VIX has remained surprisingly undervalued despite negative economic reports and not so strong earnings announcements thus far. I understand that since beginning of June, the market has been rallying. As long as this rising trend continues (as shown in blue lines), I would expect VIX to be subdued. However, I was surprised that VIX didn't even touch the 20 level when SPY tested the 133 level back on July 12th.

On Friday, Spain reared its ugly head again and negative headlines are popping up about Greece AGAIN in overnight session. Depending on AAPL earnings results and ongoing developments in Europe, I would not be surprised if SPY tests its support line again (around 134.5 level this time), but this time with higher probability of the support failing due to the fact that SPY and the VIX have priced in potentially positive news and shrugging off actually negative news. Yes, I know this can be considered a bullish sign, but that was the case over a month ago, when expectations were really negative but price action quite positive. That is no longer the case.

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Disclaimer: The information found on this site is meant for educational and informational purposes only. Nothing on this site should be construed as a recommendation or solicitation to buy or sell derivatives or securities or to trade any particular strategy. Trading of derivatives or securities has large potential risk and you must be aware of and accept all the risks. Past performance of any trading system or methodology is not necessarily indicative of future results. No representation is being made that any account will or is likely to achieve performance results similar to those discussed on this website. Hypothetical or simulated performance results have certain limitations and do not represent actual trading.

## Sunday, July 22, 2012

### Rule of Thumb Analysis on Cost of Carry for VXX

Interest in VIX and VIX futures-related ETFs & ETNs have grown exponentially over the past few years. Unfortunately, understanding of VIX futures-related ETNs, such as the most popular iPath S&P500 VIX Short-Term Futures ETN (VXX), has not kept up with the explosion of its trading.

For many who thought VXX was a good instrument to buy and hold, as a hedge against rising volatility, have suffered considerable losses. Mainly, this is because of the cost of carry in the very futures instruments that VXX holds in its portfolio.

VXX is designed to replicate, net of expenses, the S&P 500 VIX Short-Term Futures Total Return Index. Basically, what this means is that VXX holds in its portfolio a combination of front month and second month VIX futures positions in order to maintain a constant 1-month forward VIX futures positions. For example, at the start of a new expiration month (say August), VXX would be holding nearly 100% August VIX futures in its portfolio. Two weeks to go to expiration, VXX would be holding roughly 50% August VIX futures and 50% September VIX futures. As August expiration approaches, VXX would be holding closer to 100% September VIX futures position. The daily performance of VXX would be similar to the weighted average daily price changes of the first two month VIX futures positions.

VIX futures are almost always in contango. Contango means that each subsequent expiration month of VIX futures prices would be trading higher than the closer month's VIX future prices and the spot VIX overall (upward sloping curve). The top graph (in blue) shows the average premium that VIX front month futures trades over Spot VIX with X number of days to go before expiration. The red line shows the average premium that VIX second month futures trades over Spot VIX. Finally, the Green line shows the daily average cumulative cost that VXX incurs to its portfolio by selling the front month VIX futures and buying second month VIX futures on a daily basis. The average monthly cost that VXX incurs is around 6.5%. This means that on any given month, even if VIX were to remain constant, VXX price would fall by 6.5% when VIX futures prices are in contango.

Remember, that when VIX rise above 25, VIX futures usually goes into backwardation. Backwardation can be understood as the opposite situation as contango. Backwardation begins to happen when Spot VIX is higher than front month VIX futures, and complete backwardation occurs (very rarely) when VIX futures prices of each subsequent expiration month is lower than the price of VIX futures in expiration months that are closer (downward sloping curve). When VIX futures are in backwardation, VXX prices would theoretically rise as time passes, even if spot VIX were to remain constant.

The second graph above plots the actual VXX prices (in red) since the beginning of 2012. The black line represents theoretical VXX price taking into account the daily price change of VIX less the average daily cost of carry for VXX as calculated from this analysis. As you can see, while the black line does not move exactly to actual prices of VXX, on a weekly and monthly basis, it moves very similar to actual VXX prices.

For many who thought VXX was a good instrument to buy and hold, as a hedge against rising volatility, have suffered considerable losses. Mainly, this is because of the cost of carry in the very futures instruments that VXX holds in its portfolio.

VXX is designed to replicate, net of expenses, the S&P 500 VIX Short-Term Futures Total Return Index. Basically, what this means is that VXX holds in its portfolio a combination of front month and second month VIX futures positions in order to maintain a constant 1-month forward VIX futures positions. For example, at the start of a new expiration month (say August), VXX would be holding nearly 100% August VIX futures in its portfolio. Two weeks to go to expiration, VXX would be holding roughly 50% August VIX futures and 50% September VIX futures. As August expiration approaches, VXX would be holding closer to 100% September VIX futures position. The daily performance of VXX would be similar to the weighted average daily price changes of the first two month VIX futures positions.

VIX futures are almost always in contango. Contango means that each subsequent expiration month of VIX futures prices would be trading higher than the closer month's VIX future prices and the spot VIX overall (upward sloping curve). The top graph (in blue) shows the average premium that VIX front month futures trades over Spot VIX with X number of days to go before expiration. The red line shows the average premium that VIX second month futures trades over Spot VIX. Finally, the Green line shows the daily average cumulative cost that VXX incurs to its portfolio by selling the front month VIX futures and buying second month VIX futures on a daily basis. The average monthly cost that VXX incurs is around 6.5%. This means that on any given month, even if VIX were to remain constant, VXX price would fall by 6.5% when VIX futures prices are in contango.

Remember, that when VIX rise above 25, VIX futures usually goes into backwardation. Backwardation can be understood as the opposite situation as contango. Backwardation begins to happen when Spot VIX is higher than front month VIX futures, and complete backwardation occurs (very rarely) when VIX futures prices of each subsequent expiration month is lower than the price of VIX futures in expiration months that are closer (downward sloping curve). When VIX futures are in backwardation, VXX prices would theoretically rise as time passes, even if spot VIX were to remain constant.

**As a rule of thumb, from the beginning of a new expiration month, for each trading day VXX could fall on average 0.25% as a result daily roll cost from contango. With 5 days to go before expiration, VXX could fall on average 0.45% each trading day. Another way of looking at this is on a weekly basis. With 4 weeks to go before expiration, the cost of daily roll from contango could be seen as 1.25% for each passing week, but during the final week before expiration, the cost of daily roll increases significantly to 2.25% for the week!**The second graph above plots the actual VXX prices (in red) since the beginning of 2012. The black line represents theoretical VXX price taking into account the daily price change of VIX less the average daily cost of carry for VXX as calculated from this analysis. As you can see, while the black line does not move exactly to actual prices of VXX, on a weekly and monthly basis, it moves very similar to actual VXX prices.

## Tuesday, July 10, 2012

### Should SPY Fall Below 133 Level, Expect VIX To Jump 23 level.

SPY closed at 134.14 on July 10, 2012, right at its 20-day moving average. VIX closed at 18.72. Remember the chart of VIX median values from the previous post. When SPY is in an uptrend and above its major moving averages, the median value or 50/50 probability line of VIX is around 18%. The median value of VIX jumps to 22%-23.5% when SPY trades below its 20-day & 50-day moving averages.

FVE has stopped declining and has begun to rise again and currently stands at 20.89 compared to VIX of 18.72. As long as SPY remains above 133 level, I believe investors would still believe that the current rebound would continue (hence VIX to remain below 20 level). Should 133 support level fail to hold, I would expect SPY to test its 200-day moving average again and expect VIX to climb to 23 level.

FVE has stopped declining and has begun to rise again and currently stands at 20.89 compared to VIX of 18.72. As long as SPY remains above 133 level, I believe investors would still believe that the current rebound would continue (hence VIX to remain below 20 level). Should 133 support level fail to hold, I would expect SPY to test its 200-day moving average again and expect VIX to climb to 23 level.

## Wednesday, July 4, 2012

### Probability Analysis of VIX (in greater detail)

In the previous post "Assumptions Behind FVE Model", I wrote that implied volatility is a reflexive function of realized volatility of the underlying + statistical relationships on supply & demand of options based on characteristic movement of the underlying. Basically, an investor could get a good sense of the "appropriate" value of VIX based on the analysis of 1) realized (future estimate) volatility & 2) characteristic movement of the underlying. I am going to walk through this process.

First, using various GARCH models, one could calculate an annualized volatility number of the future volatility of the underlying from 1 week to 1 month out. In the case of S&P500 Index, the following link (http://vlab.stern.nyu.edu/analysis/VOL.SPX:IND-R.EGARCH) provides updated values from several GARCH models. The first chart in this post shows these numbers in graph form from one of the models. The latest value is 15.68%. One should then compare this number to the At-The-Money (ATM) implied volatility level of July/August S&P500 Index option, depending on days to go before expiration. July ATM implied volatility is around 14% while August ATM implied volatility is around 15%.

Second, I have calculated the median values of VIX dependent on where the SPY ETF price is relative to its various moving averages since 1994. As shown in the second chart (in black & grey), the median value (50/50 probability) for VIX when SPY is above its moving averages is around 18%, while it ranges from 22-26% depending on whether SPY has fallen below its corresponding moving averages. I would say the 20-day, 50-day, & 200-day moving averages are most widely used. I have also included two other "distinct" periods when VIX remained high or low for an extended period of time. Between 2003-2007, VIX remained very low, with median VIX levels around 13.6% during SPY rising trend and 16.4-24.4% during SPY falling trend (shown in blue & cyan). On the other hand, between 2008-2011, VIX remained very high with corresponding median VIX levels of 20.5% and 26-31% (shown in red & orange). I believe the long-term median values in black & grey are more befitting to the current market environment in 2012.

Finally, the third chart above shows graph of VIX relative to FVE. As described in the previous post, FVE takes in to calculation realized volatility and characteristic movement of SPY, as well as other factors. According to FVE, VIX is clearly undervalued.

However, an investor must always consider that models, even the best ones, do not predict outcomes, but only try to calculate expected or more likely outcomes. As in Texas Holdem, even with a 90% probability of winning the hand, one could lose everything especially if one bet all-in. Calculating appropriate VIX levels in the methodology described above is still much more of a challenge.

First, using various GARCH models, one could calculate an annualized volatility number of the future volatility of the underlying from 1 week to 1 month out. In the case of S&P500 Index, the following link (http://vlab.stern.nyu.edu/analysis/VOL.SPX:IND-R.EGARCH) provides updated values from several GARCH models. The first chart in this post shows these numbers in graph form from one of the models. The latest value is 15.68%. One should then compare this number to the At-The-Money (ATM) implied volatility level of July/August S&P500 Index option, depending on days to go before expiration. July ATM implied volatility is around 14% while August ATM implied volatility is around 15%.

**Based on realized (future estimate) volatility analysis, I would say that current implied volatility levels are low or undervalued.**Usually, volatility values from various GARCH models are lower than ATM implied volatility values. The reason is that investors would rather buy options than sell them, given a 50/50 outcome of a gain vs a loss, because the potential payout of unlimited gain and limited risk is far more attractive. Furthermore, if the EGARCH model estimate of 15.68% proves to be accurate, options theory tells us that one could purchase ATM options at an average14.5% implied volatility level and dynamically scalp deltas at 15.68% volatility level for a theoretical profit. Of course, commissions, slippage, and other costs would come into play, but these costs are very low for market makers. To them, the current situation would be like owning free options, and free options are always good...*should the EGARCH model estimate prove to be accurate.*Second, I have calculated the median values of VIX dependent on where the SPY ETF price is relative to its various moving averages since 1994. As shown in the second chart (in black & grey), the median value (50/50 probability) for VIX when SPY is above its moving averages is around 18%, while it ranges from 22-26% depending on whether SPY has fallen below its corresponding moving averages. I would say the 20-day, 50-day, & 200-day moving averages are most widely used. I have also included two other "distinct" periods when VIX remained high or low for an extended period of time. Between 2003-2007, VIX remained very low, with median VIX levels around 13.6% during SPY rising trend and 16.4-24.4% during SPY falling trend (shown in blue & cyan). On the other hand, between 2008-2011, VIX remained very high with corresponding median VIX levels of 20.5% and 26-31% (shown in red & orange). I believe the long-term median values in black & grey are more befitting to the current market environment in 2012.

**Based on probability analysis, current VIX value of 16.6 is low compared to 18% median value.**Finally, the third chart above shows graph of VIX relative to FVE. As described in the previous post, FVE takes in to calculation realized volatility and characteristic movement of SPY, as well as other factors. According to FVE, VIX is clearly undervalued.

However, an investor must always consider that models, even the best ones, do not predict outcomes, but only try to calculate expected or more likely outcomes. As in Texas Holdem, even with a 90% probability of winning the hand, one could lose everything especially if one bet all-in. Calculating appropriate VIX levels in the methodology described above is still much more of a challenge.

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