Moody's Analytics explains the percentile outputs of the WSG
WSG is a stochastic projection engine concerned with projecting a range of realistic possible outcomes (trials) for a set of financial quantities; these could be, for example, the projected value of an investor's fund or the amount of income generated by investments in a particular year. The outcomes for each trial are randomly, however there is an overriding structure to these outcomes that reflects the economic views built into the WSG. Indeed, because of this rational economic structure, the frequency with which particular outcomes appear within the output trials can be used to indicate their likelihood of occurrence in the real world.
For example, if only a few simulation trials yield a projected fund value greater than some particular level, then we can conclude that such a level of fund value is relatively unlikely to be achievable in the real world. We can quantify this likelihood by calculating a probability value associated with particular outcomes.
One standard way in which we describe - in a quantitative way - a distribution of outcomes from a stochastic projection is to use percentiles. A percentile has two elements – a probability level and a numerical value associated with the quantity of interest, e.g. projected fund value. So, for example, we might say that the 50th percentile for Projected Fund Value is £10,000. This is interpreted as follows: there is a 50% chance that projected Fund Value will be lower than £10,000 and a 50% chance that it will be higher. Similarly a 10th percentile of £1000 would indicate that there is a 10% probability that projected Fund Value will be lower than £1000 (and consequently a 90% chance that it will be higher than £1000).
The percentiles are calculated from the projected WSG trials using the following approach. For each quantity that we are interested in, e.g. income, fund value, annuity value etc., we arrange the simulation trials in order from the worst outcome to the best. The Kth percentile then corresponds to the outcome in the ordered trials that is K% of the way through the ordered trials, going from worst to best. For example, 100 simulation trials are ordered by Fund Value from lowest (worst outcome) to highest (best outcome). The 50th percentile corresponds to the outcome of the trial that is 50% of the way through the ordered list of trials, i.e. the trial for which 50% of all trials have a higher value and 50% have a lower value – in other words the 50th trial in the list. Similarly the 90th percentile would correspond to the 90th trial in the list, i.e. for which only 10 trials take a higher value.
In practice we use many more than 100 trials to calculate the percentile, and in some cases we need to interpolate between the values at neighbouring trials, however the basic idea described above holds true.
Percentiles can be useful in describing risk and return in investment strategies. A median outcome, which by definition corresponds to a 50th percentile, reflects a value for which there a 50% chance (1 in 2) of doing better and a 50% chance of doing worse. A measure of risk could be the 10th percentile, for example, for which there is a 10% (1 in 10) chance of doing worse but a 90% chance (9 in 10) of doing better.