If the price of the stock shoots up, your Call will be way In-The-Money, and your Put will be worthless. If the price plummets, your Put will be way In-The-Money, and your Call will be worthless. This is safer than buying either just a Call or just a Put. If you just bought a one-sided option, and the price goes the wrong way, you're looking at possibly losing your entire premium investment. In the case of Straddles, you will be safe either way, though you are spending more initially since you have to pay the premiums of both the Call and the Put.