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Platinum's Standard Deviation [SD] Bands provide you with a great reality check for positions you are evaluating and correspond to Expected Moves and Expected Ranges discussed by Optionetics' traders. The Expected Move value is based on past movement in the underlying and is an approximation of the standard deviation that can be used when looking a few days out. By adding SD Bands to your Risk Graphs you can quickly see the likelihood your position will be in a profitable or unprofitable zone over the next few days. Monitoring these values also helps with trade management once the position is established.

Although this article uses a more complex position, the 231 Modified Butterfly, focus on the price chart and trade data above the chart if the risk graph seems confusing. The discussion covers basic trade considerations such as risk, reward and breakevens. Those traders interested in reviewing the nitty-gritty statistical background can go to the information at the end of this article.

Trade Analysis

Figure 1 provides a Risk Graph 2 view of a torpedo trade discussed by Scott Kramer in his trade journal. This is an OEX (S&P 100® Index) modified butterfly trade from Feb 2009.

Figure 1: Risk Graph 2 View of Feb 2009 OEX Torpedo Trade (SV=20-days)
click here for larger view

With the OEX at 372.24 and three days to expiration, this credit trade has a downside breakeven of 344.90 and is ideally suited to an Expected Move analysis. The trade is profitable at its current level and all the way down to 344.90, which is a 7.3% move downward. The black horizontal line in Figure 1 is set at the breakeven and appears as a lighter blue line in Platinum (as seen on the risk graph portion). Profits are maximized at the short put strike of 350, while losses accrue to 9,800 below 344.90.

The type of SD Band displayed with the trade uses statistical volatility to create two bands around the current price:

• +/- 1 SD band (red) and
• +/- 2 SD band (blue).

The number of days used to determine statistical volatility [SV] is a user-defined value selected from the General Settings page in Platinum. The Finding Trades section is used to identify the number of days used in the SV calculation and includes: 6, 10, 20, 90 & 100. Using the 20-day SV and return assumptions for OEX, Figure 1 provides the following probabilities regarding the index level:

• There is a 68% chance that OEX will be between 357 & 390, and
• There is a 95% chance that OEX will be between 342 & 407.

The index levels provided are estimated values using the stock chart provided, but they do roughly translate to +1SD (390), -1SD (357), +2SD (407) and -2SD (342). More exact values can be determined with other Platinum tools, including Probability of Profit (see Analytical Toolbox: Probability of Profit from 8/24/06).

What does this mean for the position? Since the trade is profitable when the OEX closes above the breakeven level of 344.90 and this value is just within the +/- 2 SD band, there is roughly a 95% chance the position will be profitable over the next few days. Although the calculated probabilities are high, it doesn't mean you don't manage your risk for such a position. With a 1:1 risk-to-reward, the position should be monitored with a max loss level or index price/level exit identified.

When using SD Bands with your trade analysis, keep in mind that probabilities are more effective as the time horizon shortens. In this case, the bands are particularly effective since there are only three days remaining until expiration. The assumptions used for this method include those that are standard with option models and stock return analysis, and include:

1. The 20-day SV will remain the same over the next three days and
2. The average index value over the next three days will be 372.24.

Changing the SD Band

Using a shorter-term SV is clearly a reasonable choice with three days to expiration, but what if OEX SV returns to the levels that we saw last Fall? You can pretty easily get a view of such a scenario by switching the General Settings to 100-dy SV in the Finding Trades section. Figure 2 provides the revised SD Bands over 100 day period (same number of days on the previous chart). Now the SV is 58.26% versus 40.67% which was the SV for the shorter period. The breakeven level of 344.90 now appears to be just outside the lower band of the 1SD amount.

Figure 2: Risk Graph 2 View of Feb 2009 OEX Torpedo Trade (SV=100-days)

A trader reads this as, "in the event SV is closer to the 100-day level, there is a slightly better than 68% chance the position will be profitable at expiration." When applying the tool you need to keep the method assumptions in mind, but hopefully this illustrates both the usefulness and flexibility of the tool. Again, shorter time horizons have a greater chance of realizing price and index levels identified in Platinum expectations.

Accessing SD Bands

Three steps are required to set SD Bands on your Risk Graph II charts:

1. Go to the Finding Trades section of the General Settings page your Platinum application. Set Statistical Volatility to one of five SV settings.
2. Move down to the Risk Graph II and Overlay Settings section of the general Settings page and select 1 & 2 Stand Dev Bands in the Price Band field.
3. Access the charts via the Risk Graph II selection in the Trade Tools area and select Modern view in the Chart Variables and Scale Limits portion of the web page, which appears below the graphs.

The Statistics Backing It Up

Using an approximation that is based on given assumptions is the nature of the beast in trading. There are simply no guarantees, but hopefully the example provides a reasonable approach for your trade decision-making. It does represent a market maker's focus on Expected Moves and Expected Range that you can see in Scott Kramer's trading.

To add some precision to the Expected Move, Expected Range, Standard Deviation and Standard Deviation Bands terms, the following information is summarized from Platinum Help and Cajun5's coverage of the topic on the Mathematics and Theory of Options Discussion Board.

Expected Move: The Expected Move provides a statistical estimate for price one day in the future calculated as follows:

EM = Price today * Volatility / sqrt(365)

Expected Range: The expected range takes today's price and adds/subtracts the Expected Move:

ER is: Today's price - EM < Today's price < Today's price + EM

Standard Deviation: The stock price in the unknown future is assumed to have a statistical distribution based on a volatility value, V. Given the volatility, V, the stock price in the future, D days from today and 1 standard deviation (SD) from the stock price today can be computed using these equations (See Natenburg, Option Volatility and Pricing, Appendix B):

1 SD Up D days in the future = Price today * e^{[V*sqrt(D / 365.25)]}

1 SD Down D days in the future = Price today * e^{[-V*sqrt(D / 365.25)]}

Mathematical Relationship between EM and SD (discussion board): In the SD calculation, we can replace V*sqrt(D / 365.25) with e^x which has the formula: e^x = 1+x+x²/2! + x³/3! "

When x is less than 1.0, the following approximation is made:

e^x ~= 1+x, where x=Volatility*sqrt(Days/365)

Stated another way: x= Volatility/sqrt(365) when Days = 1

Substituting the above into the Standard Deviation Bands for Days = 1 we get:

1SD up = Stock Price*(1+Volatilty/sqrt(365))
= Stock Price + Stock Price * Volatility / sqrt(365)
= Stock Price + EM

So the Expected Move formula is really an approximation to the Standard Deviation Bands formula when used for just a few days expected move.

Standard Deviation Bands: A 1SD Band is generated using the current price and adding 1SD to create an upper band and subtracting 1SD to create a lower band. This calculation is completed for each day viewed on the chart, using that day's selected SV value.

A 2SD Band is generated using the current price and adding 2SD to create an upper band and subtracting 2SD to create a lower band. This calculation is completed for each day viewed on the chart.

The stock price 2 V standard deviations D days from today are:

2 StdD Up D days in the future = Price today * e^{[2*V*sqrt(D/365.25)]}

2 StdD Down D days in the future = Price today * e^{[-2*V*sqrt(D/365.25)]}

For more information on expectations for price going forward, see Analytical Toolbox: Future Prices & Standard Deviation Bands, 8/31/06. Both article references provided were jointly written by John Broussard (a.k.a. Cajun5) and Clare White.


To access other articles written by Clare White, please click here.

Clare White
Contributing Writer and Options Strategist
Optionetics.com ~ Your Options Education Site
Questions for Clare? Visit the Optionetics.com Discussion Board

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