If one portfolio always provides a return at least as high as another portfolio, then that portfolio will have a price no less than that of the other portfolio. High volatility is bad for option holders because it increases the probability that the option will expire out-of-the-money. Holding everything else constant, a longer-term American put is always worth more than a shorter-term American put. The lower the exercise price, the more valuable the call option. If an option portfolio generates a zero cash flow at expiration and a positive cash How today, an arbitrage opportunity is available