All right, here we're going to look at two spreads, option spreads, stock and option spreads. These are important for your own trading strategies, but they will also be important in future lectures for understanding option pricing, the first steps into option pricing, specifically put-call parity. And they're also very useful for understanding relationships between no arbitrage relationships between options of different strengths and calls and puts. So option spreads are a really interesting area beyond simple trading strategies. So the first two we're going to talk about is a protective put in a covered call. So the idea of a protective put strategy is one, we buy the stock. And let's say we buy the stock for $100. So we'll say we bought the stock for $100. And two, then we buy a put option. We buy a put with a strike below the stock, what you pay for the stock. So let's say we buy a put with a strike price equal to $90. And we paid for the put, the premium is, let's just say $3. So to understand the protective put, we can chart it up here. And the nice thing is we're going to chart it so we'll see the profit loss for every underlying stock price. This axis is going to be the underlying stock price on this is going to be $1.00 P&L profit loss. And it'll also give us an idea of what the max gain max loss is on this position and where we break even and so forth. So the first thing here is we bought the stock for $100. So we can put $100 here, put it right here, $100. And our P&L on a stock is just going to be aligned like that. Slope of one stock goes up to a $101. We make a dollar down to $99. We lose a dollar. And adding on here, buying a put with a strike at $90. So we can put, this is where the, this is the strike price. We paid $3 for it. So the idea here is anywhere above $90. We lose $3 on the option at $90. The option is going to be below $90. The option is going to be worth more money. Of course, we're going to break the option, break C987. So this is what the profit loss looks like on the option. Now to get the P&L on an spread, all we have to do is sum the P&L here and sum the profit on the option with the profit on the stock at each point. Keep in mind this is negative 3. And it's really useful just to start at wherever the kinks are. So here we'll just figure out what the, what the P&L on the protective put position is at $90. Where the kinks. Of course, at $90, we lose $10 on the stock. We also lose $3 on the option. So our loss here is 13. So I'll put a dot here. This is negative 13. Now the idea is below $90, we gain on the put what we lose on the stock. So these two loss set each other. So our P&L for the protective put position is just flat below $90. And I'll put a little swiggly line. So this is the combined, this is the protective put position. Now above $90, the option doesn't change, the P&L doesn't change, but the stock does. So this is going to go up along the stock here like this. And we are going to break even here at 103. So this is what the protective put position looks like. So obviously what we're doing with this position is we are giving, we're giving up upside in return for protecting us from downsides. So that's the idea. Reduce my downside, but then I also have to reduce my upside. Max gain. Our Max gain here has no limit. So just say no limit to our gain. Max loss. That's going to be our 13. So here our loss is limited to $13. And we break even. We break even when the underlying, this is of course the stock price at expiration. We break even when the stock price at the expiration of the option is 103. So this is the protective put position. Now keep in mind, you know, without doing this chart, you can always get, you know, your Max loss by simply saying, well, I'm going to lose until the strike price of the put. So here I'm losing $10. And then I lose the price of the put at 90. So you can always get this by just taking the price of which you buy the stock minus the strike price of the put option plus what you paid for the put option. That's an easy way to get the 13. Of course, we're always going to break even at the what we paid for the stock plus the price for me to pay for the put. So that's the 100 plus the $3 we paid for the put. So the idea of this is, you know, if the stock is below, what is this going to be? This this point, which is going to be 87. We are glad we put on the protective put position. Of course, any price above that, we are, we would prefer that we didn't have the protective put position on. So the idea here is, you know, we're giving, we're going to be worse off on all the states above 87 dollars here in return for not having to worry at all if the stock of being happy if the stock falls below below 87. Happy that we had the protective put position on. So the next one. So that's the protective put. And now we have a cover call or two basic spread strategies. Our cover call will still buy the stock for 110, but we'll sell will sell a call. We're usually selling a call for a strike above what we paid. So we'll say we sold a 100. Let's do 110 110 strike price call option. And of course for this, we receive, we receive all make up a number of two dollars. So this we're paid two dollars. We'll do the same chart with, and then have Max, Max loss and break even. So looking at we bought the stock for 100 call as a strike of 110. So here we'll put 100 and we'll put the strike price 110 here. P and L on the stock again, simply line. So for one. Here we receive two dollars so that the pay off on the call looks like this. The call we sold it's going to be flat up until 110. And then it's going to decrease there. This is $2. Of course, plus $2. Now the combined position all we have to do is sum at each point. Again, it makes sense to start at the kink. So at 110, we gain $10 on the stock. We gain $2 on the auction. And so plus 12. So here we have $12. When the stock is above 110, again, the, whatever we gain on the stock, we lose on the call. So this is going to be flat off in this point. And then it's going to, because this is flat here, it's going to follow this line all the way down there. And we're going to break even at 98. So we break even at 98. So now the idea here is our Max gain, $12. Our Max loss, well the stock can go all the way down to zero in which case we'll lose $100 on the stock. We'll gain $2 on the call option. So Max loss is 98. And then we break even when the underlying stock price is 98. Of course, these two will always be the same. So this, this protective put, I mean, sorry, this covered call and all. So this is the covered call position here. The idea of this spread is we're giving away upside to be better on all other states. So the idea is, you know, if the stock goes above 112, we're worse off having put on the covered call. However, if the stock is anything below 112, we are better off for having the covered call position. So again, giving away, giving away some upside and return for being better off in all the down states, which is typical. That's what we can do with up and spreads. We can gain, we can reduce downside by also reducing what we make in up states and so forth. So it's always a trade off. Good. The next thing here is to put these two together into a collar. So we can, a collar is going to be buying the stock, selling the call and buying the put. And I'll leave that for another lecture because good.