FOOL SCHOOL
How Index Trackers Work

March 11, 2005

As we saw in the last Fool School article, an index tracker attempts to match the performance of a particular 'index' of shares. In other words, it attempts to grow as closely as possible to the growth rate of that index of shares. It does this by exposing itself to the performance of the shares in that index.

To keep things relatively simple, 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 (m)	Market cap (£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.

There are basically two types of index that people might try to make out of this: weighted and unweighted. An unweighted index would give equal weight to the movements of each company. Each company would make up one fifth of the index. So, one fifth of the index's percentage movement is accounted for by each share. If Allied Pharma goes up 10 per cent, then the index will rise 2 per cent. If Exploration Oil moves up 10 per cent, then the index will also rise 2 per cent. If one rises 10 per cent and the other falls 10 per cent, then the index will be unchanged. Of course, if all the shares in the index rose 10 per cent, then the index would rise 10 per cent.

A weighted index gives different weights to the effect of each share's movement on the index according to how big the company is (by market capitalisation or total money invested). Allied Pharma, with a market cap. of £160 billion, makes up 40 per cent of the index (that is, 160 divided by 400). So, if its shares rise 10 per cent, the index will rise by 4 per cent. Exploration Oil, on the other hand, only accounts for 5 per cent of the index. A 10 per cent rise by Exploration Oil therefore only has a 0.5 per cent effect on the index.

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 which 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.

Anyway, the point of all this is that if we want a tracker which gives us the average performance of the market as a whole (which we do) 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, the FTSE 250, the FTSE 350 and the FTSE All-Share. In the US, there is S&P 500.

Perhaps the most famous index in the world, the Dow Jones Industrial Average, 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 would therefore be a fairly pointless exercise. So that's how an index is put together. Now let's look at how a tracker goes about tracking its chosen index.

How Does a Tracker Track?

There are two main ways that a tracker tracks an index: Full Replication and Statistical Sampling.

Full Replication

This is the most straightforward method of tracking an index. It involves simply creating a portfolio which includes all the shares in the index at their relevant weights. So, if you were setting up a tracker fund, let's call it the TMF 5, with £4 million to track the performance of the theoretical weighted index that we looked at above, then we would need to buy 0.001% of each company. So, we'd buy the following:

Company	Share price	Shares  purchased (m)	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

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.

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. So, if Exploration Oil shares did badly and it was overtaken, in terms of market capitalization, by Future Technologies whose shares have recently been doing well, then Future Technologies would replace it in the TMF 5 Index.

We would therefore have to sell all our shares in Exploration Oil and buy shares in Future Technologies instead. We might also have to tinker with the overall weightings of all the stocks if our correctly weighted stake in Future costs more than we get for our Exploration shares. In the UK, the FTSE indices are 'reshuffled' in this manner in March, June, September and December of each year.

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 reconstitute itself to take account of this. Assuming that the share price of Deep Hole didn't move, the new index would look like this:

Company	Share price	Shares  purchased (m)	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. Allied Pharma's weighting has fallen from 40% (160/400) to 39% per cent (160/410), while Deep Hole's weighting has increased from 10% (40/400) to 12.2%. 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.

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 (or if an existing investor decided to withdraw £100,000 from the tracker). In this case, we would have to add 2.5% to (or sell 2.5% of) the value of each of our holdings. This is happening all the time 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. All this buying and selling costs money and it is mostly borne by the new or departing investors in the form of the "bid/offer spread" on buying new units.

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 member companies, lends itself reasonably well to this.

Statistical Sampling

With an index like the FTSE All-Share (which has around 700 constituents), full replication is likely to be extremely costly to achieve. To track these larger indices, most fund management companies will therefore use a process called statistical sampling. 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 very close to it.

So, at a basic level with the TMF 5 we might decide that, since Exploration Oil only accounts for 5% 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 unless and until it increases to a level where it accounts for 6%. Of course, if Exploration 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.

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