Butterfly spreads combine the bull and bear spreads and involve three options with different strike prices and the same expiration date. If the investor expects the price of the stock to be stable (the butterfly will not flap its wings), the individual buys the options with the highest and lowest strike prices and sells two options with the strike price in the middle. If the investor expects the price of the stock to fluctuate (i.e., the butterfly will flap its wings), the process is reversed. The investor sells the outer options and buys two of the calls with the strike price in the middle. For example, suppose a stock is selling for $61 and there are three-month call options at $57, $60, and $63. The prices of the options are $6, $3, and $1, respectively.

a) The investor expects the price of the stock to be stable. What would the investor gain or lose at the options expiration from constructing an appropriate butterfly spread at the following prices of the stock: $50, $55, $57,$60, $63, $65, and $70?

b) What is the maximum possible loss?

c) What is the maximum possible gain?

d) What is the range of stock prices that produces a gain from constructing this butterfly?

e) Did the butterfly achieve its objective based on the expectation that the price of the stock would be stable?