Articles - The utility of my DC, of my DC

By Alex White FIA C.Act,Global Head of Quantitative Modelling at Gallagher

Another is psychological: perhaps many respondents were skeptical that a “50-50” bet is actually 50-50, so our instincts could lead us against it. But both explanations miss a huge point.

I’d take the gamble on the million. However, if you scale up the numbers, I would happily take a guaranteed £50m over a 50% chance of winning £1bn. The first £50 million would add far more value to my life than the next £950m. If you wouldn’t, keep scaling up the numbers until you would.

 

As an alternative framing, I’d also take £50,000 over a 1% chance of winning £100 million. In all of these scenarios I might try to sell the bet if I could, but that’s a separate question.  The key point is that it’s not simply about expected value, it’s about utility.

 

As a general principle, if you can’t afford to lose an amount of money, you shouldn’t risk it. Equally risking a life-changing amount of money may be a bad decision for a lot of people, even when the expected value of the gamble looks highly attractive. By contrast, if the choice were between £5 and a 50% chance of winning £1,000, I’d expect very different results.

 

Viewed through this lens, a lot of the results which appear to need explanations may just be outputs of utility functions. For instance, £50,000 is about $67,000[3], so it’s a bigger amount. The larger the guaranteed sum, the more you’d expect people to choose it. UK respondents may genuinely be more risk-averse than their US counterparts, but some of the differences could simply be explained by the extra $17,000, or more broadly by the relative size of the amount offered to the person’s current wealth.

 

The same logic may help explain some of the gender differences. Men may, on average, have a higher tolerance for risk. However, men also tend to hold greater wealth on average.  At least part of the gap could therefore be explained by differing financial circumstances rather than differing attitudes alone. A billionaire’s optimal decision may not be the same as someone struggling to meet immediate financial obligations.

 

One area where these findings could have real implications is in retirement planning. If the median person has such a steep and non-linear utility curve, then how we assess retirement outcomes may need to reflect that reality.

Importantly, that doesn’t always imply favoring low risk assets. In decumulation, investment horizons remain long and the liabilities are uncertain, so portfolios without enough risk can lead to very poor outcomes. Nor should we overstate the significance of a single survey when we already have more directly relevant information about behavioural preferences, such as the rate of take-up of annuities.

 

Even so, insights of this kind could influence how providers evaluate retirement strategies. For example, greater weight could be placed on avoiding particular outcomes when comparing portfolio designs, potentially increasing use of strategies like equity protection. In a totally different vein, similar questions could equally help financial advisers better understand how clients perceive risk and select the most appropriate risk categories.

 

Either way, it’s a fascinating question with answers that probably surprised quite a few people. What may initially look like irrational behaviour could simply reflect that people value outcomes differently. And if that’s true, the implications could extend well beyond a hypothetical lottery question and into how we approach financial decisions.