penny that I don't spend but every word of this post will be mooted in the most embarrassing way. 






NOTES
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[1] No doubt there is some traditional longevity pooling going on but it does not appear to my naïve eye to always be a real pool. I'd have to ask an actuary but it looks more like a pseudo-pool with a transfer of wealth from the fee-paying-living to the balance sheet of the insurer who then makes a "promise"). Maybe I'm wrong.  That makes this kind of thing feel more like a casino game where the insurer is the casino more than an intermediary. In these cases the gamer on average never wins and the long term game goes to the casino. The gambler, the glwb buyer, "pays" for the benefit through fees of course, maybe some pooling, but also via a lower payout than a pool might pay. Some will win, right? but will also become marketing fodder.  In a real pool, on the other hand, again if I have it right, the insurer is an intermediary rather than a counter party and facilitates a transfer of wealth from the early-dead to the late dead while taking a fee and retaining some risk on inefficient pooling and mortality trends that might trend against them.  Do I have that right? Anyone? Beuller-actuary? Anyone?

[2] For example, here is some one insurers fine print "No additional increases will be applied to the rider’s value once the contract’s value is reduced to $0 or after the Index Anniversary immediately following the Annuitant’s 95th birthday." That's dispositive of nothing but it does show that living to 300 will not have any accidental benefits that accidentally accrue to the 300 year old.  One is betting against a casino here.

[3] LS = lifestyle plan, SS = spend shocks, SA = superannuation risk, SR = sequence risk, MC = modest contributions to the health and welfare of my children…up to a point, O = other, because there is always other. 

[4] Or DIAs or VAs or TIPs ladders. TBD but the allocation and rationale should be opaque and uninteresting to all but me. 

[5] I just read a great book on probability that makes the case that wide swaths of probability theory originated with questions coming from issues related moral fairness (how to split a gambling pot after n games have been played, m games remain and the game has been interrupted and so forth). See Book Mention - Ten Great Ideas About Chance.

[6] This is a work around. Gordon Irlam at AAcalc uses the whole Treasury yield curve with interpolation within and beyond the data. I hope I'm not giving away secrets but it's more or less like this from an email:

"The yield curve is interpolated using Python's PchipInterpolator, par rates are converted to spot rates for every 6 months. For rates beyond 30 years the average forward rate from spot rates with a duration of 15 years or longer is used to compute the spot rates. The appropriate spot discount is used for each survival weighted probability." -- G. I.

My discount rate is a weak proxy for all of this but works ok. I'm using annual payouts and a money's worth ration of 100% btw. 

[7] here we are completely ignoring the difference between the annuity proper and the GLWB. This is just the pure delta value the price for abandoning annuitization.    


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Appendix A -- Links and Excerpts 

The Utility Value of Longevity Risk Pooling: Analytic Insights Moshe A. Milevsky1 and Huaxiong Huang 10 March 2018

Life Annuities: An Optimal Product for Retirement Income, Moshe Milevsky CFA institute 2013 

  • Here is the bottom line: To the naked eye, the VAs with GLWB might appear to have all the benefits of a life annuity—guaranteed income, risk pooling—but without the costs associated with illiquidity and irreversibility. However, although the GLWB product has merits, especially considering the research evidence that it was initially underpriced, it is not a substitute for pure life annuities because of its lower yields. For example, whereas a life annuity might pay 6% to a 65-year-old, the GLWB rate under the same market conditions would be in the vicinity of 4%.  
  • Whether the GLWB is better than the life annuity from the consumer’s perspective depends on a complex relationship between the pricing of the guarantee, the retiree’s optimal consumption strategy, and the existence of bequest motives.
Financial valuation of guaranteed minimum withdrawal benefits, Milevsky and Salisbury, http://www.math.nus.edu.sg 2005    

  • The GMWB rider/feature is being subsidized by the basic insurance fee. This is consistent with the over-pricing of standard features in VA policies. Thus, a 50 basis point fee for the rider together with a baseline 120 basis point fee might add-up to 170 basis points, which is enough to cover the risk.
  • we show how the product can be bifurcated into a type of Quanto Asian Put (QAP) plus a generic term-certain annuity
  • A recent innovation in this market is the abovereferenced GMWB ‘rider’. In contrast to all the other bells and whistles3 it contains absolutely no life insurance component and is thus well within the domain of analysis of financial economics
  • Most insurance companies charge for this downside protection by deducting an ongoing fraction of assets as opposed to an up-front fee. These unique features differentiate the pricing of this derivative security from the standard Black and Scholes (1973) approach where the option premiums are paid up-front and in advance. This fact introduces subtle hedging issues
  • we find that under a stylized product specification which guarantees a 7% withdrawal, and assuming a forward-looking investment volatility of σ = 20%, the cost of providing a GMWB ranges from 73 to 160 basis points of assets per annum… we find the recent GMWB products that have been introduced in the market are only charging 30–50 basis points, even though the underlying annuity subaccounts contain high-volatility investment choices

  • A GMWB annuity compares much more favorably against an immediate fixed annuity, which is a more relevant proxy for generating guaranteed income for life.
  • while GMWB annuities may appear to be relatively “inefficient” at an individual product level, a GMWB annuity can improve the overall efficiency of a retirement portfolio and better help a retiree generate sustainable income for life for the right situations.
  • while the GMWB annuity may be viewed as “expensive” when compared against a traditional portfolio, the cost is on par with an immediate fixed annuity.
  • When viewed from a total portfolio framework, where the goal is to maximize a utility function based on income replacement, the appeal of a GMWB annuity increases considerably, especially for retirees with lower levels of pension income, more conservative withdrawal rates, and more conservative equity allocations during retirement.


  • Another way to provide downside protection is to purchase a variable annuity with a guaranteed lifetime withdrawal benefit (VA/GLWB), or a similar product, the stand-alone living benefit (SALB), which combines mutual funds with a GLWB. This is quite different from using an options strategy, but these products achieve a similar result.
  • The level of fees makes a big difference in average bequest values. The low-cost GLWB is competitive with the option strategies in terms of average bequest, and it has the advantage of reducing the failure risk to zero. It accomplishes this by pooling longevity risk.
  • The higher-cost VA/GLWB also makes use of mortality pooling and provides this same protection against failure. But the bequest values are no longer competitive with the option strategies. Pay attention to costs in VA products.
  • For downside protection in a retirement portfolio, I would stay away from options strategies and choose an annuity-like approach providing guaranteed lifetime income. In today's environment, the Vanguard VA/GLWB is a strong contender. I would also compare financial outcomes for the Vanguard product with projected outcomes for low-cost versions of other types of annuities, such as immediate annuities and deferred-income annuities.



  • examining historical data, I have found that those riders carry a cost that will not be readily apparent to retirees: their cash flows rapidly decrease on an inflation-adjusted basis.
  • Moreover, GLWB riders, which are also known as guaranteed minimum withdrawal benefits (GMWBs), compare unfavorably to the cash flows a retiree would obtain using a systematic withdrawal plan.
  • As long as one does not exceed the allowed withdrawal amounts, guaranteed withdrawals never decrease (in nominal terms) even if the account balance falls to zero. In this regard, GLWBs share similarities with immediate annuities, though a GLWB contract can be terminated and remaining assets can be returned.
  • I remain concerned that prospective retirees may be overvaluing the guarantees in their mind because they are not properly considering how inflation will erode their real value over time. In behavioral economics, this bias is known as money illusion. People can logically understand the effects of inflation, but their emotional responses and decisions remain attached to nominal values.
  • The guarantees are not inflation-adjusted and would have been worth little in rolling periods of U.S. historical data. Moreover, it would have been rather easy to replicate the GLWB guaranteed withdrawal amounts using a systematic withdrawal plan that is not guaranteed and does not require a rider.
  • Benefiting from GLWB guarantees would require worse circumstances than any historical stretch so far. It’s important to note, however, that U.S. financial market history has been very kind to retirees. A new worst-case scenario could await those of us for whom retirement lies in the uncertain future. But these guarantees depend on the insurance company’s ability to pay, which could be at risk if the overall financial landscape gets bleaker.
  • Retirees may find “peace of mind” from the guarantees a GLWB provides. Perhaps the guarantee would stop retirees from panicking and selling stocks after a market drop. Moreover, if retirees do have a tendency to reduce their spending as they age, it may not be necessary for them to maintain a fully inflation-adjusted income. GLWB guarantees may also come in handy if people live beyond a 30-year retirement horizon. Perhaps most importantly, I have conducted research that suggests that withdrawal rates may fall dramatically below 4% for recent retirees. Should that prove to be the case, retirees could possibly benefit from the guarantees.
  • the nominal withdrawal amount guaranteed by a GLWB can become quite small in real terms, and money illusion biases may prevent clients from properly appreciating this drawback.
  • In the event that someone replicating GLWB withdrawals on his or her own runs out of wealth, an outcome that no investor has faced historically, then GLWB owners will surely worry about the risk of default for the insurer.
  • Higher fees would erode the account balance more quickly, allowing for fewer step ups, more exposure to inflation, and making it even easier for systematic withdrawals to match GLWB withdrawal amounts.
  • It is possible that purchasing a fixed single-premium immediate annuity (SPIA) would generally enable retirees to obtain a guaranteed income source more cheaply. Financial planner Joe Tomlinson refers to GLWBs as “actuaries gone wild,” due to their complex combination of downside protection and upside potential.

Understanding Variable Annuities with GMWBs by Robert Huebscher, 3/1/11 Advisor Perspectives 



  • VA/GLWBs are often costly, and the typical purchaser has few tools with which to assess the costs.
  • But when examined more closely, there are in fact more similarities than differences. [VA/GLWB vs income annuity]
  • The VA/GLWB is a more popular product than the income annuity, and it is often touted as providing stock market participation with downside protection, like "having your cake and eating it too." This is largely a mischaracterization, because the fees one pays to obtain the GLWB’s guarantees take a substantial bite out of the equity returns. Given the dictates of financial markets, it is not reasonable to expect to both hedge downside risk and enjoy equity-like returns.
  • Under the particular pricing structures for these products, the VA/GLWB provides a larger expected bequest than the income annuity. This result is sensitive to VA/GLWB fees, and I'll show an example below where the results are reversed.
  • Guaranteeing an income that lasts for life requires a significant sacrifice of expected bequest value. Advisors and clients need to give serious thought to whether guarantees are worth the cost.
  • The results are quite clear: At this higher fee level, the VA/GLWB becomes a more costly way to provide guarantees than the income annuity.
  • Income annuities will meet the needs of those who want maximum retirement income, while the VA/GLWB will work well for those who can give up some income for more liquidity and flexibility.
  • I do not see much appetite for sales forces to give up commissions in favor of improved customer value.



  • Our main practical finding is that given current design parameters in which volatility (asset allocation) is restricted to less than 20%, while guaranteed payout rate (GPR) as well as bonus (roll-up) rates are less than 5%,GLWBs that are in-the-money should be turned on by the late 50s and certainly the early 60s.
  • We conclude by suggesting that much of the non-initiation at older age is irrational (which obviously benefits the insurance industry.)

  • a deeper analysis reveals that in the end, most retirees with a GLWB rider may do little more than pay a lot in annuity costs to receive a guarantee to just spend their own original contributions and nothing more.
  • GLWB riders extract any withdrawals against the policyowner’s own cash value first, often the time horizon it takes to actually reach the point where the policyowner has worked through their own cash value and into the insurance company’s pocket via the guarantee is actually longer than the client’s own life expectancy! In other words, most clients are just receiving their own money back and may literally die before ever seeing a dime of the insurance company’s money under a GLWB rider!
  • it turns out that for those who do have annuities with GLWB riders, the best course of action may actually be not to wait, and instead to tap the annuity for permitted withdrawals as soon as possible (to the maximum allowed under the contract).
  • the benefit increases just aren’t enough to offset the shortened time window of life expectancy that results from waiting in the first place! Instead, the best course of action is to actually try to deplete the annuity as quickly as possible, in an attempt to reach the point where the policyowner can get a “return” from the insurance company

  • if the value of the rider is to guarantee a floor while taking withdrawals, then the goal should be taking withdrawals to try to hit the floor… and the older the client, the better it works!
  • Some early GLWB riders don’t actually guarantee payments for life, but only a more limited period of time. Most GMIB contracts (and the occasional withdrawal rider) require a holding period (where the benefit base grows) before withdrawals can begin, and/or the benefit base can be annuitized. Perhaps most important, contracts vary dramatically about the consequences of taking withdrawals in excess of the guaranteed growth amount of the benefit base; some are relatively favorable, while others may terminate the rider entirely for taking even $1 over the limit! To say the least, the devil is in the details,
  • The two broad categories are a Guaranteed Lifetime Withdrawal Benefit (GLWB) and a Guaranteed Minimum Income Benefit (GMIB); the key distinction being the words in the middle, “lifetime withdrawal” versus “minimum income.” Both riders rely on the use of a withdrawal or income benefit base, which is a phantom amount against which the lifetime withdrawal or minimum income guarantee applies.
  • The notable thing about the benefit base, though, is that it is not liquid; when a variable annuity states that it will grow by a guaranteed 5%, 6%, or 7%, it is not the liquid cash value that is growing, but the benefit base.

  • “Lifetime withdrawal benefits” are very popular these days; most of the indexed or variable deferred annuities sold today are bought by consumers who paid extra for this “rider”. Regrettably, all too many of those buyers believe that, for that extra cost, they will earn a guaranteed “investment return equal to the “rollup rate” of the annuity. They won’t. They will get a guaranteed amount of income, but that’s not the same thing.
  • A Guaranteed Lifetime Withdrawal Benefit is not an investment feature. Its value (a set percentage of a benefit base that is guaranteed to increase at a set rate for 10 years or until he begins withdrawals) is an insurance feature. And insurance features don’t perform like investments – because they’re not. No insurance feature, of any policy on the planet, will ever “pay off” on average.
  • If the average buyer of an insurance policy profits from buying it, the insurance company will soon go broke. The true value of an insurance feature is not its IRR (or ROI, or any investment measure), but the fact that it guarantees an outcome, no matter what.
  • the “rollup rate” and the “payout percentage” of an annuity with a lifetime income benefit is not an investment return and the buyer will not get that percentage, plus his original principal.  Those rates are simply factors producing an insurance benefit (in this case, the sure and certain income to Joe of over $10,000 per year, one tenth of his original investment, even if everything goes wrong.
  • For some consumers, this guarantee will not be worth the cost (which can run anywhere from 0.3% to over 1.3% of the benefit base each year; for others, it will. But in any case, no buyer should expect to get a “return on principal” equal to the “rollup rate”, or even the “payout percentage”.

  • Let’s suppose that you’re reasonably sure you’ll never want to take out more than your guaranteed minimum withdrawal, that you don’t care whether you leave any account balance for your heirs, or that you’re convinced the financial markets aren’t going to do very well during your retirement. In all of those cases, opting for the highest rate might make sense. But here’s the rub. By choosing and using a higher payout rate, you guarantee that you’re going to burn through your actual account value faster than you would with a lower rate. If you ever do need to make an emergency withdrawal, you’ll have a smaller lump sum available to you in your account balance. You’d also leave a smaller account balance to your heirs in the event of your death. And you would lessen the chances of enjoying an increase in your actual account value that would trigger a step-up in your benefit base, which could be important in terms of keeping pace with inflation as you get older.

Pros/Cons for GMWB (Guaranteed Minimum Withdrawal Benefit), bogleheads discussion. Circa 2013  

  • I don't see that there are any pros, none. VAs with such features have such high costs that portfolio growth is so hampered that you're all but forced to take out one of the withdrawal options. Given that outcome, you (someone) is better off investing in an entirely different vehicle from the start. If the question is to get into one in the first place or not, that's pretty obvious. If someone already has one and the market has just fallen, then there's some calculation needed. It's not like the insurance co rubs their hands together and creates money youre otherwise not entitled to. Monte Carol analysis shows that these annuities turn out better than a conventional portfolio something like 6% of the time.




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