A large car company, CarX, just performed a partial carve-out their tire division, TireX, last month in April. It's now May and the company announced that in one month (June) it will conduct the full carve out and give 1.5 shares of TireX for every share of CarX that investors own. Investors are bullish on the stock and CarX is currently trading at $95 and TireX is currently trading at $130.

Your trading department decides it wants to get in on the action and purchse CarX now so that in one month you can realize, what appears to be a risk-free profit, from the carve-out. That is, in one month (on the day of the carve-out in June) participants holding CarX will recieve 1.5 shares of TireX.

Assume you can borrow and lend at the risk free rate of 6% (annual effective). That is, you can sell a US Bond at a risk-free rate of 6% to fund your purchase of CarX shares or invest in a US Bond at a risk free rate if you sell CarX shares.

Timeline:

- May (you are here for Question 1): CarX is trading at $95 and TireX is trading at $130

- June (you are here for Question 2): full-carve out complete. CarX is now trading at $15 and TireX is trading at $85

Now assume you're restricted from trading in carve-out companies/stocks, but you've found an options desk to write options on TireX. -

- European Call options on TireX: Strike Price $95. Date of Expiry: June day of full carve-out. Price per share: $21.11

- European Put options on TireX: Strike Price $95. Date of Expiry: June day of full carve-out. Price per share: $20.65

Question 3: Assume Put-Call parity holds, explain how you can implement the TireX trade by using these options. Assume you still buy/sell 100 shares of CarX.

A) Assume in this scenario you are back in May when you put the trades on. Describe the trades you make assuming you buy/sell 100 shares of CarX and replicate TireX with above options.

B) Now move to June when the full carve-out just happens. You are ready to unwind your trades. Assume you bought or sold 100 shares of CarX. Calculate the P&L from these total trades including the option trades. Show work work clearly.