sa definitely has higher returns than ers.
That isn't quite right as you've written it. Let's see if I can be more precise (which is proving difficult on this occasion)....
For a significant span of time there's a higher
effective annualized yield on CPF Special Account funds than on CPF Retirement Account funds (those above the $60,000 bonus interest limit) fed into CPF LIFE. But it's only a "significant span of time," not "always." There are three basic time segments. (1) For deaths before payout start (which can be as late as age 70), the effective annualized yield is penny for penny identical: SA earns 4.0% interest, and RA earns 4.0% interest (above the $60,000 bonus interest limit). (2) For deaths after CPF LIFE payout start until a certain age (which varies and cannot be precisely pinned down in advance), the effective annualized yield on SA funds would end up higher. (3) For deaths after that certain age, the effective annualized yield on CPF RA funds would end up higher.
for ers, part of the money is taken out to buy insurance just in case you cannot die. because you have a lower principal, your returns will definitely be less.
As seen above, no. Effective annualized yields will be identical for deaths within segment #1, lower on RA in segment #2, and higher on RA in segment #3.
Segment #1 can be as long as 15 years, please note. Indeed, if you're in relatively poor health at 55+ and want to do something really nice for your CPF nominees, you probably ought to inject as much cash into your CPF Retirement Account as you're allowed and able, consistent with your own cash flow and liquidity needs. (And into MediSave too for that matter.) All that cash will then earn 4.0% interest and, when you die at age 67 (let's suppose) and without starting CPF LIFE payouts -- the "do nothing" default -- your nominees benefit from that juicy 4.0% annually compounded interest, every penny of it.
To put it crudely (and jokingly), CPF members age 55+ who are in relatively poor health who have some top up room in RA and/or MA can be outstanding fixed deposit banks.
There's also the important detail that cash injections into CPF RA after CPF LIFE payouts start can earn exactly the same 4.0% interest rate (while on account) as CPF SA funds...or feed into higher CPF LIFE payouts, as you prefer.