The current price of a non-dividend-paying stock is $80. Over the next six months it is expected to rise to $90 or fall to $74. An investor buys six month maturity put options with a strike price of $80. What is necessary to hedge the position?

Buy 0.8 shares for each option purchased

Explanation:

Calculation to determine What is necessary to hedge the position

Using this formula

N=Vu-Vd/U-D

U = stock price in case of an up move = $36

D = stock price in case of an down move = $26

VU = put option value if stock goes up = $0

VU = put option value if stock goes down = $32 - $26 = $6

Using this formula

N=

−

V

U

−

V

D

U

−

D

N

=

−

0

−

6

36

−

26

N

Now let calculate What is necessary to hedge the position

Value =74 x + 6

Hence,

90x=74x + 6,

x=6/(90-74)

x=6/16

x=.375