Nabil Tahani, Chris Robinson

Freedon at 55 or drudgery till 70?

Introduction

Freedon at 55 or drudgery till 70?. Navigate retirement planning uncertainty with a stochastic model. Calculate the probability of achieving your savings goals (retirement, house down payment) using variable returns, all in Excel.

Abstract

The classic preretirement problem for the financial planner is to advise a client how much to save, how much must be saved each year to reach a specified goal, and how the investments should be allocated between fixed income and equity. The traditional solution is to assume a fixed rate of return for each asset class and test scenarios until the mixture of variables yields a solution that meets the stated savings goal and seems feasible for the client. This binary result (accept or reject the plan) ignores the inherent uncertainty. In this paper, we derive a stochastic model in which the rate of return and the rate of increase of annual savings are both variable and calculate the probability that a particular goal will be achieved, given any initial savings endowment, periodic additional savings amount, mixture of assets (represented by the return distribution), and time to the goal. The calculations can be done on an Excel spreadsheet. We illustrate the use and numerical results of the model with a realistic retirement planning scenario and variations on it. While this solution is particularly important for preretirement planning, it applies generally to meeting any financial goal, such as saving a down payment for a house.

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