A portfolio manager owns a portfolio that consists of a stock market index and European puts with a strike price of $80 and a time to maturity of 6 months on the index to hedge the position. Using the information provided below, answer the following questions.

The portfolio consists of 297 Puts and 383 shares of the index. The current index price is 99. The risk free rate is .03, index volatility is .389, and the index dividend yield is .016.

If the price of the index were to fall by $5 per share, what would be the change in the portfolio's value?

If the portfolio manager wanted to buy an additional 100 puts, how much would that cost?

What is the delta of the portfolio? (Hint: find the delta of a share of the index and the delta of a single put)

If the price of the index were to fall by $5, what would the delta of the put predict the new put price to be?