How to build a powerful business index?
By: Aurélie Giraud
Tags: Economics, Business Index, Data Science, Statistics, Analyst

Economics

How to build a powerful business index?

Avoid the most common pitfalls with this reading

Indexes are potent indicators for global and country-specific economies. They are massively used by governments and traders to formulate economic policies, refine external trade and measure changes in money value.

Indexes are meant to reflect changes in a variable (or group of variables) regarding, for example, time or geographical location. That’s why they are commonly used to compare the levels of a phenomenon on a certain date with its level on a previous date or the levels of a phenomenon at different places on the same date.

ex. The price of oil in March 2020 compared to the price in March 2019 taken as the base year.

So why are indexes important anyway? Their primary function is to provide a baseline to measure your performances/portfolio or someone else’s stock picks against. This is commonly referred to as a “benchmark”.

Photo by Adam Nowakowski on Unsplash

How to build them?

Let’s take an example: Considering the COVID-19 situation in 2020, you are expecting a drop in cars utilization compared to the previous years. You want to build an index that reflects these changes.

1- Selection of Time Baseline

The first step in building indexes is to select an appropriate year as a baseline.

A Baseline is a known value against which later measurements and performance can be compared.

The baseline is supposed to reflect “regular and routine” conditions. In other words, it should be free from abnormal situations like wars, famines, floods, political instability, …COVID-19!

The base year can be selected in two ways:

(a) Fixed base method in which the base year remains unchanged

(b) Chain base method in which the base year goes on changing

In that example, for 2007 the base year will be 2006 and for 2006 it will be 2005 and so on.

Take great care in choosing the base year as all results will depend on that. Starting with an exploratory analysis of your data and looking backwards is a good idea. Look for trends and patterns as they are containing the regular and routine conditions you are seeking for. Avoid years with too many outliers or extremes “events” as they might not reflect the normal situation.

2- Selection of Variables

The second step in building indexes is the selection of the variables. Only representative variables should be selected keeping in view the purpose and type of the index number. A representative variables should be:

- recognizable,

- stable in quality over time,

- fairly large in number,

- and finally reflect the habits, customs or functioning of the feature you want to measure the change.

In our example, we could use the consumption of fuel or the total engine hours as representative variables of the utilization of cars

3- Selection of Average

Since the index numbers are, a specialised average, choosing a suitable average is an important step to build an accurate index.

There are many types of averages such as arithmetic, harmonic, geometric average, mean, median, mode.

Visualisation of the impact of Data Distribution on the different average method (Source: Minitab Blog)

Obviously, depending on the distribution of data, they are most likely producing different results. Therefore, it is essential to select the method with great care. Theoretically, the geometric mean is the best for this purpose. But, in practice, the arithmetic mean is the most used because it is the easiest to follow and to understand. Generally, the arithmetic method is combined with the chain based method to make the index more consistent.

4- Selection of Weights

Most of the time, the variables included in the construction of index numbers are not of equal importance. Therefore, proper weights should be assigned to the variables according to their relative importance. Weights should be unbiased and not be arbitrarily selected. Two common weighted indexes are used:

- Price-Weighted Indexes based on the price of each variable. For this index, the variable (stock) with the highest price will have more impact on the movement of the index than variables with lower prices.

- Value-Weighted Indexes based on the amount of each variable.

One of the most popular price-weighted indexes is the Dow Jones Industrial Average (DJIA)

In our example, the consumption of fuel could be weighted by the total number of cars.

5- Selection of Method

The selection of a suitable method is the final step to build indexes. There are many ways to calculate indexes, so let’s have a look at these 3 popular methods.

Simple Aggregative Method

In this method, the index number is equal to the sum of the variable you follow for the target year divided by the sum of the variable for the base year:

Index = [Sum(values of variable in target year) / Sum(values of variable in base year)] x 100

Let’s take this example to illustrate it:

Simple Average of Aggregative Index

In this method, the index number is equal to the average of the aggregative indexes:

Index = Sum(aggregative index) / count of variables

Weighted Aggregative Method

The first two methods are simple and fast to implement. But they are not taking into accounts the relative importance of each item. Each item has the same weight in the global index. But what if there are much more buses than trucks. Why the trucks should have the same impact on the global index?

In that kind of situation, we’d rather use weighted methods. These methods allow assigned different weights to the items according to their relative importance. Many equations have been developed to estimate index numbers on the basis of quantity weights. Here are some of the most popular:

Laspeyre’s index is built with a fixed weight of the base year (q0).

Source: Author

Paasche’s index is built with a fixed weight of the current year (q1).

Source: Author

Dorbish and Bowley’s index is an average of both method mentioned above so it takes into account the influence of both years. The arithmetic mean is used.

Source: Author

Fisher’s ideal index is also an average of Lapeyre’s index and Paasche’s index but using the geometric mean.

Source: Author

So, with the same example we obtain:

Source: Author

Which index to choose?

The table below compiles the results and the main advantages and disadvantages of the methods described above.

Source: Author

As a guideline to select which index to use, make sure that:

- it reflects a comprehensive representation of the intended market or market segment;

- it responds to the evolving market

- it reflects the data quality, distribution and variations over time (trend, seasonality, variations,…)

- the way it’s built is transparent and objective;

- you can regularly rebalance it and easily maintain it according to your computational time available and machine’s performances.