with respect to the moving average of the closing price; if not, all three trendlines may weave around one another. A volatility function can also be used to create a band. Rather than the simple percentage calculation shown first, the band may be increased at rates equal to a price-volatility relationship. All of the methods of forming bands are subject to scaling. Scaling is accomplished using a value as a multiplier or scaling factor; it will increase or reduce the sensitivity of any technique used for calculating the band, if S is a scaling factor, then the following bands can be constructed:

B=M,±ScM, (percencage smoothing)

B=M, ±ScP, (percentage smoothing using price)

B=M, ± Sx-R (fixed risk using absolute point value)

(independent smoothing of highs or lows)

Bv = Sxf{H,y B = Sf(L.)

B=M,± S{H.-L,y (volatility of hi-low)

B=M, 5 X V(P,) (volatility function at price level)

B=M, ± (volatility at moving average level)

When S = 1, the scaling effect is nullified; for S := 1, the width of the band is magnified; and for S =: 1, the band is reduced.

Different bands are not mutually exclusive. A variable band may be used to time the entries and exits subject to a maximum rid; established by another band. It may also be convenient to have separate exit and entry bands, the first more sensitive, such that a reversal of position is not ahvaj-s necessarj An exit band may be based on the intraday high or low prices while entries are determined by closing prices

Bollinger Bands

Perhaps the simplest and most robust measurement of price volatility is the standard deviation of the prices themselves over recent price history. Originally introduced by John Bollinger and popularly called Bollinger bands, the value of 2 standard deviations of price movement over the past 20 periods are plotted above and below a 20-dsj-moving average. As with other techniques, the popularity of the computer has allowed users to change both the calculation period and the number of standard deviations that form the band. Because the standard deviation represents a confidence level, the choice of 2 standard deviations equates to a 9° confidence band, while 3 standard deviations give a confidence band of 99° o.

Another way of viewing Bollinger bands is as a percentage, seen as "ob: "ob = (Close - Lower band) / (Upper band - Lower band)

In TradeStation, a function that retums the upper and lower generalized Bollinger bands, given the calculation period and standard deviation factor, is

{Function BollingerJand

Returns the width of the Bollinger band as measured from the moving average valuel irputs:period(nuner1csiniple), nsd(nunieric); Bollingerjand = nds * @stddev(close,period);

From the main program, the bands are created with the following inshnctions:

bandwidth = Bollinger Band(per1od,nsd); highband = @average(clDse,period) + band width; lowband = @average(close,period) - band width;

An excellent example of Bollinger bands uses a combination of weekly and daily data applied to the S&P 500, as seen in Figure 5-1. The price pattern follows the weekly Bollinger band higher, where the daily and weekly come together during the week of July 14.

Rules for Using Bands

Regardless of the tjpe of band that is constructed, rules for using bands to generate trading signals are limited. The first decision to be made is whether a current position will be liquidated or reversed, causing the entry into a new position in the opposite direction. Assuming a reversal from long to short and from short to long, the following rules apply:

Buy (close out shorts and go long) when the price penetrates (closes above) the upper band.

Sell (close out longs and go short) when the price penetrates (closes below) the lower band

This technique is alwajs in the market with a maximum rid; (without execution costs) equal to the width of the band at the time of entry (see Figure 5-2). If a neufral position is preferred after exiting from each hade, there are the alternative rules:

Buy (go long) when prices penetrate the upper band. Close out longs when prices reverse and go below the moving average value (the center of the band).

Sell (go shortj when prices break below the lower band. Cover your shons when prices penetrate upward through the moving average value.

The band is then used to enter into new long or short trades, and the actual frendline within the band is used onljr for liquidation. If prices are not strong enough to penetrate the opposite band on the close of the same dsy, the trade is closed out but not reversed. The next dsy, pendration of either the upper or lower band will signal a new long or short trade, reapectively.

This technique allows a trade to be reentered in the same direction in the event of a false breakout. If a pullback occurs after a closeout while no position is being held (as shown in Figure 5-3), an entry at a later date might be at a better price. A disadvantage occurs when the price changes direction and moves so fast that both the closeout and the new signal occur on the same dsy. Reversing the position immediately would be better in a fast maricet.

The high and low of the dsy may also be used as penetration criteria. Again, using the outer bands for entry and the moving average for exit, apply the following rules:

FIGLIRE 5-1 Combining daily and weekly Bollinger bands.

FIGURE 5-2 Simple trading rules for moving averages.

Buy when pncet move up through band

FIGURE 5-3 Basic rules for using bands.