What is Monte Carlo simulation?

Monte Carlo Simulation is a technique which is used in a variety of situations to give an indication of the likelihood that a particular outcome will be achieved.

(Historical note: Monte Carlo simulation was first used on the Manhattan Project, the development of the atomic bomb by the Americans towards the end of the Second World War. Until fairly recently, it was only used by major companies and institutions because only they could afford the substantial computer power required. The huge advance in computer technology has meant that “the man in the street” now has the computer power available to run these simulations on his desktop or laptop computer.)

Projections used in financial planning are dependent on the forecasts (or assumptions) used for inflation, investment return and so on. It is inevitable, given the uncertainties of investment performance and economic conditions, especially during the long periods over which financial planning is undertaken, that this single set of forecasts will not be matched in real life.

The forecasts are used for each year of the 40 year projection period. Whilst Monte Carlo simulation is inactive, the forecasts for each year are the same. When Monte Carlo simulation is active, the forecasts for each year vary in a random fashion within their respective means and standard deviations. The purpose is to attempt to replicate the uncertainties inherent in the long term financial planning. The simulation is achieved by recalculating the projections 1,000 times.

(The amount of the variation is controlled by the standard deviation for that particular forecast. Standard deviation is a measure of volatility. The defaults used are believed to be reasonable and are derived from historic data provided by Credit Suisse First Boston and the National Statistical Office.)

For each projection the value of the selected variable (i.e. LifeStyle Index, net worth, income, etc.) at the selected age is noted. These values are then plotted as a frequency distribution chart.

The heights of the bars show how many times a particular value of the variable occurred. A chart with a tall and narrow ‘bell shape’ suggests a relatively low degree of risk, i.e. the range of possible outcomes is fairly limited and there is a fairly high probability that the actual outcome will lie close to the centre of the range. Similarly, a chart with a low and wide ‘bell shape’ suggests a higher degree of uncertainty with the risk of a wider range of potential outcomes, both positive and negative.