The Cost of Contango—It’s not the Daily Roll


Saturday, March 2nd, 2013 | Vance Harwood

A while back I developed a spreadsheet that consolidates the CBOE’s historic VIX futures data into a single spreadsheet.  Using this spreadsheet I calculate the short (SPVXSTR) and medium term (SPVXMTR) rolling indexes that underlie the various volatility Exchange Traded Products (ETP) like VXX, UVXY, XIV, and ZIV  The image below shows a small sample comparing my calculations (M1-M2 Short Term Rolling Index) with the official value of the short term index.

M1-M2-Sample



The  percentage differences between my index and the official index (e.g, -0.000256%) aren’t cumulative and are probably due to rounding.

Once I had verified my index calculations I wanted to look at the nemesis of the long volatility funds like VXX and UVXY—yield losses.  These losses, which can be 5% to 10% per month occur when the CBOE S&P 500 Volatility Index (VIX) Futures that underlie these ETPs are more expensive than the market, or “spot” price.  This situation is called contango, and is typical when the overall market is bullish or flat. The graph below from VIX Central shows VIX Futures in a contango configuration.

vixcentral.com

vixcentral.com



I wanted to quantify this loss with my spreadsheet without the noise of everyday volatility moves, so I left the term structure in contango, but held the futures prices constant in my spreadsheet from day to day as an experiment. The results were surprising.

M1-M2-OnlyC



My calculations showed no daily roll costs in the index. The 0.01 upticks in the index are due to treasury bill interest.

The usual explanation for roll costs, discredited in the sample above, asserts that losses are incurred when funds sell cheaper shorter term contracts and buy more expensive longer term contracts every day as specified by the indexes they follow—a sell low, buy high situation.   A closer look illustrates the flaw in this explanation.   A simple example of a $10 million position after market close on 19-Oct-12— after the contract rolls. Fractional contracts aren’t supported, so unused money goes in the cash bucket.

Nov Contracts Nov Value % Dec Contracts Dec Value % Cash Total Value
500 $8.8 Million 88% 65 $1.19925 Million 12% $750 $10 million



Now moving to the end of the next day, neglecting transaction costs and interest, and assuming no change in the futures values.

Nov Contracts Nov Value % Dec Contracts Dec Value % Cash Total Value
477 $8.3952 Million 84% 86 $1.5867 Million 16% $18100 $10 million



The number of contracts changes, but the total value doesn’t.

There’s no doubt that these indexes lose money when the VIX Futures term structure is in contango—so where do the losses come from?

The chart below shows the real root cause:

Nov / Dec VIX Futures vs VIX

Nov / Dec VIX Futures vs VIX



Plotting actual November and December VIX futures values during a period of contango vs the CBOE’s VIX®, we see that both contracts decline in value over time, eventually converging with the “spot” VIX price at their expiration. With both sets of contracts held by the long volatility funds generally declining it’s not surprising the overall value drops. Since we are typically looking at term structures over the span of multiple months, the small daily “slide” down the curve isn’t noticeable—especially when obscured by the up and down moves in volatility driven by daily stock market fluctuations.

This analysis also explains why the mid-term volatility index SPVXMTR which holds contracts that are 4 to 7 months out also declines rapidly in contango situations, even though 2/3rds of the contracts (M5 & M6) aren’t rolled on a day to day basis.

Volatility Futures aren’t always in contango.  If the markets are panicky enough the futures contracts get less expense than the VIX index.   The chart below from VIX Central shows the June 10, 2010 situation when the VIX index closed at 36.57.

TS-7Jun10



In this configuration, called backwardation, the long volatility funds have the wind at their backs, every day the futures they hold are sliding up the curve, getting closer to the spot price.

Knowing the real reason for term structure based losses / gains hasn’t changed my volatility investment strategy, but it has removed one source of confusion in understanding the daily moves.

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Saturday, March 2nd, 2013 | Vance Harwood
  • Andrew_notPorC

    I’ve been thinking about this lately too, Vance. It seems to me that we should not necessarily be looking at the spread between M1 and M2 futures, but the 1 month constant duration (weighted average) vs spot VIX. This gives us a sense of what the roll yield is, as the front two months are falling down the curve toward the spot price.

  • vance3h

    Hi Andrew, That’s an interesting approach. Since we know the spot is the ultimate converging point, and the M1 gets flaky right before expiration, using the spot + CM would probably give us a more consistent measure.

    – Vance

  • Eli

    The M1-M2 contango causes the total number of contracts held (M1+M2) to go down. This is the way the indexes are computed. The number of total contracts only depends on the M1-M2 contango and nothing else, it is not related to the VIX.

    Now, just assume that in a month the term structure remains the same meaning that the former month’s M2 is now the M1 and has the value of the former month’s M1. What was M3 becomes M2 with the value of former month’s M2. You have the same future values for the new M1 and M2 as the previous month’s but the total number of contracts is less and that is how contango kills these indexes.

  • Eli

    And the reason the total number of contracts goes down during contango is because of the “sell low buy high”, it is just the math of how much contracts need to be bought and sold to remain with constant time to expiration.

  • Andew

    The number of contracts doesn’t matter. It’s caused by the value of contracts decreasing each day as they approach spot. If the value of the contracts doesn’t change,then the dollar exposure remains the same and the fund holds its value constant.

  • Eli

    The total number of contracts matters because the value of the index is directly proportional to the number of contracts of each future times the value of the future.

    Do the math with a constant term structure and you will see that only  the number of contracts matter as the future values (relative to future expiration) stay the same. To elucidate this point, a “constant term structure” means that what was M2 becomes M1 and what was M3 becomes M2. The term structure graph looks exactly the same month to month except that month names on the x axis have shifted to the left.

    Yes, for the term structure to remain constant the values of the specific futures must decrease even though the term structure stays the same, but it is not the decrease that is causing the loss, it is the the term structure that is causing the decrease and the loss. And the contango just describes the term structure at the short end.

  • Eli

    Try this thought experiment (or do the actual math). Take a month in which both the first and second month  futures rise every day but the contango in percentage stays the same. The VXX will be going up but because of the contago the total number of contracts keep going down. 

    Then the month after, the first and second month futures retreat back over the month to the value of the first and second month futures from 2 months ago. So one month the futures went up, and one month they went down back to the previous values. Of course, these are different contracts because the months have changed and the first and second month futures are of different months.

    The loss in VXX will be about twice the contango in percent still because the contango has caused the total number of contracts to change even though one month the futures went up all the time and the next month they just went down by the same amount. Even when the futures are rising, the contango is preparing VXX for the fall so to speak.

  • Ryan

    There are four things that describe whats going on here, and most people lump them together into two things:

    1) Contango is when a specific future has decreasing value towards expiration
    2) Backwardation is when a specific future has increasing value towards expiration
    3) A normal futures curve is when the price of future M   future M+1 on a given date

    You cannot look at a term structure on a given day and state that the futures are in contango or backwardation. What you describe in the third chart is an inverted futures curve vs a normal futures curve.

    It is possible to have an inverted futures curve that’s in contango because the individual contracts go down in value over time, but maintain their relative value on the futures curve. This happens with NG futures rolling off the winter, where winter months are more expensive than summer months, yet everything is in contango because of the storage costs (carry).

    You correctly state that the second chart is in contango because a given future decreases in value towards it’s expiration.

    In my mind, a given VIX future will generally revert to contango (decreasing value towards expiration) because the certainty about a future point in time is always increasing.

    VXX et al are losers because they hold futures that are almost always in deep contango.

  • vance3h

    Hi Eli, A couple of comments. First of all, number of contracts is not involved in the official index calculation (e.g., VXX prospectus). It’s all driven by percentage changes in the futures themselves, and the shift in allocations. Second, if you look at my example of the two days with $10 million invested the number of contacts decreases, but the value of the fund stays the same. If the number of contracts was the key variable the fund value would drop. When I get a chance I’ll run your one month one month down thought experiment on my spreadsheet.

    – Vance

  • Eli

    Hi Vance,
    Please take a look at this:
    http://investing.kuchita.com/2011/08/16/how-the-vxx-is-calculated-and-why-backwardation-amplfies-it/

    The official index calculation normalizes away the number of contracts into percentage holdings relative to an initial amount, but the principle is the same.

    As for your example, the index does not go down because it ignores the fact that you need to satisfy two constraints. The first which is a constant contango, you have accounted for. But the second constraint is that the second month future value has to converge by expiry to the first month value, otherwise the term structure is changing. That means you have to reduce the values of both futures so that when the first future expires, the second will have the value of the first when it was the same time to expiry and the percent contango is the same. So in your example 18.45 would need to go down over time and reach 17.6 and 17.6 would need to go down so that the contango would remain the same. Otherwise, you are pushing the whole term structure up. 

  • vance3h

    Hi Eli, My intent with this post was to challenge the frequently stated position that yield losses in vol ETPs result from the daily “sell low, buy high” daily turn-over of futures contracts. By setting the M1 M2 futures constant I showed that that operation does not induce losses. You are of course correct that the convergence of the far month with the near month value over time does cause losses during contango. This is a far less mechanical process, which is obscured by the normal market action.

    – Vance

  • Andrew_notPorC

    Think about it in terms of what the fund pays for each contract of a given expiry when it is the M2, then what it sells it for once it is M1. The number of contracts purchased of a given expiry always equals the number of contracts sold. The losses occur because the contracts of each expiry are sold at lower prices than they were purchased at. It has nothing to do with how many contracts are purchased on a given expiry.

  • Nau 23

    Maybe I’m thinking about this wrong, but it would take about 2 years in your example to go from 565 contracts to one contract. To break even, that one contract would have to be worth $10 million. The question is, what sort of market environment would there have to be for one contract to be worth $10 million? 

    It would require that the value of each contract owned went up proportionally to the rate that contracts evaporated via the roll.  Longs bet that the value will go up even faster than contango-induced evaporation, right? 

  • vance3h

    Hi Nau, Contango based losses in funds like VXX run about 90% a year, so after two years I would expect the number of contracts to be down to around 6 contacts. The $10 million eroded down to about $100K. There is no hope of getting back to where you started, even with 1987 / 2008 style meltdowns. Realistically longs are just betting that volatility will spike up soon enough that they can exit with profits before contango destroys their positions.

    – Vance

  • Nau 23

    I agree. Then why would anyone ever, ever want to be long VXX? If they could predict the future with the level of accuracy required to make any money on VXX, wouldn’t they be better of with other long-shot-but-high-possible-reward strategies, such as deep otm puts or highly leveraged short SPY bets?

  • vance3h

    Hi Nau,
    I think VXX is popular for people that aren’t comfortable with options. 2012 was a tough year for people long volatility. Many people did better in 2010 and 2011.

    – Vance

  • BobV

    Vance, finally someone gets it. Congrats, your post is 100% spot on. The individual futures contracts tend to decay over time when in contango and that’s what causes VXX to decay. It has nothing to do with roll yield (selling front month futures and buying more expensive second month contracts).

  • Jonathan

    Thanks for your input, Eli. I totally agree with you – the number of contracts do matter. The popular view of roll yield from moving to month 2 matters, and I don’t think can be discounted. I do also appreciate the thoughts Vance gave on the convergence to spot VIX. But I can never be convinced that when it comes to VXX pricing, that the convergence yield is of primary importance. I track the roll yield (moving to M1 to M2) and then add to it the differential between the weighted short term VIX and spot VIX to get what I call an effective roll yield. If the weighted ST VIX is below spot VIX, it brings down the effective roll yield when M1 and M2 are in contango. In other words, I look at both aspects.