Put Option - decrease portfolio Beta

How to buy a put option to derease the portoflio Beta? Let’s say portfolio Beta is 1. Portfolio size 1 mio USD, portoflio constitute is very similar to S&P500. Target: Buy S&P500 put option to decrase the portfolio beta to 0.5. What additional information do we need? Thanks.

Please disregard it. I think it’s not possible given option payoff is not linear.

Or can we buy put and long short…then it’s linear…

areyou asking for the calculation or theoretical response?

you cannot calculate this unless there is more informatoin on the delta of the put option…