Understanding Why You Need Insurance

Why Insurance Is the Only Negative EV Bet You Should Take

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This week, I will help you understand how insurance policies really work without you falling asleep. This will enable you to make better informed decisions as to what insurance coverages you should get, and what are simply a waste of money.

TLDR: Insurance is a negative expected value, but asymmetric payoff structure that protects you from catastrophic events. It is the only negative EV bet you should take.

The Principle of Pooling Risks

The key concept underlying all insurance is the principle of pooling risks. In a nutshell, it is the practice of spreading out risk amongst a group of participants.

Suppose you are Aidan, a mathematically gifted resident of San Francisco. You notice that 10 of your friends are fed up with paying $50 for parking everyday. You also notice that parking officers aren’t very vigilant - there is a slim chance that you will actually receive the $100 fine.

You run the maths, and propose to them a brilliant idea. Your friends will all give you $15 a day, and not pay for parking - this is called the premium. In return, if anyone receives a parking fine, then you will pay for it. You’re effectively selling them parking ticket insurance.

Your friends unanimously agree to this proposal. Afterall, they are each saving $35 a day - that is over $10,000 saved in a year. This deal seems too good to be true for them.

How about for you?

Everyday, you collect $150 ($15 x 10) from your friends. You gathered some statistics, and figured that on average you need to pay one parking ticket every day ($100). This puts you at an average profit of $50/day.

Remember that this is simply an average (or the expected value). Yes, this is a positive expected value bet (you obviously won’t agree to this if you are losing money). On some days with no parking fines issued, you make the full $150. On other days where two parking fines are issued, you instead lose $50. 

This is a pretty great deal for everyone - except for the local council that makes some revenue from parking fees.

Homogeneous Risk

If you have ever taken out insurance before, you may have noticed being asked several questions. This might be your age, postcode, or occupation. The purpose of this information is to group you with others with similar attributes as yourself - or being homogeneous.

Individuals in the same homogeneous unit generally have similar risk profiles. If we return back to the example with Aidan, what might happen if all 10 of his friends worked at the same office, and had parked next to each other? 

The likely outcome is that if one person receives a parking ticket, then it is very likely all 10 are fined too. This means that you are now on the line for $1000 in fines ($100 x 10). Your profit of $50, has now turned into a $850 loss.

It is important to first ask your friends where they will be parking, similar to a typical insurance questionnaire

This is why insurance firms go to great lengths to understand the risk profile of their customers. In theory with diversification, this idiosyncratic risk will be reduced as it is better spread out among a larger customer base. This is a similar concept to how diversification in ETFs reduces idiosyncratic risk.

Rising Insurance Premiums and Risk Seeking Behaviour

Suppose Amy, one of Aidan’s friends, decides to abuse the insurance and engage in more risk seeking behaviour. Rather than parking in a lowkey residential area, she parks in the middle of downtown where she will be guaranteed a fine.

Aidan, who has been enjoying the fruits of his scheme, suddenly receives 5 parking tickets from Amy in a week, rather than the usual 1. 

There are only two possibilities here. (1) The probability of receiving a parking ticket has increased, meaning that everyone needs to pay more premiums for Aidan to break even and make a profit, or (2) Amy’s risk profile has changed, and she needs to pay more premiums. 

In this instance, it is quite clear that Amy is engaging in risk seeking behaviour, and a rise in premiums should incentivise her against that. This is effectively why your car insurance increases after you have caused an accident, but is lowered after a year’s time of good behaviour.

Insurance for Insurance Companies

While Aidan has been on average making $50 per day, we have discussed previously how it may be possible for him to lose money if there were multiple fines. This means that he needs to set aside some money for a rainy day, in case he needs to pay these liabilities - this is called reserving.

There are strict requirements by regulatory bodies that stipulate how much money insurance companies and banks need to hold. Since the great financial crisis, these requirements have further tightened to ensure safety for customers.

The downside of this, is that huge amounts of a firm’s capital is being tied up in reserves. This money if used, could help grow the business faster. Wouldn’t it be nice if there was a way to limit the amount of risk exposure, to reduce the amount of capital reserves?

This is where reinsurance comes in - the insurance for insurance companies.

Suppose Aidan has been keeping a large capital reserve in case he needs to pay say 10 parking fines in a week. He really wants to access this money, as he could use it to expand his business. Here, a reinsurance firm will be able to take care of tail risks for him - say anything over $1000 in fines. 

Aidan pays the reinsurance firm $10 a week, which will limit his exposure to just $1000 - the reinsurance firm pays anything in excess of that. Now, he will be receiving a $40/day profit, but with limited downside risk. This is also called hedging your risk.

Do I Need Insurance?

In general, insurance is there to protect yourself against risks that would wipe yourself out. The reason why actuaries advocate for people to take out adequate cover for insurance such as health, life, disability, home, or car - is that any of these adverse events are usually greater than our net worth.

By risk pooling, you are obtaining the benefits of protection, for just a fraction of the cost. Worst case, nothing bad happens to you and all that’s lost is the premiums paid. In times when you truly need the insurance claim, youobtain value far greater than the premiums paid

So when should you take out insurance?

A good rule of thumb is to think about the worst case outcome, and how much it would cost. If that amount will cripple you financially, then take out the insurance. Treat it as an expense, that buys you peace of mind.

This is also why purchasing add-on insurance on kitchen appliances or phones is stupid - you are simply losing money. While it is still a lot of money to replace, it certainly won’t cripple you financially (since you could afford it in the first place). 

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