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Currently the stock of Backstreet Toys (BT) is selling for $20 per share and the risk free rate is5%.
a) Draw a payoff diagram for each of the following 3 portfolios:
i. Buy one share of BT stock and finance the purchase by borrowing $20 for 1 year at the risk free rate.
ii. Buy one call option on BT stock with a strike price of $21 that expires in 1 year. Sell a put option on BT stock with a strike price of $21 that also expires in 1 year.
iii. Enter into a one-year forward contract on BT. This contract obligates you to buy one share of BT stock for $21 at the end of 1 year, no matter what the price turns out to be.
b) Using the principle of no-arbitrage and what you know about BT's current stock price and the riskfree rate, is the price of the call option in (ii) greater than, less than or equal to the price of the put in (ii). Similarly, what can you conclude about the cost today of entering into the forward contract described in (iii)?
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