Delta hedge and risk free

Regarding a delta hedge, text says: because we are hedged, the portfolio should be earning a risk-free rate of return based on a gain in value of the short call position and the fall in value of the stock. Why do we earn the risk-free rate here with a delta hedge?

Delta Hedging: It involves hedging away the option position’s exposure to delta or price risk using either forward contracts or a spot transaction.

Only cash position left, so cash return. (Risk free rate)

To delta hedge a long stock, the no. of options to short = no. of shares hedged / delta of call option I still don’t see how we earn the risk-free here?

Long underlying + Short futures = Long risk-free bond Long Underlying = Long risk-free bond + Long futures Long underlying + Loan = Long Futures Agree for above? It’s similar to synthetic equity exposure, investors hold cash and obtain equity market exposure by using futures contracts.

Any other explanations as to why a delta hedge earns the risk-free rate?

Sorry for the bump, but any answers?

When an option position is fully delta hedge there is no more directional risk exposure.

This is also why a long-short mkt neutral fund might be expected to earn risk free rate.