Replicating portfolios: Stock ABC is currently trading at $20. There is a 60% real-world probability that six months in the future the price will go up to $23. There is a 40% real-world probability that six months in the future the price will go down to $18. These are the only two outcomes that are possible, and everyone agrees that the probability assessments are correct. No dividends will be paid on the stock in this time period. A zero-coupon bond with a $1 face amount, which matures in six months, can be bought or sold for $0.98 today.

a. What is the real-world expected return of the stock over the six-month period?

b. A European call option with a strike of $22 is available in the market today. Find a replicating portfolio of the stock and bond. Does the replicating portfolio involve going long or short stock? Does the replicating portfolio involve borrowing or lending money? What is the value of the replicating portfolio today? Note that this is the fair no-arbitrage price of the call option.

c. A European put option with a strike of $19 is available in the market today. Find a replicating portfolio of the stock and bond, i.e., determine how many shares of the stock (x) and how many units of the bond (y) will give the same cash-flows as the put option in six months time in both scenarios. Does the replicating portfolio involve going long or short stock? Does the replicating portfolio involve borrowing or lending money? What is the value of the replicating portfolio today? Note that this is the fair no-arbitrage price of the put option.