Let's think about how put options can give us leverage on a downside, or I should say, on a bet that the stock will go down relative to shorting. This one's a little bit more complicated, because shorting is a little bit less intuitive. But if you were to short a stock, in order to short it, you might say hey, I don't have to put any money up front, because I essentially just borrowed the stock immediately. And then I would sell it for $50. But the reality is that you do have to put some capital upfront, because the short can move against you. And usually you have to put at least 50% of the value of the short. So in our short scenario, you would have to put at least$25 up front. And then you would borrow the stock, sell it for $50, and so you'd essentially have$75 to play with that you would eventually have to use to buy back the stock. But the upfront capital is $25. Now, in our scenario where the stock went down, which was a good thing if you're shorting, you want the stock, that was your bet, you want it to go down. In the scenario where the stock went down to$20, you made a profit of $30. You were able to buy that stock for$20, and then give it back to the original person. So you were able to keep that $50, although net for that$20, so you made $30. So you made$30 on a $25 investment. So your gain, you make, what is that? You make$25 and then another $5, so that's 120% gain. So let me write that down. You had made 120% gain. Of course, in this scenario, you gained when the stock went down. In terms of loss here, when the stock went up, the stock went up to$80, we lost $30 by shorting. So we had 120% loss. And it's important to realize, in a short situation, the best thing that could happen for you, is your stock go to zero, in which case you can buy it back for nothing, which means you could keep your$50. So in the best possible scenario, you have to put $25 up front. You can keep the$50 that you got from borrowing and selling the stock. So you could make a 200% percent return. In the worst case scenario, so the best scenario is this is 200%, in the worst case, this would be infinite. So you have to be very careful while you're shorting. But let's think about the put option. In the put option, we only have to put $5 upfront to actually buy the put. And when the stock went down to$20, we made \$15. So this was a 300% gain. And on the other side of the equation, when the stock went up, the worst we could do is just lose all of our money. So the worst thing we could do is just lose 100%. So once again, we were able to multiply our gains relative to shorting, although it's a little bit more mixed on the downside, because the put gives you a little bit of protection there.