Low-volatility strategies in option trading (Butterfly and Condor) (Excel) transcript

hello everyone and welcome again to nettle the best platform around for distance learning in business finance economics and much much more my name is saba and today we're finishing our journey through the realm of option trading strategies with the final bit low volatility strategies in the last three videos we discussed what to do if you believe that the stock prices will go up if the stock prices will go down by a lot by a little and in the most recent video we also discussed high volatility strategies that are neutral interaction what should you do if you are sure that the stock price will change a lot but you are unsure about the direction but that doesn't cover all potential sets of beliefs that an investor might have about future stock price movements and an investor might believe that the stock price would not change much over the course of the investment period that it will remain stable and that is characteristic of some of the more well-established companies value stocks blue chips and one of the most famous examples of such a company is caterpillar that's an industrial company that's listed on the New York Stock Exchange that is a constituent of Dow Jones Industrial Average and this company is actually sometimes used by the analysts as an indicator of forward-looking economic performance whether there's going to be a recession or not this stock is believed to be extremely defensive and believed to be extremely rigid and respond a little to overall stock market movements so that stock would be perhaps the best example to discuss a low volatility strategy well if you imagine the payoffs of straddles and strangles that we discussed in the last video you might think well if we logged a call and the both at the same strike price in case of a straddle and we had infinite upside when the prices went extremely up or extremely down and we had fixed downside when the prices stay roughly the same why just short a call and put simultaneously and then grasp some payoff when the prices stay within this narrow range well that would be called a short straddle and that is by all means accessories that can be used but if you think about the payoff of a straddle you have infinite upsides and details so on the extreme positive movements of the stock price and extreme negative movements of the stock price so by analogy if you have a short straddle so you convert that type of a payoff chart to that type of a pair of chart you would have infinite downside if prices break out of this narrow range determined by the initial strike price and the option premium of the premier of the poles of boots that you shorted but there is a very neat tool a very neat option trading strategy that could allow you to take advantage of this logic of the short straddle but also limit the downside by also learning options that other strike prices so this strategy is called a butterfly the butterfly strategy involves shorting two poles or two boots at the strike price that is as close to the center price as possible so just as it would have been in the case of the short straddle with the only exemption that you short either two calls or to put not a call and a put and then you also long two calls or two put for the strike prices that are in the money out of the money respectively so in case of the butterfly strategy use in calls you would long one call that is in the money so with a strike price that's lower than the center price and one call option that is out of the money with the strike price that's higher than the center price and the share price at the start of the investment period what it would do is that it would limit your downside and for the payoff of the butterfly strategy to be symmetric so that you lose exactly the same fixed amount regardless of whether the share price moves up or down the wings of the butterfly so the distances between the center price the strike price of the call option that you are shorting and each of the strike prices of the call options that you are longing should be exactly the same in our case let's investigate the caterpillar stock and our underlying and as a training period let's consider a very short term trading period starting on the 24th of December 2019 so right before Christmas and with a maturity date of 17th of January 2020 we can see that the start of the investment period the stock price was higher in $47.48 so closer $247 $948 that would dictate the fact that our strike price for the co options that we would short for the center of our butterfly for the body of our butterfly would be 147 so we indeed short to KO options in caterpillar at the strike price of 147 and we receive the option premium for 3.3 telus per share per one call options that we shot and to pick the length of butterfly wings well first of all we have to make them equal again so our payoff our fixed downside does not depend on whether the share prices goes up or down but also this range should reflect our forecast what are the boundaries that we believe the share price would not fluctuate out of we could estimate them using technical analysis for example using lines of support and resistance if you want you could use fundamental valuations some conservative or less conservative fundamental valuations to determine those boundaries or you could just use standard deviations of the returns of the stock in specific time periods to determine this like boundaries the stock price would not breach within your investment horizon so in our case let's assume that the lower bound the strike price of the in the money call that we're longing is hundred forty four and we have to pay five dollars thirty five cents per share for this long haul and our long call out of the money is current $50 per share as a strike price and the premium is 1.9 dollars per share so we can see that the length of one wing of our butterfly is going to be three dollars and the distance from hundred forty four 247 is exactly the same as the distance from hundred fifty 247 so our payoff structure would be symmetric and that's exactly what we need because the butterfly strategy is a low volatility neutral strategy we believe that the stock price would not go in any direction it will stay roughly the same so without further ado let's calculate the net payoffs of all of those options and how could total payoff our butterfly using the calls and quite fitting we are now calculating the butterfly for the caterpillar so very fitting overall for the net payoff of our two calls that were short we need to estimate the gross player first so if the call option is in the money so the share price is lower than the strike price then Co options are not exercised and we are happy because we receive the premium for the options that we've written and we don't have to exercise anyone's right so zero but if the call options both out of the money then our counterparties have the incentive to exercise their options so they have the incentive to exercise the right to buy caterpillar from massacring 47 so we in turn have to buy it at the market for a higher price and sell it to them 147 so we receive hundred forty-seven and we pay the market price which is by definition higher and because we have shorted to calls for caterpillar we need to multiply the gross pay off that we receive by two and then because that's a short call to move from gross pay of the net pay off we need to add the option premium and again multiply by two because we shorted to call options instead of one and that would give us the payoff of two short calls now for the payoff of a long call at those two very strike prices we could implement neat technique that would allow us to just drag the formula around in Excel and would allow us not to input the formula every single time for every single option because well both what calls have exactly the same logic that have various premiere and very strike prices to accommodate for that we need to type in the following if the share price and then we need to lock the column because we would drag it to the right and therefore we don't want the column to change but we're on the road to change for different simulations in different share prices if the share price is lower than the strike price and here we'll just need to block the column because we want the strike price to change as we consider various long calls but we don't want the formula to refer to different cells at the same column because the strike price is the same for one option so again if the call option is in the money then the gross payoff is 0 and when it moves out of the money that's the long call that we are holding so we are the one that exercised in it so we can buy caterpillar 144 and sell it for a higher price on the market so the market price and again we lock the column minus the strike price and here we'll lock the row here we don't need to put multiply by anything but because we just long one call option at this particular strike price and then as that's a long call and we have to buy it so we have to pay the premium we need to subtract the option premium and in case of the option premium would still just need to lock the road not the column because we want the premium to change as we move from option to option and with that logic that logic of Excel formulas allow well allows us to drag this formula both to the right and figure out the payoff of both long calls at various share prices and bottom bracket all the way down to simulate the payoff structure and as we can see if none of the options are access so all the call options are in the money the battery of that we receive is formed only by the combination of option premium we pay and receive and due to market equilibrium reasons the some of the premier of the long call that with long calls that we have to pay should be greater than the sum of the premier for short calls that we have written because if that wasn't the case the butterfly strategy would allow us to obtain riskless profit and that is something that is unsustainable on a real world financial market so without further ado we can just calculate the total payoff of our butterfly strategy by summing up the payoffs of all options that go into our spread our option for them as usual and we can see that if the share price fluctuates out of the narrow range that we've determined by the strike prices of the calls that we long we have a fixed down side instead of the infinite downside that would have been provided by the short straddle the simple short straddle and this fixed downside is relatively small just 65 cents per share and as we are moving up we can see that as we break through the strike price of our in the money call option our payoff starts increasing and it increases until it reaches the maximum at 147 the strike price of the call options that we shorted then symmetrically it starts decreasing until it again hits negative 65 cents per share as it reaches having the $50 per share which is the strike price of our out-of-the-money long call that allows us to design this very symmetrical and bounded from both sides payoff structure that guarantees us limited positive payoff if the prices stay roughly the same and fixed negative downside if the prices fluctuate out of this narrow range that we determined by selecting the initial strike prices if we look at the graphical representation of the butterfly we can see that this is the overall cumulative payoff chart we can see that at the very tip of the graph we are obtaining the maximum payoff 2.35 dollars per share how this payoff is generated what factors into this payoff why the payoff of the butterfly is and it is well if we talk about Co options we already know that no none of the Col options are exercised in the money so when all of the options are in the money when the share price is below hundred forty-four dollars per share then all of the payoff curves are flat so this is the payoff curve for the two short calls that we're ready those are the payoff curves for them two calls that we've logged two calls that we bought so the payoff is determined just by the sum of the premiere positive or negative of those options and due to equilibrium reasons and we can see it clearly from the chart the sum of the payoffs the sum of the premiere that we have to pay should be higher than the sum of the premiere that we receive by shorting the two calls so this is what generates this fixed downside then as we break 340 for the strike price of the very first long call that we've bought we have one pair of curve of the long call creeping up but all other pair of curves still stay flat because we haven't broken through their strike prices so our payoff chart just increases one dollar at a time with one dollar increase in the share price until we reach the strike price of our short calls hundred forty seven as we reach hundred forty seven we will have one long haul payoff creeping up and two long called playoffs creeping down on that we would have one negative short call payoff creeping down so our payoff would one dollar per $1 change in the share price until we get 250 the strike price of our final long call and because we have chosen the wings of our butterfly to be symmetric to be of the same length then is what guarantees that those two points the strike price of Heinz 44 in the stripe 150 lie on the same height they guarantee the same fix downside of 0.65 dollars per share and as we reach 150 we will already have to pay of curves of Rome calls creeping up and too short call scraping down so on that the variability will be eliminated and our payoff chart of the butterfly all the way from hundred 50 and above would be just flat that is what makes the butterfly pay off as it is but we don't really need to use calls to get this butterfly pay off chance we could create exactly the same risk structured payoff structure by using put instead so whenever would have logged or shorted a call in case of the butterfly with calls we could do with boots with exactly the same logic let's proceed with that we need to short to put at the strike price that's equal to this enterprise or as close to the center price as possible and then long to puts that are in the money and out of the money and apply the very same logic of short and long puts and see where it will take us so in case of to short put if the share price is lower than the strike price then our counterparty has the incentive to exercise their short puts they have the incentive to sell the stock of Caterpillar to us at hundred forty seven dollars per share so we have to buy pay that to them and what we can sell it for is just the market price that's lower than the price that we have just paid to our counterparty because we couldn't say no to them so our payoff is the market price minus the strike price so our payoff of the short put would be negative and if the put option moves out the money then we are as their issue as the right of the Chaput we are happy because we've got the premium but didn't have to provide anything in exchange for that so the gross pay off at zero and because we have showed it to puts we just have to multiply by two and as that's a short option strategy we would have to add the option premium of the boot times two and then we can figure out that our net payoff of the two short puts if the share prices go down would be very negative ever increasingly negative potentially infinite because as the share price is going down the payoff of any short put decreases indefinitely what happens in case of hope is for those two strike prices well let again apply the same logic of locked Excel cells to just input the formula once so if the share price and we need to lock the column is lower than the strike price of this long put then we can exercise this long put we can sell caterpillar at hundred forty four haven't bought it from having put it for just the market price on the market and get positive payoff from that and if the put option moves out over the money we can no longer exercise it beneficiaries of zero and as it's a long put we have to subtract the option premium as that's the premium we have paid that we had to provide to our counterparty to guarantee this optionality for us and now what we can do is we can just drag this formula to the right and get the payoff of the second put option as well and also we can bottom right click all of those three net payoff functions to get the payoffs of the acronym side the the a person of the share prices we want to investigate and the total payoff of our butterfly using puts would be just the sum of the three of those three buyers and what we can see here even from the numerical expressions of total payoffs of those two strategies is that the total payoff of the butterfly strategies and calls is always nine cents per share lower than the respective payoff of the butterfly strategies inputs that reflects miss pricings on the option market so if you are considering a butterfly strategy you always have to consider various types of the option strategies that are equivalent in terms of risk structure and player structure but due to the fact that options are not perfectly priced might provide you with relatively better payoffs in that case the payoff of the butterfly strategy using boots is objectively better than the payoff of the same strategy using calls to look at that graphically we can see that the comparison of the two charts is the following this is the payoff of the strategies and calls and this is the payer of the strategy using puts as you can see for every single share price that the share price of caterpillar can take potentially the payoff of the butterfly studies inputs is higher so any rational investor would choose puts instead of course if they are considering the butterfly strategy theoretically what would happen on the market is that it would put additional selling pressure on oops at center prices that would drive the premium down and drive the premium of the butterfly strategies inputs down and it would put additional buying pressure on long puts at the wings so at the strike prices that are equidistant from the body of the butterfly from the center price so that would correct the relative payoffs of the butterfly strategies in calls inputs and that type of arbitrage and market movements would we'll abrade the payoffs of those two strategies eventually but as a single investor you shouldn't care about it too much you should just consider various strategies that deliver the same payoff in terms of the risk structure to you and choose the one that is objectively better if we try to consider how the butterfly strategy using puts arrives at that relatively attractive payoff structure we should consider first what happens when all of the food options are out of the money if all the my out of the money so we are going to the left from the very extremely positive share price movements closer to the center price we can see that none of the put options are exercised out of the money so everything that would contribute to our total payoff of the butterfly strategy would just be the premium the sum of the premium that we pay and receive and again due to equilibrium reasons this sum should be negative and that's why we have this negative payoff this fixed downside if the share prices fluctuates out of the narrow bound that we have determined by the initial strike prices of outputs then as we move beyond hundred 50 to the left we have one of our law puts being already exercisable so our long put at the strike price of hundred fifty so as we move from the strike price of our initial long puts 150 all the way to the strike price of our shot puts so hundred forty-seven we would have our payoff increasing by one dollar with one dollar decrease in the share price so that's exactly what happens until we reach having 47 the strike price of our shot puts all the way from there if we move further to left we can see that we'll have one lonely put creeping up and two shot puts creeping down so on that we would have our payoff decreasing by one power with every one dollar decrease in the share price so that's exactly what would happen until we reach the strike price of our final put at Holland 44 at that point all of our put options would be exercisable and we'll have to long puts crepe it up and to shotput scraping down so the variability would be eliminated and on that who would be left with a fixed downside of roughly 56 cents per share and why the downside is symmetric well because we have again selected the length of our wings the wings of the butterfly to be equal the strike prices of long puts being equidistant from the strike price of the crop put well we can see that in case of the butterfly regardless of calls or puts we grasp the maximum payoff only at one single spot when the share price is exactly equivalent to the strike price of our short course output and if the share price moves even a cent to the left or to the right of this Center price then we start losing how pay off starts decreasing to avoid that there is a modification of the butterfly strategy that's called condom in case of the condom you do not short two calls or two puts at exactly the same strike price but you pick flat plateau of sorts between the strike prices of your short column short put so for example to modify our butterfly into a corner we could make a condor out of ko options and consider a condor based on calls with short calls at hundred forty-five 849 instead of two calls and in coinciding 847 what that would do is that it would eliminate the variability of the payoff between hundred forty-five and hundred forty nine and that would mean that would secure that we guarantee maximum possible payoff in within the range of share prices that if the share prices do not fluctuate outside of this boundary and this is like the spine the body of the condor which is much thicker than the body of the butterfly because again a corner is much of a larger beast than the butterfly it is so that's the logic between the naming of the two creatures the other analogy in terms of the content I'll show you as soon as we look at the payoff chart so without further ado we need to just calculate the payoffs of the short course on 4549 that are again symmetric in terms of the initial center price of hundred forty seven and we also need to pick the wings of the content as the two strike prices for long calls that's very analogous to the process that we used when constructing the butterfly the length of each condors wings should be exactly the same so the strike prices of the long calls should be equidistant from the strike prices of the respective short calls in that case we have picked the in the money loan call at the stripers of hundred thirty nine and out of the money alone called to be at the strike price of hundred fifty fifty five it means that the length of each of our wings or the wings of our Condor six dollars each so one wing the left wing is from 139 245 six dollars the right wing is from hundred forty nine 255 again six dollars that would again guarantee that the payoff structure of our Condor is symmetric so in case of the short call again we have two short calls here so we can apply the very same logic that we already did if the share price and we lock the column is lower than the strike price and we'll lock the row so if the call option is in the money then our country party doesn't want to exercise that and we are happy and the grass payoff of this short call is zero if on the other hand the call option moves out of the money our counts body wants to exercise it they want to buy caterpillar from us at current forty five per share so we have to sell it to them at $145 per share so that's what we receive but what we have to pay for getting the stock at the first place is the market price which is higher so that's why the gross pay off of the short call in that case would be negative and then as it's a short call again we need to add the premium because that's what we receive for writing the option for taking on the risk so add that and look just the row and we can drag that and apply the formula for both short calls in case of the long cause we already have the formulas for any lone call for any strike price and any premium written over there so we could just copy those two cells and paste them over here and get correct payoff structures calculated automatically just for the sake of the fact that we have locked correct rows and columns please do follow this procedure as well when you have lots of various payoffs to estimate and you want to save time now we can just bottom right click this function and see how the payoffs of those long and short calls change with time and figure out the total payoff of our Condor which would be the sum of those four payoffs again the total payoff of the option portfolio is just the sum of the net payoffs of all of the options that go into that so over here we can see that we've got fixed downside of minus four point seven dollars per share if the share prices fluctuate wildly out of the boundaries we have projected then as we pass through the initial strike price of our long haul which is hundred thirty nine so we pass 239 and our playoff starts creeping up and then as we pass through the wing so we climb onto the left wing on the corner and we climb onto the spine of the contract at hundred forty-five we start receiving the maximum payoff possible one point three dollars per share and this payoff at this plateau remains exactly the same all the way until we reach the right wing of our condom the 149 strike price the second strike price of our shot cold and then our playoff starts decreasing as we climb down the right wing of the content and then it remains fixed since we have passed 355 that's the final strike price of the long haul and because the wings of the Condor that we've constructed of the same length they are equidistant from the center prices they are six dollars each the payoff structure is symmetric we're losing the fixed amount and this fixed amount is exactly the same minus four point seven dollars per share regardless of whether the price moves extremely to the right or extremely to the left if we look at the graphical representation we can see this plateau being formed in case of the Condor and here the logic is very similar as none of the options are being exercised variability is eliminated we have fixed downside then as we pass through currently 39 the first strike price of the long call we start creeping up then we have one short call kicking in at 145 the start of the body of our condo on the left-hand side then we have one long call creeping up one short call creeping down that would mean that our variability is again eliminated and we have fixed payoff fixed positive pay off all the way until we get 249 that's the right-hand side of the body of our Condor and then we start getting negative payoff from our second short call at the strike price of 149 so then we have two short calls creeping down and one long call creeping up so again we would have one short call creeping down on that so PF will be reduced by $1 per share with every $1 increase in the underlying share price and that would continue all the way until we reach the and of the right wing of the content and by the virtue of the fact that our wings of equal length the payoffs are symmetric regardless of whether the price moves extremely to the right or extremely to the left the final thing that we would consider today is the strategy that implements the Condor spread using puts fee logic is exactly the same it's just that we have two short two puts and the strike prices that are close to the center price and that equidistant from it roughly and we have too long to put to specify the wings of our Condor and here we'll choose exactly the same strike prices we'll just choose puts instead of calls and we can see that the premier for the boots and calls change respectively we can see that again the logic is preserved that the higher strike price means a more valuable put option and a less valuable call option which stems from the fact that it's more valuable to buy something cheap and it's more valuable to sell something expensive now for the payoff of the short put we can implement exactly the same logic if the underlying share price and we need to lock the column is lower than the strike price and here we need to lock the row then our counterparty has the incentive to exercise their put option so they have the right to sell caterpillar to us at hundred forty-five and then we can just sell it on the market for a lower price so we receive the market price and we have to pay the strike price so that's why our gross payoff if the short put is in the money's negative and if the short put moves out of the money that was paid for zero and we're happy about it because we have received the premium now we can drag it to the right and implement the very same logic for another shot put with a different strike percent premium and then we can implement the very same logic for the long puts because room we have written the same formulas for our butterfly spread so we can copy those paste them over here and then we'll be able to bottom right click the functions for all four options that go into our spread now we can sum up V for that option payoffs that go into an spread and see that indeed the risk structure of our condor has not changed we have fixed downside when the price goes down the limited upside when the price stays roughly the same with this nice plateau of 2.75 dollars per share when we are at this body of the condor between the two strike prices of the short boots and then it starts decreasing again and it reaches minus three point twenty two dollars which is exactly the same than our fixed downside when the prices went significantly down if we look at this graphically we can see that the logic is exactly the same but slightly reverse to the logic of the Condor using course so we have various amounts of food options been exercisable either burn us about our counterparty at very strike prices so our payoff chart it is either flat variabilities eliminated or it's creeping up or down depending on how many short or long boots are exercisable at every single strike price and comparing the two payoff charts we can see that again the total payoff of the Condor spread using boots is always significantly higher than the total payoff of the Condor spread using calls and here the difference is much greater than in the example of the butterfly we and a riskless profit of almost 1.5 dollars per share by moving from a corner with close to a condo with puts by no means it's always the case sometimes spreads based on calls are more effective and they have objectively better payoffs that's just the lesson that you have to learn that you always should look for the best strategy available if you have a number of equivalent strategies that you can consider and that's all for low volatility strategies and I'm afraid we have covered all basic and even advanced option strategies together in this short series of videos hope it has been helpful to you hope this topic in investment management and derivatives was at least relatively exciting to you if you would like to see some more content regarding other types of derivatives or more advanced content on options please leave your suggestions in the comments below as for now don't forget to leave a like under this video subscribe to our Channel and stay tuned thank you very much