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Fair Volatility (VIX) Estimate Model & Indicator 8-19-13

|Includes: SPY, iPath S&P 500 VIX Short-Term Futures ETN (VXX)

Here is a section of content that I have written and have yet to write much more. I do not know what the final structure of the amalgamation of my research over the years would be, whether that would take shape in an ebook, an educational manual, or just many more posts in my blog. This blog has served as a personal journal of my interests in the financial markets and in volatility. Perhaps it is time I start to engage more with those that visit this site. I would highly appreciate any feedback you could provide. Thank you.

Fair Volatility (VIX) Estimate Model & Indicator 8-19-13

I designed Fair Volatility (VIX) Estimate Model & Indicator back in May 2010. I had left the professional trading world the previous year. Computers & high frequency trading had taken away most of the profitability of my once very small but highly lucrative options market making business. Yet, the allure of trying to understand the markets kept me engaged, so in my spare time I tinkered with a crude econometric model with the combination of parameters that could mimic the CBOE Volatility Index (VIX).

VIX is calculated from a weighted average of implied volatilities from options prices of multiple strikes on the S&P500 Index with a constant maturity of 30 days to expiration. For example, a VIX number of 15 technically reflects the option market participants' expectation that the S&P 500 Index would move within a ~4.33% range up or down (with confidence of one standard deviation or 68%), within a one-month time frame. Because VIX represents an annualized volatility number, we need to divide 15 by the square root of 12 (months in a year) in order to come up with a one-month equivalent number.

In reality, however, VIX reflects the market's expectation of price volatility, fluctuation AND behavior of the S&P500 Index looking 30-days into the future.

S&P500 Index options are bought as insurance to protect against potential decline in the value of equity portfolios. Obviously, the higher the demand, higher the value of protection and thus higher VIX levels. This is why VIX is commonly referred to as the "Fear Index". It is well known that VIX usually moves in opposite direction as the S&P500 Index. This inverse correlation is seen 70 - 80% of the time. Therefore, in building a VIX model, we should look at more than just volatility.

VIX is a function of Volatility Factor & "Fear" Factor.

Before I delve in to these factors, I wanted to explain why I consider my model to be crude. I am not a mathematician, nor do I have the skills to come up with a beautiful theory. I compare myself to that of an amateur airplane model builder with great reluctance and concern that my model would crash and burn. However, the desire to fly has always been strong, even if the flight has been under a simulator. I have simulated the Fair Volatility Estimate indicator using simple trading rules on VIX futures and VXX for over three years now. I believe it is time now to share my designs.

I do not have expectations that my designs would have any commercial success. However, I believe it could provide educational value and perhaps ideas and insights for others to achieve their goals. In particular, to the vast majority of traders and investors that do not fully grasp complex mathematical concepts and options theory, I am in the same vehicle as you. Yet, perhaps it is someone like me that can speak the same language and serve as a guide to your journey in trading and in financial markets. The attractiveness and utility in trading volatility as an asset class is too good not to learn more about it.

Chart of FVE & VIX 8-19-13

FVE Trading Simulation on Front Month VIX Futures 8-16-13

Volatility Factor:

Based in options theory, it is my understanding that the core component of any volatility model is a way to efficiently calculate realized volatility, otherwise known as historical volatility or statistical volatility. I prefer the term "realized volatility" because there is a strategy in options volatility trading known as gamma scalping, which is a form of volatility arbitrage

In gamma scalping, one would buy for example the options straddle of an underlying stock or index and then at certain price or time intervals hedge the delta exposure of the options straddle by buying or selling the underlying instrument. Let me explain this process in greater detail.

For example, let us say you bought 100 September straddles (long Sep 37 call, long Sep 37 put, each 100 contracts) for the combined price of 2.25 and implied volatility of 24% on XXX stock. This straddle purchase would cost you $22,500. Now let us also imagine an extreme case that XXX stock price for the next one-month period remains unchanged on a day-to-day closing price of 37. In this case, at expiration, you would lose the entire $22,500 by holding the straddle as it expires completely worthless

However, let us also assume in this extreme example that intraday, XXX stock price fluctuates up or down by $1 and back to the closing price of 37. Let us also assume that you hedge your delta exposure of the straddle by buying and selling XXX stock as the price fluctuates intraday. If the gamma on the 37 strike options is 0.14, then with XXX stock $1 lower to 36 intraday, the delta of the calls would change from +0.50 to +0.36, and the delta of the puts would change from -0.50 to -0.64. The new net delta of the straddle with stock price at $36 would have changed to -0.28 from zero. On an options position of 100 straddles, this would mean buying 2800 shares (-0.28 * 100 straddles * 100 unit shares/per option) of XXX stock at the price of 36 to bring the net delta exposure to zero. Finally, as the price of XXX stock moves back to 37 by market close, you would sell the 2800 shares that were bought at XXX stock price of 36 in order to bring the net delta exposure back to zero. On the flip side, if the stock moves up from 37 to 38 intraday, then you would short sell 2800 shares of XXX stock at 38 to hedge the new delta exposure of the straddle of +0.28. Once again, as the stock price closes at 37, you would buy back the 2800 shares stock sold short at 38.

This is a simplistic and unrealistic example which does not account for the change in gamma over time as well as execution costs. However, if you were to repeat this process each and every day for 21 trading days or one month time frame, you would have lost the entire $22,500 you paid for the options straddle but profited $58,800 from the delta hedging process of buying and selling stock for a net profit of $36,300!

This is where the term "realized volatility" comes from. A $1 price fluctuation intraday of a $37 stock is equivalent to a 42.9% volatility (1/37 * square root of 252-- # of trading days per year). Remember that the September 37 straddle was bought at 24% implied volatility. The rule in any profitable trading is to buy/sell lower/higher and sell/buy higher/lower. In gamma scalping, one is buying/selling implied volatility of options and selling/buying by capturing or "realizing" stock volatility.

Let us take a look at an example of selling implied volatility or selling the straddle using the same scenario as above, except that instead of $1, XXX stock is assumed to fluctuate just $0.30 intraday. To hedge the delta exposure with stock price at 36.70 and 37.30, you would buy and sell 840 shares of XXX stock. The net result would be $22,500 profit from options less $5,292 from delta hedging process for a net profit of $17,208. A $0.30 price fluctuation on a 37 stock price is equivalent to a 12.9% realized volatility. In this reverse example, one would have sold 24% implied volatility and bought at a 12.9% realized volatility.

Volatility arbitrage is the main reason why implied volatility and realized volatility move hand in hand. If they did not, then there would be tremendous opportunities to buy or sell implied volatility against stock volatility. The most important and critical challenge, however, in deciding whether to buy or sell volatility is to determine future volatility of the underlying instrument. Ah, of course! The future is unknown and uncertain.

However, volatility I believe is actually more predictable than the price direction of a stock. Think of volatility as a volt meter. We know from physical reality, that energy moves back and forth from high intensity to low intensity, unlike stock prices which could continue to move up or down.

There are several ways to measure a stock's price volatility. Historical volatility of closing prices is the simplest & most widely known. The following lists other more efficient ways.

1) Historical volatility: close to close

2) Exponentially Weighted

3) Parkinson: High to Low

4) Garman-Klass: Open/High/Low/Close

5) Rogers-Satchell: Open/High/Low/Close

6) Yang-Zhang: Open/High/Low/Close

7) GARCH & EGARCH models[1]

8) Average True Range[2]

9) My "Realized Volatility" calculation

The following report provides an excellent summary of the various ways to measuring historical volatility from 1 - 6 in the above list--(http://www.todaysgroep.nl/media/236846/measuring_historic_volatility.pdf.

GARCH models are also widely looked at as a way to predict future volatility. The Average True Range indicator is widely used in technical analysis, but seldom mentioned in volatility modeling circles.

When designing my "Realized Volatility" measure, I wanted something that was both simple and usable. I analyzed my own delta hedging actions while I was an options market maker and came up with the following formula.

Realized Volatility = 11 trading day exponential moving average of [If (Absolute Value(Log(High/Prior Close))>Absolute Value(Log(Low/Prior Close)), then Absolute Value(Log(High/Prior Close))*square root(252), else Absolute Value(Log(Low/Prior Close))*square root(252))*Adjustment Factor].

Basically, I look at how much the market pushes the price up or down from the prior closing price and translate this into an annualized volatility measure. Then I take the 11-day exponential moving average of those values to come up with my Realized Volatility calculation. The adjustment factor can be 0.80 - 1.00, depending on the longer-term implied volatility levels of the underlying instrument. This Realized Volatility measure does not take into account the general rise in implied volatility levels prior to earnings announcements or other events, therefore, should not be applied to stocks, except for periods one month prior and 2 weeks after such events. It is appropriate for indices, commodities and sector ETFs. The adjustment factor also serves as a tool to use if I want to have a bias of being short or long options, in general, but this adjustment factor makes this measure a tool and not a model.

Here is what the Realized Volatility indicator looks (red), compared to VIX (black) and the traditional historical volatility measure 11-days (green).


[1] http://vlab.stern.nyu.edu/doc/1?topic=apps

[2] http://en.wikipedia.org/wiki/Average_true_range