Contributions F r a n k | M i t c h e l l | B l a n c h e t t An Age-Based, Three-Dimensional Distribution Model incorporating Sequence and longevity risks by Larry R. Frank Sr., CFP®; John B. Mitchell, D.B.A.; and David M. Blanchett, CFP®, CLU, AIFA®, QPA, CFA Larry R. Frank Sr., CFP®, is a registered investment adviser with an M.B.A. and B.S. cum laude in physics, Executive Summary living in Rocklin, California. (LarryFrankSr@ BetterFinancialEducation.com) • The authors develop an age-based, tion periods. The model developed three-dimensional distribution in this paper demonstrates: John B. Mitchell, D.B.A., is professor of finance at Central model that illustrates a retiree’s » How longevity probability can be Michigan University. ([email protected]) yearly transition through retirement, developed into dynamic, yearly including superannuated years (very adjustable distribution periods David M. Blanchett, CFP®, CLU, AIFA®, QPA, CFA, is a old age), to demonstrate the impact » These dynamic distribution research consultant for Morningstar Investment Man- of longevity risk periods can then be combined agement in Chicago, Illinois. Blanchett has published • The model builds on “Probability- with stochastic (Monte Carlo) more than 30 papers in various industry journals and has of-Failure-Based Decision Rules real returns an M.B.A. from the University of Chicago, Booth School to Manage Sequence Risk in • The distribution period (DP) can be of Business. ([email protected]) Retirement” by Frank, Mitchell, and dynamically managed, as the retiree Blanchett (2011) to simultaneously: ages, by varying the percentiles of » Establish an age-based distribu- longevity ithdrawal rates are sensi- tion model • The withdrawal rate is very sensitive tive to two fundamental » Incorporate current-age life to DP, and the DP is very sensitive Wcomponents: the distribu- expectancy to life expectancy; thus more atten- tion period (DP) and the market returns’ » Address survivorship into tion should be paid to longevity risk effect on portfolio values (through the superannuated ages than has been in past research basic formula in which withdrawal rate » Address market sequence risk • The probability of failure (POF) equals the annual dollars distributed » Develop a method to rationally remains a useful metric to evaluate divided by the portfolio value). How incorporate retiree goals of either exposure of a retiree’s portfolio to do retirement planners separate these consumption or inheritance, and market sequence risk, and a POF- two components when helping retirees switch between the two as desired based decision rule applies to both make decisions about the sustainability • Past research has primarily focused the asset allocation effect and the of their distributions? Frank, Mitchell, on fixed, non-age-specific distribu- age effect on withdrawal rates and Blanchett (hereinafter FMB) (2011) described how to measure the market returns component. This paper builds on life expectancies define the length of the risk decision rule in which portfolio that work by addressing the distribution current distribution period (DP) based withdrawal amounts are adjusted based on period component. on the current age of the retiree. The market returns. Rather than use generic fixed distribu- current DP changes dynamically each tion periods not necessarily associated year as the retiree ages and/or by adjusting Brief Overview with a specific retirement age, the authors the longevity percentile (how long the This paper develops an age-based, three- have developed an age-based model that retiree is expected to live). Additionally, dimensional distribution model for retire- uses period life table statistics so that the authors introduce a market sequence ment. The model plots the results of many 52 JournAl oF FinAnciAl PlAnning | March 2012 www.FPAnet.org/Journal F r a n k | M i t c h e l l | B l a n c h e t t Contributions simulations relative to each other—each periods. For the application of withdrawal The model developed in this paper will simulation represents a transient state rate research in any given country, the help the reader determine what the effect a retiree may dynamically pass through expected longevity of that country should on withdrawal rate, more importantly as time and portfolio values change. The be used. POF, is of surviving into the “next” concept of transitory states suggests a Making decisions based on a single distribution period (DP)—the “next” dynamic process of change the retiree’s simulation into perpetuity is unrealistic DP is the then current life expectancy for decumulation goes through over time because conditions continually change the then current retiree’s age. The model and market changes. A range of transient with time. Proactive or strategic decision dynamically adjusts as the retiree ages states is okay for a retiree, but beyond making requires a larger context of how a through rolling distribution periods that that range, spending retrenchment (with decision to solve one issue (for example, decrease slightly in length each year. bad market returns, commonly referred longevity risk) may affect another issue The authors’ hypothesis is that sequence to as sequence risk) is recommended to (for example, sequence risk), and may risk occurs more often and throughout increase the probability the portfolio does need to include other factors relevant to retirement relative to the occurrence not fail during that DP. The transient overall strategic decisions such as asset of longevity risk; hence the POF-based state concept was initially developed and allocation, time frame, retiree goals, etc.— techniques that manage exposure to explained by FMB (2011). all of which come from within a model and sequence risk also simultaneously manage The lack of a specific distribution period methodology to evaluate choices. In other aging into and through superannuation. based on the retiree’s current age is prob- words, how do a multitude of possible The authors’ model no longer shows lematic because, as the authors will show, coexisting transient states relate to each generic distribution periods. Instead, the withdrawal rates are sensitive to distribu- other? Second, models can be developed current age of the retiree is used as the tion periods. What is an age-appropriate to compare strategies; for example, starting point for each year during simula- DP? The model here removes much of this different retrenchment strategy models to tion. The DP is derived by subtracting the DP uncertainty. The authors also evaluate the baseline model or allocation change current age from the percentile longevity the transition between “early” retiree ages strategy models to the baseline model. age (from periodic life tables). Joint (with corresponding expected longevities) Last, the methodology should be consis- couples are assumed to be the same age to “older” retiree ages (superannuated); tent throughout all models and include for concept development purposes. For specifically, how outliving early/younger the three dimensions of distributions example, a 65-year-old couple in which DP estimates affects later/older distribu- (allocation, withdrawal rate, time) with a either, or both, have a 20 percent chance tion feasibility. focus on probability of failure1 (POF)—a to live beyond age 95: DP = 95 – 65 = The sustainable withdrawal rate variable that does not depend on time and 30 years. This DP calculation is updated available from a retiree’s portfolio depends is therefore a proper variable with which to annually within the simulation. on a number of factors. The withdrawal make key decisions (FMB 2011). The overall effect of using joint data rate itself is a variable that depends The model and methodology in this initially is for longer DPs in the model, directly on time because it changes as paper extend the work of Mitchell (2010 thus making the model more conservative the retiree ages—it goes up as the retiree and 2011) and combine Mitchell’s work than would be the case for either single ages or the expected distribution period with the methodology first developed female or single male scenarios. Further shortens. Thus, longevity probability is a by FMB (2011) to address the follow- model development and research is very important variable when determin- ing issues simultaneously: (1) applying needed for situations of singles, although ing proper age-specific distribution expected longevity as the distribution the effect would be slightly shorter DPs periods. Life expectancies in this paper are period to an age-specific model, (2) compared with joint data, thus resulting in based on the Social Security Administra- evaluating sequence risk as the retiree slightly higher withdrawal rates. Various tion’s 2006 periodic life table. Annual ages through this model, (3) developing age differences within couples would also changes to the life table have not been a method to address early on the effect affect DPs and therefore withdrawal rates. material, and therefore should not make a of a retiree continuing to survive beyond The authors combine male and large difference in findings and methodol- longevity estimates, and (4) incorporating female life expectancy statistics and ogy. However, just as market data may decisions for both poor or good market assume independence to determine joint update results over time, periodic life table effects (sequence risk). The objective is probabilities. For example, if the prob- adjustments should also be applied so to develop