“Fear”
Factors:
The “fear” factor is the second part that goes into my Fair
Volatility (VIX) Estimate Model. VIX is
a measure of the implied volatility levels of options on the S&P500 Index
with 30-day constant maturity. VIX
reflects the supply and demand for those options. If demand/supply gets stronger relative to the other, VIX rises/falls. Therefore, in order to model the “fear”
factor, I thought about the several factors that would increase or decrease the
demand & supply of options. The
following table summarizes those factors.
Demand & Supply Factors / Expression
|
Explanation
|
Volatility Factor |
|
Expected Future Volatility
/ Use Realized Volatility Measure
|
Volatility Arbitrage looks at opportunities to profit from
differences between expected future volatility of the underlying relative to current
implied volatility (IV) level of options.
Demand/Supply for options will increase/decrease if current IV levels
are low/high relative to expected volatility.
|
Fear Factors |
|
Falling Prices
/ Inverse Correlation
|
While options are great instruments for use in any type of
trading strategy, demand for options is strongest as protection against
falling portfolio value. The shape of
the normal IV curve or skew would show the usual relationship between underlying’s
price and IV direction. For the
S&P500 Index, there is a strong inverse relationship between VIX & the
S&P500 Index.
|
Speed/Acceleration of Price changes
/Slope of Trend
|
Speed is related to but different than volatility. A stock in a strong uptrend could have low
to stable volatility, but the speed would be relatively high. Demand for options is strong when the
speed of decline is high.
|
Price Trend of the underlying instrument
/ Relative Strength of Prices
|
Demand for options increases when the S&P500 index is
in a down trend while supply of options increases when S&P500 Index is in
a steady uptrend. This is similar to inverse
correlation, but more specific to the price trend.
|
Leading Factor, Wave Factor
/ Stochastic RSI of Prices
|
Options prices reflect the expectation of future price
behavior of the underlying instrument. In other words, the changes to implied volatility levels is
believed to be a leading indicator to changes to volatility of the
underlying. While historically this
has not always been the case, we should accommodate this assumption in our
model, which is built using the underlying prices. In technical analysis, oscillating indicators such as Stochastic
Oscillator has some properties of turning before the actual prices do.
|
Let us try to model all the factors and assumptions
described in the table by combining several technical analysis indicators[1].
Fair Volatility (VIX) Estimate or FVE Model & Indicator is
a function of:
1)
Realized Volatility
2)
Inverse Correlation
3)
Slope of Price Trend
4)
Relative Strength Index (RSI)
5)
Stochastic RSI
6)
Adjustment Weight of each Indicator
7)
Adjustment constant for best fit with VIX.
First & major factor is the volatility of the S&P500
Index itself. I developed the “Realized
Volatility” measure discussed in the “Volatility Factor” section to model volatility.
Next, we can combine the inverse correlation and slope of a price
trend factors by using the Linear Regression Slope (LRS) indicator. The LRS indicator moves above zero if the
price trend over a specific time period is calculated to be rising and below
zero if the price trend is calculated to be falling. For inverse correlation, I subtract values from the FVE model when
the LRS is positive and add values if the LRS is negative. More specifically, however, instead of
looking at the speed of a price trend, I believe looking at the acceleration of
the price trend would be more optimal. This can be accomplished by comparing the distance between the LRS
indicator and its moving average. Algorithmically,
this is expressed by the following formula:
Negative of (Linear Regression Slope 11 day – simple 11-day
moving average of the LRS (11)) * Adjustment Weight
Furthermore, we want to look at the current price of the S&P500
Index in relation to its past prices given a time frame. This insight came to me after conducting
analysis on historical VIX values. The
following chart shows the median VIX values when the S&P500 Index is in an
uptrend or downtrend relative to several of its moving averages
The way to interpret this chart is as follows. The black & grey lines show the long-term
median VIX values since 1994. The black
line represents the median value of all VIX values when the S&P500 Index
was above its moving averages, from 5-days to 240 days. The grey line represents the median value of
all VIX values when the S&P500 Index was below its moving averages. The red and orange lines look at median VIX
values during specific times of high volatility, for example between 2008-2012.
The blue and cyan lines look at median VIX values during specific times of low
volatility, for example between 2003-2007.
The current market since 2012 is that of a low volatility
environment. Therefore, given the
current environment, as the S&P500 Index fluctuates above (for example) its
20-day moving average, we can expect with 50/50 probability that VIX would be
around 13 (blue line). When the S&P500 Index
moves below its 20-day moving average, we can expect with 50/50 probability
that VIX would be around 17 (cyan line).
We can use moving averages to express whether VIX values are
expected to be lower or higher, but the 22-day Relative Strength Index
expresses this more efficiently and is easier to calculate. Therefore, the following formula represents expected
incremental changes to VIX dependent on the price trend of the S&P500
Index.
(100 – RSI(22))*0.01
* Adjustment Weight
The leading or wave factor tries to take into account the
assumption that implied volatility level of options is a leading indicator to
price volatility of the underlying instrument.
Even when the S&P500 Index is moving in a clear trend, intraday or
daily prices moves up & down in wave form.
VIX is not only affected by price trends but also is affected by
intraday & day to day price behavior. The Stochastic Relative Strength Index indicator moves quickly up
& down with high sensitivity based on the intraday and day to day price
behavior of the S&P500 Index.
We should take caution that no price based technical
indicator acts as a true leading indicator.
They are lagging indicators. Using them would be like driving a car looking at the rear-view mirror. However, the sensitivity of the Stochastic RSI indicator serves the
purpose of anticipating possible changes to VIX quickly and in combination with other factors serves its purpose better. The algorithm for this leading or wave factor is as follows.
((100 – Stochastic
RSI)*.01)*Adjustment Weight
You probably have noticed the “Adjustment Weight” attached to the three factors described above. Honestly,
this Adjustment Weight is a blunt calculation to adjust the weighting of the
various factors to the absolute value of volatility. In other words, a 10% move in VIX when VIX is at 30 is twice the
amount as when VIX is at 15. Since the
FVE model takes the base Volatility Factor and adds the various components of
the Fear Factors, I needed to increase the value of those components as
volatility rises. The Adjustment
Weight was calculated as follows:
1 + (75% of
Realized Volatility / long-term average of VIX which is around 21.5)
The final component of the FVE model is the Adjustment Constant. This Adjustment Constant was used as a value
for best fit to the actual VIX values. Yes, this is curve fitting, but if we take a look at the
long-term, 6-month average of the difference between VIX and FVE model without this
Adjustment Constant, we can see that the difference has been ranged from 2.0 – 7.0 most of the time. I have used 3.2 since
developing the FVE model since May 2010. Furthermore, this Adjustment Constant is in of itself a good
indicator to show structural changes to VIX. For example, one of the reasons why the FVE model’s trading
performance has been lackluster since October of 2012 could be that volatility
has been aggressively sold since the ECB’s OTM policy announcement on September
6, 2012, when much of the fear of Euro’s collapse that was built into
volatility markets quickly subsided. With
the Adjustment Constant untouched, FVE Model has perhaps been overvaluing VIX
in recent months. Nevertheless, this
Adjustment Constant can be but should not be changed.
Compiling all the factors together, the FVE indicator is
built as follows:
1)
11-day exponential moving average of 75% of Realized
Volatility Calculation Value[2]
+
2)
Negative of (Linear Regression Slope 11 day – simple 11-day moving
average of the LRS (11)) * Adjustment Weight +
3)
(100 – RSI(22))*0.01 * Adjustment Weight +
4)
((100 – Stochastic RSI)*.01)*Adjustment Weight +
5)
Adjustment Constant of 3.2
The following chart shows graphically each component of the
FVE indicator.
In summary, the Fair Volatility (VIX) Estimate Model and
Indicator is just that--an attempt to model VIX.
FVE indicator is a graphical representation of all the assumptions used
to construct the model in its attempt to show how VIX would move in real-time
based on prices of SPY. Because of the numerous variables and the crudeness of the math, the danger that FVE model over fits past data is ever present. However, I have analyzed FVE model on VIX for over three years now since its creation. The efficacy of the FVE model (I believe) lends support to the assumptions that I have built into the model.
Of course, because FVE model is represented as an indicator,
trading strategies can be devised rather easily using the FVE indicator. For example, let us assume the following
simple strategy.
Buy front month VIX futures if FVE > FVE 11 days ago AND
VIX futures price < FVE,
Sell front month VIX futures if FVEVIX futures price < FVE,
Or
Buy VXX if FVE > FVE 11 days ago AND VIX futures price < FVE,
Sell VXX if FVE < FVE 11 days ago AND VIX futures price > FVE. |
| includes 0.075 points slippage & $2.50 per contract commission costs |
 |
| includes 0.05 cents slippage & $25 commissions cost |
 |
| includes 0.075 points slippage & $2.50 per contract commission costs |
Steven Lee
[1] There are
many resources to describe the formulas and assumptions behind most widely used
and known technical analysis indicators.
Just search for them on the web.
[2] I actually
use a filtered version of Realized Volatility Measure that takes out the
outlier effects, for example flash crash of 2010
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