Premium Growth: Which Half of the Line Actually Moved

An insurer's premium line is two different businesses added together. New business premium is what was sold in the period being reported. Renewal premium is what is still being paid on policies sold in earlier periods. The two grow for unrelated reasons, so a premium line that moved says nothing until it has been split, and only the first half is anything sold recently.

The sheet above carries the arithmetic of a premium line worked on an invented insurer, with every division shown happening on the screen. Where it walks into something an authority decides, the row is drawn with the authority inside it and the value column left blank.

The sheet opens on the worked example, set out here in plain text as well. New business premium of Rs 5,200 crore and renewal premium of Rs 10,400 crore add to total premium received of Rs 15,600 crore. With new business premium held at Rs 5,200 crore next period and 66.67 per cent of this period's total still being paid, Rs 10,400 crore carries forward, total premium received next period is Rs 15,600 crore again, and the line is flat: no change at all, and 0.00 per cent of this period's total. The third box opens on Rs 12,800 crore for the period before this one. Against that earlier base, this period is a rise of 21.88 per cent.

Now press the second button under the boxes. A renewing share of 80.00 per cent carries Rs 12,480 crore forward, new business premium falls a fifth to Rs 4,160 crore, and total premium received next period is Rs 16,640 crore. The rise of Rs 1,040 crore is 6.67 per cent of this period's total premium received. The reported line went up by a fifteenth in the same period that everything sold went down by a fifth, and the sheet says so in words on the screen. A line rising while selling falls is the reading the split exists to catch, and the sheet produces it rather than asserting it.

Here is the shape of the problem. A single line arrives: total premium received went from one figure to a bigger figure. Did the business grow? The line is a sum of two things that had nothing to do with each other, so no amount of care with the total alone will answer that question.

Think of a tailor's shop on a busy street. Some of this month's takings are from people who walked in this month and ordered something. The rest is the final instalment on a set of wedding outfits ordered eighteen months ago. Added together they make a number that is perfectly true and answers no question at all. Asked how business is, the tailor will not quote the total; the answer will be how many people walked in.

An insurer is that shop with the second half made enormous. The split, worked on an invented insurer's figures, ends at a single setting where the whole line stands perfectly still.

What does an insurer's premium line actually consist of?

Two named halves, and they are named the same way everywhere, so the split is always available. New business premium is premium on policies sold during the period being reported. Renewal premium is premium on policies sold in earlier periods and still being paid. Every rupee of premium an insurer receives falls into exactly one of those two, and the two add to the total.

Take Chandrika Life Insurance Limited, an invented life insurer with one stated year of figures here. New business premium of Rs 5,200 crore and renewal premium of Rs 10,400 crore add to total premium received of Rs 15,600 crore.

The drawing below works the three divisions rather than asserting them. The new business half is 33.33 per cent of total premium received, the renewal half is 66.67 per cent of it, and renewal over new business is exactly 2.0 times. The multiple and the share are the same fact stated two ways. Two rupees in every three arriving at this insurer this year came from something sold in an earlier period.

Two rupees in every three is the whole of the split in one line. The largest part of what looks like this year's business is not this year's business: it is the visible edge of contracts signed in earlier years, still running, still in forceThe state of a policy that is still running, still covered and still capable of producing a claim, as against one that has ended., and still owed forward. Because a life contract can run for decades, the renewal half at a life insurer accumulates layer on layer until it dwarfs whatever was sold most recently.

A second reason the split matters here more than at almost any other business sits underneath the arithmetic rather than inside it. A renewal premium arriving this year is a contract still running. The insurer is still carrying everything it promised on that contract. The money set against those promises is held as policyholder fundsThe money an insurer holds against what it will have to pay out on contracts already written. The money sits on the insurer's books but the claim on it belongs to somebody else., and none of it is the insurer's own.

One qualification is the commonest exception to the whole picture, so it belongs here rather than later. Not every contract produces a renewal at all. A single premiumAn amount paid once at the start of a contract, with no further payment due on it and therefore no renewal to follow. is paid once and nothing follows it, so it lands wholly in the new business half in the period it was paid and contributes nothing to any later renewal half. An insurer selling a great deal of that kind of cover has two halves sitting in a proportion that says nothing about how well its older book is holding. This record carries no split of this insurer's premium by product, so nothing further is said about it here.

Why do the two halves move for completely different reasons?

Because they are answers to two questions asked years apart. New business premium moves with what was sold in the period being reported. Renewal premium moves with how much of what was already sold is still running and still being paid. Nothing an insurer does to the first this period reaches the second this period, and nothing that happens to the second says anything about the first.

Look at what sits behind each half. Behind new business premium is a selling year: how much cover was offered, at what price, through which intermediaryAny party standing between an insurer and the person buying cover, such as an agent or a broker, whose registration and permitted activity are set by the authority named further down., into what conditions. Behind renewal premium is a book of contracts written across many earlier years, each still capable of continuing or of stopping, and what happens to that book turns on decisions taken long ago.

A contract stops when a premium due on it is not paid, and the name for that stopping is lapseWhat the contract does when a premium falling due on it is not paid within the time the contract allows. Lapse is a mechanism written into the arrangement, not a judgement about anybody.. Lapse is a mechanism rather than a verdict on anybody: a contract that stops being paid stops contributing to renewal premium from that point on. The mirror image of it is persistenceHow much of what an insurer already sold is still running and still being paid, read as a share of what was sold.. Both are properties of the older book and neither is touched by this period's selling.

Now go back to the street. A stall outside one office building takes money from people walking past today, and it also takes money from a standing monthly order a company placed two years ago for its Monday meetings. A very good day at the counter says nothing about the standing order, and the standing order continuing says nothing about whether anybody walked past today. The two halves answer different questions, run on different clocks, and can move in opposite directions in the same year without anything strange having happened at all.

The possibility of opposite directions is what catches people. Most business lines have halves driven by the same demand in the same year, so they move together. Here they are not, so a year in which new business premium fell hard while renewal premium rose is an ordinary year rather than a paradox needing an explanation.

What does this tool compute, and from which five figures?

Five inputs, all in rupees crore, and the sheet returns both totals, the movement of each half with its direction in a word, and three separate sets of percentages. The bases matter more than the percentages do. A share of premium can be struck on total premium received, on premium net of what was passed to a reinsurer, or on the slice belonging to cover already given, and those are three different denominators producing three different answers out of the same rupees. So every percentage the sheet prints names its own base inside its own line, and the three sets are kept apart on purpose: the headline and the two contributions sit on this period's total, each half's own rate sits on that half, and the rates across periods sit on the earlier period's total.

Two of the five inputs are always looked up. Those two are the halves of this period. Two more are the earlier period's total and next period's new business premium, and both can be looked up once a report exists that carries them. The fifth is not looked up anywhere: the share of this period's premium still being paid next period is not in this record, is not published anywhere, and is an assumption. The sheet prints it as an assumption every single time. An arithmetic sheet that quietly turned an assumption into a projection would be the most dangerous thing on the screen.

At what point does a premium line stop growing altogether?

Hold new business premium completely still at Rs 5,200 crore and ask what next period's total premium received becomes. Next period's total is whatever share of this period's Rs 15,600 crore is still being paid, plus that Rs 5,200 crore. At a renewing share of 66.67 per cent the carry forward is Rs 10,400 crore, next period's total is Rs 15,600 crore again, and the line is exactly flat.

Now notice what that number is. The share at which the line stands perfectly still, 66.67 per cent, is precisely the share renewal already occupies of this period's total premium received. The match is not a coincidence and not a property of these particular figures. Renewal premium already is total premium received less new business premium, so as long as new business premium is unchanged, the share needed to hold the line still is exactly the share renewal already is, at any insurer and on any figures.

Stated as a rule it becomes usable. An insurer's renewal share, read off the split, is in the same breath how much of the existing book has to keep being paid for the premium line to do nothing at all. Everything above that share is a line growing on the older book. Everything below it is a line falling, with new business premium unchanged and nothing whatsoever wrong with this period's selling.

An insurer whose renewal half is two thirds of the line needs two thirds of everything it received to keep arriving before a single rupee of growth appears, and an insurer with a smaller renewal half needs less. The larger the renewal half, the higher the bar the older book has to clear merely to keep the total level. The bar is a fact about the shape of the business rather than about anybody's effort.

What does a rising premium line establish, and what does it not?

A total premium line can rise for three quite different reasons. More was sold. More of what had already been sold kept being paid. Or a little of both happened while one of the two was actually going backwards. The total is the one figure that cannot distinguish which of the three has happened.

Every business has some version of this problem and on most of them it is mild. An insurer has it severely: two thirds of the line is renewal premium, and the book behind that half was written over many years and moves slowly. A half that large and that slow arrives in this year's statement, in this year's column, under this year's heading, and nothing about where it sits warns that it is evidence about earlier years.

Write the arithmetic down and the confusion has nowhere to hide. The change in the total is the change in the renewal half plus the change in the new business half. Two terms, and each carries its own direction independently. The two terms can point in opposite directions, and when they do, the sum reports whichever of them was larger and says nothing whatsoever about the other.

The mistake is avoidable rather than unavoidable: both halves are ordinarily published side by side, so the fix costs one subtraction and about four seconds. People skip it anyway. The total looks like a finished answer, and a finished answer is hard to argue with until it has been taken apart.

What has to be seen to tell the two halves apart?

Two things, and only the first of them is arithmetic. The first is the new business and renewal split for both periods. The split gives the change in each half and confirms that the two add to the change in the total. The subtraction is one step, and the sheet above does it and prints what is left over.

The second is a measure of how much of the older book is still running. Inside an insurer that measure is built by an actuaryThe specialist who builds the basis on which an insurer's expected costs and long dated obligations are estimated, using the mathematics of probability. against the assumptions the contracts were priced on. From outside, what is visible of it is whatever has to be disclosed, and the disclosure requirement is set elsewhere. The rule on what an insurer must disclose about how many of its policies stay in force, and over which periods that is measured, is set by IRDAI at irdai.gov.in, and it moves.

One thing about that measure is arithmetic rather than regulation, and it is worth understanding even without the requirement. A share of policies still running is meaningless without the measurement periodThe length of time over which a share of policies still running is read. Different lengths give different shares from exactly the same book. it was read over. The drawing below takes one invented book of 1,000 policies and reads it over two lengths of time. The shorter reading leaves 900 policies still running, or 90.00 per cent of the book. The longer reading leaves 620, or 62.00 per cent of the same book. Same policies, same insurer, two completely different numbers.

So the period has to be named alongside the share, every time, or the figure cannot be compared with anything. Two insurers each reporting a share of policies still running, over lengths of time that have not been stated, are not comparable, and setting the two side by side ranks measurement conventions rather than businesses.

The absence, plainly: this record carries no figure at all for how much of Chandrika Life Insurance Limited's book stays in force, no earlier year and no later year of any kind, no split by product and no split by how the cover was sold. None of those is supplied here: every period on the sheet other than the stated one is a supplied figure.