Suppose the current price of ACME Ltd. shares is $20 and in 3 months it will be either $18 or $22. Assume that the ACME stock does not pay any dividends, the continuously compounded risk-free interest rate is 12% per annum and markets are frictionless. Assume you have a portfolio of 10,000 ACME shares and you want to use portfolio insurance to protect the value of the portfolio from falling below $21 per share in 3 months.

a) What steps should be taken now to protect the portfolio? Show your calculations.

b) Show the cashflows on the insured portfolio now and in 3 months when the stock price is $18 or $22. Show your calculations.