VXX is composed of a certain number of first month and 2nd month VIX futures.
Suppose you have :
n1: number of 1st month futures contracts
n2: number of 2nd month futures contracts
n1, n2 are chosen so that the average future lifetime of the VXX contracts is 1 month. The initial n1, n2 values you use can be chosen arbitrarily, they are later adjusted so that the calculated VXX matches the market one.
Lets call p1 and p2 the prices of the first and second month vix futures, which are readily available here from the CBOE where I originally gathered it. The processed data ready to use to calculate the VXX can be downloaded here (data since March 2004).
The price of the VXX is calculated as :
VXX = (p1*n1+p2*n2)/c
As of now
VIX 33.60 +1.73
VX Q1-CF 33.67 +1.57
VX U1-CF 27.65 +0.95
VX V1-CF 26.80 +0.85
VX X1-CF 26.20 +0.75
So
p1=33.67
p2=27.65
and
n1=9.36
n2=91.66
c=85.32
So by replacing you get VXX=33.4, the slight difference with the market value is simply due to daily demand/offer dynamics.
Note that n1, and n2 change every day
Defining by
r: the number of remaining days until the expiration of the first future
Then n1 is reduced by n1/r every day, and with that amount you can buy more n2.
So if there are r days left to expiry of future 1 then as of tomorrow n2 will become:
n2+(n1/r)*p1/p2
and n1 = n1-n1/r
Therefore when there is backwardation the contract base (n1+n2) gets bigger every day because n1/r 1st month contracts are sold every day to buy more second month ones, but for every 1 contract sold of the 1st month you can buy p1/p2 contracts of the second month and p1/p2>1 by backwardation definition. When you have contango the opposite happens and n1+n2 decreases every day because p1/p2<1.
So the contract base expands in backwardation days giving the VXX quite a considerable tailwind and decreases in contango periods. Even though most of the time VIX futures are in contango, empirically backwardation periods are of higher strength than contango periods as you can see here. Strong persistent backwardation accompanied with increasing prices creates high VXX prices in a short period of time as evidenced by he graph available in this post: the great recession VXX values, making VXX a dangerous instrument to short.
The following implications are good things to understand and remember, they can be easily demonstrated. Based on how the VXX is priced you have the following consequences:
(For a financial math demonstration of these corollaries use the definition that VXX = (p1*n1+p2*n2)/c so if n2 is increasing/decreasing faster due to the presence of backwardation/contango then that affects over time the VXX value directly and more than if there was none or if it was smaller. Also use the fact that futures converge to spot prices.)
0) The Level of backwardation/contango affects the VXX valuation, the bigger the more influence.
1) Backwardation with increasing futures makes the VXX go up fast because not only the are futures growing which directly influence it but also the number of contracts is increasing.
2) Backwardation with decreasing future prices will make the VXX fall or go up depending on the strength but will act as a bias pushing it up since future prices converge to the spot VIX value.
3) Contango with increasing future prices will make the VXX fall or go up depending on the strength but will act as a bias pushing it down since future prices converge to the spot VIX value.
4) Contango with decreasing future prices will make the VXX fall faster because not only are the future prices decreasing but also the contract base is shrinking.
How and why c is used?:
Its because you start with an arbitrary number of contracts but then you get a huge VXX number or small, but definitely different than then market VXX, but proportional to it, that’s what matters.
You can use as initial value n1=100 and n2=0 just the day after the expiration date of a future. That will correspond to the day when all contracts are 1st month contracts which are exactly one month away.
You can start with c=1 and then chose another c to adjust it to the market data. Otherwise the VXX you calculated by starting with an arbitrary number of contracts will be proportional to the VXX values only but not like them. So you use c to adjust it. For that you take any date where you have a VXX market value like the previous closing date and you calculate c such that the calculated VXX matches the VXX of the previous VXX market close price
so
c=(n1_*p1_+n2_*p2_)/VXX_
where
n1_ : number future 1 contracts previous day
n2_ : number future 2 contracts previous day
p1_ : close price future 1 contracts previous day
p2_ : close price future 1 contracts previous day
VXX_ : close price VXX market price contracts previous day
So when you divide by c you get that the calculated VXX matches exactly the market VXX on the previous day and all the other calculated VXX will be very similar if the calculations you did were right, if not there is a mistake 
, but the calculations are easy because you know by how many contracts to decrease n1 every day (just the available number divided by the days left to expiration) and also how many to increase n2 (based on the future prices relation multiplied by the future 1 contracts sold).
You can like this basically create your own vxx calculation the hardest part is getting the futures data, but that is available in this blog. That can allow you make forecasts, like this one for example, based on futures “future” prices and see how they are influenced by the contango/backwardation periods. Or at least you will be better off to make decisions once you understand its dynamics.
If you did not understand anything just come over here and we discuss it over a caipirinha!
Hope it helped.
Cheers!
Juan
Questions:
“But I don’t understand
how futures are priced when VIX falls
10% in a week?”
The futures are priced based on market expectations, demand and offer, so even though the VIX fell from 48 the 2nd month future was never too high and did not fall much:
Date/1st month future/2nd month future/VIX
08/08/2011 36.55 30.20 48
08/09/2011 30.50 25.40 35.06
08/10/2011 36.00 28.75 42.99
08/11/2011 35.15 27.65 39
08/12/2011 35.00 27.85 36.36
08/15/2011 32.10 26.70 31.87
As you can see the VIX fell from 48 to 31.87 but the 2nd month future just fell from 30.2 to 26.7, and its that future who determines more veavily the VXX price (because the 1st future is about to expire and VXX has little first month futures left)
Plus the contract base is expanding at around a 1% rate per day given backwardation (more 2nd months futures can be bought by selling 1st month ones), so the VXX price is boosted by that contract expansion.
“That’s what I’m saying…
30.2 to 26.7 = 11.67%
VXX isn’t down that much.”
Here is the data:
Date 1st mth 2nd mth Days left VXX (NAV) VXX (market) VIX #Contr 1m #Contr 2m Tot contracts
08/01/2011-20.70-20.60-13-22.42-22.41-23.66-60.82-31.76-92.57
08/02/2011-22.30-22.00-12-24.08-23.97-24.79-56.14-36.50-92.64
08/03/2011-22.00-21.85-11-23.82-24.08-23.38-51.46-41.21-92.67
08/04/2011-27.45-25.90-10-29.07-28.89-31.66-46.78-46.17-92.95
08/05/2011-29.15-26.20-9-30.16-30.31-32 42.11-51.37-93.48
08/08/2011-36.55-30.20-8-36.22-34.78-48 37.43-57.03-94.46
08/09/2011-30.50-25.40-7-30.36-31.26-35.06-32.75-62.65-95.40
08/10/2011-36.00-28.75-6-34.93-35.17-42.99-28.07-68.51-96.58
08/11/2011-35.15-27.65-5-33.77-33.78-39 23.39-74.46-97.85
08/12/2011-35.00-27.85-4-33.90-34.13-36.36-18.71-80.34-99.05
08/15/2011-32.10-26.70-3-32.18-32.18-31.87-14.04-85.96-100.00
The day that the second future was @30.2 you had the 1st one @36.55 and the VXX @36.22
And yesterday with the 2nd future @26.7 and the 1st one @32.1 and the VXX @32.18
So actually the VXX fell from 36.22 to 32.18 just a bit less percentually than the 2nd future fall.
Not that the contract base augmented in total from 92.57 to 100 due to backwardation.
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Howdy Juan. I’ve got a question and thought I might ask it here rather than on Yahoo, but feel free to answer it here or there, or not at all…
Do you have any thoughts on the divergence between the VIX index and the CBOE volatility futures recently? I’m talking about since the VIX hit its high, say 8/08 or 8/09. The trend showed no signs of slowing yesterday, with VIX down 3.8% and VXX up 1.x%.
Maybe I’m being lazy and asking you to do my homework for me. So I’ll look into it myself and report back.
Thanks!
Hi John, Excellent question to illustrate the boost given by backwardation.
When the vix reached its high on the 08/08/2011 you had this situation:
1st month vix future contract closing price: 36.55
2nd month vix future contract closing price: 30.20
Days left to 1st month expiry: 8
Calclated VXX clsing price: 36.07
Market VXX closing price: 34.78
VIX closing price: 48
30 day vix future price: 32.72
Total number of contracts base: 92.64
Now on the 08/17/2011
1st month vix future contract closing price: 32.73
2nd month vix future contract closing price: 27.95
Days left to 1st month expiry: 1
Calculated/market VXX closing price: 33.53
VIX closing price: 31.58
30 day vix future price: 28.17
Total number of contracts base: 100.00
So even though the 30 day vix price went from 32.72 to 28.12 the contract base expanded due to backwardation from 92.64 to 100 making the vxx just go down from 34.78 to 33.78 while the vix fell from 48 to 31.58
So in simple words the futures that determine the price hardly went down while the contract base increased making the vxx hardly fall.
Hope it clarifies!
Cheers!
Juan
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Hi Juan, just discovered your great blog today and going over it.
I can see r the remaining days of the month is also a factor in the calculation. it means we get bigger effect of backwardaion /contango depends on how close we are to rolling contracts ?
backwardation peaked immediatly @20% more than a month ago, since the 1st month future spiked but not the second . Since then the backwardation is going down, except the last 2 days where it went back up, but never over 10% again
vxx went up because the futures did and also due to the positive bacwardation (even if its decreasing)
it could be that close to the expiration date the first month future approaches to the vix (because futures converge to spot price) and you have a bit more of backwardation then but what really matters is the spread between the first and second vix futures and since both (also the second month vix future) are quite high now the spread is smaller therefore backwardation too
so if you have a situation when the 1st vix future is 38 and the second is 37 then both are very quite high (like now) and backwardation is quite small (38 is less than 3% over 37), then if the vix falls the futures would follow, backwardation could even get smaller or pass to contango and the fall of the futures would directly hit the vxx price, even if there is backwardation, since it is too small to help,
of course the vix could go to 50 but if it doesnt and it goes under 40 then vxx would fall due to its falling futures which directly affect its price
BTW Juan just checked the vix contracts , the front one is 39.05 and the second is 35.90 quite strong backwardation not as you mentioned.
i looked at another time of the day when the vix was lower, that shows how fast the futures change depending when exactly you look at it, and it shows how fast the 1st month follows the spot vix price, conversely if the vix goes under 40 backwardation could be erased for that same reason or also if it remains over 40 and the second contract goes up,
it is still way under the initial 20% peak we had a month ago, that tailwind will be hard to be seen again because futures are already both high, note that there is no backwardation along the whole futures spectrum anymore just on the front months, the rear end months are in contango or flat and at quite lower values, which means future expectations point to a vix fall
if the rumor is true and Europe this weekend announces to buy banks corporate debt (bonds) and lowers the official interest rates volatility could go down that’s the reason European markets recovered by the end of the session, that’s what some say is the reason why Spanish banks jumped more than 5% just at the end of the day
Amazing blog and analysis! The math all makes sense. What do you think, Juan, are the reasons that the VIX near-term futures tend to be in contango more often and for longer periods than in backwardation, translating into a greater negative area under (or over) the curve over time on the backwardation-contango plot you created? If one thinks about the VIX itself (a basket of out-of-the money near-term S&P options) it would follow that long-term VIX futures should be closer to the historical VIX average than nearer term futures (which are closer to the spot VIX) leading to a tendency for strong backwardation when the VIX is higher than its historical mean and a tendency for contango when the spot VIX is below its historical mean. I imagine the explanation results from the notion of using VIX futures as a hedge to protect their long S&P equity positions in case of market turmoil and that the nearer expiry time of nearer-term VIX futures tends to make the value of VIX futures decay over time (as expiry approaches) and no market turmoil appears to be developing. But what is the psychology and/or strategic basis behind the willingness to pay a potential premium for longer term VIX futures in general? Why are investors more fearful (on average) of potential market turmoil a few months away than potential market turmoil in the nearer term? Perhaps if one looks outside and sees a sunny day, flood insurance seems unappealing. But I suspect this is not the only explanation since there are plenty of cloudy days and near-term market turmoil may be more devastating to a portfolio since there is less time to prepare (eg, diversify).
Hi Daniel, Vix futures have only been traded since 2004, there are several month futures traded and the vxx is just made of the 1st and 2nd months. Since that date more than 90% of the time the 1st future has been cheaper than the 2nd (contango). Just a few percentage points but enough to cause a big decay on the vxx. I do not know for sure of why its like that I can only speculate. I think it has to do with information and the certainty that it carries with it. People perceive in average, based on the lack of future information compared to present information, that there is more uncertainty after 30 days than before 30 days, the reason being that there is more information data pointing to the present than to the future and the lack of information causes uncertainty and that lack of information is compensated by higher prices, the price of uncertainty which is almost always positive except in extreme volatile times, therefore a slightly higher price for the second month future. Maybe for that same reason longer term interest rates (and oil futures) are generally almost always higher than shorter term ones.
But no one can really give you the real reason, just observe the historical fact that it has been like that. In any case vix futures are very recent it could have been that in other periods it was not like that so there is not even really any historical guarantee of that behavior persisting.
What is historically a fact is that the VIX oscillates around its mean and it has always traded within a range. It makes sense because the vix is calculated as a ratio. So if you short when the vix and its futures are quite higher than their mean you should do ok if contango remains the norm and you hold long enough. But on the short term you could have big paper losses so you have to make sure that they do not cause you problems like margin calls or liquidity limitations to better investments opportunities. You can manage those problems by using hedges or shorting small quantities only when you are very sure the odds are on your favor by trading very seldomly when its really worth it.
what happened to VXX vs VIX today? Right now VIX is up 3%, meanwhile VXX is down a bit. Given that the futures point to a backwardation scenario, how could this happen?
Kai
VXX is priced based on futures not on the VIX
VIX is up as of now but the futures remained at the same price as yesterdays close that’s why the vxx is not up:
VIX 32.37 +0.81
VX X1-CF 31.10 +0.10
VX Z1-CF 29.95 0.00
Most of the contracts are on the 2nd month future who is not up as of today and that’s the one who carries more weight to price VXX.
Also price differences between the real and theoretical price happen due to daily demand and offer dynamics.
I was thinking if this has to do with the Oct VIX option expires today…
Does it play a role in this disparity in addition to supply/demand dynamics ?
October future expiring today means that the price of vxx is basically fully determined by the November future, that’s what matters to price it (today)
Hi Juan,
I just finished reading this article, and I found it very useful!
The first thing I do after finish reading it is downloading VXX data since Mar. 2004 provided in this article, then I tried to fill up the blank by myself.
I put the VXX market price (10/31/2011 – 11/11/2011) into the chart first in order to find out if I can predict the VXX market price in the near future by doing like you.
Then, I noticed that the calculated VXX price does not match VXX market price.
I don’t understand what happened here.
I guess it’s because November 2011 future price has change dramatically after you stop calculating VXX price since 10/28/2011, or the data used to calculate in this chart is not up-to-date, am I correct?
Hi Ted, It should match almost exactly, I have to go to the dentist now but as soon as I return I will update and post the updated data for you to download to compare with yours.
Hi Ted, I just updated the data, the VXX on the market is almost the same as the one calculated, you can download the data and compare.
Hi Juan,
Here is the screenshot of the original VXX data sheet(vxx…15.xls).
I didn’t change anything of it, I just fill it up with latest VXX market price.
In the original one, the calculated price doesn’t match the market price.
In the revised version(vxx…..16.xls), everything is alright again!
What’s the difference between the 2 .xls files mentioned above?
The data/future prices used to calculate the VXX price?
Hi Ted, it because that version does not have the formulas included, the values are just fictitious, simulated.
Hi Juan,
I’ve just downloaded the updated spreadsheet.
Now I will start paying attention to the calculated price and market price everyday until the end of 2011.
I’d be very happy to pay you via Paypal to receive further calculation/prediction of VXX for the first half of 2012 (just like what you said in another article.) if nothing’s wrong with the calculation.
The processed data really helps in determining when to buy/sell and protecting protfolio!
Hey Juan,
Love the blog dude! Post some more good stuff so I have something to read besides nitwits preaching nonsense. Anyway I devote most of my time trading Volatility products (VXX, XIV, VIX futures and some Vol plays on indexes (mostly butterflies and diagonals on the RUT, and I’m really digging playing the weeklies on some of these) I was curious to hear your opinion on VXX heading back into the contango shuffle. I’ve been wondering how big of an effect it will have since the futures just rolled and it’s such a small slice of the monthly pie. Have you ever researched how big of an effect it has on price in relation to where they are during the futures lifecycle? I only trade the options on VXX so I’m really interested in seeing how option prices react when its in full contango again after all of the people who blew out selling naked calls dive back into the shark tank!
Scott
Hi Scott,
From the historical data since 2004 on the vxx it seems like the best moment to short is when all the vix futures are high and backwardation is falling or contango is starting again, so based on that it would be good to short now the vxx.
I was already short and 100% hedged with calls so I just sold 50% of my calls now remaining half hedged. I am quite surprised to see that the second vix future is quite high, forcing contango to appear and hopefully stay. If it remains like that vxx will suffer a headwind. It seems like speculators are manipulating the contango/backwardation, but who knows… maybe not.
I am shorting more based on fundamental reasons, I do not think the economy will get much worse than now and plan to stay for long on my shorts, but its reassuring to see that historically contango is more present than not and that the vix futures are quite above their averages and revert to the mean, therefore I guess that combining that with the bet that the economy will not get much worse the vxx short should play good on the long run.
PD: There are some other posts you may read, by searching vxx data on the blog search box you may find more info.
Cheers!
Juan
How about that?!? SPX is flat and VXX down 3% today! We all knew it would happen but I didn’t think it would be that fast. Are you doing way OTM calls (they decay a bit faster) out into Jan-Mar or the Dec expiration? The theta doesn’t really seem to move these things so I’ve been doing a mixture of short calls and long XIV just to see where I get the most bang for the buck. XIV sucks just as much as VXX but I’m wondering how far it will fill the gap if VXX really tanks. Hedging these things in some way that works would be a great find if it’s out there. Vols are so high longs won’t really work. Narrow butterflies don’t seem to work. I’m looking at some spreads in the weeklies that may be a possibility. Any thoughts?
Scott
Hi Scott, this is what I have been doing lately with vxx: http://investing.kuchita.com/2011/11/19/sold-half-of-my-vxx-volatility-hedges/
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Juan,do not understand all the xs and os you post here,but can you tell me when the VXX will change its trend and start going up.thanks
crewser, I can’t predict that because that depends on the expected future market volatility which I have no idea when it will change.
Cheers,
Juan
Jan,
I don’t much about vxx, but a decent position which is now substantially in the red.
Have been trying to stay in the game by selling calls, but it keeps going down and I’m getting worried.
Now I hear different stories that make me even more unconfortable.
My question to you is this: is there a chance that vxx value evaporates to nothing in the long run?
I had intention to grind out this down period by selling options thinking of vxx as a stock that could not go to zero. Is this totally wrong?
Your help will be very much appreciated.
Franco
Hi Franco,
I personally think that the vxx will go down to 0 in the long run. That’s why I keep a long term short position.
In the short term here is what I think: http://investing.kuchita.com/2011/08/21/vxx-data-since-vix-futures-avilable-march-2003/#comment-10477
On the other hand if there is a market scare you can make a small fortune on you vxx, that’s why my short position is not big. It all depends on how likely that is.
Cheers!
Juan
Sorry, that should read: Idon’t know much abot vxx, but have a decent………..etc.
Hi Juan
Hello everyone , I m new and would like join in this group i look forward to learn from all of you here . I have been following vix and trading HVU around 3months and i would like to learn more about vix .
Hi Mike, Here is what I think about volatility and contango lately: http://investing.kuchita.com/2011/08/21/vxx-data-since-vix-futures-avilable-march-2003/#comment-10477.
Do not doubt to comment or post about your investing or trading ideas.
Hope it helps!
Cheers!
Juan