Stocks are among the most popular instruments to invest money
in. There are many different stocks; even in small countries like the
Netherlands, there may be more than 100. Now, for many reasons, people want
to have an idea how well the general stock market is doing. For this
reason, people have invented the stock market index, or index for short.
An index is the value of a collection of stocks. The publisher of the
index, often the stock exchange, selects a certain number of companies.
This number is often fixed, such as 225 in the Nikkei index, 25 in the
AEX index, or 100 in the FTSE index. Of these companies, a certain
number of shares is bought. We then add the value of all these
shares together to come up with a value of the index.
Let’s build or own index to illustrate this. To keep things simple, we want
to build an index out of only three companies, but these three should be
representative of three major sectors of the economy, namely
energy, banking and IT. Let’s pick Exxon, Citigroup and Google as an
example. Now, we could make an index by just taking one share of Exxon, one
of Citigroup and one of Google. Exxon is worth $70.12 a share, Citigroup is
worth $ 5.23 a share, Google is worth $ 464.75 a share, making our index
worth $540.10. Now, imagine that Citigroup were to double overnight. This is
of course great news for many people owning the stock, and should have a
large impact on our index. Unfortunately, our index will rise by less than
1%: it will be worth $ 70.12 + $ 10.64 + $ 464.75 = $545.33.
The solution to this is by taking multiples of each stock. Let’s say we take
one Google share, add 10 shares of Exxon to that (because Exxon is a bigger
company) and add 50 shares of Citigroup (because Citigroup is a lot smaller
– around 20 times smaller than Exxon at the moment I’m typing this). This
would make our index worth 1427.45.
One finishing touch we could add is to scale our index a bit. This is often
done in practice. If one, for instance, has 50 shares, adding even a small
number of each share produces an index value that is very large. Therefore,
many indices are determined as a set of stocks that make up a certain number
of indices, for instance 100. In our case, we could say that our stock
basket – that’s the technical term for it – of 28 shares of Google, 602
shares of Exxon and 5895 shares of Citi. This package of shares is almost $
100.000, and we could say we have 100 indices of 1000.
With this, we can compute both how much one cent and one percent move in one
of the stocks changes the index. For instance, a 1 cent move in Google moves
our index by 28/100, or 0.28 points, while a 1 cent move in Citi moves our
index by 5895/100, or 5 points. A 1 percent change in Google, on the other
hand, changes our index by 28 * 0.01 * 464.75/100 = 2.7 points, while a 1
cent change in Citi changes our index by 2895 * 0.01 * 5.23 /100 = 3.8
points. We hence see that the weight of Google and Citi in the index is
nearly the same, even though the share price of both companies is very
Having seen how the value of an index is computed, we essentially know what
it is. The next step is trading one. It’s all nice to hear the
Eurostoxx 50 index rose by 13 points, but how can we profit from this?
There are three common ways of going long an index.
The first and most obvious way is just buying all the shares in an index, in
the right proportion. This is a bit of a hassle for three reasons. Firstly,
we might need to trade shares in a lot of different companies. That is a lot
of work, and also costly, as exchanges often charge a fee per trade. Buying
shares in 225 companies, like the Nikkei has, means paying this fee 225
times. Other transaction costs could also accrue. Secondly, as mentioned,
one basket is often multiple times the index. For instance, the AEX index is
currently at 300. However, the basket is 100 times the index – and that
basket contains a fractional number of shares, so to be precise, we need 4
basket, or 120.000 euros to buy all shares. That’s a considerable amount of
money, and often too much to invest in a single index. Thirdly, the
composition an index can change as companies shrink, grow, get taken over or
go bankrupt. This means that keeping the basket up-to-date requires work. As
a final point, not all indices even have futures.
The second, and far more common way, is to buy a futures contract on the
index. Such a futures contract gives us the right and obligation to
buy the index at a point in time in the future, for the price we currently
pay. In practice, what happens is that we receive or pay money every day
for changes in the index, in order to build a buffer. There are other fine
points to trading futures, such as margining, the interest and
dividend exposure of futures, and the fact that futures will only give the
exposure until the time when we are in effect “buying” the index. These
points are deserving of a write-up on their own, and those who don’t
understand these finer points are well advised to stay away from futures, as
it is really easy to lose an enormous amount of money. A second, more
pragmatic point, is that futures are often a few times the index. For
instance, one DAX future is 25 DAX indices, so it is an exposure of around
25 * 5500 = 138.000 euros. Professionals love futures, but
for private investors, they are not the instrument of choice.
A third way of buying an index is buying a tracker. In essence, when
buying trackers, someone will use the money to buy index baskets. Because
trackers are bought and sold in large amount, economy of
scale applies, and the person buying and selling the baskets can do so in
such large volumes that his costs per basket are modest. Buying a tracker
does have a disadvantage: an annual fee is charged. This fee, however, is
typically small, around 0.2 to 0.5% of the value of the tracker. For a
private investor, this is typically a lot less than the trading costs that
would be incurred by buying the basket. For additional convenience, trackers may represent only a fraction of one index. For instance, it may require 100 27-euro Eurostoxx trackers to "build" one Eurostoxx index. Because trackers pay dividends at different times than the stocks in the basket, there might be a slight difference in value between the set of trackers and the index. We'll see below that this is not a real issue in practice. It is noted that note all indices have trackers; on
the other hand, some indices have multiple trackers.
One might ask whether all these three products have the same value. The
answer is a rather firm yes. There are many market participants who can
compute the value of a future rather precisely from the index basket and
vice-versa. Something similar goes for trackers. If a profit can be made by
for instance selling the future and buying the basket, they will do this.
Because there are so many people watching this, even a tiny profit is enough
to trigger a trade, as otherwise, someone else will do it. People doing this
are called arbitrageurs. They typically trade huge
volumes for tiny profits, guaranteeing an efficient
market and receiving a modest profit from it.
We now know what an index is, and even how to trade one. This is quite
useful to know, because there are many different indices. In general,
indices are sorted by four criteria:
- Location: This can be one or more countries, a continent or the
entire world. For instance, the DAX-index contains German stocks, whereas
the Eurostoxx –index contains Euro-denominated stocks
- Size: of the companies: There are many indices for big
companies, but also indices for mid cap and small cap stocks. For
instance, the MDAX index consists of German stocks that are one size too
small to be in the DAX-index
- Sector: There are many sector indices, such as the Nasdaq-index
(technology), but also gold mine indices.
- Product: In the discussion above, I’ve focused on stock indices.
Stock indices are not the only type of index around; we can build an index
around a pool of bonds to create a bond index, for instance.
In summary, indices are tools to indicate how (a part of) the (stock) market
is behaving. Investing in indices is not straightforward, but handy
proxies for an index may exists. Investors should not only decide
what index they want to invest in and for what size, but also what proxy
One small thing: this isn’t investment advice. So don’t come complaining
when you make an investment decision based on this write up and it goes
wrong. By the way, exchange websites provide excellent
- I looked up the present stock values at Yahoo Finance.