> You can't just reduce risk without also reducing gains.

You can (assuming you haven’t exhausted all available independent investment opportunities with equivalent risk/reward profile) reduce risk without reducing expected gains.

Doing so (assuming you were investing suboptimally for your the prior risk level and expected returns) involves reducing in the part of the distribution above the mean offsetting the increase in the part below the mean.

Buying a 10% interest in each of 10 lottery tickets (ignoring practical risks associated with deals to split winnings) doesn't reduce your gains compared to buying one lottery ticket, it just reduces your risk.

This is the whole point of diversification.

But in the case of something like a pension, reducing risk is often the goal, right?

The goal is to make enough money for pensioners to live off.

If the goal was to reduce risk then pensions would be better off being held in cash. But pension funds dont have enough cash to meet needs so they have to grow.

Pension pots actually often do follow a path of minimising risk, with the percentage held in cash and government bonds increasing as pensionable age nears.

They have a specific percentage growth targets which gets adjusted periodically based on interest rates and life expectancy.