  # Monte Carlo Simulation

#### Market Influence on Fund Performance

For each of the funds in our database we have a measure of the extent to which the fund's performance is correlated with that of the FTSE 100. By comparing the current FTSE value with the statistical range of future values, it is a straightforward calculation to determine the potential mean return and the risks for that market dependent element of the fund's future performance.

If the fund were a FTSE tracker fund, the correlation with the market would be 100% and that would be pretty much all that is necessary because the underlying returns that are left when we take out the market-dependent element are fairly constant - or, more correctly, statistically not particularly significant. The majority of funds available to the UK investor have a much less predictable pattern of their underlying returns (once the market-dependent element is accounted for). This particular fund has a similar market-based element to the earlier tracker fund but the variation in the underlying returns is much more significant and needs to be fully accounted for if we want to quantify the associated risks.

Just as we produced a statistical model of the FTSE 100/GDP relationship it is an easy matter to calculate the mean value and standard deviation for these underlying returns.

#### The Monte Carlo Method

Predicting the risks that a fund will achieve a particular target level when we have more than one random statistical element is a much more complex task and this is where we turn to the Monte Carlo Method.

The method involves making a simple calculation of the fund's future value based on random values for the two 'unpredictable' values (the future values of the FTSE 100 and the underlying fund return). The result of this prediction will undoubtedly be wrong but, if we repeat this calculation thousands of times with different random values of the two unpredictable variables, we can determine what proportion of these calculations achieve the desired outcome and we have a measure of the risk!

This makes it possible to quantify the risk that the investment will be worth less than its current value in a year's time or indeed, achieve a required target return at any future time.

#### Whole Portfolio Testing

A natural extension of this approach is to apply the method to a complete portfolio of funds.

The method is exactly the same but now involves many more calculations and applies the final test based on the outcome for the complete portfolio.

#### Diversified Risks

Most investors will seek to reduce risk in their portfolio by diversification of assets. In these cases our algorithm will use different random values to determine the underlying returns of funds within each iteration thereby reducing the final risk values. However, diversification based on asset class alone can often include funds whose returns are closely correlated - in these cases the same random value is used in the model so as not to understate the risk.