Ask yourself this question: if a tossed coin landing on “heads” wins you £1, but the same coin landing on “tails” wins you nothing, how much would you be willing to pay to play the game? 25p? 50p? Or more?

Here, there is no right answer – it all depends on your attitude to risk. For the academically minded, the amount you’re willing to pay – or the minimum amount you’ll accept for certain to give up your chance of winning – is known as the “certainty equivalent” (for any students reading, think of the banker’s offer in the daytime TV show Deal or No Deal).

It is a measure of risk-taking in a field of “game theory”. And, as such, it is related to the “expected utility hypothesis”, which states that your betting preferences on uncertain outcomes will be a mathematical function of the size of the payout, the probability, the utility of the payout and your risk aversion. But this is all rather, well, hypothetical, isn’t it?

Not until you ask yourself this question: if a with-profits endowment policy wins you a real return of 2.9 per cent a year on average, but the same policy loses you 0.9 per cent a year at worst, how much would you be willing to invest? Or how much would you want for certain in a savings account to give up this opportunity? £1,000? £2,000? Or £12,000?

Here, the answer has been becoming all too clear of late – there has been too much money, put to too much risk. For anyone advised to invest £50 a month in a with-profits endowment 20 years ago, the “certainty equivalent” has been £12,000 – but the gamble has delivered as little as £16,192 in some cases, which is a negative return after inflation, and less than the certain £17,451 that could have been had from the average 90-day notice account.

It is a game that too many policyholders appear to be losing. And, as the past week has shown, it is now turning into a losing streak.

Last Friday, Norwich Union – the second-largest with-profits provider with 2.3m endowments, bonds and pension funds – announced that it was cutting payouts by up to 15 per cent, after its main fund lost 12 per cent in 2008.

A week earlier, Friends Provident announced cuts to the bonuses on its 1.2m with-profits policies of up to 20 per cent.

Advocates of with-profits investments would make two observations here: these cuts were still less than the 31 per cent fall in the FTSE 100 index last year; and the sums quoted above, from FT magazine Money Management, are the payouts from the average and the worst 20-year policies – not the best.

But the crux of the matter is that the annual and terminal bonuses added to with-profits policies – which are supposed to smooth out years of good and bad investment performance over the long term – are so arbitrary, opaque and uncertain as to make choosing one a mug’s game.

Money Management figures show that, while the best 20-year with-profits endowment returned 12.7 per cent, turning £50 a month into £49,792, the worst returned 2.9 per cent, giving that payout of £16,192. Four other 20-year policies returned less than 4 per cent, meaning that they produced less than cash.

By contrast, the same monthly sum invested in a UK index tracker fund produced an average of £22,855, with far less variation between providers.

Why are these with-profits outcomes so much more uncertain than trackers? Because they are not determined by the market, but by the actuaries who set the bonus levels – and whose interests are aligned with the life assurance company, not with the policyholder. Why, then, were millions of people advised to buy with-profits policies, instead of a diversified portfolio of equity or gilt index trackers?

Ask yourself this question: if selling a with-profits bond earns you 7 per cent commission, but recommending an equity or gilt exchange traded fund earns you nothing, what’s the only game in town?

Independent financial advisers would argue that they only sell products that meet clients’ needs, and the smoothing effect of with-profits policies theoretically suits risk-averse investors.

But I can’t help remembering the story told by one of my colleagues who, as a student, took a holiday job with a financial advice firm (rather than watching daytime TV). One day, having printed off hundreds of pro forma letters to new clients, she couldn’t help but ask herself: why does every single letter conclude with: “We recommend that you take out a with-profits bond”?

Now an award-winning financial journalist, she realises that advisers don’t gamble with profits – they just leave clients to.

Copyright The Financial Times Limited 2018. All rights reserved.

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