The Finance and Investment Column This column provides informative commentary on financial matters and is written by Patrick van Beek, managing Proprietor of Caribbean Actuarial & Financial Services.
An index is an average of a series of numbers. Though this does not sound too exciting, once a series of numbers has been converted into an index it has myriad uses. Probably the most commonly referred to index in Guyana is the Georgetown urban consumer price index (or CPI for short). The series of numbers in this case is the cost to buy particular goods and services eg food, clothing, rent, fuel and light. The average of these costs is weighted such that the index is representative of the proportion the average household spends on each particular item. In this way, changes in the index represent changes to the cost of living, commonly referred to as price inflation.
In financial indices the series of numbers is usually the changes in the prices of securities. In some stock market indices the average is un-weighted - so the change in the index is the price change for each stock summed and divided by the number of stocks. The Dow Jones Industrial average and the Nikkei 225 are constructed in this manner. Although popular and often quoted these indices should not be used for tracking the value of the market as a whole, since each company's performance carries exactly the same weight, whereas in reality each company's contribution to the value of the market will depend on its market capitalisation (the market value of the shares times the number of shares in issue).
An extreme example may illustrate the point. Consider a market in which only two companies trade: LargeCap and SmallCap, which have share prices of $10 per share and $100 per share respectively. LargeCap has 1,000,000 shares so its market capitalisation is $10 million. Small Cap on the other hand only has 20,000 shares so its market capitalisation is only $2 million. The value of the market is $12 million. Now consider what happens if the value of SmallCap falls to $5 (and LargeCap remains the same). The change in the prices is 0% and -50% respectively. An un-weighted index would thus fall 25%. However the value of the market has gone from $12 million to $11 million, a fall of only 8.3% or so. So the index is wholly unrepresentative of changes in the value of the market.
For this reason, most modern indices, including the Standard & Poor's 500, Topix and the FTSE Actuaries Share Indices published by FTSE International in conjunction with the Faculty and Institute of Actuaries, are all weighted by the market capitalisation at the end of the previous close. In the above example, the price movements would be weighted by 10 and 2 respectively. So the change in the index would be (10*0+2*-50%)/12 = -8.33% - exactly representative of the fall in the market.
This mirroring of changes in the value of the market and changes in the index can be shown to be a general property of indices weighted by market capitalisation. Using it provides a convenient short cut to calculating an index: the change in the index is the change in market capitalisation. In fact, it is not even necessary to calculate the index iteratively from a date some time ago to the present since intermediate sessions cancel in the calculation. All that is needed is the divisor, the ratio of the market capitalisation and the value of the index at the previous point in time. The current value of the index is then simply the current market capitalisation divided by the divisor. In practice it is not quite that simple since the divisor must be adjusted if there are rights issues and as and when new stocks are added or removed.
To see how this might work in practice I show how my index, the vBI (which is Guyana's first stock market index) is constructed:
van Beek Index (vBI) Construction
The first stage in the index construction is to calculate for each stock the market capitalisation which is the number of shares in issue multiplied by the market weighted average price (MWAP) from the trading session (or if no trades took place the MWAP from the last session when shares were traded is taken). The market capitalisation can be viewed as the price it would cost to buy the entire company in the market if all the shares could be bought at the current MWAP.
The total market capitalisation is the sum of the market capitalisations for all shares which have been traded. This is then divided by the divisor which as explained above is broadly the total market capitalisation when the index begun divided by the starting value of the index. The divisor is adjusted each time there is capital change to the index, which is done so that the value of the index before and after the change remains the same.
The simplicity in construction means that the value of index can be verified using just the price data published at www.gasci.com, the number of shares in issue and the latest divisor.
Example
Consider the price data as of the end of session 66 (September 27). The MWAP for Banks DIH Ltd was G$4.5 per share. Given there are 881,718,750 shares on issue this puts the market capitalisation of Banks DIH Ltd at G$3,967.7 million. Working the calculation for each stock in turn gives the total market capitalisation of the market as the following table shows:
The current divisor is 20,778,328 so this puts the index at 21,585,975,242/20,778,328 = 1,038.9
Calculating capital returns over a period is simply a case of dividing the value of the index at the end of the period over the value of the index at the beginning of the period.
Changes to divisor
The divisor has changed five times since the first trade on July 8, 2003.
Date Divisor Stocks Added
08/07/2003 6,410,312.50 BTI, DIH
14/07/2003 12,185,312.50 DDL
21/07/2003 17,583,614.08 DTC, NBI
08/09/2003 18,407,528.66 CBI
06/10/2003 20,262,498.30 GSI, PHI
04/05/2004 20,778,327.79 SPL
The reason the divisor changes when a new stock is added is that if it was not done the index would rise simply because new stocks have been added, making it inappropriate for performance measurement. A real portfolio, invested in the same proportions that each stock makes up of the total market capitalisation, would have to sell some of its holdings and invest in the new stock. By adjusting the divisor, changes in the index reflect the capital returns which would be achieved on this portfolio.
Next week I will look at how indices can be used to compare returns on asset classes and to see if they have beaten the inflation watershed over various periods in time.