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Tuesday, August 20, 2013

Fair Volatility (VIX) Estimate Model & Indicator, Part II 8-20-13

This is the second part of the contents of the FVE Model & Indicator.  Once again, the purpose of the two posts is to share ideas.  Your feedback would be highly appreciated.

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

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 FVE < FVE 11 days ago AND
VIX futures price > FVE.


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.

The simulated results would be as follows on VIX front month futures since 1/30/2008

includes 0.075 points slippage & $2.50 per contract commission costs

The simulated results would be as follows on VXX since 1/30/2009

includes 0.05 cents slippage & $25 commissions cost

However, the potential for FVE model utilized in a trading system is much greater.  Recently, I have simulated a trading system with an additional factor included in the FVE model for the purposes of using it as a trading model.  Once again, however, I am reluctant to disclose the adjustment to the FVE model and trading rules because I am highly aware that the adjustments could just be curve fitting or over optimization to past data.  This adjustment and new rules would need to stand the test of time.

I am, however, very interested to find out if my insights to making the adjustment to the FVE model would prove to be sound.  Once again, please take the simulated results with heavy skepticism.  This next graph only shows the maximum potential, not the likelihood of performance.

includes 0.075 points slippage & $2.50 per contract commission costs

Thank you for reading these latest two posts on FVE model & indicator and my blog.  I hope you found it educational.  I have built the FVE indicator in Metastock and had them built for eSignal platforms.  I will try to share these in the not too distant future (although I may have to charge a small fee for processing...sorry).  Finally, I am sharing my research and ideas freely.  However, if you utilize them, please at least acknowledge my research and efforts.  Better yet, share these posts.  As you can see, I am not trying to profit from them.  Thanks.

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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