You own a stock trading at $50. The stock does not pay any dividend. You

are worried about the risk of stock price movement but cannot sell or short the stock. You

want to reduce your exposure to stock price movement but do not want to incur any cash

expense for doing so. Use a collar so that the value of your hedged stock after six months

will lie within a range. That is, lock a price range between A and B such that your position

will be worth A if stock price after six months is less than A, B if stock price after six

months exceeds B, and equal to the stock price if stock price after six months is between A

and B. What collar strategy will provide you a $20 range (that is, B - A = 20) at zero

cost? Ignore commissions or transaction costs. The risk-free rate is 5% per annum with

continuous compounding and the volatility of the stock is 40%. Structure the collar using

European options. Assume option prices are given by Black-Scholes formulas.