Insurance Ratio Calculator: Where Each Line Comes From

Three figures from an insurer's reported results go in: claims, the cost of running the arrangement and the premium those two sit on. Back come the loss ratio, the expense ratio and the two added, with the premium base printed inside every line. The same three readings come back on a second base at the same time, together with the rupee amount of premium left over.

Where the figures came from. Every rupee amount divided in this calculator belongs to Chandrika Life Insurance Limited, an invented life insurer, and every amount was built to be divided. The record behind this calculator carries no ceded premium figure at all, so the net premium base is a supposition and is flagged as one everywhere it appears.

The arithmetic between the boxes and the answers is two divisions and one addition, and it could be done on the back of a bus ticket. So why a tool at all. Because the hard part of this calculation has never been the arithmetic. The hard part is knowing which figures are in hand. A published result puts four numbers that could all plausibly be called claims within about a centimetre of each other, and it puts the premium figure in at least three different forms depending on which part of the document was opened.

One sentence carries the whole tool. The division is trivial and the choice of what to divide is not, so this calculator asks for the base to be named out loud and then prints that name inside every answer it hands back.

Both settings above are printed here as plain text as well, so they survive without the tool. Take total premium received of Rs 15,600 crore as the whole. Claims of Rs 6,720 crore come to 43.08 per cent of it, expenses of Rs 2,496 crore come to 16.00 per cent of the same whole, the two together take 59.08 per cent of it, and Rs 6,384 crore is left standing. Now put the very same two rupee amounts over the supposed net premium of Rs 14,040 crore. The readings become 47.86 per cent of that base, 17.78 per cent of it, 65.64 per cent when added, and Rs 4,824 crore left standing.

A result that cannot be retraced is a result taken on trust, so two things sit between the boxes and the answers. The build up prints each division as its own numerator over its own denominator, and the line beneath it proves that the two halves add to the third answer and that the third answer and the premium left standing come to one hundred. The pairing control above the boxes carries three named settings and a fourth for figures supplied by the reader, and the third of the named three is the mistake this calculator is built around.

The drawing under the answers redraws on every keystroke. A ratio is drawn rather than only printed because a ratio is a position rather than a quantity, and a position is something that can be watched moving.

The meaning of the answers is covered separately, under the three insurance ratios: what each of them measures, what the hundred line is, and the four things none of them contain. Here the voice is a field noteA note about location. Which line of a reported result a figure sits on, and what sits immediately above and below it, rather than what it signifies once it is in hand. throughout: where a figure is found, what sits beside it, and which neighbour a first-time reader picks up by mistake. Never what it means.

What does this calculator work out?

Four rupee amounts for one stated period, three choices that are names rather than numbers, and six answers back. The shape of the output shows the shape of the question, so the six are worth noting before anything is touched.

The loss ratio, with its base named inside the line. The expense ratio, with its base named inside the line. The two added, with its base named inside the line. The rupee amount of premium left standing after both have been taken out. The same three readings computed again on a second base supplied alongside the first. And the base itself, handed back as an output line in its own right, where it can never be an assumption sitting quietly in somebody's head.

The sixth output looks like a waste of space and is the most useful thing on the tool. A ratio that has been separated from its denominator is not a number anybody can use, and the way a ratio gets separated from its denominator is that somebody copies the percentage out of the box and leaves the box behind. Printing the base inside the string means the base travels with the figure into the note, the message and the slide it ends up on.

The premium left standing and the combined reading are one statement said twice, once as a share and once as an amount, and the tool prints both because people trust the two differently. A reader who shrugs at 59.08 per cent of total premium received sits up at Rs 6,384 crore, and a reader who cannot hold Rs 6,384 crore in their head can hold four tenths of the premium. Same split, same period, same insurer, two vocabularies.

Where does the claims figure come from, and what is inside it?

The claims line is what the insurer paid out during the period on losses it had covered. In a published result it does not sit alone. The claims line sits inside a small cluster of lines that are all about money going out on policies, and every one of that cluster is a perfectly respectable number that answers a different question from the one being asked.

Three neighbours get picked up by mistake, and all three are within a few lines of the one wanted. The first is the difference between what was paid before anything was recovered from a reinsurerAn insurer's own insurer, which agrees to carry part of what the first insurer has taken on. What it costs and how it is arranged are worked through separately. and what was paid after that recovery. Both figures are usually there, one under the other, and they differ by exactly the part somebody else is carrying. The second is the movement in the reserve held against claims not yet settledAn amount set aside for claims that have been made or are expected but have not been paid out yet. How it is worked out and valued is covered separately.. The reserve movement sits directly beside the paid figure and is a change in an amount held rather than a payment made. The third, on a life insurer specifically, is the benefit paid when a contract reaches its maturityThe date a contract runs to, when an amount falls due because the contract has ended rather than because anything went wrong. date. A maturity benefit is a payment falling due on a promise that ran its course rather than a loss claimed against cover.

Using this tool does not require deciding which of these is the philosophically correct numerator. Only one thing has to be decided: whichever version is taken, the premium figure underneath it has to be the matching version, so a numerator taken before any recovery sits over a premium taken before any recovery, and one taken after sits over one taken after. The matching discipline is worth more than any amount of care about the rest, and the failure block further down is entirely about what happens when it slips.

Where does the expenses figure come from, and which lines belong in it?

The expenses figure is what the insurer spent getting the business in and running it. In a published result that almost never arrives as one line. The expenses figure usually arrives in at least two parts. The two parts sit in different places and are counted in different ways, and that is why this is the input people most often get half right.

The first part is what was paid to bring the business in. Bringing it in means commissionWhat an agent or a broker is paid for bringing a policy in. Who may be paid it, and on what conditions, is covered separately. to whoever sold the policy, and everything of the same character that goes with it. The second part is what was spent operating: the offices, the people, the systems, the printing, the whole cost of being an organisation that answers the telephone.

Both parts go into the box, so a split presentation needs adding up rather than choosing between. Taking only the operating half is the single most common way the expense input goes wrong, and it goes wrong in the direction that flatters. A reader who does that has quietly removed the entire cost of distribution from the arrangement. On Chandrika Life Insurance Limited the figure standing in this box for the stated period is Rs 2,496 crore, and that is the whole of the cost of getting and running the business rather than one half of it.

Three lines stay out, and it is worth knowing that they stay out for three different reasons rather than one. Claims stay out because they are the other half of the stack and putting them in here would count them twice. The movement in the reserve stays out because it is not a cost of running anything, it is a change in an amount held against something that has not been paid yet. And tax stays out because it is neither half of what this tool measures, and a tool that has not reached a result yet cannot be taxing one.

Which premium figure goes in, and what does the calculator do with that choice?

There are at least three figures in a reported result that a reasonable person would call the premium, they are different sizes, and the ratio that comes out depends entirely on which one was reached for. The premium base is the input that decides everything, and that is why the tool asks instead of assuming.

Total premium received is everything taken in during the period, before anything has been taken out of it. On Chandrika Life Insurance Limited that is Rs 15,600 crore for the stated period, being Rs 5,200 crore of new business premium and Rs 10,400 crore of renewal premium. Net premium is what is left after the part cededHanded on to a reinsurer, together with the premium that goes with it. How much may be handed on, and on what conditions, is covered separately. to a reinsurer has been removed, so it is always the smaller of the two and it is smaller by exactly the amount somebody else is now carrying. Earned premium is the premium for cover the insurer actually provided during the period rather than the premium it collected during the period. The two are different whenever a policy straddles the end of a period, and most policies do.

No earned premium figure for this insurer sits anywhere in this record, so the third choice is named as a base a reader may hold independently and is never filled in here. The refusal is worth stating out loud rather than quietly leaving the box empty. A tool that made up an earned premium number would produce an answer that looks exactly as solid as the two that are real.

The choice drives the whole design. The calculator takes the name picked and prints it inside the answer string, in the same breath as the number, so the output reads 43.08 per cent of total premium received rather than 43.08 per cent. A ratio separated from its base is the commonest wrong number in this entire subject, and printing the base inside the line is the cheapest guard anybody has ever built against it.

Why do the same three ratios come back on two bases rather than one?

Because the size of the gap between them is the teaching, and a reader who is shown one number believes the number instead of the base. Show two and the base becomes visible. The base is now the only thing that could possibly have caused the difference.

Hold every rupee figure completely still. Claims of Rs 6,720 crore, expenses of Rs 2,496 crore, nothing touched. Measure them first against a whole of Rs 15,600 crore, being total premium received: the readings are 43.08 per cent of it for claims, 16.00 per cent of it for expenses, 59.08 per cent when the two are added, and Rs 6,384 crore standing at the end. Now measure the identical pair against a whole of Rs 14,040 crore, being the supposed net premium: 47.86 per cent for claims, 17.78 per cent for expenses, 65.64 per cent added, and Rs 4,824 crore standing.

The insurer did absolutely nothing in the gap between one reading and the other. No claim was paid, no rupee was spent, and the added figure moved by more than six points anyway. Every point of that movement came out of the denominator. Isolating the denominator is what the exercise was built to do: pin the numerators down and the base is the only thing left that can shift the answer.

The second reading is a sensitivity test rather than a report, and confusing the two would undo the demonstration. Holding the numerators still while the base moves measures how far the answer can travel on the choice alone. In a genuine net reading the claims figure comes down too, so this is not how an insurer would publish a net reading. The genuine net case is worked out in full in the failure block below.

What does the output not settle?

Four lines, and the tool prints all four under its own result. Every one of them is something a first-time user assumes the number already contains.

On a life insurer, the premium taken in during a period and the risk carried during that period are related much more loosely than the words suggest. A large part of what arrives is renewal premium on contracts written years ago, and a large part of what will be paid out falls due decades from now. The sum of two ratios struck on a life insurer's total premium received is a perfectly respectable arithmetic fact and it is not a combined ratio in the sense a general insurer uses that phrase, so setting the two side by side compares two different constructions wearing the same name.

Refusing to divide would be a strange thing for a calculator to do, so the tool will still compute it. The tool states instead what it was not told, and that is the honest version of the same protection.

What was never in this record to work with?

Carrying this arithmetic past where the calculator leaves it starts with knowing where the supply of figures runs out.

Two facts hold at once, and the less pleasing one carries as much weight as the other. Every division above closes exactly, and the set of questions it can answer is very small. Being exact and being far reaching are unrelated qualities that get confused constantly. Exactness feels like authority. A tool that let its exactness stand in for its reach would be the more dangerous of the two, and it would be dangerous precisely because it worked.