In this workout, a trader expects a stock price to be range bound between $46 and 54 over the next three months, and they're looking to monetize this view. Using the following option table answer the questions below. So we've got some calls for 3M, we've got their strike and premium, and we've got some puts for 3M. Again, we've got their strike and premium. Which option should the trader buy or sell given the information above? Well, if the trader is convinced that the price is going to be somewhere between $46 and $54, then we want to try and make money from people who think it will be above that or below that. So if someone else thinks, oh, I think the price will go to 55, 56, 57, we want to get them to give us money. So they're going to want to buy a call at $54. If the price went to 55, then they could buy at 54, sell at 55, and make lots of money. So the call we're going to go for here is the 54 strike call with a premium of 1.30.

But what if someone else thinks the price will go below 46? Again, we want to try and make money from their belief, even though we think they're wrong. So we're going to sell a put with a strike of 46 and a premium of 1.15.

So we're going to put those two together.

The trader can set up a short strangled position selling $54 strike calls and selling $46. strike puts. Onto question two, it says, draw the combined profit and loss or p and l profile of this trade. What is the maximum profit? What is the maximum loss of this trade? And we'll see it appear in this chart on the right hand side.

Well, let's start with our short call P&L at a very low price of 40 or anything of $54 and below we will make money, which is great. We'll only lose money if the price goes above 54. So at any price of 54 or below, what are we going to be earning? We will earn the premium from selling that 54 strike call. So I'm linking up to cell C14.

I'm going to lock onto that. That's our initial premium. Great, but what if the price did go up? What if the price went up to 60? Oh dear. We'd make a loss then because the other party would get to buy from us at a fixed price of 54. Where would we get the stock at 60? Oh dear. We'd make a loss between the 60 and the 54.

So how are we going to put this together? Well, I'm going to say we're going to make a loss of $54 minus. If we were down at the $60, it would be the 60 and we'd make a loss of $6 there. In this row, I'm going to link to the 40. Now that's a bit strange because we're not going to make a loss at this price. The other party is not going to exercise their option. We're not going to make any loss in this situation. So I need to put a little min function around this. The moment this is coming up with 54 minus 40 coming up with a positive 14, we're not going to make any profit here. We're not going to make any loss here. So I want to put the min function and zero.

It'll become more clear when I copy this down. So at low prices, like $40, we just earned the premium and watch at all of these low prices. We just earned the premium, but as I drag this down and copy it down to the cells below, we notice that at the higher prices we start to make a loss. So let's just work it out again. My min function here is creating a loss for me of 54 minus the 60. Oh dear. We make a loss of $6 there. Oh, but hang on. We earned $1.30 from the premium, giving us a net loss of 4.70.

Okay, what about the short puts? Well, with the short puts, again, we sold these and we're earning a premium. The premium we're earning is that $1.15. I'm going to lock onto that, but again, we might make some losses here. With the short put, we make losses. If the price goes below $46, we think it won't happen. But if it does go below that, maybe it's a 40. Oh dear. We would make a loss of the $40 and the 46, the $6 in between.

So to put this into my formula, I'm going to add on open B23 minus the 46. So there's my $6 loss.

However, I'll only make that loss if the prices below 46. If the prices above 46, I won't make any profits. So I need to make sure this only gives us a figure if it comes out as negative. So again, I'll put a min function in front of it, min of everything inside there and zero Only a negative number can come out of this now. So let's check that that works. I press enter. Great. We made a loss, unfortunately of the $6 here. So the difference between the $40 and 46, but we earned a premium of a $1.15. They net out to $4.85 loss. Let's copy that down.

And we see at any price above $46, we're just earning the premium, earning the premium, earning the premium.

So if I now combine these two together, I'm going to take the short call P&L, add the short put P&L, and then copy that down.

I can now work out what's my maximum profit. Well, my maximum profit is when we are in the middle of the range that we think the stock price is going to stay between. It's going to stay between 46 and 54. Our maximum profit here is 2.45, and that's the two premiums added together.

2.45 the total premium income. If both options expire worthless. What's our maximum loss? Well, if the price goes down below $46 down to 40, we start to make losses.

The maximum loss we would make there would be an asset price of zero.

However, if the price goes above 54, in this example up to 60, we start making losses, but that price could go up to an infinite level, so our losses could be infinites. So our maximum loss infinites, a short call has infinite loss potential.

Lastly then, what are the advantages and considerations of this strategy compared to a short straddle? Well, in comparison to a short straddle position, a larger price range can be tolerated before a loss occurs. In our example, we were able to tolerate a price range from $46 up to 54. However, in exchange for that, a lower initial premium is generated.

The combined column, we can see that in the payoff diagram on the right hand side here, that's being shown by the gray line on the charts. It combines the blue short called P&L and the orange short put P&L. And we can see that we make a profits definitely between the 46 and the 54 and smaller profits up to 55 and down to 45.