General Methodology for the AMF Indices
The Arab Monetary Fund (AMF) calculates a composite index measuring the performance of Arab Capital Markets combined. The (AMF) also calculates an index for each Capital Market. These indices are Market capitalization weighted, using a chained Paasche Method, prices are calculated in U.S dollar terms, using end of period data.
Changes of the value of the components are adjusted to accommodate changes in market capitalization resulted from the addition or deletion of shares in the samples of the indices.
The mathematical equation for the indices (x) is :
When time period i < 1,
Xi= (Mi/Bi) * 100
Bi=Bi-1 * (Mi / Mad)
and when i=1,
Xi= 100 * Bi = Mi
i = time period
Xi = index at time i
Bi = base value of index. when i=1 (the first period), market capitalization=base value of index
Mi = market capitalization of constituents at time i
Mad = adjusted market capitalization (adjusted for , rights issues , new issues of stock , stock cancellations for constituents, and the addition or deletion of constituents).
Market capitalization (Mi) is the sum of the market value of all stocks included in the index. The market value of each stock is equal to:
Mi = Pi * ni
Pi = the last transaction price for the stock in period i
ni = the number of shares issued and outstanding at the end of the period i.
Adjusted Market Capitalization
Adjustments to the basic method of measuring change in capitalization are needed when a company issues new shares or declares a rights issue. The purpose of the adjustment is to neutralize the change so the change has no effect on the index. For example, when a company sells additional shares of stock, it adds market capitalization that would distort the index by implying that the market capitalization of the index increased from the period before the new shares were issued to the period after the new issue.
Mad = Mi-Ii-Ni-Ri+Qi-1
Mi : market capitalization of constituents at time I ( the sum of the market capitalization of all stocks included in the index)
Mad : adjusted market capitalization at time i.
Ii : market capitalization of new shares issued by a company included in the index and listed at time i
Ni : market capitalization of the company added to the index at time i
Ri : market capitalization of rights issues
Qi-1 : market capitalization of the company at time (i-1) which deleted of the index at time i
No adjustment is made, however, in case of stock split, bonus shares (stock dividend) and a decrease in paid-in capital, since such corporate actions do not affect the current market capitalization. Thus, adjustments are done for any changes in index sample or any corporate action affecting the market capitalization on index stocks. This can be achieved by using the adjustments factor Mad.
The formula above is used to calculate the adjusted market capitalization (Mad) in local currencies, and then converted to U.S dollar to calculate the index for each market.
The Composite Index
The (AMF) daily composite index, includes as of now , the indices of the 14 markets, which are the markets of Abu-Dhabi, Bahrain, Dubai, Egypt, Jordan, Kuwait, Lebanon, Morocco, Oman, Palestine, Qatar, Saudi Arabia, Syria, and Tunisia.
The shares included in the samples of the indices are treated in the composite index as if they are shares of one single market. The composite index is calculated in U.S dollar terms, not in domestic currencies.
The shares selected to be included in the sample of the (AMF) indices, are selected based on:
- Market capitalization
- Turnover ratio
- Company sector representation