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9 A stock is trading at $50. An investor wants you to design her a portfolio whose value after one year will depend on the price of the stock at that time as shown in the figure below. Don't ask why she wants such a portfolio. How can you structure such a portfolio for her? How much will it cost her? Use a spreadsheet for Black-Scholes pricing. Assume that the stock does not pay dividend and its volatility is 40%. The risk-free rate is 5% per annum with continuous compounding. Ignore transaction costs and you will not charge her for your time as you have nothing better to do. 100 40, 100 90 70 30,70 50 0, 50 90,50 100, 50 20, 50 30 0 10 20 30 40060708090100 Stock Price 9 A stock is trading at $50. An investor wants you to design her a portfolio whose value after one year will depend on the price of the stock at that time as shown in the figure below. Don't ask why she wants such a portfolio. How can you structure such a portfolio for her? How much will it cost her? Use a spreadsheet for Black-Scholes pricing. Assume that the stock does not pay dividend and its volatility is 40%. The risk-free rate is 5% per annum with continuous compounding. Ignore transaction costs and you will not charge her for your time as you have nothing better to do. 100 40, 100 90 70 30,70 50 0, 50 90,50 100, 50 20, 50 30 0 10 20 30 40060708090100 Stock Price

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