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Author: Jonathan Osters

This lesson will introduce the concept of risk.

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This tutorial is going to explain to you the concept of risk from a probability standpoint. So risk is essentially the negative average value, the expected value, you would incur by losing something. So we'll go through some examples and decide if something is risky or not. So diamonds, diamonds are very valuable. But consider diamonds in a safe. This is not very high risk. Even though the diamonds themselves are valuable and losing them would mean a huge loss of money, the probability of losing them is so small that it offsets their large value and makes it not very risky.

Let's look at another example. Firefighters-- their lives obviously are very, very important to them. Economists would say that those are valuable assets. Your life is a valuable asset. However, in his profession, his profession carries with it a fairly high probability of losing his life, so a high probability of losing something that's very valuable. And that high value combined with a high probability of loss is what makes fighting fires defined as being a high risk occupation.

Last example, let's consider a paper clip that you have in your pocket. Almost certainly, you'll use it or lose it by the end of the day. So the probability of loss is very high. However, it's still not considered risky. Because the paper clip isn't a very valuable asset to you. So what are we seeing here? We're seeing that the risk associated with having an item is equal to the value that you would incur by losing it times the probability of losing it. And this is what makes it an expected value.

So let's take a look. Suppose that a house that costs $300,000 has a maybe like a one in 5,000 chance of burning down, a total loss. So what people will do is they will take that negative $60 of risk and buy insurance. They'll pay the insurance company a little bit more than $60 to assume that $300,000 risk. So buying insurance protects against loss by agreeing to pay you back for if you do lose it. So since they're assuming the risk, you have to compensate them for that. So you have to compensate them with the $60 and then some. And you do that through paying premiums.

Now risk is a very unpredictable issue here. So when you're talking about the expected value, you would think about it in terms of that negative $60 mean. But also think about 5,000 homeowners with $300,000 homes. 4,999 homeowners don't lose anything at all. And one of them loses the whole hog. So now what would that happen to be like? The standard deviation of the data set here would be 4,999 zeroes and a negative $300,000. And the standard deviation of that data set is over $4,200.

Compare that with the fact that almost all the values are the same, that standard deviation is awfully high. So it's a very unpredictable quantity with a lot of variability to it. And because of the high variability, it's not beneficial to have only a few policies out there. Suppose that you are an upstart insurance company and you only have like five policies. It would be possible that one of your five policies would be one of the ones that burned down. And you wouldn't have enough money coming in to offset what you would have to pay to that homeowner.

So the more policies an insurance company issues, the more predictable the gains and losses become. The more policies they have out there, the more of a guarantee it is that they'll have a few large payouts to pay. But the more policies they have out there, the more premiums they'll be able to collect. They'll be able to collect relatively small amounts from people who don't need them to pay them. So they're going to more than offset their large payouts by collecting many, many small premiums. So it becomes less risky for them, because it becomes so much more predictable with more policies out there.

So to recap, risk is the product of the value of something times the probability of losing it. So it's an expected value. It's a negative expected value. And to offset that negative expected value and protect against loss, insurance companies assume the risk for multiple people and their homes. So whoever purchases insurance policies agrees to pay premiums to the insurance company. And in exchange, insurance company assumes the risk and will pay you in the case of your loss. People will pay good money for that kind of peace of mind.

So we talked about the idea of risk from a probability standpoint. Good luck. And we'll see you next time.

Terms to Know

The negative expected value of losing something. Something becomes less risky if it is not worth much, or if the probability of loss is very small.

Formulas to Know

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