ISAs and Investment Funds

Published on:

March 18, 2010

8. How Trackers Track

An index tracker attempts to match the performance of a particular 'index' of shares. In other words, it attempts to follow the ups and downs of the index as closely as possible. It does this by exposing itself to the performance of the shares in that index. But how exactly does it do this?

Let's imagine that the following are the biggest five companies on a theoretical stock market and that we want to create an index of them.

Company Share price Shares in issue
(millions)
Market value
(£bn)
Allied Pharma 1,600p 10,000 160
British Banking 500p 20,000 100
Cable Telecoms 800p 10,000 80
Deep Hole Mining 100p 40,000 40
Exploration Oil 1,000p 2,000 20
Total 400

The market capitalisation is the figure for the total value of all the shares in each company. It is therefore the sum of the value of every shareholder's shareholdings. So £400bn is the sum total invested in these five companies.

There are basically two types of index that people might try to make out of this: weighted and unweighted.

Unweighted index

An unweighted index would give equal weight to the movements of each company. Each company would make up one fifth of the index, and one fifth of the index's percentage movement is accounted for by each share.

So if Allied Pharma goes up 10% in a day, then the index will rise 2%. Similarly, if Exploration Oil moves up 10%, then the index will also rise 2%.

If both Allied and Exploration rise 10%, then the index will rise 4%. If one rises 10% and the other falls 10%, then the index will be unchanged. You get the picture.

Weighted index

A weighted index gives different weights to the effect of each share's movement on the index, according to how large its market value is, as a proportion of the total value of the market. Allied Pharma, with a market value of £160bn, makes up 40% of the index (£160bn being 40% of £400bn). So, if its shares rise 10%, the index will rise by 4%.

Exploration Oil, on the other hand, only accounts for 5% of the index. A 10% rise in Exploration Oil will therefore only increase the index by 0.5%. In other words, movements in Exploration Oil's share price only have one eighth of the effect on the index that movements in Allied Pharma's have. This is because Exploration only has one eighth as much money invested in it, and is therefore only an eighth of the size of Allied Pharma.

The important thing about weighted indices is that they reflect the average performance of every pound in the index. You can think of a weighted index as being like a portfolio that owns all the shares in all the companies. Whatever happens to the share price of the companies in the index, a weighted index matches the performance of the average pound invested in it.

To weight or not?

Anyway, the point of all this is that if we want a tracker that gives us the average performance of the market as a whole then we need to be tracking a weighted index. For this reason, the majority of indices are weighted. Examples from the UK include the FTSE 100 and the FTSE All-Share. In the US there is the S&P 500.

However, perhaps the most famous index in the world, the Dow-Jones Industrial Average (DJIA, or just 'the Dow'), is an unweighted index. Other unweighted indices are the FT 30 in the UK and the Nikkei 225 in Japan. Tracking these (unweighted) indices would not necessarily give you anything like the average performance of the US, UK and Japanese stock markets and therefore isn't ideal.

So that's how an index is put together. Now let's look at how a tracker goes about tracking its chosen index. There are two main ways that a tracker can track an index: Full Replication and Statistical Sampling.

Full Replication

The main advantage of the full replication tracking approach is that you can expect to match the index very closely. The disadvantage is that it can be expensive and it is only really very practical where you have a relatively small number of shares in an index. The FTSE 100, with its 100 constituent companies, lends itself reasonably well to this.

Full replication simply involves creating a portfolio that includes all the shares in the index at their relevant weights. So, if you were setting up a tracker fund with £4 million to track the performance of the theoretical weighted index that we looked at above -- which we'll call the TMF 5 -- then we would need to buy 0.001% of each company (that is, our fund of £4m as a proportion of total value of the index of £400bn). So, we'd buy the following:

Company Share price Shares purchased Value
(£m)
Allied Pharma 1,600p 100,000 1.6
British Banking 500p 200,000 1.0
Cable Telecoms 800p 100,000 0.8
Deep Hole Mining 100p 400,000 0.4
Exploration Oil 1,000p 20,000 0.2
Total 4

Once we've bought these shares, then all things being equal, we can just leave the tracker to do its job. We basically only have to buy and sell the shares in three situations.

1. Index changes

The TMF 5 is designed to follow the performance of the average pound invested in the five biggest companies on our theoretical stock market. Say Exploration Oil shares did badly and it was overtaken, in terms of market value, by Future Technologies.

The shares of Future Technologies would replace Exploration in the TMF 5 Index. We would therefore have to sell all our shares in Exploration Oil and buy shares in Future instead. We might also have to tinker with the overall weightings of all the stocks if our correctly weighted stake in Future Technologies costs more than we get for our Exploration shares.

In the UK the FTSE indices are rebalanced in this manner on a quarterly basis. However, some changes occur at other times when, for example, a company is taken over and its shares are no longer listed on the stock market. In this instance, the highest placed company on the 'reserve list' is normally promoted to the index.

2. Share capital changes

This is when the member companies issue new shares or cancel any of their existing shares. Imagine that Deep Hole Mining issued 1 new share for every 4 of its existing shares to buy the Australian company, Gold Diggers Pty Ltd. The TMF 5 would have to adjust itself to take account of this. Assuming that the market was ambivalent towards the deal and the share price of Deep Hole didn't move, the new index would look like this:

Company Share price Shares in issue
(millions)
Market value
(£bn)
Allied Pharma 1,600p 10,000 160
British Banking 500p 20,000 100
Cable Telecoms 800p 10,000 80
Deep Hole Mining 100p 50,000 50
Exploration Oil 1,000p 2,000 20
Total 410

So all the other companies' weightings have fallen. For example, Allied Pharma's weighting has fallen from 40% to 39% (160/410). Deep Hole's weighting has increased from 10% to 12.2% (50/410). As a result, a little of each of the other companies will need to be sold and the money used to buy shares in Deep Hole.

3. New money from investors

The third reason for buying and selling would be if a new investor came along and asked to invest £100,000 in the tracker fund. In this case, we would have to add 2.5%. This happens frequently with most index trackers. Every day, people are coming along to put more money in or to take money out.

If there is a pound put in for every pound that gets taken out, the balance is maintained. However, if, overall, money is flowing into the fund, then it will need to be buying shares in each company each day to maintain its correct exposures. If there is net money flowing out, then it needs to be selling shares in each company each day to maintain the balance.

Statistical Sampling

With an index like the FTSE All-Share (which consists of around 600 companies), full replication is likely to be extremely costly to achieve. To track these larger indices, a process called statistical sampling is often used. The fund doesn't try to hold every share in the index, but it analyzes the index and works out its investments so that it is very confident of achieving a performance that is very close to it.

So, at a basic level, with the TMF 5 we might decide that, since Exploration Oil only accounts for 5 per cent of the index's value, then we don't actually need to hold it to ensure a performance very close to the index. We do, though, have to keep a close eye on it. If it increases by 20% relative to the rest of the index, then we will underperform by 1% and we certainly don't want to risk underperforming by more than that.

We might therefore decide that we can afford to save costs by not holding Exploration Oil unless and until it increases to a level where it accounts for 6% of the index. Of course, if Exploration Oil underperformed the rest of the index then we would benefit from not holding it.

Statistical sampling is a bit of a fudge. If money flows into the fund from new investors, shares of one sort or another will certainly have to be bought, but we might be able to save a bit on costs by not sticking rigidly to buying exactly the right amount of every single company. With a large index such as the FTSE All-Share, the relationships between the different shares will be examined, so that the tracker's manager can be very confident of not departing very far from the index.

Phew! That's a lot to take in one go. We suggest a nice cup of tea before reading the next part of this guide.

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