Euan Sinclair once said teaching and writing is an essential part of learning (probably not the first person to say it but I will give him credit here). After spending the last 3 months vigorously learning and trading the term structure with calendar spreads I have decided to write a piece on how they should be traded. There is almost zero good content on trading calendar spreads so most of my learning had to be done by myself with the help of some friends and people from this board. The goal for this article is to write my thoughts down as well as educate others and receive feedback. I am not scared of giving edge away here as it will be a general and not specific to certain leaks in the term structure. Spotting the leaks is a totally different discussion and is hard to find with out the technology/coding skills required (as it should be).
This will be focused on the 1:1 long calendar with a front month (30 days) and a back month (60 days) spread however, this applies to short calendars and of different maturities. Also note I am using calendars as a stand alone strategy in these examples and not a way to hedge although they can be great ways to hedge a portfolio.
A calendar is the sale of the front month option and the purchase of the back month option on the same underlying. To intuitively think about it I will be breaking it down into two separate positions, a short front month call and a long back month call.
The short call
short vega
short gamma
long theta
You sell the front month call because:
you believe that the implied volatility(IV) is relatively expensive vs the realized volatility(RV). To realize the spread between IV and RV we need to trade the RV otherwise known as delta hedging. Our PnL at the end of the trade will be the Vega of the original position multiplied by the difference of IV and RV (Vega * (IV-RV)). This being said if you decide not to delta hedge your vega and theta gain must outweigh your gamma loss.
The long call
long vega
long gamma
short theta
You buy the back month call because you believe that the implied volatility (IV) is relatively cheap vs the realized volatility (RV). You would also need to delta hedge this until expiration to realize it. However, because you have much more vega in the back month, your theta/vega ratio is much lower and therefor you may prefer not to delta hedge if you think your gamma/vega gains will out weigh your theta loss in the short term. Our PnL is also Vega*(IV-RV). There is an instantaneous formula as well but my intention is to not turn this into a math paper.
The calendar spread
Long Vega
Long Theta
Short Gamma
Now that we have an understanding of the 2 parts that go into our calendar spread. Lets see what happens when we combine the 2. At first glance the calendar spread looks very attractive because it is long vega and long theta, HOWEVER this is sort of an illusion. Many "option gurus" fail to realize how volatility moves through the term structure. The calendar will only gain in price if the implied volatility moves the same amount for both expiration. For example if the front month increases by 10% and the back month increases by 10% then the calendar will gain in price. Volatility moves with square root time. Meaning if the front month volatility moves up by 10% than we have:
Annualized vol = .10*sqrt(1/12)
Back month vol change = Annualized vol/sqrt(2/12)
Back month vol change = .07 or 7%. By converting to annualized vol we can back solve for any time period.
Here is a before and after picture demonstrating what happens to a calendar spread when implied volatility increases.
View attachment 187755
View attachment 187756
When we use our example of increasing front month vol by 10 and back month by 7 we get no change in PnL (for the geeks out there, you can also divide front month vega by back month vega to see how much your the vols need to change by to make money). What is very obvious tho is that the spread widens. What is happening here? Because volatility is synthetic time ie. if vol goes up that is the same as time increasing! (tree diagrams do a good job at demonstrating this). So because vol has increased it is like we are putting on a calendar spread with longer time to expiration. This new calendar might now resemble a 2 month 4 month calendar spread at previous vol levels. If vol contracts a few days later the calendar break even points will also contract. Our theta increases, so as long as the volatility stays elevated then each day will bring us larger profits than if the vols were not elevated.
This brings us to how we can make money trading calendar spreads. Calendar spreads can be traded in 2 ways. However they are both a guess on forward volatility. The first example is trading the forward realized vol and the second example is the forward implied vol. You are making a guess on what the volatility will be between the 2 expirations at a future date. The two ways of trading a calendar are:
1. Using the front month premium to reduce the cost of the back month, maybe because we think realized vol will be higher in the second month. Remember how we broke down the calendar into 2 parts? Imagine we think the front month vol is fairly priced but we think the back month is under priced. We can buy the calendar and when the front month expires, we are left with the back month at a reduced cost and can now gamma scalp the realized vol all the way until expiration of the second month.
2. Pricing in an event. Lets say we have earnings in the second month cycle and the front month spot vol is 30% and back month vol (with earnings) is 28%. Well then its a no brainer we can buy the back month with earnings and sell the front month without the earnings and profit once the back month vol rises. We can then close the position for a gain.
Calculating forward vol and event vol is something you can do on your own time.
Calculating the PnL of the calendar
on average Our PnL will be: vega1 * (IV1 - RV1) + vega2* (IV2 - RV2). This is assuming we keep our calendar delta neutral.
Conclusion: Spot volatility is easy to see but forward implied vol can sometimes quietly fall off the track. Calendar spreads are a great tool to use to take advantage of the term structure. Remember that although calendars are long vega they do not usually increase when volatility increases. Delta hedging calendars is an effective way to reduce the risk of a calendar and isolate the spread of volatility.
Once again I want to thank those on this forum who continue to make me think and who I have learned a lot from.
@Secret Santa @srinir @JackRab @Maverick74 @spindr0 and most importantly
@sle I wonder what ever happened to him.
TheBigShort
