Does it make sense to insure something when you could financially bear its loss?

Question

I'm wondering whether it makes sense to insure something if its loss would not be life-changing. I want to buy a boat to live on while I attend university. It would cost about 10,000 dollars and my financial situation is good enough so that I would not live on the street if it suddenly sank.

My father suggests I insure the boat, but I'm not sure this makes sense. Insurance companies on average make money by selling insurance, which means you lose money on average by dealing with them. Hence, insurance seems to only makes sense if you couldn't bear the loss.

Consider for example, Aganju's answer to a health insurance question:

Insurance - in its basic idea - is supposed to protect you from exceptional and potentially life-changing financial situations; not from day-to-day cost. That means that covering the first 1000 $ is pretty much useless; for any serious sickness the insurance would be without merit. [From Aganju's answer to this question].

I agree with this. Am I missing anything here? Why do people get boat insurance at all if they could bear the loss of their boat?

Answer 1

Some brief research suggest that boat insurance is ~1.5% of boat cost/year. So a $10,000 boat might be about $150. Other sites say average boat insurance is $300-500/year. So a bit of a range to work with.

Though the risk is relatively low, people would rather a small planned expense than risk a large unplanned expense.

In addition, most policies cover liability, so if someone were to get hurt on your boat, or you caused damage with your boat, insurance adds protection.

Answer 2

Insurance is a financial product to control risk. The fact that a loss would not be catastrophic simply makes the decision to carry insurance less critical. It is perfectly reasonable to be "self-insured" in this case.

This is assuming we are discussing replacement of your property vs liability (which you have made clear).

Like many other products one buys, a fine reason to purchase insurance is simply because one wants to. Just because you can absorb the loss, does not mean that you want to take on the full risk.

I would be careful of your analysis here:

Insurance companies on average make money by selling insurance, which means you lose money on average by dealing with them

Insurance companies make money based on the cumulative probability that they will have to pay on multiple policies. To make money, they analyze the risk that in a given period they will only pay on a portion of their hundreds of thousands or millions of policies.

This is a different analysis than the probability that you will have a loss on your specific asset.

Your risk of a loss is not equivalent to their risk of loss here. The argument that they only 'win' if you individually 'lose' is not a good one.

Answer 3

Even if you can afford the loss of the boat because you have other housing options available, can you also afford to lose all your possessions if the boat sinks or is stolen?

All of your clothing, electronics, etc can add up to thousands of dollars easily. A significant fraction of that amount are things you'd need to replace quickly, even if you're confident of having somewhere else to live for as long as it takes you get a new boat/apartment/etc.

Answer 4

They get insurance when they believe that the cost of replacing the boat does impact their lives.

We are also assuming that liability insurance is something you will purchase, since if your boat breaks loose and smashes into a $1,000,000 boat that is cash you probably don't have. It will also cover you if somebody falls on the boat.

In your comment you mention that the cost will be $2,000 for 4 years. The issue is are you willing to save $2,000 by foregoing insurance but risk the $10,000 boat.

Answer 5

Insurance companies on average make money by selling insurance, which means you lose money on average by dealing with them.

The insurance is not gambling where the house always wins. This expression is literal in gambling, because that's how they set the odds. Insurance isn't necessarily similar.

Example. Suppose there's 10% chance that $10,000 the boat sinks due to a defect. So, on average your loss is going to be $1,000. The variability of your loss measured as its standard deviation is $2,846. The variability of loss is a measure of risk.

Now, let's look at two $10,000 boats. There's 1% chance that they both sink, and 18% chance that only one of them sinks. So, the expected loss is, unsurprisingly, $2,000. However, the variability of expected loss is $3,842, not quite twice the risk (variability) of a single boat accident.

If you imagine that instead of a couple of boats the insurance has 100 boats, the variability of their loss (hence their risk) will increase only by a factor of 10, not 100 compared to a single boat. This means that their risk in relative terms is smaller than yours, the individual insurer's.

What I tried to show was that it is possible to both of you and the insurer to benefit from the arrangement. It doesn't mean that it happens in every case, but generally it does. That's why in actuarial science there's a term fair price.

UPDATE I was trying to avoid talking about utility here, because it's an involved subject, but you're dragging the discussion in this direction :) You're right that expected value cannot explain the insurance. The reason is that there's another concept that's necessary in addition to the objective measures such as expected value and risk: I mean the utility function or risk-aversion. So, in short you need to maximize expected utility, not the expected payout.

Here's a toy example with the same boat. Assume that insurance is $150, and they pay the entire boat's value in case of accident, i.e. $10,000.

You're given two choices effectively. At the end of the year, you have either of the following:

1. 10000-150 = $9,850, certainly. If you lose a boat, then insurance pays you $10,000, if you keep the boat then it's still worth $10,000, but you lose your insurance premium in any case
2. $10,000 most likely, and $0 with some low probability.

You're right that the expected value in the second option can be higher in the second option. Let's say the probability of the loss is 10%, in this case the expected value would $9,900, which is higher than certain value of option 1.

Why then some people choose option 2? The reason is that we don't maximize the expected payout, but we maximize the utility, according to modern microeconomics and game theory.

Utility is some kind of an function that reflects your preference given the uncertain choices. Every person has their own preferences, and utility function.

Let's say that yours is exponential with a=10000. In this case we can calculate the expected utility as follows:

1. 6265.60773063
2. 5689.08502946

The math works out in such a way that it accounts for your risk tolerance. Depending on how much you love or hate risk, your expected utilities for these option will come out differently. For this given toy example it turned out that the expected utility is higher with insurance, so this person should get it. However, for different values of a parameter "a" in the function, it may not make a sense to insure.

Some people are risk averse, some are risk lovers in certain situations. That's the reason why given the same options we make different choices. You may say that you don't value certainty enough to buy this insurance. The bottom line is that nobody can tell you that you're wrong to not buy an insurance. If your risk tolerance is high it may not make a sense for you.

Having said this all, I must note that sometimes the society doesn't accept your preferences and utility function. Yes, you tell me today that you accept the risk, but tomorrow when the boat sinks you may come to me and say that you can't pay the student loan because of the hardship. That's the reason why it's mandatory to get liability insurance on cars, for instance.

Answer 6

All of the insurance policies I'm familiar with have different costs for liability vs replacement coverage of the specific item. Typically liability insurance is very cheap by comparison, and is therefore a "must-strongly-consider". Insuring your specific item is up to you, and depends on how badly you'll feel if you lose it to theft or destruction. Even if you choose not to insure your boat for replacement value, don't forgo liability though, for if you hit something expensive, or if someone is severely injured or killed as a result of an action related to your boat, your outlay could be extremely high.

Answer 7

Keep in mind that if you choose a loan for the boat, you may be required by the lender to maintain a minimum coverage of insurance during the term of the loan.

Further, some states require you to carry some level of liability insurance on your boat, and some entities require liability insurance when using certain bodies of water within their jurisdiction.

If neither apply to you, and if you could suffer the loss of the boat itself, could you similarly suffer the damages caused by your boat if you lose control? Let's say you hit a much larger, more expensive boat, or your boat breaks free from it's dock and damages the dock well beyond the cost of your boat.

Are you also able to withstand these costs?

If not, you may want to invest in minimum liability insurance.

If, at this point, you are still convinced that you are not at financial risk due to the boat, I'd strongly suggest a plan of self insurance. Take the money you would normally spend on insurance, and invest it in low risk investments that can be liquidated in a matter of months.

If you do have a problem with the boat, your risk is mitigated by the self-insurance. If you don't, then you have not only saved that money, but increased its value.

Answer 8

An answer from a psychological viewpoint: money does not have a linear value to people. If you have $10.000, losing one dollar doesn't really matter. Losing all $10.000 is more than 10.000 times as bad.

As a simple example of a non-linear function, let's use the "square root" function. Let's say that having $100 is ten times as good as having $1, and having $10000 is ten times as good as having $100.

Now, this means that an insurance may have a negative expectation when expressed in dollars (since the insurance company is making a profit), but the expected value still can be positive.

Let's assume the premium is $150 and there's a 1% chance it will pay $10.000. Clearly in dollars the expected loss is $50. But in the value to you (using that same square root function), the premium is just -0.75 (sqrt(9850)-sqrt(10000) and the expected payout is 1 (sqrt(10000)*1%).

Intuitive: you won't notice the premium, if you're rich enough that you don't need the insurance. But once you do need the insurance, you could now be so poor that you appreciate the payout.

As a side effect - this also shows that you want an insurance with a fairly high deductible. If a $10.000 loss is a risk you can bear, then you don't need insurance for losses in the order of $100. And that's even ignoring the fact that such small payouts have relatively high administrative costs for insurance companies, which is why the premium discount for high deductibles can be disproportionally high.

Answer 9

Another reason to buy insurance, though not applicable in this case, is that the insurance company is a big buyer of services and will be able to buy any services covered under the policy much more cheaply than you will. So they can charge you less than your expected payouts if you were uninsured and still make a profit. This particularly applies to things like medical and veterinary insurance.

Answer 10

There are cases where it makes sense to insure something, even if you can bear its loss. Insurance is a tool to control risk. One reason you might want to control risk is indeed if you cannot afford to bear it's loss. However, there are other reasons you might wish to insure something when you look at your life in totality.

Let's say you have $100 to work with, and you have an item A that costs $30. Perhaps you really need A in your life, but its clear here that you can afford to replace it, so maybe you don't insure it. Then you get item B, which also costs $30, and item C which costs $30. We can see that you can cover all three of these (total value $90), so one might argue that you don't need to insure it.

Now let's add item D onto the plate, also at a cost of $30. Now you're in an interesting position, with 4 items you depend on, A B C and D, which have a sum total replacement cost of $120. Now if all of these break or are stolen, you no longer have the funds to replace them. Of course, what are the odds that all of them break at the same time? You may be able to do the math to determine the probability of going broke, and use that to determine whether you want to insure the item or not.

Now consider that you will have to make a similar mathematical analysis for every additional purchase you make. You will also have items which you can "bear to lose" but you really don't want to. These can add a large amount of effort to every decision you make. It may be worth getting insurance in such a case. One could think of the purchase in two parts. There is the part that accounts for the statistical expectation of loss, and the other is the insurance company's profits. The profits could be thought of as paying the insurance company for a service which makes it easier for you to think through complicated decisions by removing risk.

Answer 11

Look at it from the other side

So far all insurances start from the perspective of the insurance taker. However, I find it much more intuitive to look from the perspective of the insurance giver:

For each dollar that is paid out, two dollars go in

Note that the exact amount may differ, but management fees of a few dozen percent are quite realistic. Note that it is not as unreasonable as it may sound at first, some costs:

1. Payout of risk
2. Fund and risk management
3. Registration/Administration
4. Risk assesment

And of course most insurance companies will want to keep some profit as well.

Conclusion

If you are completely risk averse, typically it is only financial beneficial to get insurance if you have a significantly higher risk profile. Examples of this (not an expert on boats):

• You park the boat in a bad neighborhood
• You often sail between big rocks
• You use the boat much more often than average

Note that piece of mind may also be worth getting the insurance for, for instance if you frequently put others in the position to crash your boat, and don't want to create an awkward financial discussion when they do.

Answer 12

There are (at least) two problems with the argument suggested in the OP.

First, the ability to cover the cost, doesn't mean willingness, ease, or no major side effects of doing so. Second is the mitigation of "upside risk". It might be true that the most usual loss is small and manageable, but 10% of incidents could be considerably larger and 1% may be very much larger - without limit.

Your own attitude to risk and loss will determine how much these are seen as unlikely+ignore, or worst case situation+avoid.

Answer 13

This is a generic answer to this question, since I believe the UK requirements mean you have no choice in this particular situation.

Ask yourself this question: If the boat sank, would you buy another boat? If the answer to that is "yes" then insurance is often worthwhile.