I understand the combinations of calls/puts/underlying. The charts are straightforward. I’m also fine with the corresponsing profit function as it could be derived from the positions.
HOWEVER, I have no idea how to derive the max profit, max loss, and breakeven equations. Schweser doesn’t explain how they are derived (or is it even possible?).
One option is to memorize but I’d rather learn them. What’s your strategy?
You should use this strategy when you expect a stock to go up, so it makes sense that you start by buying a call.
If you were purely bullish, you would stop there, but a Bull Spread strategy involves selling a call with a higher strike price
By the way, we’ll call these positions low X and high X.
So your starting point is net negative because you paid more for the low X call then you received for the high X call, which means that the underlying has to move that far above the low X price in order for you to break even.
Now we get to the “Spread” part - and this is important.
If the underlying tanks, goes to $0, both call options are worthless and you end up at the same place you started - a loss of the difference between what you paid for the low X premium and what you received for the high X premium.
That would be your worst possible result, you can’t lose more than your net premiums paid at the outset.
If the underlying goes way up, you receive a huge payoff on your long call position, but you make a huge payout on your short call position.
The most money that you can make on this strategy is the SPREAD between the high X price and the low X price, but you adjust for your net negative starting point after buying and selling the calls.
The net effect of this strategy (see below) is that you are not obligated to buy the underlying if the price tanks, but you give away any upside if the stock price moves above the higher strike price (in exchange for a partial offset of the premium that you paid for your low X call).
Now, to bear spread, you dont have all day, so i’ll be quicker:
You’re in luck because it is just the mirror image of the Bull Spread strategy.
You use it when you expect the price of the underlying to go down.
Start by buying a put, then selling a lower X put, which leaves you in a net negative cash position at the outset (this is the only way these strategies are the same).
Therefore, the price of the underlying has to below the strike price by the amount of the cash hole that you put yourself in at the starting point before you break even.
If the underlying goes way up, both options are useless and you’re only out by the amount of your original cash hole.
If the underlying goes way down, you can only make the SPREAD between the high X put that your bought and the low X put that you sold, but you have to adjust for the amount of your original cash hole.
By selling the low X put, you gave any any “upside” from the underlying dropping below the low X price
What about the Butterfly Spread strategy?
Use this when you expect the price of the underlying to remain at its current level.
It is built buy establishing TWO long positions - one high, one low - and selling TWO call positions at the current price of the underlying (and, for exam purposes, assume that this also the halfway point between the strike prices on your two long call positions).
You start out with a net positive cash position because you received more in premiums for the calls that you sold than you paid in premiums for the calls that you purchased. This is also your maximum profit - you can only go down.
If the price of the underlying moves EITHER up or down by the amount of your net positive cash position, you break even.
If the price moves further, you start looking money, but your downside is protected if the price of the underlying finishes above the highest strike price or below the lowest strike price.
Your maximum loss is limited to the difference between the midpoint and either the high or low strike prices, but adjusted for your net positive cash starting point.
The payoff diagram for a Zero-cost collar looks a lot like a Bull Spread.
Be careful, because the payoff diagram looks similar, but it is NOT the same.
In this case we also own the underlying, so we are buying options with that position in mind.
Specifically, we buy (long) a put, which is a simple insurance policy against a drop in the price of the underlying.
We then offset this premium by selling a call with the EXACT same premium as what we paid for our long put position.
Because these premiums offset each other, our starting point is “zero-cost”.
Note that you’ve already broken even on your options position.
Because you own the underlying, your payoff is calculated in reference to its price at the starting point.
If the price of the underlying goes way up, you make the difference between the starting price of the underlying and the high X,
If the price of the underlying goes way down, your loss is the difference between the starting price of the underlying and the low X.
Thanks Rogue Trader. However, I am looking for something more specific and mathematical.
As I mentioned, the purpose and combinations of calls/puts/underlying to create the option strategy are understandable. For example, it’s easy to derive the profit function for a protective put.
long put
long stock
profit = max (0, X-ST) - P0 + ST - S0
We can do the same approach with any combination because the profit function is a summation of every component of the option strategy.
However, I am struggling to come up with the max profit, max loss, and breakeven functions by doing it mathematically.
My concern is that if the exam asks, just like in the BB, “what is the max loss equation for XXX option strategy?”. I don’t know if a graph, or a short answer paragraph would suffice.
A bull or bear spread can never be worth more than the strikes between them, so a 10 pt spread can only be worth a max of $10 ever (so a 30-40 call spread or a 25-35 put spread). They can also never be worth less than zero.
A butterfly can never be worth more than the strike width. So a 35-40-45 fly can never be worth more than $5.00. They can also never be worth less than zero.
A box is worth the distance between strikes at expiration, so a 500 point box (say 1200-1700 box) will epxire to $500. If today it can be bought for $991.50 then the difference is the implicit interest rate like a zero-coupon bond given its time to expiration
A straddle has breakevens at the strike price +/- premium paid.
I think you’re wasting your time by trying to know each and every payoff formula, especially this lateam iN the game. If you understand the payoff charts for each strategy, as long as you have to strike prices and option premiums you can figure out everything you need to know For the exam.