Loss Ratio, Expense Ratio and Combined Ratio Together

The loss ratio is claims over premium. The expense ratio is what the insurer spent on running itself over premium. The combined ratio adds the two, and answers whether the premium covered both before any return on the money held in between. All three move when the premium figure underneath them changes, so a ratio quoted without its base named in the same sentence cannot be compared with anything.

Each of these is one division and nothing more. The whole of the difficulty sits in the denominator. Premium received during a period, premium left after part of the risk has been handed on to somebody else, and premium earned for cover actually provided during that period are three different quantities, and a percentage struck on one of them reveals nothing about a percentage struck on another. The choice of denominator is not a technicality to file away for later. Three different denominators are the reason two people can read the same published account, do the arithmetic correctly, and finish with numbers that will not sit beside each other.

What are the three ratios, and which premium sits under each?

Start with the one that gets quoted most. The loss ratio is claims over premium, and it answers a single question: what share of the premium went back out again as claims. The expense ratio is the cost of running the arrangement over premium, and it answers a different single question: what share went on getting the business in and looking after it afterwards. The combined ratio is those two added together, and it answers a third question that neither of the first two can answer alone. Did the premium cover both?

Write the base inside the sentence. Not in a footnote under the table, not in a column heading above the number, in the sentence itself. Chandrika Life Insurance Limited, an invented life insurer, reports claims of Rs 6,720 crore against total premium received of Rs 15,600 crore for the stated year. The division runs as follows: Rs 6,720 crore against Rs 15,600 crore gives 43.08 per cent of total premium received. The last four words of that sentence are carrying as much weight as the digits. Dropped, they leave a number that looks portable and is not.

One note on that figure before it travels any further. The recorded description of this insurer carries the claims share to one decimal, as 43.1 per cent. Two decimals is what the rest of the arithmetic needs, so the same quantity is carried below as 43.08 per cent. One quantity has one value, printed at two levels of precision.

Expense Ratio Forms: why does one expense figure give three answers?

Most of the confusion in the subject lives in one detail, usually left to a line in somebody's footnote. The expenses are one figure. The ratio is not. There are at least three denominators in ordinary use, and a reader meets all of them.

Form one is expenses over total premium received. Both halves of it are printed, so a reader can usually build this form from what an insurer publishes. Form two is expenses over net premium, meaning premium after the part cededHanded on to another insurer, along with the share of the risk that goes with it. Ceded premium leaves the premium the first insurer keeps. to a reinsurerAn insurer that takes on part of a risk from the insurer who wrote it, in return for part of the premium. Reinsurance, and how it is priced, is covered separately. has been taken out. Net premium is a smaller denominator, so the same expenses produce a larger ratio. Form three is expenses over earned premium, meaning premium for cover actually provided during the period rather than premium that arrived during it.

A fourth split runs across all three. The money paid to bring the business in, being commissionWhat is paid to the person or business that brought a policy in, most often a share of the premium on that policy. and everything shaped like it, is a different kind of spending from the cost of running the arrangement afterwards. Some presentations keep them apart and some add them together, and the two presentations produce two different expense ratios from the same accounts.

Here is the demonstration, on this insurer's own figures, and neither answer is the wrong one. Chandrika Life Insurance, a life insurer, spent Rs 2,496 crore in the stated year. Put that Rs 2,496 crore over the Rs 15,600 crore of total premium received and it lands on 16.00 per cent of total premium received. Now suppose, purely as a supposition, that one rupee in every ten of premium had been ceded. Ceding one rupee in ten leaves net premium at Rs 14,040 crore, and the same Rs 2,496 crore measured against it lands on 17.78 per cent of net premium. Same insurer, same year, same rupees spent, two correct answers to two different questions. No ceded figure for this insurer exists, so the second base is a supposition and is labelled as one at every appearance.

Loss Ratio vs Combined Ratio: what does the second one answer that the first does not?

A reader meeting these two for the first time usually assumes the second is a fuller version of the first, the way a total is a fuller version of a subtotal. The combined ratio is not a fuller version of the loss ratio, and the difference matters. The loss ratio answers how much of the premium the claims took. The combined ratio answers whether the premium covered the claims and the cost of running the arrangement together, before any return on the money the insurer is holding in the meantime. The two questions are about two different parts of the arrangement, and one part can improve while the other gets worse.

Everything separating two insurers with exactly the same loss ratio sits in the expense half, so the two can end on opposite sides of the hundred line. That is the consequence a reader has to walk away with. Handed a loss ratio alone and asked to judge the period on it, the honest answer is that half the arithmetic is missing and which way it points cannot be told.

The second consequence follows from the same structure. A falling loss ratio alongside a rising combined ratio is not a contradiction and not a misprint. The pattern belongs to an insurer whose claims got better and whose cost of bringing business in got worse by more than the claims improved. Because the total is just the two halves added, the movement can always be attributed, and attributing it is the entire reason for keeping the halves visible instead of quoting the sum on its own.

What does the hundred line mean on each side of it?

Below one hundred, the premium covered the claims and the running costs, and whatever the insurer earned on the money it held in between sits on top of that. Above one hundred, the premium did not cover them, and the difference has to come from somewhere else. In practice the difference comes from the return on the money held. The hundred line carries nothing beyond that reading, and the flat terms are worth stating before anybody attaches a verdict.

A stack above one hundred is not automatically a loss for the business, and a stack below one hundred is not automatically a profit. Neither figure contains the return earned on money held between the premium and the claim, and neither carries whatever the reserveAn amount set aside now for claims expected to be paid later. How it is valued is a specialist calculation and is covered separately. behind claims not yet made had to absorb. Two large parts of the economics sit outside the arithmetic. The two missing parts are why the hundred line is a reading and not a verdict, and why anyone who treats crossing it as a result has answered a question the number never asked.

How far does the answer move when only the base moves?

Now the demonstration, worked through on one set of figures. Take the same claims of Rs 6,720 crore and the same expenses of Rs 2,496 crore, and change nothing else at all. Measured against total premium received of Rs 15,600 crore they read 43.08 per cent and 16.00 per cent, and the two come to 59.08 per cent of total premium received. Swap the denominator for the supposed net premium of Rs 14,040 crore and those very same two amounts read 47.86 per cent and 17.78 per cent, coming to 65.64 per cent of net premium.

Not one thing happened at the insurer in between, and the total shifted by 6.56 percentage points. No claim was made or settled, not a rupee left the building, nobody sold a policy. One number underneath was replaced by another number underneath, and a reader who saw only the two totals would reasonably conclude that something serious had changed. The rest of the subject rests on one standing habit. A percentage is a fraction of something, and a percentage whose something is not printed beside it is not yet a number anybody can use.

Why is a life insurer not read on a combined ratio at all?

The combined ratio is a general insurance measure, and it is struck on earned premium. Earned premium works as a base there. The cover runs for a stated period, and the premium for it is earned across that period. Cover a shop against fire for a year. By the sixth month roughly half the cover has been provided, so roughly half the premium has been earned. Received and earned line up.

Cover on a life does not behave like that. The premium received in a year buys an obligation that may not fall due for decades, so premium received in the year is nowhere near premium earned for the risk carried in that year. Put the two halves of a combined ratio on top of a base that does not correspond to what happened, and the result is a number that looks like a combined ratio and answers nothing. The mismatch is also why an actuaryThe specialist who works out what an insurer's future obligations are worth today, and what has to be set aside now to meet them. is doing a different job at a life insurer than a period ratio can stand in for.

Chandrika Life Insurance is a life insurer, so the arithmetic above works on a life insurer's figures to show the mechanism. The 43.08 per cent and the 16.00 per cent of total premium received are two real divisions of two real rupee figures, and their sum of 59.08 per cent of total premium received is not what a general insurer means by a combined ratio, so it must never be laid alongside one.

What do these three ratios leave unanswered?

Four things sit outside all three of them, and a reader who carries the four will not misuse the ratios. The first is the return on the money held between the premium and the claim. On a long contract that return is the larger half of the economics, and it sits in none of the three divisions. The second is whatever the reserve behind claims not yet made had to absorb during the period. A reserve movement can shift a result further than the claims actually settled in the period did.

The third is timing. A loss that has happened and has not yet reached the insurer as a claim, which the trade calls incurred but not reportedA loss that has already occurred and has not yet been told to the insurer. The loss belongs to the period even though no claim has arrived for it., belongs to the period and is not sitting in the numerator anybody just divided. The fourth is growth. A book that grew quickly during the period has fresh premium in the denominator and claims from older, smaller years in the numerator. The mismatch moves all three ratios at once and has nothing to do with how well anything was priced.

The four are not caveats to bolt onto the end of a sentence. The four are the questions to ask next. Two of them, being the return on money held and the reserve movement, are covered separately and worked in full there. A reader who quotes a combined ratio as a verdict on a period has quietly assumed all four are zero, and none of them is.

Where does anybody actually use these three divisions?

Think of a tiffin service run out of one kitchen. In a month it takes in a certain amount from subscribers. Some of that goes on the food actually delivered, and some goes on the scooter, the rent and the boy who takes the orders. Two different divisions on one month's takings, and the person running it needs both. A month where the vegetables got expensive and a month where the scooter needed repairs look identical if only one total is ever computed.

An analyst reading an insurer's published account does the same thing and is careful about one extra step. The analyst takes the rupee figures the insurer printed, runs both divisions afresh, and writes the base into the label rather than trusting the label handed over. The movement is what carries the information, so the two halves get read across two periods. A claims half that improved while the expense half worsened is a completely different story from both halves moving the same way, and the total on its own hides which happened.

Somebody running the insurer uses them differently again. The expense half is the one they can act on within the period, since underwritingDeciding which risks to take on and at what price. Underwriting is settled before any of this arithmetic and is covered separately. decisions made two years ago are what turn up in this year's claims half. The lag is why a claims ratio in a single year is a report on old decisions rather than current ones. And a person holding shares in a listed insurer reads all three as a check on the story rather than as the story: the ratios describe one period of the insuring side, and the money held against policyholder fundsMoney sitting with an insurer that belongs, in the end, to the people holding its policies. At this insurer it is the largest number on the balance sheet. is a separate question entirely.

The worked instance, in full

Chandrika Life Insurance Limited is a life insurer, and every figure below belongs to one stated year. Total premium received is Rs 15,600 crore, being new business premium of Rs 5,200 crore and renewal premium of Rs 10,400 crore. Claims are Rs 6,720 crore and expenses are Rs 2,496 crore. Each percentage in the table is recomputed from the two rupee figures printed beside it.

Say plainly what the Rs 6,384 crore is not. It is not profit. No addition to the reserve behind future claims appears in this arithmetic, and neither does anything earned on the money held in between. Calling premium received less claims less expenses a profit is the shortest route to a wrong number in this whole subject, and the earnings question is covered separately.

Which of these numbers is somebody else's to set?

Several of the quantities circled around above are not an insurer's to set. An authority sets them, and an authority revises them. The rows below name that authority in place of the number.