Data. So-102:X= 116, 1 + r= 1.08. The two possibilities for ST are 150 and 82. a. The range of S is 68 while that of P is 34 across the two states. What is the hedge ratio of the put?b. Form a portfolio of one shares of stock and two puts. What is the (nonrandom) payoff to this portfolio?

P1

a.

-41.47%

b.

8%

Explanation:

a.

Hedge ratio can be calculate as follow

Hedge ratio = Put option payoff - Stock option Payoff

Hedge ratio = ( P1 - P0 ) / ( S1 - S0 )

Where

P1 = 0

P0 = 34

S1 = 150

S0 = 68

Placing vlaues in the formula

Hedge ratio = ( 0 - 34 ) / ( 150 - 68 )

Hedge ratio = -34 / 82

Hedge ratio = -0.4147 = -41.47%

b.

First calculate the Payoff

Possibility 1

Payoff = 150 + 0 = 150

Possibility 2

Payoff = 82 + 68 = 150

So payoff will be same in both possibilities

So

1 + r = 1.08

r = 1.08 - 1

r = 0.08

r = 8%

Payoff of portfolio of one shares of stock and two puts is 8%.

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