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Statistical techniques are increasingly used to predict financial returns and reduce portfolio volatility.

I have recently been talking to a financial adviser who has mentioned using a financial planning system that uses processes called Monte Carlo simulation and stochastic modelling. Can you explain to me what these are and how they apply to financial and investment planning?

Projections used in most financial planning systems are usually dependent on a number of forecasts or assumptions used for things such inflation, earnings’ growth, tax rates, investment growth and so on.

Quite often, the system will calculate a future value of, say, a pension fund based simply on the FSA approved growth rates, often using the mid rate (6 per cent) to forecast the eventual fund that will be produced.

However, it is quite illogical to base future expected returns on a simple growth rate of 4, 6 or 8 per cent without taking into account the likelihood of these growth rates actually being achieved. In other words, simple forecasts used by many systems can be vastly misleading if account is not taken of the actual asset mix that is contained within the funds that the client invests in.

For example, is it sensible to use the mid rate in an illustration if the fund is a cash or fixed-interest fund when, after tax and expenses, these asset classes have not historically produced this sort of return on a long-term basis?

With some more modern systems, estimates of potential returns and volatility from different asset classes are created by looking back for as long a period as there is good and comparable data and finding the average returns and variance for them.

There are problems with taking an historical average, however, in that it will not always reflect the breadth of possible returns that were achieved, only what did happen.

Also, it is inevitable, given the uncertainties of investment performance and economic conditions during the long periods over which financial planning is undertaken, that a single set of forecasts will not be matched in real life. To overcome this limitation and in recognition of the uncertainty of future outcomes, statistical techniques are sometimes used. These techniques require assumptions about the statistical properties of returns, principally, the statistical distribution of returns.

A well established statistical technique called Monte Carlo simulation is therefore often used in more modern financial planning systems. Monte Carlo simulation is so named because it is based on a large number of random outcomes, just like you would find at a casino in Monte Carlo.

In Monte Carlo, one can never be certain if a particular gambler will win or lose but one can be certain that, overall, the casino will never lose. This is because the games played in casinos have a slight advantage to the casino so, given a large number of gamblers – some winning and some losing – the average result will always be in the casino’s favour.

Monte Carlo simulation depends on the fact that the results of a large number of individual random events will accurately describe the probability distribution of the individual event. In financial planning systems, this process takes the assumed pattern (statistically, the distribution) of returns and simulates a possible future scenario. The simulations produce a population of possible returns on which valid statistical calculations can be based.

Inflation and the impact of taxation can also be factored in to the forecasts.

One of the most significant developments in the retail investment market over the last few years has been the use of financial planning systems using techniques previously only available in institutional investing, Stochastic modelling being one of these techniques.

The growth in the use of this technique has been magnified by the volatility of stockmarket performance in the last six years. This has exposed the weaknesses in many investors’ portfolios, mainly the lack of coherent asset allocation strategies.

Stochastic modelling relies on computer technology which allows a large number of simulations to be created, that is, guesses about asset allocation, with each one being slightly different from the next. From these results, it is possible to calculate all of the possible portfolio returns from all the various asset combinations.

Most important of all, the process is iterative so the outcome of one set of simulations can be fed in to the next in order to uncover the best combination of assets that over time produces less volatility.

Stochastic modelling is therefore a predictive technique used to decide the best asset allocation within a portfolio based on a combination of historical and expected returns from each asset class. The aim of this process is to reduce the range of possible outcomes over time, making the portfolio’s returns less volatile or, in other words, reducing the risk.

Patrick Murphy is director of investment management services at Thinc Destini.

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