# Underlying Fund Returns

#### Sensitivity of Fund Returns

The first step in determining the risk/return profile of any investment fund is to determine the extent to which the fund's performance is dependent on changes in the market index. This involves performing a regression analysis of annual fund performance against corresponding market performance. The resulting figure is a measure of how sensitive a fund has been to market fluctuations.

The results of this analysis will typically yield a value of 1.0 for a FTSE tracker fund and 0.0 for a cash fund. Other funds may even exceed 1.0 or have a negative correlation.

The chart above shows that even a bond fund like Fidelity Extra Income has a significant sensitivity to changes in the market: in fact, three quarters of UK funds have a strong correlation in excess of 70% with the FTSE 100 index.

#### Underlying Fund Returns

Having established the sensitivity of a particular fund, it is then possible to compensate for the element of the fund's performance that results from changes in the market to produce a profile of returns over time that reflect the underlying returns arising from other factors such as stock picking decisions, commodity prices, currency exchange rates etc.

These underlying returns represent the fund's performance as it would have been without the effects of variations in the stock market - they might also be termed 'market-neutral' returns.

It is also a straightforward process to make an estimate of the fund's future potential return by taking into account the current market and the sensitivity of the fund - on the assumption that the most likely value of the Market Index at the end of the period will be 100.

#### Some Examples

The graph above shows the rolling underlying annual returns for a FTSE 100 tracker fund. This fund has a sensitivity of 1 as should be expected from a tracker fund. The returns are relatively stable and are effectively comprised of GDP growth (gross) and dividend return. The dip in the returns in 2009 is a consequence of the recession during that period.

As with the Market Index, these underlying returns can be expressed as a normal curve, in this case, with a mean of 6.5% and a standard deviation of 1.2%.

This second example of an emerging markets fund has a very different profile with higher returns but with associated higher volatility and hence risks.

This fund's underlying returns have a mean value of 16% with a standard deviation of 17%.

#### Putting All This to Use

When using statistical data to predict the chance of a certain outcome for the FTSE 100 it is a straightforward process because we only have one variable that is described by a statistical function and it's simply a matter of looking up the appropriate value in a set of tables.

Performing the same task for a specific fund there is the added complication of using two sets of normal distribution functions and a more complex approach is needed - Monte Carlo Simulation.