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ps4_solution

# ps4_solution - Riccardo Colacito Division of Finance...

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Riccardo Colacito Division of Finance Problem Set 4 Investments Answer key 1. (a) The value of the call will be \$30 if the stock price goes up and zero otherwise. (b) The hedge ratio is H = 30 - 0 110 - 20 = 1 / 3. (c) For each call written, you should buy 1 / 3 of a share to perfectly hedge your portfolio. (d) Since the portfolio is perfectly hedged, its value will be equal no matter what happens tomorrow. The portfolio value is 1 3 × 110 - 30 = 20 / 3 or \$6.67. (e) The present value of \$6.67 at a risk-free rate of 6.5% is 6 . 67 1 . 065 = 6 . 26. (f) By no arbitrage the cost of the portfolio must equal the present value found in the previous part: 1 3 × 60 - C = 6 . 26 that is C = \$13 . 74. (g) If the call sell at \$14.50, you could make an arbitrage by buying the same portfolio of part c and borrow its cost at the risk free rate. This amounts to borrowing 1 3 × 60 - 14 . 50 = 5 . 50. The cash flows are documented in the table below: Today Tomorrow if S=110 Tomorrow if S=20 Buy 1/3 shares -20 36.67 6.67 Write 1 call 14.50 -30 0 Loan 5.50 -5.8575 -5.8575 Total 0 0.8125 0.8125 With this strategy you pay nothing today and get a positive of 0 .

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ps4_solution - Riccardo Colacito Division of Finance...

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