Abstract
This study addresses the question of how long a given amount of capital will be able to fund a living annuitant if the following five parameters are known: expected retirement duration (i.e. years between date of retirement and date of death), return on investment, inflation, annual withdrawal amount and initial capital amount available. A model (the Pension Model) that graphically depicts the relationship between these parameters was developed. This model facilitates retirement planning by showing how retirement duration and withdrawal rates change the financial “Survival Probability” (SP), which is the probability of having enough capital to maintain a desired withdrawal rate for the expected retirement duration. The underlying model is based on long-term historical investment yields of equities, bonds and cash in South Africa using Monte Carlo simulation with Cholesky factorisation.
Highlights
This study addresses the question of how long a given amount of capital will be able to fund a living annuitant if the following five parameters are known: expected retirement duration, return on investment, inflation, annual withdrawal amount, and capital amount available
This allows for retirement planning by showing how retirement duration and withdrawal rates change the financial “Survival Probability” (SP), which is the probability of having enough capital to maintain a desired withdrawal rate for the expected retirement duration
If reference is made to the probability of money death (MD), it is the complement of the SP
Summary
This study addresses the question of how long a given amount of capital will be able to fund a living annuitant if the following five parameters are known: expected retirement duration (i.e. years between retirement and death), return on investment, inflation, annual withdrawal amount, and capital amount available. A model (the Pension Model) that graphically depicts the relationship between the parameters listed above was developed This allows for retirement planning by showing how retirement duration and withdrawal rates change the financial “Survival Probability” (SP), which is the probability of having enough capital to maintain a desired withdrawal rate for the expected retirement duration. In order to calculate what the financial SP was for a given age at death, the actual yearly benefit as a percentage of the funds available was compared to the desired benefit as specified by the living annuitant for each possible return scenario. These limitations are set out in the Association for Savings and Investment South Africa (ASISA) guidelines and impact the probabilities given the fact that they place limits on the amount of funds that can be withdrawn at any time.
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