Is your car worth less than $5,000? Consider canning your comprehensive insurance.

Chances are if you are as frugal as the Armchair Fiduciary at some point you will end up driving a car worth less than $5,000. If you find yourself in this position, it might be time to cancel your comprehensive insurance and save yourself a few hundred dollars annually. In case you don't know comprehensive insurance is one of two types of car insurance. Comprehensive car insurance covers non-accident related damages such as hail, vandalism, and theft. Collision insurance is the other kind of insurance and it covers damage to property and people (i.e. medical bills) as a result of an accident. It is generally required by law in the United States.

Before delving too deeply into why one would cancel comprehensive insurance, let's understand the basic concept of insurance. Insurance companies sell policies to individuals to protect them from adverse events. The insurance company, a little like a casino, doesn't mind losing once in a while because they use statistics and the law of large numbers to predict what their losses will be and then they price their policies such that the house will win over the long term.
Individuals buy insurance because they are risk averse (and in the case of auto insurance because they are often required to by law). Risk aversion means that you don't like big negative surprises. For instance, if there is a 1/100th chance that you will lose $99 and there is a 99% chance that you will make $1 the expected value of the situation to you is $0. A risk neutral individual should not care about the outcome because their expected value is $0. A risk averse person might be willing to pay slightly more than $1.00 for insurance to protect against the $99 potential loss. This guarantees a return of slightly less than $0, but also avoids the off chance of a big loss. This may seem irrational at first but lets consider a slightly different situation where the loss is $99,000,000 and there is a a 1/100,000,000th chance of that outcome but the gain is still $1.00 the rest of the time. In this scenario giving up a few pennies might seem like a more rational decision than risking a huge fortune even if the chances of losing it are remote. When the pain of losing a lot of money is a lot more than the benefit of a higher expected value, that is risk aversion.

While insurance companies can spread their risks over thousands of customers, an individual customer only gets one shot and they therefore have a reason to be risk averse, nobody wants to be the one out of 100,000,000 and lose everything just because they are unlucky. Buying insurance helps you avoid “becoming a statistic,” but the insurance company will charge you something for the privilege.

So by now you may understand why getting rid of comprehensive on a cheaper old car may make sense. You can increase your expected return because the insurance company is going to charge you a little more for comprehensive insurance than is statistically fair so that they can make a profit. If losing your car would not bother you that much and you can afford taking a $5,000 risk then you should cancel your comprehensive insurance and just carry the collision/liability insurance required by law. This should yield you several hundred dollars of savings per year and improve your expected value while exposing you to the remote risk of a $5,000 loss if your car was totaled due to vandalism, hail, etc.