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