A Comparative Analysis of Retirement Portfolio Success Rates: Simulation versus Overlapping Periods

Article excerpt

Abstract

One of the risks faced by retirees is the possibility of outliving money saved for the retirement years. Knowing the sustainability of withdrawal rates from a portfolio, or at least the risks associated with them, would greatly help retirees deal with this problem. Two procedures proposed to analyze the problem are Monte Carlo simulation and the overlapping periods methodology. This study compares and contrasts the implications of these two procedures for sustainable withdrawal rates from a retirement portfolio. Under some conditions, the procedures produce similar results, but in others the differences are quite large. (C) 2003 Academy of Financial Services. All rights reserved.

JEL classification: G1; G2

Keywords: Retirement portfolio; Sustainable withdrawal rates; Monte Carlo/overlapping periods

1. Introduction

One of the many changes that the Internet has brought to retirement planning is the use of mathematical simulations to assist in retirement investment planning. Investors nearing retirement age become especially interested in how much income their portfolios will provide at reasonable risk-return tradeoffs. In other words, what would be a reasonable withdrawal rate from a retirement portfolio? Withdraw too much and the retiree dies broke, but withdraw too little and the retiree unnecessarily sacrifices a higher standard of living. A portfolio is successful only if it lasts as long as required by the retiree.

Money Tree, U.S. News, Fidelity, Vanguard, Financial Engines, and NETirement are examples of companies that offer net-based simulations to help retirees. The typical simulation program provides Monte Carlo simulations that require input assumptions regarding personal characteristics and expected investment performance. The program then outputs estimates of the probability of retirement portfolio success assuming various initial withdrawal rates, portfolio compositions, and payout periods.

For retirees who are unfamiliar with mathematical simulation, the process may well be regarded as a "black box" out of which flows investment advice. The alternative approach to simulation relies on actual historical security returns and inflation rates. Referred to as the overlapping (or rolling) periods method, it makes intensive use of historical market returns to calculate periodic portfolio returns and end-of-period values net of planned retirement withdrawals. The sample size in the overlapping periods approach is limited to the available historical returns data, whereas simulation programs can simulate very large numbers of market returns from which a large number of hypothetical portfolios and payout periods may be evaluated. Special care, however, must be taken in simulating security returns so that the underlying time series properties (such as mean reversion) are preserved.

An obvious concern for retirees is which methodology produces more reliable results. If one approach reports significantly different portfolio success rates for the same range of withdrawal rates, portfolio compositions, and payout periods, retirees must make a methodological choice. Theoretically, if the simulation faithfully incorporates all meaningful market properties, the simulation methodology should produce highly robust results, looking at the effects of different portfolio withdrawal rates over potentially thousands of simulated holding periods. However, if actual security returns are generated from unstable distributions or different distributions over time, it might not be possible to build a realistic simulation. In such a situation, the overlapping periods methodology would be a more accurate predictor of sustainable withdrawal rates.

Fortunately, in many cases we find that the alternative methods produce similar results and no methodological choice is required. In these cases, the simulation methodology closely matches the market conditions of the overlapping methodology. …