Private equity funds, especially some quantitative hedge funds, use various hedging strategies to earn absolute returns, that is, they make money regardless of market ups and downs, which is called market neutrality.
As for your specific question, if it is a hedging strategy, you can look at the relevant information of hedging calculation. It depends on the setting of stock options, such as how much is the first hand? Treasury bond futures represent1100,000 par value stocks. If one hand represents 1000 shares, buy one hand.
The second question, as I have actually said, is that few people buy a stock and then short it with options. That is to say, no matter whether the market goes up or down, you will not lose money or make money, and you will also spend the waiver fee. This doesn't support it? Sometimes it is used like this. You buy your own stock, but there are rumors that it is not good, you don't want to sell it, or you can't sell it. In order to prevent losses, you can not sell stocks, temporarily short options, do some hedging, and then close options when things are clear.