Hull Chapter 19 Greeks EOC Question 18.16

In Reference to Hull Chapter 19 Greeks End-Of-Chapter Question 18.16 :-

A fund manager has a well-diversified portfolio that mirrors the performance of the S&P 500 and is worth $360 million. The value of the S&P 500 is 1,200, and the portfolio manager would like to buy insurance against a reduction of more than 5% in the value of the portfolio over the next six months. The risk-free interest rate is 6% per annum. The dividend yield on both the portfolio and the S&P 500 is 3%, and the volatility of the index is 30% per annum.

  1. If the fund manager buys traded European put options, how much would the insurance cost?
  2. Explain carefully alternative strategies open to the fund manager involving traded European call options, and show that they lead to the same result.
  3. If the fund manager decides to provide insurance by keeping part of the portfolio in risk-free securities, what should the initial position be?
  4. If the fund manager decides to provide insurance by using nine-month index futures, what should the initial position be?

_ For Part C of this Question, _ which states that " If the fund manager decides to provide insurance by keeping part of the portfolio in risk-free securities, what should the initial position be?"

The Hull-Problem-Solution calculates the Delta of the Put to be = .3327 which is fine

But then states "This indicates that 33.27% of the portfolio (i.e., $119.77 million) should be initially sold and invested in risk-free securities."

Why & How is the Put Delta * (The Size of the PortFolio) = be the Amount that should be initially sold and invested in risk-free securities …? Shouldn’t the Amount that should be initially sold and invested in risk-free securities be= K.e-rT…?

Can someone please the explanation of Hull Problem Solutions for Part C of this Question