What it means
Imagine tracking the cost of a basket of goods over twenty years. The raw dollar figures are hard to read, but if you pick one year as the starting line and call it 100, every other year can be shown as a number above or below that line.
A reading of 125 simply means that the cost is 25% higher than in the base period. Statistical agencies and businesses use base periods for price indices, production indices, sales trackers and share price indices.
The choice of base period is a matter of convenience and clarity. Many official indices are rebased every so often so that the base stays reasonably recent and the figures stay easy to interpret.
The base period matters for comparison. Two indices can look very different if they use different base years, even when the underlying data are the same.
Before comparing them, a careful reader converts both to the same base so that they start from the same line. Rebasing is a simple calculation.
To move an index to a new base period, divide each value by the value in the new base period and multiply by 100. The shape of the series does not change, only the numbers on the scale.
A good base period is one that is representative and not distorted by an unusual event. If the base year had a recession or a spike in prices, every later comparison will look better or worse than it should.
Analysts therefore pick a base that reflects normal conditions or state clearly why they chose the one they did. Businesses can build their own indices too.
A procurement team might index the price of its main raw materials to the first quarter of the year, which makes it easy to see which costs have moved most. A chart of several indexed lines starting at 100 lets managers compare items with very different dollar values on one page.
In practice
Real-world examples.
Example
A government statistics office publishes a consumer price index with the base year set to 100. A reading of 118 tells a payroll manager that prices are 18% above the base year, which is useful when she negotiates a cost-of-living increase.
Example
A food manufacturer indexes the price of wheat, sugar and cooking oil to the first quarter of last year at 100. The chart shows sugar at 140 and wheat at 105, so the buyer concentrates on contracts for sugar.
Example
An investment analyst compares a fund with its benchmark by setting both to 100 on the day the fund started. The fund ends the period at 132 and the benchmark at 125, which shows the fund beat the benchmark by seven index points.
Formula
Calculation
Index value = (value in current period / value in base period) x 100
Suppose a basket of materials cost $2,400 in the base period, which is set at 100, and costs $2,640 today. The ratio 2,640 / 2,400 = 1.10, so the index = 1.10 x 100 = 110. The basket is 10% more expensive than in the base period. To rebase, if the index was 110 today and 125 two years later, and today becomes the new base, the new value is (125 / 110) x 100 = 113.6, which means costs are 13.6% above today's level.Case study
Seen in the real world.
Maple Quay Foods is an illustrative, fictional company that supplies bakeries. Its purchasing team had two price trackers, one built by its own staff and one bought from a data provider, and the lines on the two charts disagreed sharply.
The finance analyst noticed that the internal tracker used last January as its base while the supplier's used a base five years earlier. She rebased both to last January, and the two lines turned out to tell almost the same story, with prices up about 12%.
The team then set a rule that every index in the monthly pack must state its base period on the chart. The illustrative lesson is that numbers on different bases cannot be compared until they are converted to a common starting line.
Watch out
Common mistakes.
- Comparing two indices that use different base periods without rebasing them first.
- Reading an index value as a percentage change when it is a level, since 118 means 18% above base and not 118% growth.
- Choosing an unusual year as the base, which distorts every later comparison.
Questions
People also ask.
Why is 100 the usual starting value?
It makes the maths simple, because the distance from 100 reads directly as a percentage change from the base period.
How do I change the base period of an index?
Divide every value by the value in the new base period and multiply by 100, and the new base will equal 100.
Does changing the base alter the trend?
No, only the scale changes, and the percentage movement between any two dates stays the same.
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