Stock markets – putting your money where your math is
Key text
This topic is sponsored by the Australian Government's National Innovation Awareness Strategy.
Unlocking the secret ‘codes’ of the stock market with some simple mathematics will help you understand the way our free-market economy operates.
Those stock market tables in the business section of the newspaper seem to be written in code. You’ve probably seen those rows and rows of numbers, headed by terms like ‘Last sale’, ‘% yield’, ‘PE ratio’ and ‘Share indexes’. But you don’t need a business degree to decode these unfamiliar terms, all you need is some simple mathematics.
What is a stock market?
A stock market (also known as a stock exchange) has two main functions. The first function is to provide companies with a way of issuing shares to people who want to invest in the company. This can be illustrated by an example:
Suppose a company has a mining lease over an area with some rich ore deposits. It wants to exploit these deposits, but it doesn’t have any equipment. To buy the equipment it needs money. One way to raise money is through the stock market. The company issues a prospectus, which is a sort of advertisement informing people about the prospects of the company and inviting them to invest some money in it. When the company is ‘floated’ (established) on the stock market, interested investors can become part-owners of the company by buying ‘shares’. If the company operates at a profit, shareholders benefit in two ways – through the issuing of dividends in the form of cash or more shares, and through growth in the value of the shares. On the other hand, if the company does not operate at a profit (eg, if the price of the product dips), the shareholders will probably lose money.
The second function of the stock market, related to the first, is to provide a venue for the buying and selling of shares.
Stock markets are big business
The buying and selling of shares on the world’s stock markets is big business, which is why we hear so much about it in the news. In 2007, the New York Stock Exchange turned over around $US74.5 billion every day (that's about $A79.5 billion). Even the Australian Stock Exchange (the world’s twelfth largest) will turn over about a billion dollars worth of shares on a quiet day.
Shares actually constitute a relatively small proportion of a stock market’s turnover, with vast sums of money being channelled through other financial instruments such as derivatives, futures, options and bonds. There isn’t space enough here to describe what these are, but one example will show the sorts of numbers involved. In 2007, the world financial markets are reported to have traded $US3.2 trillion worth of currency each day. By comparison, Australia’s gross domestic product (which is the estimated total value of all goods and services produced in the country) for the whole year in 2007 was $US890 billion – or less than a third of a single day’s currency trading.
Many Australians have investments in shares listed on the Australian Stock Exchange; some make a living by trading shares on a daily basis, while many others keep the same shares for years, hoping they will grow in value over time.
But how do these investors know what stocks to buy, and when? Making good investment decisions depends on obtaining as much information about the market as possible. Cracking the codes used by the stock market would be a good start.
Assessing company performance
If you were contemplating buying some shares in a company, you would first need to do a bit of research. One source of information is the share listings in the business section of a newspaper. Information about company shares is listed something like this:
| Company | Last sale | + or - | No. sold (100s) |
Year’s range High Low |
Div ¢ per share | Div yield (%) | PE ratio |
| AGL | 9.78 | +37.0 | 16020 | 12.29-9.059 | 43.00 | 4.40 | 14.3 |
| Coles-Myer | 8.66 | -6.8 | 16842 | 9.22-5.92 | 24.50 | 2.83 | 25.5 |
| Lend Lease | 20.78 | +58.6 | 6356 | 24.00-15.28 | 56.00 | 2.69 | 28.8 |
| Makeshift Construction | 4.20 | +8.0 | 3422 | 4.27-2.18 | 14.90 | 3.55 | 13.6 |
Makeshift Construction Pty Ltd is a fictitious name, but the numbers presented are for an actual company listed on the Australian Stock Exchange. We will use Makeshift as an example to help ‘decode’ the columns of numbers.
Share price and turnover
In the column headed ‘Last sale’ for Makeshift Construction is the number 4.20. This means that each Makeshift Construction share is currently worth $4.20. (If you were to buy 500 shares, you would pay 500 x $4.20 = $2,100, plus a stockbroking fee, which is paid to the firm that actually goes to the stock market and makes the purchase for you or runs the on-line system that lets you buy shares yourself.)
The value in the next column (‘+ or –’) is +8: this tells you that the share value increased by 8 cents over the last sale on the previous trading day. The column labelled ‘No. sold’ tells you how many shares were sold during the day. The value for this column for Makeshift Construction is 3422 – since it is presented in units of a hundred, the actual turnover for the day was 342,200 shares.
The ‘Year’s range’ (sometimes labelled as ‘52 week high low’) shows you the highest and lowest share prices achieved by the stock over the previous year. Makeshift Construction traded in the range $2.18-$4.27. (If you had bought at $2.18 you would make a nice profit if you sold now!)
Financial indicators of companies
‘Div yield %’ (often referred to as % yield) is a measure of the return to shareholders on their investment. It is calculated by dividing the dividend earned by each share ('Div ¢ per share') by the latest share price and multiplying by 100. In the case of Makeshift Construction:
This means that you are earning 3.55% on your investment – probably about the same as you could earn in a high-interest bank account.
The last value in most market tables is the ‘PE ratio’ (price earnings ratio). This is the ratio of the share price to its earnings per share (EPS). EPS is calculated by dividing the net operating profit of the company by the number of ordinary shares on issue. This figure isn’t given in the table, but we happen to know that its EPS is $0.309. The PE ratio then becomes 4.2 divided by 0.309, which is 13.6 – middle-of-the-road for a stock of this type.
By looking at the way the PE ratio is calculated we can see that it increases as EPS decreases and as share price increases. A high PE ratio indicates that the share price is high relative to its current earning power, possibly indicating that the stock is over-valued and that a ‘market adjustment’ (that is, a rapid fall in price) might be expected. Alternatively, it might indicate that the company has good prospects for growth – so investors are prepared to put up with low earnings for now in the expectation that these will increase in the future.
This snapshot view of Makeshift Construction does give us some important information about the company. But most indicators of company performance, including the Div yield % and the PE ratio, are best viewed over time, so that trends in performance become evident. For example, while the Div yield % for Makeshift Construction is quite low at the moment, it may be moving upwards.
Even at their best, though, market indicators only tell us about what has already happened, not what will happen in the future.
Assessing market performance
On the same day that the share price of Makeshift Construction rose 8 cents, the All Ordinaries Index (or ‘All Ords’) rose 10.5 points to 2934.5. What does this mean?
The All Ords is the main share index for the Australian Stock Exchange, providing a general measure of stock market performance. All stock markets have a host of such indexes. The most famous of these are New York’s Dow Jones Industrial Average, Hong Kong’s Hang Seng and London’s FTSE 100.
The All Ords is based on the share prices of 500 major companies listed on the Australian Stock Exchange. These prices are ‘weighted’ according to the market capitalisation of those companies. This means that a company with 5 per cent of the total value of stock listed in the index would constitute 5 per cent of the index. The All Ords, then, is calculated by adding the ‘weighted’ share price (in cents) of each company in the index, then dividing this sum by the total number of those companies.
The All Ords, like other indexes in other stock markets, is regarded as an indicator of the general ‘health’ of the market. The actual number doesn’t mean anything, except as it relates to previous index values. Market analysts look at trends – is the index rising or falling?
Where will the market head next?
Share prices, and therefore the stock market, are affected by a wide range of factors (eg, interest rates, social unrest, changes in government policy), some of which defy prediction. It follows, then, that while stock market indicators such as the All Ords provide a good guide to what has happened, they may not be very useful for predicting the future.
Mathematicians, traders and financiers have studied stock markets ever since they were invented several hundred years ago, but no one has yet managed to devise a foolproof system for working out what will happen next. But financial analysts can use historical data and mathematical calculations, such as moving averages, on balance volume and the stochastic oscillator, to try to predict future changes in the stock market.
What the smart money says
You may have no impulse – or money – to invest in the stock market, but this would not be a reason to remain ignorant of it. Whether we like it or not, what happens on Wall Street and on Bond Street (the location of the Australian Stock Exchange in Sydney) affects the way we live our lives. The smart money says that understanding it will pay dividends.
Page updated May 2008.