Regression

The purpose of regression is to determine what have been the major factors causing a fund to perform the way it has. By selecting benchmarks and regressing the fund against them we hope to see how exposure selected benchmarks has influenced the fund.

The goal of every regression model is to explain what part of the fund's performance can be explained by the movement of specified benchmarks. If your model is accurate enough you can then infer what part of the fund's performance has been down to the manager.

For example, you may be considering investing in a UK Equity fund. You work for a small printing firm listed on the London Stock Exchange, and feel that your wealth is already reliant on the performance of a small cap company and would like to focus your investment on large and mid cap stocks.

You have decided that the Blackrock UK Equity fund looks appealing, and perform regression analysis to see where the manager has been making his investments.

From the regression model you see that the fund makes 89% of its returns from large and mid cap stocks. The manager has an active management style and over the last 36 months his active management has added an additional 25% to the value of the fund than would otherwise have been earned from just passively tracking this asset allocation.

 

The model also shows that the benchmarks selected for the analysis are all highly significant. The high significance test scores (STS) of each benchmark make the probability that the manager really is investing in these markets and that the correlation between them isn't just coincidence as well above 95% (represented by a STS of two and the threshold for passing the significance test).

The adjusted R squared of 0.93 tells us that the model explains 93% of the fund's performance, which is high enough for us to consider the information gained as relevant. The unexplained 7% of the fund is likely to consist of some cash and maybe one or two percent in fixed income or international equities.

This additional information allows you to make better choices when constructing your portfolio.

Pre-selected models

Regression relies upon having a set of benchmarks that represent a fund's market exposure to regress against. The less accurately the benchmarks in your model resemble the fund's market exposure, the less accurate the results from the model will be. To this end, we've suggested a set of benchmarks that should be appropriate for the sector and, hopefully, provide a useful insight into the style of the fund.

For each sector we have tried to identify the most practical application of regression and suggested a model to that end. In most cases the model tries to identify either the geographical breakdown, asset class break down or capitalisation break down of the fund.

While the suggested benchmarks for each sector are a good guide to the sort of model to be used, it is impossible to cater for every fund in the sector. That said, the suggested model should offer a clue to the sort of analysis that could be carried out on the fund, and be a source of ideas when creating a model of your own.

Constructing a model

When selecting benchmarks, three things are key:

• The benchmarks should be representative of the markets the fund is exposed to.

The key to obtaining meaningful results is to use meaningful benchmarks. Avoid adding benchmarks irrelevant to the fund, there will likely be some spurious correlation that will distort the results.

• Use as few benchmarks as possible

Less is most definitely more when building a style analysis model. The tool allows for a maximum of ten benchmarks to be used, but the ideal would be to use no more than five. The more benchmarks are added the harder it becomes to accurately determine the influence of any one factor on the fund's performance.

• Pick benchmarks that have a low correlation to each other

While it is impossible to completely avoid correlated benchmarks, it is important to pick unrelated benchmarks when specifying your model. Too much overlap will cause some factors to be double counted.

For example there is a high correlation between the FTSE 100, FTSE 250 and FTSE Small Cap but this is acceptable as the benchmarks represent different factors, and the model provides a reasonable insight into the capitalisation split of a UK Equity fund.

A model trying to evaluate the split between US, UK and European Equities containing the FTSE 100, S&P 500, DJ Eurostoxx 50 and the FTSE 250 will likely bring back inaccurate results. In this instance the FTSE 100 and FTSE 250 will be too highly correlated to be distinguished between. The influence of UK Equities will likely be overstated.

Testing the model

Once a model has been constructed, Analytics runs two tests to try and spot weaknesses in the model. The two tests are:

• Significance of the benchmarks

Each benchmark that is selected has its correlation with the target fund tested for significance at the 95% confidence level.

The basis of this test is to see whether there is a chance that the correlation of the benchmark to the fund is genuine. By passing the test we've determined that there is at least a 95% chance that the correlation is indeed genuine.

The benchmarks significance is measured by its STS (Significance Test Statistic). The higher the number, the greater the chance the benchmark is significant to the fund. For a benchmark to pass the significance test the STS must be greater than two.

• Correlation between benchmarks

The correlation test tries to spot benchmarks whose correlation is out of sync with the rest of the model. It does this by comparing correlation between benchmarks to the average correlation between all the benchmarks in the model. If the correlation between two benchmarks is more than a certain percentage greater than the average, the benchmark fails the test.

Failing either test will produce a warning, explaining which benchmark is problematic and why. You then have the option to proceed or alter the model.

Results of Regression

The results page shows what weightings of your chosen benchmarks best explains the performance if the fund. Every regression model is subjective and is unlikely to perfectly highlight every factor influencing that fund. However some statistical analysis on the model can help you decide if your model is accurate enough for the results to be meaningful.

The two statistics on the models accuracy are:

• Adjusted R-Squared

R-Squared is often referred to as the strength of the model. It explains what proportion of the fund's performance is explained by the model. For example an R-Squared of 0.98 means 98% of the fund's performance can be explained by the model.

Adjusted R-Squared takes into account of the number of benchmarks used and stops the R-Squared figure from being inflated just by adding additional benchmarks.

• Excess Tracking Error

The tracking error measures the standard deviation of a fund's excess returns over the returns of the model. A low tracking error suggests the manager is taking a passive approach and tracking the benchmarks in the model. A high tracking error suggests a more aggressive active approach.

The Excess Tracking Error will be affected by the strength of the model. The better the models ability to explain the performance of the fund, the more the accurately the Tracking Error will describe a passive of active approach

As well as statistics, the results page displays two graphs. One is a fairly straight forward pie chart showing the weightings to each benchmark used in the model.

The other shows the performance of the fund relative to the model. Provided the strength of the model is enough to accurately describe the fund's investments, this graph reveals some very interesting information.

It shows what the costs or benefits are from the manager not taking a passive approach. In other words what the Tracking Error actually means in terms of fund performance. If the fund's performance is above that of the model, the managers active approach has paid off and provided higher returns than if they had tracked the market. If the performance of the fund is below the models, then the manager has lost money from his approach.

If the model is strong enough, what this chart offers is a graphical representation of the manager's value or alpha. If they are increasing or decreasing your return compared to just tracking the market.

Other considerations

Any calculation of this sort is sensitive to small factors, so it is important, in addition to the above, to ensure the following:

• Currency

Do not let currency factors get in the way of the true numerical relationships, so make sure you are using a single set of currencies in the fund and the benchmarks, or use the facility to rebase to a particular currency.

• Time Periods

Excessively short or long periods may not lead to useful results. Probably 1-3 years is best.

How to use Regression

Add the fund that you want to run regression to your active list.

Select the regression option from the Reports tab dropdown.

Step 1

Ensure that your target fund is your desired fund.

 

Step 2

Either choose your benchmarks manually (Indices only) or click on the "Suggest Indices" button if you are unsure of what to use.

In this example, I will ask the system to suggest some Indices for me that I could regress against.

Simply click on the Suggest Indices button and the suggestion will become available (where we have them) in the screen below your target, as shown below.

Note: Suggestions are not available for all funds and are based on sectors so they may not be relevant to your fund and may fail the significance test.

 

If you are happy with the suggestions made and would like to regress against them, you will need to add them to your active list via the add to active list icon.

Step 3

Click on the "Go" button to run the regression model if you are happy with your target and benchmark selection. When you do this, a couple of things will happen:

• Test each benchmark in the model, ascertain if its valid for use with fund (using t-value method). Failing the test returns a warning to the user detailing which benchmark is unsuitable, and gives them the option to remove it.
• Test correlation of benchmarks between themselves; determine if correlation is too high between 2 benchmarks, compared with correlation of others. Based on correlation of 2 benchmarks, compared to average correlation across all benchmarks. Again produce a warning with suggested resolution steps.

Note: You do have the option to turn off the test.

If all your tests pass, a pop-up will ask you if you would like to continue (you may want to test many benchmarks and not actually run the model, hence we have a confirmation window).

If any of your benchmarks fail the tests, a pop-up will warn you of this.

 

If you click "Cancel" the display window will show you which benchmarks failed the tests.

 

If you remove the problematic benchmark and re-run the test, they should all pass and display a message like below,

 

On the Regression modelling page, we show the Optimum %, Significance test score, Adjusted R squared and Excess tracking error.

A pie chart of the optimum % weighting is shown (the colours in the pie chart are taken from the ones selected in your active list) and a relative line chart is shown of your target fund vs. your benchmark composite.

 

To save the regression model click on the save icon . You will be prompted to give the model a name and it will be saved in your directory.

To print the model click on the print portrait  icon.