You are a provider of portfolio insurance and are establishing a $4-$year program. The portfolio you manage is worth $$108$ million, and you hope to provide a minimum return of $0\%.$ The equity portfolio has a standard deviation of $21\%$ per year, and T$-$bills pay $8\%$ per year. Assume that the portfolio pays no dividends.

Required:

a$-1.$ What is the delta of the implicit put option conveyed by the portfolio insurance?

a$-2.$ How much of the portfolio should be sold and placed in bills?

b$-1.$ What is the delta if the new portfolio falls by $5\%$ on the first day of trading?

b$-2.$ Complete the following: Assuming the portfolio does fall $5\%$ the manger should sell how much in stock?