Excel - Pension Withdrawal Rates using UK Market Data

Pension Withdrawal Rates using UK Market Data

Introduction

One of the toughest questions asked by clients of a financial adviser is, “I want as much income as I can without running a risk of depleting my pension pot and I would also like to pass on whatever capital is left to my children”. This is a complex question which compounds many of the issues that financial planners face including pension size, investments, expected growth, long term asset class growth, income levels, tax regimes and tax efficient investments.

Research in this area started in 1994 with an article by Mr W Bengen Oct 1994, where the main aim for the paper was to analyse the worst case scenarios in the period from 1926 to 1976 (specifically the “Big Bang” 1973-74 which included a period of very high inflation and very poor equity returns) to define a minimum initial withdrawal rate that would ensure that no client would run out of money within 30 years of retirement income being taken. The Conclusion from this which Bengen termed the ‘Safe-Max’ was an initial withdrawal rate of 4%pa rising with inflation. In addition the paper concludes that an asset allocation of between 50-100% equities is required to maintain the portfolio value.

Decision Rules

Guyton and Klinger (2006) showed that using decision rules to modify withdrawals can result in significantly higher total withdrawals than one could achieve with only increases for inflation, with the same success rate. Two of their decision rules are designed to protect retirees’ investment assets from running out. Obviously, poor investment returns alone will reduce investments. Investments also could be depleted during periods of high inflation relative to investment returns. To protect against running out of money, the following decision rules were defined:

·         Modified Withdrawal Rule

·         Capital Preservation Rule

·         Prosperity Rule

*See Guyton & Klinger (2006)

Approach & Simulator

The approach taken in this research applies Monte Carlo techniques to simulate retirees’ portfolios during their retirement. A Monte Carlo simulator written in Microsoft Excel was used to simulate retirement portfolios.  A conservative 40-year retirement period was chosen to simulate retirements because many people now expect to live for more than 30 years after retirement at age 65, hence I feel that a 40-year period is appropriate. This research assumes a retirement portfolio value of £1 million with the below asset allocations using Initial Withdrawal Rates of 4.5%, 5%, 5.5% and 6%.

Portfolio	Cash (%)	Fixed Interest UK (%)	Equities UK (%)	Total (%)
Equities 50%	10	40	50	100
Equities 65%	10	25	65	100
Equities 80%	10	10	80	100

Each year’s entire withdrawal is made from the portfolio’s assets on the first day of the simulated year. Withdrawals rise annually by the prior year’s inflation rate, modified by any decision rules in effect using the formulas presented earlier and are deducted from the retirement assets. At that time, the asset classes are rebalanced to the target asset allocation. Simple rebalancing was used for this research.

Sector	Cash	Fixed Interest UK	Equities UK	Inflation
Mean	3	5	8.25	3
Standard Deviation	2	5.75	21	3

For each year, the simulated return is obtained by generating (using the relevant correlations) a random number from the normal distribution with the appropriate mean and standard deviation to obtain the relative return value r.

Retirees’ portfolios are simulated by performing the above calculations for each retirement year, such as 40 times for an assumed retirement period of 40 years. If the sum of all assets becomes negative during a simulated period, the simulation is considered a failure.

I have decided to apply the following values for Exceeds, Cut, Fall and Raise when applying the decision rules.

Rule Values
Exceeds	Cut	Fall	Raise
20.00%	10.00%	20.00%	10.00%

The simulator is used to test different scenarios. Firstly to establish the end portfolio value, then the total withdrawal rates to test for differences in the total withdrawals paid to the retirees, finally the portfolio longevity is investigated to see if the models and the Initial withdrawal rate s show a significant increase in the longevity of the portfolio.

For more please click the link for the full paper - Link to paper