Question

# A) Assume you bought 100 shares of stock DEF at a price of \$30/share. Now, the...

A) Assume you bought 100 shares of stock DEF at a price of \$30/share. Now, the price has risen to \$80/share. Assume 3-month 80-strike puts on DEF cost \$6/share and 3-month 80-strike calls on DEF cost \$7/share. If you want to fully protect your gains for the next 3 months using options, what could you do? B) If you implement this option strategy, what would your net profit or loss be (ignoring transaction costs) if DEF falls to \$50? C) Again, assuming you implemented the option strategy, what would your net profit or loss be (ignoring transaction costs) if DEF continues to rise and goes to \$100/share?

A) We hedge using the collar strategy. In this strategy, while holding the stock, we buy put options at strike price 80 and sell call option at strike price 80. The initial cost = \$6 - \$7 = -\$1 to implement the strategy ie. we have a positive payoff of \$1 to implement this strategy

B) If DEF falls to \$50

Profit from stock = \$50-\$30 = +\$20

From the short call = +\$7 (this is the premium receiveed from short call since short call payoff is 0)

From the long put = \$80-\$50-\$6 = \$24

Hence, net profit = \$(20+7+24) = \$51

C)

If DEF rises to \$100

Profit from stock = \$100-\$30 = +\$70

From the short call = \$80-\$100+\$7 = -\$13

From the long put = -\$6 = -\$6

Hence, net profit = \$(70-13-6) = \$51

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