The Expected Value of Insurance - Why You Should Still Buy It Even When the Math Says No

5 min read

Only Part of Your Premium Ever Becomes a Claim

A life insurance premium is made up of three components.

Net premium. The portion that actually funds claim payouts. It is calculated from statistical data such as mortality rates and hospitalization rates.

Loading premium. The insurer's operating expenses: salaries for sales agents, advertising, office rent, and IT systems. At insurers that sell mainly face-to-face, agent compensation is said to account for a large share of this loading.

Profit. The insurer's margin.

How these three split varies by company and by product, and the breakdown is often not shown in the documents handed to policyholders. The order of operations, however, never changes. A premium is the money needed to fund claims plus the costs and profit stacked on top, so across all policyholders the total paid in is necessarily larger than the total paid out. It shares that structure with the expected value of the lottery: something is always taken off the top.

Mathematically, insurance is a negative-expected-value bet. So why does it exist, and why do so many people buy it?

Insurance Is Not About Expected Value - It Is About Risk Transfer

Evaluating insurance by expected value alone is actually a mistake. The real purpose of insurance is to convert a "low-probability but catastrophic loss" into a "certain but small expense (the premium)."

Try it with an assumed number. Suppose a 30-year-old has a 5% chance of dying before age 60. If he buys a term life policy with a 30-million-yen death benefit at 3,000 yen per month, his total outlay over 30 years is 1.08 million yen, while the expected payout is 30 million yen times 5%, or 1.5 million yen. Under that assumption the policy looks like a "win." But the calculation ignores the costs and profit stacked on top, and nudging the assumed probability down slightly flips the conclusion. The real premium is set at the level the insurer's own estimate implies, plus expenses and margin.

The point, however, is not expected value. Compare "a 5% chance that your family loses 30 million yen" with "a guaranteed outlay of 3,000 yen per month." Which scenario is more devastating to a household budget? The answer is obvious.

Insurance is a product that buys peace of mind, not profit. As we discussed in the real cost of extended warranties, the scale of risk is fundamentally different. A broken appliance will not ruin your life, but losing the primary breadwinner can bankrupt a family.

Public Benefits: The Insurance You Already Have

Before shopping for a private policy, there is something worth checking first. If you are a company employee or a public servant in Japan, the social insurance contributions deducted from your pay have already bought you a substantial amount of coverage.

If the household's earner dies, the survivor's pension pays out, with the amount depending on which system you belonged to and how many children you have. If illness or injury keeps you from working, health insurance pays a sickness and injury allowance. If a hospital stay or surgery pushes medical bills high, the high-cost medical care system caps your out-of-pocket spending at a ceiling set by income.

What a private policy should cover is only the gap those benefits leave. Yet insurance conversations often start from "how much you would need in an emergency" before anything is subtracted for public benefits. Change the starting point and the coverage you appear to need changes dramatically.

Look up your own public benefits first, then calculate what is missing. Keeping that order is the first step toward not overpaying for coverage.

See all referral & invitation codes

Insurance You Need vs. Insurance You Can Skip

The guiding principle is simple: insure only against "low-probability, high-damage" risks. Paying premiums to cover losses you can absorb out of pocket is a losing proposition in expected-value terms.

Insurance worth buying. Auto liability insurance: a single accident can generate tens of millions of yen in damages. Fire insurance: a total loss of your home means a multi-million-yen hit. Life insurance (if you have dependents): losing the household's income stream is an existential threat. These are losses you cannot recover from on your own.

Insurance you can skip. Smartphone insurance (a few hundred yen per month): repair costs top out at tens of thousands of yen, well within savings range. Pet insurance: treatment costs have a visible ceiling. Cancer insurance (if you have substantial savings): Japan's high-cost medical care system caps out-of-pocket expenses at roughly 80,000-90,000 yen per month.

The decision rule is straightforward. "If this loss occurred, could I cover it from savings?" If yes, skip the insurance. If no, buy it. Just like the math behind discounts, the key is to decide with numbers, not emotions.

When in Doubt, Start With "Could I Pay It From Savings?"

When you run into a policy you cannot decide on, having a fixed order of questions keeps the answer stable. The figure below lays out the criteria from this article, top to bottom.

The order for deciding whether to buy a policy
1
Could you absorb the loss yourself?Look at the worst-case outlay and ask whether savings would cover it
No → go to 2Yes → handle it with savings, not insurance
2
Do public benefits already cover it?Subtract what the survivor's pension, sickness allowance, and high-cost medical care system fill in
Not fully → go to 3Yes → no need to stack a private policy on top
3
Is the event genuinely unlikely?For things that happen often, the costs and profit added to the premium work against you
Unlikely → consider buyingHappens often → fix the budget before buying cover
Only a loss that clears all three is a good fit for insurance

The three questions restate the criteria discussed above; no new standard has been introduced. Where you draw each line depends on your own finances.

The advantage of this order is that it is hard to sway with a polished sales pitch or a moment of anxiety. Judge by "it would be awful if this happened" and almost every product looks necessary. Judge by "I could not pay if this happened" and the list gets short.

The answer to question 1 also changes over time. As savings grow, the range you can absorb yourself widens, and coverage you need today may be unnecessary later. Rather than signing and forgetting, it is worth walking through the same order again every few years.

Four Ways to Lower Your Premiums

Once you have identified the insurance you need, the next step is minimizing what you pay for it.

  1. Choose an online insurer. Policies sold face-to-face bundle the agent's commission into the premium. Online insurers (such as Lifenet and SBI Life) cut that cost, offering the same coverage for 20-40% less.
  2. Right-size your coverage. Instead of defaulting to a 50-million-yen death benefit, calculate the actual need: your family's living expenses, the remaining mortgage balance, and your children's education costs. Set the benefit to the minimum required. Excess coverage is wasted premium.
  3. Review regularly. Once your children are financially independent, reduce the death benefit. After paying off the mortgage, drop the corresponding coverage. Adjusting your policy as life circumstances change eliminates premiums you no longer need. Think of it as auditing your subscriptions applied to insurance.
  4. Understand public benefits. Japan's social safety net is generous. Survivor's pension, the high-cost medical care system, and sickness and injury allowances already cover a significant portion of risk. There is no need to duplicate that coverage with a private policy.

Three Patterns Behind Premiums That Never Go Down

Households that review their insurance and still see no savings tend to share a few patterns.

Riders piled on top of riders. The base policy is small, but outpatient, advanced medical treatment, women's illness, and cancer diagnosis riders are all bolted on. Each one is minor, yet together they can rival the base premium. Riders are usually added on a recommendation at signing and then forgotten. Open the policy documents and write down what you are actually paying for; that is where the review starts.

Protection and saving living in one product. Whole life and education endowment policies bundle coverage with an investment component. Trying to cut the premium touches the savings portion as well, and cancelling early can leave the surrender value below what you paid in. The difficulty comes not from the product being bad but from two goals being tied into one contract. If you are buying new, keeping protection and saving separate leaves you far more room to adjust later.

Policies bought out of anxiety. Contracts signed after a relative's illness, or after a presentation full of statistics. Because the amount was never derived from a calculation, there is no ceiling on how much peace of mind costs. Policies of this kind tend to creep back up even after they are trimmed.

All three share the same root: the reason for buying was reassurance in the moment rather than a household calculation. The flip side is that once you work out the amount you genuinely need, premiums come down on their own.

Frequently Asked Questions

Is a savings-type policy a better deal than term insurance?

You can only judge that against the alternative of keeping protection and saving separate. A savings-type premium still contains the cost of the coverage plus the insurer's expenses, so the portion that goes into the savings component is smaller than what you pay in. Cancel partway through and the surrender value can sit below your total contributions, which makes the policy hard to unwind exactly when money is tight. Buy term coverage and save separately, and you can keep the protection you need while changing your savings plan freely. The real question is whether you value the forced-saving mechanism itself.

Is medical insurance really unnecessary?

It is not unnecessary across the board; it depends on whether savings and public benefits already cover the gap. Japan's health insurance includes the high-cost medical care system, which caps out-of-pocket medical spending at a ceiling set by income, and employees also receive a sickness and injury allowance. That structure makes it unlikely that a hospital stay alone will wreck a household. So if you have several months of living expenses saved, medical insurance is a lower priority. If your savings are thin, if you are self-employed with no sickness allowance, or if you want private rooms and newer treatments to stay on the table, buying it makes sense.

Online insurers are cheaper, so is the coverage weaker?

The price gap comes mainly from how the policy is sold. Face-to-face sales load agent compensation into the premium, and buying online shrinks that component. For the same coverage the benefit paid is the same, every insurer operates under the same regulator, and the policyholder protection framework is shared. What you do give up is breadth: online line-ups are narrower, and designs that assume complex riders or in-person consultation are not on offer. The more comfortable you are specifying your own coverage, the more of that price difference you keep.

Is it cheaper to buy while you are young?

The monthly premium is set lower for younger buyers, but you also pay it for far longer, so buying early does not reliably cost less in total. The more important question is whether you have anything to protect yet. Carrying a large death benefit while no one depends on your income means paying premiums with nothing on the other side. "It is cheaper while you are young" is often used to hurry a decision; the default should be to buy when the need appears. The chance that a future health condition limits your options is not, on its own, enough to overturn that.

Was this helpful?