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Why the Fundamental Insurance Equation is Fundamental to Actuaries | CAS Exam 5 - YouTube
Channel: Actuary elle
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Thank you for clicking on a video about insurance.聽
Hi my name is Michelle this is actuary elle,聽聽
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my actuarial youtube channel. You've made it to聽
a very weird niche on the internet, I'm not gonna聽聽
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lie to you. I'm a fellow of the casualty actuarial聽
society, a fellow of the Canadian institute of聽聽
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actuaries. Currently working as a personal lines聽
pricing actuary at a major car and home insurer聽聽
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here in Toronto, Canada. So if I asked you, "What聽
are the two main ways that insurance companies聽聽
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make money?" Would you know? I'm going to give聽
you the answer because we can't have a live聽聽
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dialogue right now in this pre-recorded video. The聽
first way is by selling insurance that's pretty聽聽
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obvious you sell the policies and you try to make聽
money off of it and then the second way is by聽聽
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investing the money that you make from selling the聽
policies. Insurance companies are a financial聽聽
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institution, we collect large amounts of money and聽
then we take that money we invest it and then we聽聽
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make money off of those investments. That part of聽
it is not what we're going to talk about today聽聽
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today we're really going to be focusing on the聽
part of actually selling the insurance policies聽聽
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making money by selling insurance if you want聽
the real proper insurance term for this it would聽聽
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be called underwriting income or underwriting聽
profit we earn income by underwriting policies聽聽
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and then we earn profit off of that underwriting聽
policy if you know everything goes to plan i聽聽
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mentioned it before and i'll mention it again聽
the fun actuarial challenge with insurance is聽聽
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the timing problem first you sell the insurance聽
policy then maybe someone has an insurance claim聽聽
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we don't know how much that's going to be we聽
don't know when the claim is going to happen聽聽
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and then along the way there's expenses that come聽
up and then maybe if it's priced properly we get聽聽
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some profit when i sell you the car insurance聽
policy i don't know if you're gonna have no claim聽聽
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probably or if you're gonna have a $300 claim or聽
if you're gonna have a 10 million dollar claim i聽聽
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don't know how much this is going to cost in the聽
end we sell the policy first and then we find out聽聽
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the expenses later i like to talk about this in a聽
timeline because it makes it more clear at least聽聽
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in my mind of what's sort of happening but if聽
we're gonna get mathy about it let's just shove聽聽
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an equal sign so premium is equal to losses or聽
claims i use the terms interchangeably basically聽聽
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the amount that we're paying when someone gets into聽
a car accident or when someone's house burns down聽聽
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plus expenses plus profit that my friends is the聽
fundamental insurance equation it's a reserving聽聽
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actuaries job to make sure that we set aside聽
enough money to pay off our claim liabilities聽聽
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depending on the type of policy it can take a聽
year three years 10 years before we know how much聽聽
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the total claims are going to be on a given policy聽
and it's the pricing actuaries job it's my job聽聽
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to make sure that we collect enough premium聽
in the first place a pricing actuary does two聽聽
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main things one is price segmentation figuring聽
out that i charge this person thousand dollars聽聽
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and this person five thousand dollars because this聽
person is less risky and this person is more risky聽聽
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not what we're talking about the next thing聽
that the pricing actually does is make sure聽聽
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that we collect enough premium in aggregate we聽
do this with rate indications and rate level聽聽
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indications come from the fundamental insurance聽
equation is that nice aren't we tying things back聽聽
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unless you're a new insurance startup there聽
are already insurance prices like i don't聽聽
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have to touch them people can keep selling聽
insurance policies for as long as they want聽聽
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next year they can still sell a whole bunch of聽
policies we will collect a whole bunch of premium聽聽
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people will have claims we will have to pay聽
out those claims the expenses will happen聽聽
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and then the part of the equation that will聽
either dip up or down is going to be that聽聽
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profit part profit can be very positive or profit聽
can be very negative it really just depends on聽聽
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the balance between premium and losses if we sell聽
100 million dollars worth of premium but have 200聽聽
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million dollars worth of losses that seems like a聽
whole lot of negative profit what we do is we use聽聽
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the fundamental insurance equation to look at the聽
balance to look at how profitable we expect to be聽聽
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i'm not going to teach you all about indications聽
today but just know that it's a way for us to know聽聽
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do we need to raise prices or do we need to lower聽
prices to keep this equation in balance there are聽聽
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a couple other key metrics from the fundamental聽
insurance equation that i do want to teach you聽聽
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about but what we have to do is we have to take聽
this equation and divide it all by premium so聽聽
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if we look at the left hand side premium divided聽
by premium is 100% of premium we're saying this is聽聽
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the whole pie this is 100% of all the premium that聽
we got and then if we look at the right hand side聽聽
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of the equation we're saying where is this premium聽
going what percent of the premium is being paid聽聽
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towards losses what percent of the premium is聽
paying paid towards expenses what percent of聽聽
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the premium is being kept as profit if i sell a聽
hundred dollars in premium we have sixty dollars聽聽
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in losses thirty dollars in expenses and ten聽
dollars in profit that sixty percent is called聽聽
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a loss ratio the loss ratio tells us how much聽
of the premium is going towards paying claims聽聽
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the expense ratio in this case would be thirty聽
percent thirty percent of premium is going聽聽
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towards expenses and then ten percent is going聽
into profit that would be a really nice really聽聽
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nice idea like situation that does sometimes聽
happen a combined ratio is the combination聽聽
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of the loss ratio and the expense ratio so 100%聽
of premium goes to the combined ratio which is聽聽
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losses and expenses plus the profit ratio now if聽
the combined ratio is below 100 then that means聽聽
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you've made profit if the combined ratio is above聽
100 that means that you have not made any profit聽聽
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as soon as your combined ratio goes above 100%聽
then your profits become negative because there's聽聽
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no more premium to allocate towards profit lower聽
combined ratio means more profit means more better聽聽
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as an insurance company we don't aim for excessive聽
profits that's not the goal the goal is not to聽聽
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gouge people out of as much money as possible but聽
we definitely want a combined ratio below 100. if聽聽
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you want to hear about how reserving actuaries set聽
aside enough money to pay off the insurance claims聽聽
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do click that video right here thank you聽
for calling i love you guys thumbs up bye
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