Question

17. The current price for a stock index is 1,000. The following premiums exist for various options to buy or sell the stock index six months from now: Strike Price Call Premium Put Premium 950 120.41 51.78 1,000 93.81 74.20 1,050 71.80 101.21 Strategy I is to buy the 1,050-strike call and to sell the 950-strike call. Strategy II is to buy the 1,050-strike put and to sell the 950-strike put. Strategy III is to buy the 950-strike call, sell the 1,000-strike call, sell the 950-strike put, and buy the 1,000-strike put. Assume that the price of the stock index in 6 months will be between 950 and 1,050. Determine which, if any, of the three strategies will have greater payoffs in six months for lower prices of the stock index than for relatively higher prices. (A) (C) (D) (E) None I and II only I and III only II and III only The correct answer is not given by (A), (B), (C), or (D)

Answer 1

First let us calculate payoff assuming lowest price of stock index @ 950 & calculate the payoff

Assuming the lowest price for stock index@ 950 StrategyI Payoff Buy 1050 call Sell 950 call 0 Premium -71.8 120.41 Profit/Loss -71.8 120.41 Net Payoff 48.61 Assuming the lowest price for stock index@ 950 Buy 1050 put Sell 950 put Strategy II Payoff 100 Premium -101.21 101.21 Profit/Loss -1.21 101.21 Net Payoff 100 Assuming the lowest price for stock index@ Buy 950 call Sell 1000 call Buy 1000 put Sell 950 put Strategy II Payoff 0 0 50 0 Premium -120.41 93.81 -74.2 51.78 Profit/Loss -120.41 93.81 -24.2 51.78 Net Payoff 0.98

Next let us calculate payoffs for higher stock index @ 1050

Assuming the highest price for stock index@ 1050 Strategy I Buy 1050 call Sell 950 call Payoff 0 0 120.41 Premium -71.8 Profit/Loss -71.8 120.41 Net Payoff 48.61 Assuming the highest price for stock index@ 1050 Strategy II Buy 1050 put Sell 950 put Payoff 0 101.21 Premium -101.21 Profit/Loss -101.21 101.21 Net Payoff 0 Assuming the highest price for stock index@ Strategy II Buy 950 call Sell 1000 call Buy 1000 put Sell 950 put Payoff 100 0 -74.2 Premium -120.41 93.81 51.78 Profit/Loss -74.2 -20.41 93.81 51.78 Net Payoff 50.98

Only Strategy II gives higher payoffs when stock index is @ lower levels than higher stock index.

There are no answer options showing only Strategy II.

Hence the answer is Option (E) The correct answer is not shown by A, B, C or D