White Paper – Introduction, Component Stocks And Calculation Of Tekedia Broad Industrial Average (TBIA)

Preamble

The Nigerian Stock Exchange (NSE), established in 1960, has about 300 listed companies (283 companies as at March 9, 2007) with all listings included in only one index, the Nigerian Stock Exchange All Shares Index. The goal of TBIA is to use twenty stocks to represent the market dynamics and simplify things for analysts, economists, policy makers, investors, among others.

Introduction

Tekedia Broad Industrial Average (TBIA) is a stock market index created by Tekedia Intelligence, a division of Fasmicro. It is an index that shows how twenty large, publicly owned companies, based in Nigeria have traded during a standard trading session in the stock market. To emphasis that this index is not restricted to any particular industry such as technology, transportation or banking, we included the word “Broad”. The word, “industrial”, was used within the constructs of different markets. For example, we have the banking industry, hotel and tourism industry, and so one with no implied connotation to the industrial era. We understand that many of the companies in the index are knowledge driven, yet, they operate in an industry.

TBIA is not a mean or actual average of the prices of the component stocks. The average is price-weighted and tested over a period of six months to ascertain its correlation with the All Share Index of the Nigerian Stock Exchange.   We also included a scaled average model in case there are stock splits, stock dividends or similar adjustments in the future; we acknowledge that these are not common in the Nigerian Stock Exchange.  The scaled average will re-calibrate the index and ensure no historical distortion is introduced. Accordingly, we will update for any adjustment immediately the NSE makes that information public.

Our goal is to generate a reliable and consistent value of TBIA or TBIA 20 for investors, economists and the general public. Possibly, TBIA could become a benchmark index to track the Nigerian Stock Exchange (and futuristically Nigeria’s economy if it begins to correlate with the exchange performance) using 20 stocks instead of nearly 300 companies in the exchange’s All Share Index.

Because this index is price-weighed, it was very hard to choose the components since most of the large caps in the exchange, especially banks, are price-depressed. For instance, the total sum of all (individual) bank prices is about N85 while Nestle trades at N400, yet, most of the banks have solid capitalizations. Take UBA, for an example, it trades at N4.45. Any average with UBA and Nestle will be skewed. So, we had to more some statistical modeling to ensure we zero-out the skew. In other words, UBA will be inconsequential in an Index with a stock more than 90 times its value. To overcome this problem, we introduced a divisor, cap devisor, which helps us to capture the large caps, though price-depressed and statistically adjusted the index for relevance. A total of two divisors were used.

(On July 1 2011, originally planned debut day, the decision was to remove any stock with value of N200 or more in TBIA. But after more statistical data analyses, it was decided to find a novel way to accommodate the top market caps despite the depressed prices in the exchange. The extra time gave rise to using two divisors).

We understand that economies change and markets are disrupted with new players emerging and old ones dislodged.  When we notice that any of the components in the index has lost relevance, we will replace it. When that is done, we will adjust the scale factor which we have used in the calculation to ensure the value of the Index remains the same. That scale factor is the second divisor.

TBIA Calculation

As noted above, there are two divisors for TBIA calculation and it is by no means a simple mathematical average. To obtain the daily value of TBIA, the sum of the prices of all 30 stocks is divided by two divisors. The divisors are adjusted in case of stock adjustments like splits, spinoffs, etc. The goal is to ensure that none of such events distort or alter the numerical value of TBIA. We categorized the stocks into two groups:  A and B (more on the classification later). All chosen stocks in the index have fair market cap in the exchange. The equation for TBIA calculation is as follows:

In the equation above, p represents the prices of the component stocks and d is the divisor. Any stock with price of N85 was included in Category B. The value of d_a is 0.1343330 while d_b is 0.5064900. With these numbers, the Index will not be overly affected by one stock movement. It is also important to emphasis that for Category A, one Naira stock movement contributes N7.50 while for Category B, it will have an effect of about N2. Heavy hitters like Nestle and Guinness are in Category B and we have statistically adjusted for their influence in the index.

For TBIA to remain undistorted despite structural changes like splits, spinoffs, etc which ideally can change the sum of the component prices, it will be updated whenever Nigerian Stock Exchange announces a change. The optimization goal is for value of TBIA before and after the event to coincide:

Components Stocks

There are many standards we put in place before a stock could make it into TBIA. It must have an appreciable market capitalization, at least N10 price, among other factors. By the close of business on Friday, August 12, 2011, we cutoff and qualified those with above N10 and respectable cap. We now apportioned so that most of the industries could be included.  So, there are some industries you will not see in the Index and what that means those industries may not be having huge impacts in the stock exchange All Share Index. Insurance has no representative and only three banks made it. To ensure a technology company is included, we qualified NCR despite not meeting our price criterion, an exception.

Now with the selection of the stocks, we moved any stock that is more than N85 into the high price Category B. Others went into Category B.  Using the formula explained above, we automated the process. Daily updates will be done.

Review and Listing Update

We hope to review the list in six months. If you have an idea, please email [email protected] (Attn: Bode). We will include any suggestion and criticism as we improve on this project. If you use the equation we have presented above and the value of the stocks at the close of business in the NSE, you will get exactly what we have. If you have any problem, please email us. Whenever NSE does a structural change, check TBIA page, we will activate the magic number to balance the equation as presented above. We have excluded it in this discussion to avoid unnecessary complexity when there is no need for it. But it is simple, we are engineers, and it is easy to optimize two things given some constraints.

TBIA Web Page for Daily Update

https://www.tekedia.com/tekedia-broad-industrial-average-tbia-daily-records/

http://fasmicro.com/TBIA.aspx  (INDEX PLOT)

Ndubuisi Ekekwe

TBIA Creator

August 14, 2011

Disclaimer: We have presented TBIA “as it is”. You are free to share and distribute; NO rights reserved.

Register for Tekedia Mini-MBA (Jun 3 - Sep 2, 2024), and join Prof Ndubuisi Ekekwe and our global faculty; click here.