When Is Travel Insurance Worth It? The EV Case

An insurer has to charge more than the average claim, or it goes bust. Staff, marketing, capital and profit all sit on top of the expected payout. That loading is why buying insurance is, on average, a slow leak of money.

Here is an illustrative single-trip policy - the numbers are made up to show the mechanism, not quoted from any insurer. Say the policy costs £40. The distribution of what you might claim looks something like this:

Add those contributions and the total expected payout is roughly £33, against a £40 premium. Your expected value as the buyer is about minus £7 per trip. Repeat that across a hundred trips and you would expect to be several hundred pounds down. On the maths alone, you should never buy it.

Because the losing bet removes a number you could not survive. Look again at that last row: a roughly 1-in-8,000 chance of a £200,000 bill. On its own, that single risk has an expected cost of 0.0125% multiplied by £200,000, which is about £25. Tiny, on average. But there is no NHS in a Florida hospital, and an air-ambulance repatriation from the United States can genuinely run into six figures.

Now ask what a £200,000 loss would actually do to you. For almost anyone, it is not a setback - it is the end of the financial game. Savings gone, house remortgaged or sold, years of earnings committed to a debt. You cannot shrug it off and let the average work itself out over your next hundred holidays, because there is no hundred-holiday average for a household that has just been wiped out.

That is the difference between expected value and expected utility (the value of an outcome to you, which for most people rises far more slowly than the money itself, and falls off a cliff near ruin). Money you do not have is worth vastly more than money you can spare. Paying £40 to delete a £200,000 tail is a bad deal in pounds and an excellent deal in utility. We cover the full mechanism in expected value vs expected utility.

The deciding factor is not how likely the loss is, or even its expected size. It is whether the worst plausible outcome is recoverable. A risk worth insuring has a tail that could knock you out of the game entirely.

This is the same idea as ergodicity (whether the average across many parallel gamblers matches the average of one gambler's path through time). Expected value is an average across thousands of imaginary versions of your trip. You only ever live one. If one bad outcome ends that single path - bankruptcy, a debt you can never clear - then the comforting ensemble average never reaches you. A loss that can be absorbed is ergodic in the way that matters: you take the hit, recover, and carry on. A loss that ruins you is not. We unpack this in ergodicity explained.

So insurance earns its keep on exactly the risks that are rare, large, and non-recoverable. It is a terrible deal on risks that are common, small, and easily absorbed - which is most of the insurance the market tries to sell you.

Take phone or gadget cover. Say it costs £9 a month, or £108 a year. The worst realistic outcome is a cracked screen at around £140, or a full replacement near £900. Suppose there is a 1-in-6 chance you damage the screen in a given year. The expected payout is roughly 17% multiplied by £140, plus a slim chance of a bigger loss - call it £30 a year in total.

That is an expected value of about minus £78 every year. Far worse, proportionally, than the travel policy. And crucially, the worst case here is affordable. A £140 repair, or even a £900 replacement, is annoying - it is not ruin. There is no catastrophe tail to hedge, so the utility argument that rescues travel insurance simply is not available. You are paying a hefty premium to smooth out a bump you could pay for in cash.

The rational move is to self-insure: skip the cover, keep the £108, and pay the occasional repair yourself. Over a typical phone's life you would expect to be well over £300 ahead. The same logic sinks most extended warranties and explains why a higher voluntary excess usually pays: you happily absorb the small, frequent stuff to stop bleeding premium on it.

Watch your own psychology here too. The instinct to insure a £140 screen is loss aversion - the pull of avoiding any loss at all - not rational risk management. Rational risk-aversion caps catastrophes; loss aversion insures inconveniences.

You can compress all of this into one decision. Buy insurance against a risk only when both of these hold:

If either test fails, self-insure and keep the premium - the negative expected value is then a pure cost with no catastrophe to justify it. A useful heuristic: if losing it would change your life, insure it; if losing it would just annoy you, do not.

The entire case for travel insurance rests on one line item: emergency medical treatment and repatriation abroad, where costs are effectively uncapped and no NHS is standing behind you. That is the catastrophe. The cancellation, delay and baggage cover bundled alongside it is the inconvenience - pleasant to have, but on its own it would be as poor a buy as phone insurance.

Two practical points for UK travellers. First, a GHIC (the Global Health Insurance Card, the UK's post-Brexit replacement for the EHIC) gives you access to state-provided healthcare in the EU on the same terms as a local - but it does not cover repatriation, private treatment, or travel outside the EU, so it is not a substitute for insurance. Second, the UK's Foreign, Commonwealth & Development Office is blunt about this: it advises taking out travel insurance for any overseas trip, and warns that being uninsured can cost you or your family many thousands of pounds. See the official gov.uk guidance on foreign travel insurance and the GHIC details.

So insure the medical catastrophe on every trip that involves one - a fortnight in the US, a ski week in the Alps, anywhere a serious injury means a private bill. Do not agonise over the baggage limit or lose sleep because the policy is, on average, a small loss. That small average loss is exactly the point: it is the price of deleting the one outcome you could not survive.

• GOV.UK - Foreign travel insurance (FCDO guidance on why to insure and what to check)
• GOV.UK - Global Health Insurance Card (GHIC) (what state-healthcare access covers and excludes)

Worked figures in this article are illustrative models chosen to show the underlying mechanism, not prices quoted from any insurer.