Aug 20, 2019

Combining Annuities and Tontines

On the Optimal Combination of Annuities and Tontines

33 Pages Posted: 5 Aug 2019

An Chen

University of Ulm

Manuel Rach

University of Ulm - Institute of Insurance Science

Thorsten Sehner

University of Ulm - Department of Mathematics and Economics
Date Written: August 1, 2019


Tontines, retirement products constructed in such a way that the longevity risk is shared in a pool of policyholders, have recently gained vast attention from researchers and practitioners. Typically, these products are cheaper than annuities, but do not provide stable payments to policyholders. This raises the question whether, from the policyholders' viewpoint, the advantages of annuities and tontines can be combined to form a retirement plan which is cheaper than an annuity and carries less risk than a tontine. In this article, we analyze and compare three approaches of combining annuities and tontines in an expected utility framework: The “tonuity” introduced in Chen et al. (2019), a product very similar to the tonuity which we call “antine” and a portfolio consisting of an annuity and a tontine. We show that the payoffs of a tonuity or an antine can be replicated by a portfolio consisting of an annuity and a tontine. Consequently, policyholders achieve higher expected utility levels when choosing the portfolio over the novel retirement products tonuity and antine.
Keywords: Optimal retirement products, annuity, tontine, tonuity, antine
JEL Classification: G22, J32

Loss Aversion Risk Preferences ... Lead to Greater Retirement Income Certainty [SSRN]

Investing for Retirement: How Loss Aversion Risk Preferences Naturally Leads to Greater Retirement Income Certainty

47 Pages Posted: 30 Jul 2019

William Lim

Australian National University (ANU)

Catherine Donnelly

Heriot-Watt University

Gaurav Khemka

Australian National University (ANU)
Date Written: July 26, 2019


We analyze the ability of different investment strategies to give pre-retirees more certainty about their income in retirement, while allowing them to benefit from taking investment risk. Specifically, we look at the optimal strategies that maximize the expected values of a loss aversion utility function and a constant relative risk aversion (CRRA) utility function. We also include a typical lifestyle strategy. 

We find that the loss aversion utility function gives a high degree of certainty about its reference point, the latter chosen to give the desired replacement ratio. Adding in constraints on the income purchased at retirement does not improve the certainty of achieving the desired replacement ratio enough to counter-balance the increased chance of obtaining an income far below it. A CRRA utility function fails to get adequate certainty on the retirement income, and becomes too risk-averse when constraints are added. The lifestyle strategy performs well but is overall out-performed by the loss aversion-derived strategy.

We include inflation in our model, and allow for inflation-indexed bonds in our investment universe. Our results are analyzed in both a Brownian motion-driven financial market model and usi
ng UK historical data.
Keywords: finance, retirement planning, optimal asset allocation, stochastic optimal control, constrained optimization

Aug 17, 2019

A reminder

I had a really nice recommendation from abnormalreturns the other day to come here for retirement math. I just wanted to remind my readers:

- I have no formal training in math. My last calc class was in 1977.

- I have no formal training in statistics or probability. My last statistics class was intro in grad school circa 1987, probability theory never.

- My formal training in finance is limited to a concentration in an MBA program (again ~1987) which, if you know MBA programs, is typically shallow. Mine was.

- I am a student here, reporting what I learn, rather than a teacher.

- I am not an academic nor am I a finance professional. I have no designations or titles and I make no income off this blog or any profession related to finance other than managing my own wodge.

- Everything I report is incremental, one straw on top of another, all of them no doubt on a camel's back.

- If you come here for retirement math as a reference you will be sorely disappointed if you look too closely.  I'd rather that you defer to someone like earlyrirementnow, in, say, this post.

- The most I can say is that I read a lot and am willing to pick up excel and R for test drives and I have no conflicts of interest.

Aug 16, 2019

Fun little artifact from the "Spending, Rules and Habit" post

I don't know if this is just a coincidental, statistical artifact kind of thing or something more meaningful but thought I'd compare -- from the last post Spending, Rules and Habit -- the following:  
(a) The mean real spend from the "close to optimal" scenario using the fake parameters (50k spend on $1M with .05/.12 r and sd and a little bit of spend adaptation) used to generate one of the illustrations in that last post linked above. I took the mean real spend for each of the first 30 periods of the simulation scenario mentioned in that post.  Might be better to use median. Also, note that the distribution is defective btw because some percentage of the spends "fail" or snap to income at some point which creates two distributions, the regular one and the ones that fail.  Mean probably makes less sense in this case but at least it makes a pretty picture below, and   
(b) the Blanchett  (2016) regression formula that fits, or tries to fit, observed evidence for how people spend in real life in retirement.  I was just curious but now the overlay looks interesting. Since the regression model is sensitive to the level of spend I used 50k since that is what we did in (a). Here is the Blanchett (2016) Formula (p 15):  
Charting (a) (orange) and (b) (blue) over 30 periods, it looks like this when rendered in absolute real dollars

Does this mean anything? Probably not but if it did, maybe it means that real retirees are not all that irrational when they try to spend in practice over a lifetime.  Maybe one doesn't need a PhD to get it right after all...  

Blanchett, D. (2016), Estimating the True Cost of Retirement, Morningstar

Aug 15, 2019

Spending, Rules and Habit

The Point of This Post

I can think of no reason, other than when we consider what is already embedded in common sense, for why this post would be of practical use.  How's that for sandbagging, huh?  But I had a thought and the thought was:
"if I had a 'slider' that could slip spending between "constant" and "percent-of-portfolio" in a continuous fashion, what would happen in a consumption utility model, especially one that knows that wealth depletes and spending snaps to income when that depletion event happens?"
If you are an avid reader of this blog, and I have my eye on all three of you, you may have noticed that I do not trade much in spend rules (except for my own RH40 rule and that was half tongue-in-cheek). Spend rules seem to be a big thing in retirement lit.  I don't trade in them because rules tend to be a wee bit ad-hoc, arbitrary, and not always mathematically necessary, not to mention blind to optimality along some dimension or other.  This is a point that Patrick Collins made in Monitoring and Managing a Retirement Income Portfolio.  But rules, when they are thrown out there into the ret-fin universe, generally try to do one thing if they are honest. They adapt to the circumstances that arise after retirement-initiation vs., say, a Bengen 4% rule or academic papers that use constant inflation adjusted spending for convenience. Let's also ignore a strict application of macro econ and consumption smoothing for now even thought that is more or less what we are doing in this post. In my 5-process paper I made a case (that, embarrassingly, I can't remember) that this smoothing can sometimes be self-contradicting when put into practice. 

Aug 13, 2019

Retirement Finance and Herding Goats

The oldest form of capital management on earth is probably, I'm guessing here, goat herding. Me? I think that that particular activity has a lot of affinities with retirement finance.  I even have an academic ag paper somewhere in my pile on the economics of North American goat herding in order to prove that point but I had a hard time penetrating the prose and data for my use here so I thought I'd just do an amateur quick-riff which is what I seem to often do here.

Aug 2, 2019

Health, Preventable Disease and Retirement Finance

Having been on a health kick lately for its own merits, whether for vanity or longevity I won't say, I found myself in an interesting Twitter dialogue recently about a nexus between health and retirement finance.

There appears to be a mounting pile of evidence (not provided here maybe start here with PD Mangan or with a book I read) that implicates diet (e.g., sugar, processed food, protein intake, fasting etc) and fitness choices in preventable chronic disease, insulin resistance, inflammation, longevity etc.  That evidence can be translated into a retirement finance discussion in addition to usual one about personal well-being and quality of life.

I originally viewed my own health choices as a quality of life thing but it's more than that as Alli Covington (@allicovington) reminded me in this [edited] thread on Twitter and about which I should have already been aware:
The cost of healthcare after you’ve poisoned your body with years of bad food will astound your retirement savings. Imagine being crippled, unable to move easily, in pain AND broke. Put down the down the donut and pick up a dumbbell. Don’t be left broke and broken  
The real matrix […is…] the trap of eating processed food labeled as “healthy” that eventually leads to disease, which siphons all your available cash preventing you from being free…
That got my attention.  So I asked her what she meant.  She's still working privately on something yet to be published but the concept as I understand it seems pretty sound as she explained in a follow-up DM...   
I researched the annual cost for specific conditions that are 1) prevalent and 2) preventable and reversible with diet and exercise  
If they start fit, they avoid millions in spent dollars with interest. If they allow themselves to get a chronic disease like diabetes, they will lose out on millions.
Ahhh, she's singing retirement finance lullabies to me there. And we can test this a little bit even without the data.  I'd love to see the research and analysis but the underlying dynamic is super simple at its core: this is just retirement spending.  And we've beaten that to death here before. But lets just re-color things a bit and take in hand a subset of health spending in particular (the part attached to preventable chronic disease that can be influenced by self-care choices), which before might have seemed an inevitable and fixed cost of future retirement, and now we make it discretionary! Willful ignorance of health choices and future spending will no longer be tolerated here at RH.