# Options Formula - Call Ratio Backspread ???



## rapidex (18 July 2007)

I'm just running through some examples of *Call Ratio Backspreads* (learning how to do them is probably more accurate):

I'm having issues with what formula/equations to use. I have found 2 formula for *Max Risk* and *Lower Breakeven* but the answers aren't equal ??

Can anyone see what I'm doing wrong - Thanks.

Heres what I have:
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MER trading @ $86.20 (live example from 18th July)

Buy 3 MER Jan $95 Calls @ $3.80
Sell 2 MER Dec $75 Call @ $14.90

Net Credit = (Short Premiums – Long Premiums) x 100 = ($14.90 x 2 – $3.80 x 3) x 100 = $1840

Max Risk: (2 formulae for this)
(1) = (Difference in strikes x 100) – Net Credit = ($20 x 100) - $1840 = *$160* *???*
(2) = [(# Short Calls x Diff. in Strikes) – Net Credit) x 100 = [(2 x $20) – $18.40)] x 100 = *$1270* *???*

Max Reward = Unlimited to the upside beyond breakeven

Breakeven Upper: (2 formulae for this)
(1) = (# Short Calls x Diff. in strikes) + Higher Strike – Net Credit = (2 x $20) + $95 – $18.40 = $116.60
(2) = Higher Strike + [(Diff. in strikes x # Short Calls) / (# Long Calls - # Short Calls)] – Net Credit = $95 + [($20 x 2) / (3 - 2)] – $18.40 = $116.60

Breakeven Lower: (2 formulae for this)
(1) = (Net Credit / # Short Calls) + Lower Strike = ($18.40 / 2) + $75 = *$84.20* *???*
(2) = Lower Strike + Net Credit = $75 + $18.40 = *$93.40* *???*
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## wayneL (18 July 2007)

rapidex said:


> I'm just running through some examples of *Call Ratio Backspreads* (learning how to do them is probably more accurate):
> 
> I'm having issues with what formula/equations to use. I have found 2 formula for *Max Risk* and *Lower Breakeven* but the answers aren't equal ??
> 
> ...



It's not a call ratio backspread. It's a *calenderized* call ratio backspread. This will mess up your calcs big time. Yo can only use set equations if all options expire together

In fact, you can't calculate precise figures because you don't know the IV of the Jan call at Dec expiry. You can only make projections (read: guesses), but a strategy modeler such as Hoadley's will be a big help.

Here is a payoff diagram, presuming IV stays constant


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## Magdoran (19 July 2007)

wayneL said:


> It's not a call ratio backspread. It's a *calenderized* call ratio backspread. This will mess up your calcs big time. Yo can only use set equations if all options expire together
> 
> In fact, you can't calculate precise figures because you don't know the IV of the Jan call at Dec expiry. You can only make projections (read: guesses), but a strategy modeler such as Hoadley's will be a big help.
> 
> Here is a payoff diagram, presuming IV stays constant



Absolutely right Wayne!  Fully agree...



Hello rapidex, 


You are doing a diagonal version of a ratio back spread as Wayne points out (or “Calendarised” if you prefer).  

I thought I’d illustrate how this can be used in practice as food for thought, so that you aren’t just looking at the theoretical side, but start to see how you can trade these, and the conditions you are looking for, and the types of situations you may consider deploying one strategy or another…  Just beware though, I’d advise paper trading these for a LONG time before doing this for real.

These are great in specific conditions, but you really need to be highly experienced to use these effectively, knowing when to use them, and when they are attractive to use in terms of taking in premium - aiming for high volatility on the SOLD leg.

The rules I use for these is determined by what I think the underlying is likely to do.  Personally, I use this as a morphing strategy to either hedge or profit from swing trading around a core position which is aligned with the main trend in the time frame I am trading, and has a reasonable amount of time value in the main position.

If long, the idea is to sell a ratio of contracts deeper on the money with less time to expiry to the core position (which is usually out of the money or near the money while the underlying moves up with the idea these will go into the money much later).  

The objective is to buy the sold contracts back where and when the bearish counter trend to the bullish trend (in this case, or the reverse if trading a bearish trend) is likely to reverse in order to resume the net long position.  This is essentially a combined profit taking exercise and hedging exercise, but can also be viewed as a short term counter trend trade, trading the opposite direction to the main trend.

I tend to sell enough time in the sold contracts to ensure I can wind out the position BEFORE expiry since the real risk in these positions is the underlying ending in the money for the sold position while the bought position is still out of the money (not really a problem if you have more time in the bought position, but something to be aware of – work through various pay off diagrams to see what the combined position will do as different attributes change).

Hence even though it looks a bit like a kind of “mutant calendar” spread, I don’t treat it this way since I seldom aim for the sold position to expire worthless, I just look to capture the value in the counter trend as a directional play and hedge while there is still around 12-15 days left to expiry in the SOLD leg (the bought position should have more time value in a diagonal scenario).

If you can calculate it correctly, and time it right, the move can hedge your position since if selling when the underlying has been trending in your direction, then even if the underlying falls significantly, the position overall should have a profit locked in (providing the move down is significant enough), and still has unlimited reward to the upside.

The danger is that the underlying trades sideways, where the OTM/ATM bought position expires worthless if you held it to expiry.  

Hence the rule is to wind out the sold position before say 12-15 days to expiry, and wind out the bought position if still OTM or ATM around 30 days to expiry (exceptions do exist but are involved – but one for instance is when the bought position is under 30 days to expiry (after the sold position had been wound out long before), to exit a portion of the bought position if deeply ITM if expecting further movement in your direction, and riding the other portion until the trend is at risk even right down to expiry if the underlying is accelerating deeper ITM – perhaps exiting portions on the way up if inclined aiming not to overstay the trade – this is in a blow off scenario having entered at a basing or consolidation phase preferably with low volatility and OTM at eth time of entry looking for an ITM exit).

Entering this kind of position requires a lot of options knowledge – especially in volatility, delta and theta decay.  You are aiming to trade the counter trend on one level, and lock in profit by hedging on the other in case of a strong reversal.  This is usually in a strongly trending volatile underlying, hence the selling of volatility at or near the top of a leg of a strong trend should yield significant premium, but still leaves a net long position with unlimited reward to the upside because of the ratio effect (you need to understand how to do this), and locked in profit if the underlying moves sharply against the core position.  The main weakness is if the underlying trades sideways, but if exiting according to a plan via time, this weakness can be ameliorated and managed.

Try studying the shape of a ratio back spread using strikes with the same expiry date as suggested by Wayne.  In order to see these better, discount the volatility for the bought leg and inflate the volatility for the sold leg (this is what you aim to do if entering a conventional back spread opening both sides at the same time – you’re looking for a significant skew in your favour).

Hope that is of interest!


Regards


Magdoran

P.S. This is just my style, and the way I use these... of course there are many alternative uses – examples are where you may sell for premium in a diagonal ratio back spread in order to take in premium in long slow counter trends...  Mag


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## rapidex (19 July 2007)

Damn  sorry, the expiration dates are supposed to be the same.

Here's what the options should have read in my original post:

---------------------------------------------
Buy 3 MER *Jan* $95 Calls @ $3.80
Sell 2 MER *Jan* $75 Call @ $14.90
----------------------------------------------

So it's meant to be a vertical spread (not a horizontal or calendar spread).

So taking that into account, I should be able to use an equation, right? if so, why aren't mine working.

Sorry for the confusion.

I'll read through your responses and learn from them anyway, but if you could respond taking the above correction into account it would be greatly appreciated.

Thanks.


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## Magdoran (19 July 2007)

rapidex said:


> Damn  sorry, the expiration dates are supposed to be the same.
> 
> Here's what the options should have read in my original post:
> 
> ...



Hello rapidex,


Your maximum loss AT EXPIRY should you hold till then would be if MER (US Market) closed on $95 for the scenario you outlined would be $2160 ($4000 - $1840).

The 2 sold calls are (US options are 100 shares per contract) worth $20 per share ($75 calls with the underlying at $95), hence 200 shares times $20 = $4000.  This is the maximum loss for the sold component.

You entered the position with a credit of $1840.

Subtract the credit ($1840) from the loss ($4000), and the theoretical maximum loss at expiry is $2160.


Now, why are you trying to work out the break evens?  The Maximum loss is at the tip of the “V”, while the theoretical break evens (AT EXPIRY) are above and below this in price.  They are different things – have a look at the attached graph.

Have a read of my comments below, and I’ll explain why what you are doing (while admirable as a learning exercise) is not going to help you in the actual execution of this kind of spread (which I love, but you have to know how to use these in practice, and WHEN – and in what situation).

Also, I just looked at your original post more closely – the original version had the sold call with the longer time to expiry – an altogether different animal!  (Not possible I think with most brokers, and not advisable).


*Rapidex – READ THIS PART!!!*

Trying to work this out at expiry while helpful in a theoretical sense is actually a waste of time in practice because you’re looking at the wrong end of the trade – you’re looking at what it would look like at expiry, something some brokers tend to look at to determine margin (erroneously in my view).  Certainly you need to know the maximum risk, but a good options program should automatically tell you this.

In my view your trading rules should have you exiting this kind of spread well and truly before expiry would allow this kind of significant loss to occur.  Hence only experienced players should get involved with this kind of spread and have developed risk mitigating rules to avoid the worst case scenario.

What you should be looking at very closely is the positive and negative effect of VOLATILITY (BIG HINT) which is if you know what you’re doing going to be a major threat to this kind of position, and being able to simulate the effect of volatility crush or rush is critical since even if the underlying moves in the way you think it will, volatility can turn a theoretical winner into a market loser.  Watch out! (Incidentally, theoretical losers can actually do ok in volatility rush scenarios, but you need to work through this via trial and error).

Since you are likely to exit well before expiry (at least I’d hope so), you need to work out the time value component and the volatility component, and to some extent the effect of theta decay.  The strikes you choose, the ratio you choose, the space between the strikes, and the time to expiry are all going to matter a lot, and of course there is Volatility!  

Each strategy will have unique characteristics, and it is your job to work out the best strategy based on an assessment of the probabilities in part based on straight risk to reward, but also on your assessment of how volatility and price action will play out, and when.

See the chart below which has different lines running through it based on different times (see the small analysis table with legend) and this is assuming flat volatility.  Volatility rush and crush can greatly effect the theoretical values even for this, hence you have to work out where MER will be (in price) and WHEN.

The break evens are only relevant to the expiry line, hence in my view potentially misleading unless you intend to sit through to expiry…  

Break evens are fine with vertical spreads you intend to hold through to expiry, but I’d suggest looking at different strategies to do this, straight ratio back spreads are generally either for very aggressive directional plays, or in some cases for highly volatile markets where a large move is expected in a direction, but an adverse move is possible of great magnitude.  It is the alternative spread of choice for those who prefer back spreads over straddles and strangles, eliminating many of the problems with theta decay, but for a trade off.

In my experience it is rare to find a good ratio back spread to trade straight off the bat in terms of finding enough skew (although it is possible, just unlikely, and you need to be set up to take advantage of these).  

In practice unless you are an expert fully set up to trade these strategies, it is often far better to sell the second leg to lock in profit at a time where the volatility has increased, aiming to buy low volatility, wait, and sell at a point where volatility spikes up later irrespective of the price (although playing the price and counter trends of course can be important depending on how you want to play these, just don’t forget the importance of VOLATILITY).


I hope that answers your question, and I added some food for thought as a measure too...



Kind Regards



Magdoran


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## rapidex (19 July 2007)

Hello Magdoran,

Thanks for the response.

I'm working through the DVD set of the Optionetics course and they use equations at numerous points. That's why I was trying to calculate the values at expiry (even though with a Call Ratio Backspread one of the exit rules is to be out before the last 30 days). I was getting ahead of myself and trying to calculate a 2:3 spread using the equations they use in the DVD and also the equations in a book I have (hence the two different formula which didn't match up). I understand there's not much point to this because (a) you would have a software program like optiongear doing this for you and (b) you should be out before last 30 days (as a general rule - I know there are adjustments).

Also, one of the other reasons I was trying to work this out was to understand the worst case scenario (max risk) both for a profit point of view and a 'required margin' point of view (if that makes sense)

I understand volatility is crucial to trading options, and that often you are actually, you might say, trading entirely with volatility and it's effect on said options.

I've a while to go yet to understanding options, but things are starting to click and it feels good.

Thanks again, it's onto Put Ratio Backspreads tonight for me


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