I thought it could be fun to start making actuarial videos about advanced
actuarial topics I've seen people posting videos on YouTube about the
preliminary exams but I haven't come across anybody making free study resources for
advanced actuarial exams. So I thought I'd take a break from talking about my
life as an actuary and actually try to teach you some things, if you want to
learn it. The fun thing about advanced actuarial exams is that the math
actually isn't very hard. My parents always tell people, "Oh I couldn't even
begin to understand the math that Michelle does every day!" Yeah, yeah they
could. The preliminary exams are full of advanced mathematical topics statistics,
infinite series, Monte Carlo simulation. Advanced exams at least the
ones that I wrote mostly stick to addition multiplication and in the case
of what I'm gonna show you today the tiniest little bit of geometry. Today I
want to show you how actuaries read parallelograms eventually this goes on
to do things like on leveling premium aggregating exposures but today we're
just gonna go over the basics of when I see an actuarial parallelogram what am I
looking at first I want you guys to remember the main reason why we need
actuaries at insurance company it's the timing problem first insurance companies
collect your money then they pay out your claim if you happen to have one
since insurance companies want to charge a fair price for a person's expected
losses and insurance companies want to make sure that they hold enough money to
pay out those losses when they do come in we need some fancy math and some
fancy parallelograms. Insert clip from PowerPoint let's see
if the PowerPoint clip works let's say that you sell a one-year insurance
policy on January 1st 2017 that means that the insurance policy is going to be
inforce, effective, on the book until December 31st 2017 and
then on January 1st 2018 the policy would either get renewed or expire for
what I'm doing today we're not thinking about renewals we're just thinking about
the one year time period right now the image that you should be seeing if my
animations are working properly looks a lot like a flat line to make it
two-dimensional what we do is we double up the timeline
the bottom line represents the moment that the policy sells top line
represents the moment when the policy expires and we draw a diagonal line from
start to finish to represent the policy now if I add a few more policies are you
starting to see some parallelograms great because of the ever famous
insurance timing problem actuaries and insurance companies in
general have many ways of looking at years. I know, I said it at the beginning,
the math not super hard the concepts tough to get your head around. Calendar
year is probably your most basic way of looking at years I'm gonna keep talking
in terms of years but this can also be done for a month a quarter a decade it
doesn't have to be a year on our parallelogram timeline if everything is
drawn to scale each calendar year is represented by a square if we want to
know the number of policies that were written or sold in that year just look
at the lower timeline of the square in this case for if you want to know the
number of policies that expired in that year you look at the upper timeline of
the square in this case two things get interesting when you look at policy D or
any line that crosses outside of its calendar year square for that matter
it starts in one calendar year and ends in another calendar year when you throw
insurance claims in the mix this gets very interesting let's say their house
burns down in 2018 it might take three years before the
insurer pays the claim so you collect the premium in 2017 the claim happens in
2018 and the claim is paid in 2021 if we only came up with insurance prices by
looking at calendar year you would look at the year the policy was sold and say
we collected five hundred dollars from this person they cost us nothing maybe
the policy is overpriced jump forward to the year when you actually make the
claim payment and there's no policy to associate it with anymore
I'm not gonna get into the specifics of aggregation and on leveling in this
video because it would make the video even longer than it already is
but if you're interested there's always that like button and the comment section
let's say that instead of looking at calendar year we want to look at a
policy year instead of a square this time we want to follow the start date of
the first possible policy sold in the year through
the expiration of the last possible policy sold I say possible policy
because the insurer doesn't have to have sold a policy on January 1st for you to
start your policy or on January 1st we just wanted 12 month period when we're
talking years if we're talking months you just want a one month period policy
years show up as a parallelogram in our timeline the interesting thing about a
policy year is that it actually spans two calendar years this particular
policy year starts on January 1st 2017 but ends all the way on December 31st
2018 one of the advantages of the first type of year that I showed the calendar
year is that at the end of the year you know your results with the policy year
it takes two years before you've got all your results in let's add back some more
policies if we want to know the number of policies that were written or souls
in that policy year just look at the lower timeline of the parallelogram in
this case four if we want to know the number of policies that expired in that
policy year you look at the upper timeline and assuming that no one
cancelled their policy before it expired it's gonna be the same number as the
ones sold in that year the last quick thing that I'm gonna show you guys today
is how to calculate the number of inforce policies inforce just means a
snapshot view of the number of policies that are effective on a given date using
our timeline if we want to know how many policies are inforce on November 1st we
just draw a straight line through November 1st and count the number of
policies that it intersects with so for the policies that are already expired
we're not responsible for any new accidents they have on November 1st and
for the policies that haven't started yet we're not responsible either it's
just the ones that touch the vertical line well I think that is enough actuarial
content for one day be sure to click that subscribe button if you want
to learn more about real actuarial concepts or just join me in my actuarial
youtuber journey thank you for calling byeeeeeeeeee