Implied equity market
volatility (as measured by VIX) is determined by a reflexive loop between the
derivative and underlying markets based on future estimate of realized
volatility of the underlying (S&P500 Index) + characteristic movements of
the underlying. There are of course many more factors that affect the VIX--such
as skew of implied volatility curve, day of the week, holidays in a given
month, upcoming events that could impact the market--just to name a few.

Unlike determining the
direction of stock prices, forecasting volatility can be a matter with which
investors are unfamiliar. While this
may sound like a complex concept, it can be easily broken down into three parts.

*I. Forecasting Market Volatility (VIX)*

*II. Understanding VIX Futures Related ETNs (VXX)*
*III. Forecasting VXX Prices*

*I. Forecasting Market
Volatility (VIX)*

In a nutshell, an
investor could get a good sense of whether equity market volatility or VIX is
cheap or expensive based on following the analysis of 1) Various GARCH model
estimates and 2) Median Curve of VIX dependent on (SPY)
prices in relation to its various moving averages.

The first step
involves looking at estimates of future realized volatility. V-Lab
is an excellent website to get up-to-date estimates of the future realized
volatility of the S&P500 Index based on various GARCH models. (Wikipedia is an excellent resource to
understand the technical definitions of GARCH
Models). In V-Lab, click on SPX, and
several analyses of S&P500 Index will show. I like to look at EGARCH return series (just a personal
preference). The graph below is from
V-Lab and shows EGARCH volatility prediction for future realized volatility of
the S&P500 Index. As of August 23,
2012, the value for 1-month prediction was 15.13%.

One should then
compare this number to the At-The-Money (ATM) implied volatility level of
S&P500 Index options, depending on number of days to go before
expiration. Since we have two weeks
remaining to August expiration, we should average the implied volatility levels
of SPY August & September 139/140 strike options, which are
At-the-money. ATM implied volatility
numbers can be found in Morningstar's
website under "Options" tab for SPY and the average currently stands
at 14.4%.

Usually, volatility
values from EGARCH model are a couple of points lower than implied volatility
values of ATM options. 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 15.13% proves to be
accurate, options theory tells us that one could purchase an ATM options
straddle at 14.4% volatility level and dynamically scalp deltas at 15.13%
volatility level for a small, but riskless profit. Commissions, slippage and other costs could make this trade less
attractive, but these costs are very low for market makers. To market makers, the current situation
would be like owning almost free options, and almost free options are always a
good to own. **Based on realized
(future estimate) volatility analysis, I would say that current implied
volatility levels are undervalued.**

The second step is to
look at median values of VIX dependent on where SPY prices are relative to its
various moving averages because changes in VIX are dependent not only in the
volatility of SPY prices, but also in how comfortable investors are about the
market. The chart below shows analysis
that I conducted. Median values
represent 50/50 probability of VIX being above or below a specified level based
on historical data.

For example, since
1994, shown in black & grey, when SPY prices were in an up trend and above
its moving averages, the median VIX levels were around 18%. On the other hand, when SPY prices were in
correction and below its moving averages, the median levels were between
22-26%. I would say that the 20-day,
50-day, & 200-day moving averages are most widely followed.

I also included two
other plots showing "distinct" periods when VIX remained high or low
for extended periods of time. Between
2003-2007, shown in blue & cyan, VIX levels remained low. The median VIX level when SPY prices were
above its moving averages was around 13.6%, while when SPY prices were below
its moving averages, median VIX levels ranged from 16.4-24.4%. On the other hand, between 2008-2011, shown
in red & orange, VIX levels remained high. The median VIX levels during
this period were 20.5% and 26-31%, respectively. I believe the long-term median VIX values in black & grey are
befitting to the recent market environment in 2012

If we look at the
current graph of SPY below, SPY closed on August 3, 2012 at 139.35 and remains
above all moving averages and is moving within a clearly defined uptrend. Based on median VIX value analysis, I would
think VIX levels around 17 would be considered “fair value”. VIX closed at 15.64 on August 3^{rd}**,
therefore, probability analysis also confirms that current VIX level is
undervalued****.**

Finally, the third
chart below shows the graph of VIX relative to my custom built, Fair Volatility
Estimate (FVE) Indicator. FVE takes
into calculation 1) the future realized volatility estimate and 2)
characteristic movements of SPY, as well as other factors, in a visually simple
indicator. According to FVE, VIX remains below FVE’s value of 18.9 and thus
visually illustrates the conclusions we drew from the two separate analyses
above that VIX remains “undervalued”.

Now that we have
walked through this process and determined that VIX is indeed undervalued based
on 1) estimate of future realized volatility and 2) historical probability, how
can we make money off of this analysis?

*II. Understanding VIX
Futures Related ETNs (VXX)*

Unfortunately, VIX is
not an instrument one could realistically trade. There are instruments that have been created based on VIX
futures, but these instruments have complex idiosyncrasies of their own. Let us look at iPath S&P500 VIX
short-Term Futures ETN (VXX) because it is by far the most popular VIX-related
instrument available to retail investors.

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. With 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 monthly VIX futures
positions.

Many investors who
thought VXX was a good instrument to buy and hold or use it as a hedge against
rising volatility have suffered considerable losses. Mainly, this is
because of the cost of carry as a result of contango in the very futures
instruments that VXX holds in its portfolio.
Contango means that each subsequent expiration month of VIX futures
prices are trading higher than the closer month’s VIX futures prices and the
spot VIX overall (upward sloping curve).
The effects of contango on VXX can be seen visually in the graph below. The graph shows the average premium the
front month and second month VIX futures trades over spot VIX over time, along
with cumulative average cost per month that puts significant downward pressure
on VXX prices.

When in contango, VIX
front month futures (in blue) on average start off 10% higher than the spot VIX
with 21 trading days to go before expiration.
As expiration approaches, this premium goes to zero. Likewise, VIX second month futures (in red)
on average start off 15% higher than spot VIX.
The premium on this goes down as well as time passes. The net effect (shown in Green) is that VIX
futures contango has reduced on average the price of VXX by 6.5% per month!

Remember,
when VIX rises above 25 level, VIX futures usually goes into
backwardation. Backwardation can be
understood as the opposite phenomenon 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.

To
test the accuracy of how contango affects VXX prices, I plotted VXX prices from
the beginning of 2012 and compared this to the theoretical VXX price taking
into account the daily price change of VIX less the average daily cost burden
from VIX futures contango. As you can see over time, theoretical VXX
prices mirrored actual VXX prices as shown in the graph below.

**As a rule of thumb, from the beginning of a new
expiration month, the average daily cost from contango has been 0.25% for each
trading day. With 5 days to go before
expiration, however, the cost has jumped to 0.45% for each trading day. More appropriate way of looking at this is
on a weekly basis. With 4 weeks to go before expiration, the effects of
contango has eaten away on average 1.25% from the price of VXX each passing
week, but during the final week 2.25% has been chomped off!**

*III. Forecasting VXX
Prices*

Now that we have
understood what VXX is and how contango affects the price of VXX, let us
revisit our VIX forecast from above and translate this into a forecast for VXX
prices. Let us assume that fair value
of VIX is around 18 level, and VIX will rise to 18 sometime in the next two
weeks before August VIX Expiration. As
long as SPY prices continue to trade within its rising channel, VIX is expected
to fluctuate from 16-19 level for the next two weeks as well. VIX August futures price closed at 17.20,
and VIX September futures price closed at 19.40 on August 3rd.

If VIX were to rise to
18 level one week from now (15.1% higher from 15.64 level), VIX August &
September Futures prices could be expected to trade around 18.85 & 20.25,
respectively, according to the average premiums VIX futures trade over spot VIX
when in contango with 7 trading days to go before expiration. Calculating for the weighted average rise in
VXX’s portfolio of VIX August & September futures positions, VXX is then
expected to rise 6.9% to 13.0 from August 3^{rd} closing price of
12.16. Following the same methodology,
if VIX were to rise to 18 level right before August expiration (slightly over
two weeks from now), VXX is expected to be trading around 12.55, or just 3.0%
higher than August 3^{rd} closing price! Finally, if VIX were to move within 16-19 range until VIX August
expiration, VXX prices could trade between 11.15 to 13.70. **Please consider how different VXX moves
in comparison to spot VIX and understand how important it is to not only to
forecast VIX but to carry out analysis to forecast VXX when one wants to trade
volatility instruments.**

A
superior risk adjusted trading strategy to execute based on the above forecasts
would be to buy August VIX futures while simultaneously selling September VIX
futures as a spread. The logic behind
this trade is that the front month futures would rise a greater percentage than
the second month futures if VIX were to rise as expected, but at current price
levels, the spread is not expected to lose much if VIX does not rise. Another strategy would be to sell the VXX
August monthly 13/14 call spread and sell the VXX 12 puts for close to 0.70
credit, which should generate a profit if spot VIX moves within our forecast,
but should VXX fall close to 11 level, it would be worth owning VXX outright
for a short-time to recover any losses from this options spread.

By:
Steven Lee

Disclosure: I am slightly long VXX and because VXX is an
instrument to trade, I could exit out of this position in the next 72 hours.