If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content
Current time:0:00Total duration:3:54

Video transcript

so I claimed in the last video that we made a five-dollar risk-free profit by spending thirty-eight dollars to buy a call and a bond and we got $43 by shorting a stock and essentially writing a put option what I want to do in this video is verify that we really do have all of our bases covered so let's just think about all of the different scenarios for the underlying stock price at option expiration because that's the date that we care about so let's take the situation where the stock just becomes where the stock just goes to zero so in that situation the call that we own is worthless the call is worthless no reason why you would want to exercise the option to buy it for $35 when the stock is worth zero but the good thing is is that we when we now have to cover our short remember when you short something you're borrowing the stock and selling it and in the future you have to buy the stock to cover your short to buy the stock and return it to whomever you borrowed it from so now we can spend $0 we can now spend $0 $0 to buy stock and essentially give it back to whom we borrowed it from or essentially cover the short to buy stock to cover or unwind short to cover the short the bad thing is is that put option that we wrote remember we wrote it we sold the put option we're giving someone else the right to sell to sell the stock to us for $35 and if the stock price is worth the 0 they're going to exercise that option because they can then they can buy the stock for 0 they can sell it to us for $35 so we have to spend we have to spend $35 to buy to to kind of buy the stock from put holder from put holder but the good thing is is that we have this bond we own this bond that's not worth $35 we have a $35 bond 35 we have a $35 bond so we can use the $35 bond to to spend the $35 and since you give that $35 to the holder of the put and everything cancels out so we can still keep original $5 so that's the situation where the stock price went to zero what about the situation where the stock price goes to something crazy let's say the stock price goes to 70 so the stock price goes up let me draw a little column over here so now let's think about the scenario where the stock price goes to 70 now all of a sudden the call option we have remember it's an option to buy the stock at $35 the call the call is worth is worth $35 the call is worth $35 we have a bond that's going to be worth $35 a bond worth 35 the put option is worthless so the person who we get who we wrote the put forth they won't exercise it so the put is worthless the put is worthless but we still have to cover our short we have to buy back the stock and return the stock to whomever we borrowed it from and now to cover our short to buy the stock it's going to cost us $70 so we're going to have to use this $70 so $35 from the call and $35 from the bond to actually cover our short position so $70 to buy stock and cover short and what you'll see is I just picked kind of a low a low stock price and a high stock price but no matter what the stock price is you're going to be able to cover all of your obligations and break even at expiration and keep your original risk free $5 now the reality of the situation is that opportunities like the seldom exist because frankly people can write computer programs to find these these arbitrage opportunities and just exploit them really really really fast