Tag Archives | delta

Probability of Profit

Hi Mark,

I would like to know how to correctly calculate (and use) the “probability of profit” tool…

Everywhere I look amongst the options sellers I read about it, and, behind the obvious, I think it may be an useful tool, but only if correctly understood (and used).

Do you calculate it by yourself? Do you trust any site in particular?

Thanks, as always


Hi Roberto,

‘Probability of profit’ is not something I calculate.  Too many variables are involved (see below).

However, these items can be calculated

a) Probability that an option will finish in the money (i.e., be ITM) at expiration

b) Probability that any underlying asset will move to touch the strike price (i.e., the option becomes ATM or ITM) of any of your short options at any time during its lifetime, even when it does not ‘finish’ ITM

c) Probability that an underlying will move to touch any specific price (presumably your target exit price) at any time during the lifetime of the option.  And you can set the ‘expiration’ date of the option to coincide with your planned exit date – for traders who prefer not to hold through expiration.

We cannot determine probability of profit because certain events may occur and each of them affects the final outcome: profit or loss.  For example, you may make an adjustment or exit quickly with a small profit.

There is no way to determine WHEN the underlying may reach the point at which you plan to exit.  You can determine the probability of reaching that price, but the time elapsed before that occurs determines whether you earned a profit [If you exit when the option is still OTM for example, you could have a profit if enough time has elapsed]

There is no way to know the implied volatility of the options at whatever future time you would choose to exit.  If you close the position on at unknown date and when options are trading with an unknown implied volatility, there is no way to know if the position will be profitable.

No. I do NOT calculate this myself.  Some brokers offer the tool that calculates ‘the probability of touching.’  I prefer to use, and trust, the free software made available by Peter Hoadley.

To make it work, set the strike price (or any other stock price of interest) and expiration day (or any other date.  If you plan to exit early, there is no reason to use the option expiration date.  Use your planned exit).  Select a volatility for the calculations, with your best bet being the current IV of the specific option that concerns you.

The calculator output gives the probability of touching at some point.  It does not give probability of profit.  Note:  Even when option finishes ITM, it may be a profitable trade – if it is ITM by a small amount.


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Adjusting a position: Using the underlying


I have maybe a naive question. Is it possible to make adjustments to already open positions, that might be 'in danger' of losing money, using stocks (or indexes if applicable) instead of options?

From "The Rookie's Guide to Options" I know that it is possible to create 'synthetic' positions and sometimes it makes sense to trade them.

One example: A put spread where short side is ATM (or very little out), probably too late, but at this point the put should be bought back.  Instead one might short the stock and buy a call to protect from a big upside move.

Could you please explain what are pros and cons of such adjustments.



Good question.  Let me reply by making some points

1) Yes, you can use stocks or futures or any underlying asset for adjustments.  Remember that these adjustments provide only delta (positive or negative), and do not reduce gamma, vega, or theta risk

2) Any trade that reduces risk and leaves the trader feeling comfortable with the adjusted position – is a satisfactory adjustment.  That is one of the goals of risk management.

3) Buying or selling shares is a very appealing adjustment method, but in my opinion, it's a poor idea.  Many traders use stock as their adjustment of choice, believing that 'fixing' delta is all that is needed to make a satisfactory adjustment.

Think about why the position is in trouble in the first place.  The ATM put contributes significant negative gamma to the position.  Buying, or in your example, selling, stock does nothing to reduce that gamma risk.  It does take the immediate delta risk out of play.  And that's good enough for some traders.

The advantage of using stock is that the trader doesn't have to pay for any gamma and does not have to sacrifice any theta (time decay).  After all, thinks the trader, I'm in this position to collect theta, so why would I want to make a trade that cuts my positive theta?

Answer: Because buying gamma comes with negative theta. And reducing both delta and gamma is going to make the position safer than only reducing delta.  If you – an individual decision – are comfortable with maintaining the negative gamma position, then by all means – adjust with stock.  However, I feel more comfortable reducing delta and gamma risk, rather than delta only.  There's no right or wrong here.  It's a personal choice.

There is also risk of getting whipsawed.  Although that possibility exists with any adjustment, it is especially painful when the adjustment was made with stock becasue it results in a buy high, sell low scenario.

My recommendation is that it's okay to adjust with stock when you cannot figure out what else to do – but the adjustment should be temporary.  As soon as you have the chance to unload the stock position and replace it with a positive gamma trade, that will give you a better position.  'Better' from the perspective of less risk in the future.

4) Consider your example.  You are long delta because of a short put spread.  Apparently you don't want to buy any puts, but you are considering selling stock short and buying calls to protect the upside.

Ask yourself: Why don't you want to buy puts?  Is it that if you buy the put you sold earlier that you would be locking in a loss?  Is it that puts seem to be too costly?  Is it that you hate paying the time decay present in the puts?  Is it that it feels more 'professional' to make an adjustment, rather than closing the position?

None of those is reasonable.

When you short stock and buy calls to protect the upside, you are buying synthetic puts.  Stock plus a call is the same as owing a put at the same strike as the call.  If you make the suggested trade, you are complicating a position (and raising margin requirements) for no good reason.  Buying the synthetic put is the same as buying the 'real put' – and if determined to make the stock plus call play, then I strongly recommend buying the appropriate put instead.

To answer, I cannot think of a single 'pro' for making that play , only 'cons'- unless the prices of the options are so far out of line that buying stock plus puts is a lot cheaper than buying the call (do not forget that it costs money to own stock).  The 'cons' have it.

Robert – just because you can trade a synthetic (or equivalent) position, it does not follow that it's always a good idea.  Here, buying protection in the form of puts makes the most sense (unless exiting makes you feel better).  As an aside:  DO NOT refuse to exit this trade to avoid locking in a loss.  If this position no longer feels right to hold, then please don't hold it.  On the other hand, if you like the adjusted trade and want it as part of your portfolio, then adjusting is the better choice.


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Elementary Questions on the Greeks

Don has some questions regarding delta and gamma that are worth posting (edited for brevity, when possible). 

If you understand the principles, then using the Greeks becomes far less frightening. 

The Greeks serve one purpose.  They allow a trader to measure risk.  That's it.  They do no more than that.  If the risk is within your boundaries, you can be comfortable with the trade.  If not, you can easily change any specific risk factor.  That's the beauty of using options.  Risk is readily measured and controlled. You cannot do that with stock, currencies, commodities etc.  Options are special.


Hi Mark,

You often mention the effect of Gamma on front
month trading. Are there strategies that use Gamma advantageously for
the trader? 


Advantageously?  Are you saying that + gamma is advantageous and negative gamma is not?  If you want positive gamma, you must PAY for it.  It is not free. If you want gamma, there are strategies to suit: long options, buy straddles, back spreads etc.

You freely choose iron condors (and others) that benefit from positive time decay.  Negative gamma is part of the package. 

Time decay of options is not linear, and graphs show that the last six weeks prior to
expiry has the most dramatic theta effect. Would you explain the positive
and negatives of this trade and have you ever considered trading IC's
in this time frame? 

1) That is not anywhere close to having the 'most dramatic theta effect.'  Any position with less time is even more dramatic. 

The 'most' dramatic theta effect occurs when your option is exactly ATM, it is one minute prior to the closing bell on the 3rd Friday, and news is pending within the next 10 seconds.

2) The positives and negatives of this trade are exactly the same as ANY OTHER iron condor trade.  More time = higher premium, less theta, and less negative gamma. It's always a compromise.  Choose the combination of pluses and minuses that suit you.  Don't let anyone tell you that there is a 'best' time frame for you.

3) I consider trading iron condors in ANY time frame.  For me, front-month trades almost never survive the first elimination round.

Buying LEAPS and selling calls against them: Let's say that an option
trader believes that a stock will rally in less
than 24 months.

If a trader continued to sell options against LEAPS [MDW: assuming the shorts conveniently expire worthless], by the time the long option approached expiry, that could pay for the call and he/she would still own the Jan 15 calls – an ITM option.

Yes,the stock may go below 15, with the LEAPS losing value – but are there other negatives to this strategy? 

Don, I have discussed the idea of using LEAPS in 'covered call' and collar strategies a bunch of times.

Bottom line: Yes, there's big risk.  A big market move or a big decline in implied volatility demolishes this strategy.  See those, and other, posts for explanations.

PUT: if a trader were bearish on a stock, how would the LEAPS work with
Puts? Buy the ITM Put and sell OTM puts against it? 

That's one method.

A web site I saw recommended selling calls and puts on a stock
you like – at the same time. I get worried about this. Anytime you sell,
you have an OBLIGATION rather than a RIGHT and you never know when a
black swan event will hit an individual stock. But I was thinking that
this may be more acceptable on an index, I'd like to hear your opinion.

Who in his/her right mind would sell a naked call on a stock he/she likes?  I assume you already own, or are willing to buy the stock to make this play.  Don, this is merely covered call writing.  The long stock and short call is a covered call.  The naked put is equivalent to a covered call.

Covered call writing has downside risk.  If you don't like the risk, don't make the play.  If you don't want to be obligated to buy shares at the strike, then don't sell puts.

Indexes tend to be less volatile than individual stocks, so yet, this idea is a bit better when using index options.  You would have to buy something to represent the underlying stock.

A follow up on Gamma. Today F is trading at 13.20 and the
Sep 13 Call has a 57 Delta and 22 Gamma (am I correct that like Delta
you simply remove the decimal to factor in Gamma?)  Meaning (to me) that  Delta of the 13 Call will be 77
if it moves up and 35 if it moves down. Is this right? 

The gamma is per share, so multiply by 100 to get gamma per contract. 

Is this right? To a point.  I thought you would know that gamma is not constant and changes as the stock price changes.  Thus, the call delta changes by more than you anticipate (higher gamma at the end of the move than at the start) when the stock rises and by less when it declines (final gamma declines during stock price slide).  But what you have is a reasonable estimate.

If I move out to Dec, gamma is
less. The
reasoning behind this is: as the front month option moves into the money and it is
near expiration, gamma is more pronounced due to the reduction in
time, is this the correct view? 

Yes.  When there is less time, there is less chance that the option will move OTM or ITM.  Thus, delta moves towards 100 or 0 much more quickly.  For delta to change so rapidly, gamma must be higher. 


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Gamma, Vega and Risk Management

When trading options, holding positions with too much gamma – positive or negative – can be dangerous. It's necessary to avoid getting hurt by the two most destructive emotions for traders: fear and greed.

On Monday, Jun 28, 2010 the markets fell hard.  That 1040 SPX price level – that many believe is a vital support area – was tested.  Option prices rose sharply as is seen in the performance of VIX and RVX.

Tuesday (as I write this) the markets are slightly higher and option prices are once more coming down to earth.  I had better rephrase that.  Option prices and implied volatility are decreasing, giving up a significant portion of yesterday's gains.  In my opinion, prices are still high.  ADDENDUM: By the end of the day, the markets closed lower.  SPX broke down by trading below 1030.

When IV moves sharply higher, the trader who is not vega neutral, and that includes most of us, must demonstrate the ability to handle and manage risk.  If you are a clear thinker and make good trading decisions, your portfolio is probably in good shape.  The same can be said for most traders who prepared a trading plan in advance.  That plan is designed to save any trader (and especially the inexperienced) from panicking in a stressful situation.

Positive gamma and vega

As the markets get more volatile, and especially as markets decline, traders who own positive gamma and positive vega are well positioned to profit.  Nevertheless, that trader cannot afford to idly watch the markets as the days pass and theta takes its toll. 

Positive gamma is a delight in that it allows the trader to pick the time and place for making an adjustment.  This adjustment locks in profits and can include the sale of some options to reduce both gamma and vega, or it can be made in the form of shares of the underlying (stock or futures contracts).  It's tempting to hold the position, but a minor reversal, such as seen Tuesday morning threatens much of the profits.  Greed makes the trader hold out for larger gains.  Fear makes the trader panic and sell (what is probably) an inappropriate portion of the position.

However, a well-thought out plan, or sound risk management, allows the trader to reduce risk by moving closer to neutral in gamma, vega, and delta.  Ignoring greed, the successful trader adjusts the position – retaining some vega and gamma.

Negative gamma and vega

Iron condor traders seldom find themselves in the positive gamma/vega boat.  The only exception occurs when extra options are owned as insurance, and these extra options are in play (not too far away from being ATM).

Thus, they (we) may be floundering when the positive gamma group is sailing along smoothly in those choppy waters.

If your positions have too much negative gamma, if your short options are not too far OTM, then it's time (or past time for many conservative traders) to adjust the position.  Panicking in a sudden meltdown is unlike to produce good results.  However, ignoring problems, hoping they will disappear, represents a different type of panic decision – being too afraid to act.

If you have a trade plan in place, it's probably right to take the action as prescribed in the plan.  Lacking a plan, it's not too late to create one now.  If you are capable of making sound decisions as losses mount, then good for you.  Take advantage of that skill by taking sound steps to protect your assets.  Be aware of potential loss, your pain threshold and comfort zone boundaries.

If you lock in a loss and the market reverses, so be it.  Your goal is to pay attention to rule #1: Don't go broke.

If you are not yet in trouble on this decline, you have the luxury to plan ahead.  I'm planning to sell extra vega by doing a ratio roll down* for some RUT Aug and/or September put spreads.

* Close current short put spread and sell a larger quantity – perhaps 3 for every 2 bought – of farther OTM put spreads.  I prefer to move the strike of the short option by at least 3 strikes.  Collect a small cash credit for the trade.  I only do this when my portfolio is not already at its maximum size.  Make no mistake about this trade: it does increase ultimate risk.  it looks good because the probability of the large loss is reduced.

Example buy two 560/550 put spreads and sell three 500/510 (or perhaps 510/520) put spreads.


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How Much do I Lose on a 5% Market Decline?

Here's a very simple question from a reader.  And to be honest it's an excellent question and it's something I have never specifically addressed.  I've told readers to do it, but without details.


Just read your post and would like your help on how to most accurately determine how much a portfolio will lose from say a 5% fall?

Underlying:  RUT. 

Here are the Greeks: -50 delta, -5 gamma, +300 Theta, -800 vega.
Thanks for your help,



That's a lot of vega!  You did not supply enough information, so I'll make assumptions.  I need the current IV (so we can estimate the new IV, post decline).  I'll use RVX, which is near 35.

Most accurately?  That's a tough one.  You must have a very good estimate of how much IV is going to increase, especially when your vega risk is substantial.  That is difficult all by itself.

A) I would use software – hopefully provided by your broker – that plots positions on a graph.  Look at the position with RUT down 32 points to 614.  Then increase IV by ?? Try 10 and 20% as guesses. Change the date to one day later.

If such software is unavailable to you – consider opening an account at TOS.  No need to fund it.  That should allow you to use their excellent software.

B) Lacking good software, then your next best answer is to break down your position into it's individual option components.  I understand that you may have so many different option series that this is going to be too time consuming.  However, if you own just one or two different positions, then it's probably worth the time to do it.  Find an options calculator.

For each single option in your portfolio, determine the option's value at today's price and tomorrow's price.  For tomorrow's price, use the 5% decline number and once again make a guess as to the future IV.  There is no way around that.  We don't know of there will be panic or relative calm in the marketplace.

Multiply each option by the quantity in your portfolio and determine how much is lost.  It's a good idea to record the new Greeks to help make a similar estimate in the future.  By that I mean it's good to know how gamma, vega change and theta change.

C) If you are willing to accept a less accurate method, then we have to do a 'quick and dirty' calculation – and that's the basis for this post.

1) Gamma.  We don't know the rate at which gamma changes, so let's guess. Gamma is now -5 and will be -10 after the 5% decline.  I admit this is just a guess.  Thus, we have a 32 point decline with an average gamma of -7.5.

2) Delta is -50 and will (negatively) increase by 32 * 7.5.  New delta: -290.

Average delta over the decline: -170 (avg 50 and 290).

32 * 170 = $5,440.   This is the loss from delta

3) Theta.  You get your $300, but theta is almost certain to be higher tomorrow.

4) Vega.  Assuming vega remains near 800, and assuming that IV increases by 10%.  That's an increase of 3.5 points or a loss of 3.5 * 800 = $2,800

Simon, please remember that each of these Greeks is changing.  Just as gamma changes delta, so to do gamma and vega and theta change as the underlying price changes.  Thus,these are merely good guesses.  They work as a ballpark figure.  they allow you to decide whether this risk is too large for you to accept.

Here's where it gets tricky. 

a) The problem is that if panic were to set in, then IV could double to 70.  If that happened, the estimated loss – just from vega alone – would be $800 * 35, or $28,000.  If you were to incur that loss – and if you did not have an margin call and were allowed to continue to hold the position – the question is would you do so.

NOTE: If using Reg T margin and if your positions are protected (i.e., no naked short options), then you will not get a margin call.

b) There is a limit to possible losses.  If you own (for example) 20 iron condors, then it's impossible for the loss to exceed $20,000 minus today's position value.  And I'm sure you understand it would never get that high. 

If the markets were very wide, then your position could get 'strange' closing marks, but I do not believe it's possible for your account to be placed in jeopardy.  But this is a question for your broker, not for me. [What happens if my 10-point iron condor is market a 15 points?  Could I be forced to liquidate?]

Markets can be very wide, but when options are being quoted, the is every reason to believe that it will be impossible to collect >$10 for a 10-point iron condor and I assume that means your end-of-day marks must be in the rational range.  Thus, I assume liquidation is something we can all safely ignore.  But, it is an assumption.

c) If the market does drop that far and if IV does rise that much, I cannot imagine that your loss to vega could be that high.  It fact, at that level, your portfolio could easily be short far less vega.  In fact, when your LONG options are closer to being ATM that the shorts, you will be positive vega.  So the vega estimate is fraught with potential inaccuracies.  That's why the risk graph works so much better than anything else – for your needs.


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