Academic journal article Financial Services Review

How Risky Is Your Retirement Income Risk Model?

Academic journal article Financial Services Review

How Risky Is Your Retirement Income Risk Model?

Article excerpt

1. Introduction

Sustainability of adequate lifetime income is a critical portfolio objective for retired investors. Commentators often define sustainability in terms of (1) a portfolio's ability to continue to make withdrawals throughout the applicable planning horizon, or (2) a portfolio's ability to fund a minimum level of target income at every interval during the planning horizon. The first approach focuses on the likelihood of ending with positive wealth, or, if wealth is depleted before the end of the planning horizon, on the magnitude and duration of the shortfall; the second focuses on the likelihood of consistently meeting all period-by-period minimum cash flow requirements.

Risk models help advisors assess a portfolio's ability to provide adequate cash flow throughout retirement. Conclusions about cash flow sustainability are usually reached by determining the likelihood that withdrawals (fixed amounts, percentage of corpus, or "dynamic") can be maintained for either deterministic or stochastic time periods under various asset allocations and longevity assumptions. Expressed in terms of a Venn diagram, portfolio success lies at the intersection of the three elements in Fig. 1:

"Sustainability" differs from the concept of "feasibility." Feasibility depends on an actuarial calculation to determine if a retirement income portfolio is technically solvent-current market value of assets equals or exceeds the stochastic present value of the cash-flow liabilities. If the current market value of assets is less than the cost of a lifetime annuity, the targeted periodic withdrawals exceed the resources available to fund them. In short, the portfolio violates the feasibility condition. Determination of the feasibility of retirement income objectives is not subject to model risk because the determination rests on current observables-annuity cost versus asset value-rather than on projections of financial asset evolutions and the distribution of longevity. Although it is important to track both risk metrics-sustainability and feasibility-as part of prudent portfolio surveillance and monitoring, the remainder of this article focuses on the sustainability or shortfall probability risk metric.

2. Sources of retirement income model risk

Probability assessments are only as good as the models upon which they are based-that is to say, assessments are prone to "model risk." In general, model risk arises from several sources:

1. Variables of Interest: Projected model outcomes may differ considerably depending on the range of input variables. Health shocks, inheritance expectations, life insurance availability, and other variables may or may not improve the calculated probability of a successful retirement investment and consumption strategy.

2. Model Sensitivity to Changes in the Value of Input Variables: Output can be notoriously sensitive to small changes in input values; likewise, compounding over long planning horizons can produce large differences in outcome values and likelihoods given small changes in input values.

3. Model Structure: Deterministic inputs will likely project outcomes different than those generated by a model that treats investment, inflation, and longevity variables stochastically. The nature of the model's covariance matrix may be an additional source of estimation error.

4. Model Assumptions: The choice of utility function can influence model output. For example, assumption of Constant Relative Risk Aversion may rank outcomes differently from those flowing from models assuming a Hyperbolic Risk Aversion function.1 Likewise, the functional form chosen to generate inflation or investment returns will often influence investment recommendations.

Econometricians often discuss model risk in terms of specification error. Errors may arise as a result of including irrelevant variables in the model, failure to incorporate relevant variables, and inaccurate estimation of input variable values. …

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