QUESTION $3$

You are a pension fund manager. Today is May. You OWN $100$ shares of XYZ$.$ Today's XYZ share price is $$1,330$ per share. There exist call and put options with an expiration date of June $11.$ Each option is on one share of XYZ$.$ The call has an exercise price of $$1400$ and a premium of $$3\mathrm{.}00$ per share. The put has an exercise price of $$1200$ and a premium of $$4\mathrm{.}00$ per share. Suppose that the riskless interest rate is zero and that XYZ does not pay dividends.

A$)$ Design a hedging $($insurance$)$ strategy against a SUBSTANTIAL DECLINE in the share price using either put or call options. Calculate the initial cost $($of the strategy$)$ and your maximum gain and maximum loss on expiration day, per share.

STRATEGY: $...$

INITIAL COST: $...$ MAX. GAIN: $...$ MAX. LOSS: $...$

B$)$ You are concerned about the high cost of the insurance provided by the strategy above. Using the options above, design a hedging strategy that will cost less money today and will have lower maximum losses on expiration day. Calculate the initial cost $($of the strategy$)$ and your maximum gain and loss on expiration day, per share.

STRATEGY: $...$

INITIAL COST: $...$ MAX. GAIN: $...$ MAX. LOSS:

C$)$ Compare the two strategies above. Which strategy is better?