$200$ shares of the stock at $$28$ per share and $70$ six$-$month European put options with an exercise price of $$26.$ Each put option $$1.$

$($b$)$ Discuss the value of the portfolio with and without the European put options.

The lower the stock price, the

beneficial the put options. The options are worth nothing at a stock price of $

or

put options to the overall portfolio for stock prices of $