Hey aspiring actuaries! If we haven't met before, my name is Michelle, this is
actuary elle, the channel where I teach you: things
actuaries know, show you how actuaries live and help guide you along your
actuarial journey. Today I'm gonna try to teach you something that
actuaries know which is how to read actuarial triangles. We're gonna take this
all the way from data aggregation to a real, actuarial reserving technique known as
the loss development method or the chain ladder method and I'm here to tell you
that you are about to learn that being an actuary is not a math heavy job. In
the actuarial exam process, the preliminary exams are full of scary math, there is
calculus, there are Greek letters all over the place and then once you get to
the advanced exams which more accurately represents what I do every day at the
office, the math behind reading and using actuarial triangles is real simple. Little
multiplication division and a little bit of averages and you're golden. The
concept behind actuarial triangles will make your brain hurt the first twenty
times that you care about it so if you don't understand what I'm talking about
please feel free to ask questions below, re-watch the video a couple times
because this is something that you're going to learn about in your exams
especially if you are a Property and Casualty actuary like I am. I've
mentioned in the past that I am a pricing actuary, but I do have to review
reserves in my pricing exercises. If you want to learn about all of this on your
own time, it is available for free on the casualty actual society's website, so
feel free to go check it out otherwise let's go to the PowerPoint. If
you're a regular viewer of my channel you know the lesson that I try to pass
on to you every time is that the insurance time line is weird. First a
person buys an insurance policy then twelve months later the policy expires
the question is: will they have a claim? maybe at some point in that twelve month
period. Along the way from the insurance company's perspective some expenses are
incurred and at the end of the timeline well maybe if I'm doing my job right we
even manage to find some profit. The first thing to
notice is that the policy is sold before the costs are known. We don't know if the
person's gonna have a claim, we don't know when the claim is gonna happen and
we don't know how much that claim is gonna cost us but what we do have is we
have reserves to make sure that we keep enough money to pay out all the claims
that is the actuary's job and that is what we're gonna talk about today how we
set reserves or at least one reserving method specifically the chain ladder or
lost development method. Let's learn a little bit of vocabulary I know this is
starting to feel a little bit like school but I promise you it's gonna be
so helpful so write this down remember this because these are important
insurance terms. A "case reserve" is money set aside for a specific claim. That
means, you have a claim, you call the insurance company and the adjuster will
say I think this claim is gonna cost us $5,000 so they set aside $5,000 for the
expected future cost of that one specific known claim. That doesn't mean
that they pay the person $5,000 it's just hypothetical money that is set
aside because we know that the claim already happened
"Paid loss" is money that we actually paid to a specific claim so if you call and
you say I had this accident a car accident and we pay some money out to
the garage to fix your car that would be some paid loss. When you add case
reserves and paid loss together then you get "incurred loss". Incurred loss is
the total amount of money that the insurance company expects to pay for
specific claims so let's say you have a car that got into an accident they call
the insurance company and the adjuster decides to set aside two thousand
dollars in case reserves. Well, the case reserve is two thousand dollars, paid loss
is nothing and our incurred loss right now is two thousand dollars. Let's say we
find out a little bit more information, we start to pay out $700 on this claim.
well now the case reserve is reduced to thirteen hundred dollars, our paid loss
is seven hundred dollars and our incurred is still two thousand dollars
because thirteen hundred plus seven hundred = two
thousand and we know that case reserve has played loss equals incurred loss
finally we learn a little bit more about the claim we make another final payout
of thirteen hundred dollars and now our case reserve is zero, our paid loss is two
thousand dollars and our incurred loss is still sitting at a whopping two
thousand dollars. But how often do you think our case reserves are exact on the
first try? I mean that would be very impressive and if adjusters could do
that well they probably need a raise because that's very impressive
forecasting on their part. In reality incurred loss on a claim will go up and
down as reserves change when we get new information about that claim maybe we
didn't know that someone got injured before and now they did maybe once the
garage mechanic gets under the hood of the car they see that there's way more
damage than they actually thought or vice versa
maybe they thought it was way worse damage than it actually was and it
wasn't really that hard to repair we don't know which claim costs are gonna
go up and which claim costs are gonna go down if we did we would change the case
reserves immediately what we have to do is we look at all the claims in
aggregate. First we group all cars that had claims in the same year we put all
their incurred loss together then add a buffer layer for two reasons, for cars
that have case reserves that are too low and for cars that are had accidents but
haven't told their insurance company yet this buffer layer is called IBNR this is
incurred but not reported reserves this is a very important insurance term to
understand incurred but not reported and it's made up of IBNER: incurred but not
enough reported, that's when we have money set aside for a claim but it's not
enough because we didn't know XYZ about the claim and so it when we thought
originally it was $5,000 but it ends up being $50,000 we didn't put enough money
aside that would fall under IBNER, and we also have pure IBNR, cars that have
had accidents but haven't told us about it yet so we haven't set any money aside
for that claim even though we are responsible for paying out the claim so
case reserve plus paid loss adds up to incurred loss
incurred loss plus IBNR adds up to ultimate loss. Now let's talk about this
asterisk that I have next to the word year. how do you group claims by year
here we have three examples of three cars all three bought a policy in 2020
first and the third car had an accident in 2020 the second car had its accident
in 2021 and they all have different timings of when they tell the insurance
company and when we make payments on that claim we can group claims by policy
year, meaning allocate all the money that we pay out to the year that the policy
was purchased, we can group claims by accident here which means allocating all the
money to the year the accident happened in this case the second vehicle because
it had the accident in 2021 instead of 2020 we would allocate all
the money that we pay out to 2021 maybe we group it by reported year the
year that the accident is reported to the insurance company maybe we group it
by calendar year the year the payment is made on the claim the reason why I'm
showing you all of these years is to tell you that the way that we group our
data very much will impact the way that our results turn out you saw all the
little green arrows moving from left to right based off of how I decide to
aggregate my data and if you're doing an actuarial analysis one of the
fundamental assumptions one of the base things that you need to understand while
doing that analysis is what is the aggregation method used when I'm looking
at this claim information? Calendar year would be most commonly used for things
like financial statements whereas accident year would be most
likely the year aggregation that you'd be using as an actuary although there
are situations where you would look at it by a different basis but the majority
of the time you're going to be aggregating by the year the accident
happened. Let's get a new fake accident accident happens in 2020. In 2021 they
call let us know about the claim we set aside two thousand dollars, later in the
year we pay out the two thousand dollars the claim is closed. The claim never
reopens. What accident year does this claim belong to? Since the accident
happened in 2020, the accident year is 2020. Shat is the incurred loss at the
end of 2020? I'm gonna give you a second to think about it
if you said $0 you are correct because at the end of 2020 we have no case
reserve set aside and we have no paid losses on this claim because we don't
even know that this happened so at the end of 2020 the incurred loss is zero
dollars. what is the incurred loss at the end of
2021? well in this case the incurred loss is
two thousand dollars because we have paid out the claim for two thousand
dollars, we have no more case reserve set aside for it, so our case reserve of zero
plus our paid loss of two thousand equals two thousand in incurred. What I
want you to see here is that the information that we know about the claim
develops at different moments in time even though the accident had already
happened at the end of 2020 we didn't know about it so we didn't set aside any
money for it but at the end of twenty twenty one we did and this is what we
mean when we say a claim develops we find out more information about this
claim and so we set aside a different amount of money with different amount of
information on the claim it develops finally moving on to the information
about triangles every row in an actuarial triangle represents one year
of accidents that means information about accidents that happen in that
specific year the highlighted row would be accidents that happened in 2015
every column in an actuarial triangle would represent the information that we
know after a certain amount of time since the beginning of the accident
period the highlighted column that I have right now would be 12 months after
the beginning of the accident period so in this case it would be December 31st
2015 December 31st 2016 2017 2018 2019
because the year starts January 1st and ends December 31st the pattern of the
triangle is going to be incurred loss to gross INBR to ultimate loss. If we
look at the first row again now we see that as more months pass we get more
information about the incurred loss so after 12 months from the beginning of
2015 the incurred loss for accidents that happened in 2015 was thirty-four
thousand eight hundred and seventy one dollars after 24 months so that would be
December 31st 2016 now incurred loss has gone up to 38,000
another 12 months it's gone up to 40,000 41,000 and then back down to 40,000 it
is possible for incurred loss to go down there are a few reasons that this would
happen the first being over reserving if you
set aside too much case reserve and then it turns out that we don't have to pay
out that much maybe it'll go down another reason that it could go down
is something called salvage and subrogation. This would be in a situation
where we pay out a claim but then we're able to recoup some of the money by
selling off the parts or by suing a third party if we let this triangle go
on forever eventually we would get to an ultimate amount in this case for year
2015 we think the ultimate claim amount for accidents that happen in 2015 is
going to be 41 thousand 77 dollars once we fill in the incurred loss for the
rest of the accident years are you starting to see the triangle the reason
why we call this an actuarial triangle is because we know a different amount of
information for each of the different years this triangle would be dated
December 31st 2019 at that moment in time we have 12 months of information
about 2019, 24 months of information about 2018, 36 months about 2017 etc etc
forming a triangle we have more information about years that are further
in the past than we do about the most recent year which means that we're gonna
have more IBNR on the more recent year than we would on years further in the
past accidents that happened long ago are probably close to ultimate we've
probably finished paying them off nothing really is gonna change but
something that happened two months ago we're gonna see a lot of development
each diagonal in the triangle represents the same moment in time in this case the
purple squares are December 31st 2019 on December 31st 2020 we would be able to
add another diagonal to this triangle because we would have 12 months of
additional information for each of the accident years so how do we set reserves
first what we do is we ask the question how do we get
the 12-month information to the 24-month information for 2015 it was times one
point one times one point one times one point two five times one point one and
then we say okay we don't have the answer for 2019 but what do we think is
gonna happen the one point two five that we see in 2017 kinda seems like an
outlier because all the other months have a one point one multiplier so in
this case I'd probably choose a one point one and say that at 24 months it's
probably somewhere around 47,000 then we play the same game to get from 24 months
to 36 months we look at 2015 to 2017 and we say what factor did we use to get
from 24 months to 36 months and when I say did we use I mean what really
happened because these are real I mean fake because this is a fake
example but real hypothetical incurred loss triangles 1.05 1.05 1.07 so to
project 2018 and 2019 forward I'd pick something like 1.055 which brings us up
to 47,000 for 2018 and 49,000 for 2019 these factors that we're selecting are
called loss development factors or LDFs now in these fake examples it seems
pretty straightforward but in reality there's a lot of actuarial knowledge
that goes into how to select these loss development factors because in reality
claims don't develop like 1.1 1.1 1.1 1.1 every single time you might see
trends like in this case where it's going from 1.05 up to 1.07 and you
might say well are there changes in the way that we're handling our claims now
if we're closing claims faster than we would expect our earlier LDFs to be
higher and are later LDFs to be lower than historical LDFs so it's really
important to have a good understanding of what's changing in the insurance
business what's changing in your company to understand how to interpret these LDFs
And that's reserving all you're trying to do is fill in the bottom half
of the triangle. badda-bing badda-boom you
done set some money aside easy-peasy! No Greek letters involved not a
whiff of calculus I hope you found this helpful if you want to learn more real
actuarial techniques let me know in the comments below and I'll be sure to put
together some sort of a PowerPoint. Do thumbs it up and subscribe because this
did take me a long time to put together thank you for calling bye