Minimum acceptable annualized return

What is the minimum annualized return you can accept for a trading system? and why?

Thank you

Typically you don't just look at annualized return but rather at risk adjusted return compared to risk free rate. You have to incorporate drawdowns (risk) somehow in your metrics.

And typically you look for Sharpe ratio > 1. Note that this is not "minimum" this is actually a very, very good to have Sharpe ratio > 1 over long term.
The problem with Sharpe ratio is that it depends on analysis period. The longer period, the more difficult is to achieve Sharpe ratios > 1.

For less complicated measure, look for CAR/MDD (annualized return by maximum drawdown %) to be > 2. If CAR/MDD is less than 1 it means that you risk more than you effectively gain.