Stochastic models let you discuss projected future values, such as annual pension incomes from different withdrawal strategies, in terms of how likely each one is to happen.

They work by assigning probabilities to specific outcomes, based on real world analysis, which are then run through hundreds of simulations.

The result is a range of possible outcomes, each ranked in terms of how likely it is to happen.

Nothing is guaranteed, but a result based on real world analysis is far more trustworthy than one which assumes nothing will change over 40 or more years.

Building a trustworthy stochastic modelling engine is not a simple undertaking.

The scale of initial analysis and ongoing effort that is needed to keep one working and passing repeated due-diligence checks is significant. Fortunately, there are some problems that you don’t need to solve yourself, especially where an excellent solution already exists.

There aren’t many companies that provide stochastic modelling engines, and there aren’t any who can equal the depth of experience and range of expertise that Moody’s Analytics provides, which is why we've partnered with them.

Their underlying engine is widely recognized as an industry standard for valuing and projecting assets and liabilities, and assessing risk and capital positions.

Moody’s Analytics, a unit of Moody’s Corporation, helps capital markets and credit risk management professionals worldwide respond to an evolving marketplace with confidence.

The company offers unique tools and best practices for measuring and managing risk through expertise and experience in credit analysis, economic research and financial risk management.

Their stochastic modelling tool is integrated into enterprise risk management platforms, consumer advice tools, and valuation processes around the world.

- Regularly passes due-diligence processes across a range of organisations.

- Captures key retirement risk factors: asset returns, interest rates, inflation and mortality.
- More granular asset classes across wider range of currency and economies than any other vendor.

- Models across multiple markets, including real estate, alternatives, hedge, commodities, infrastructure, and emerging market debt.

- Updated each quarter with current market prices and market conditions.

- Comprehensive documentation of all models and quarterly economic assumptions.

- Model a wide range of sophisticated product features: asset allocation glide-paths, constant proportion portfolio insurance (CPPI), guarantees, investment-linked and variable annuities.

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.