# The Financial Model Behind Tekedia Broad Industrial Average (TBIA)

TBIA Calculation

As noted in a white paper, 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 da is 0.1343330 while db 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.