) ispresented as a stepped line. The 4 days of interest are marked by the letters A, B, C,and D and appear on both (a) and (6) of Figure 19-2.
2. The 50-minute HiLo Activator (seen in Figure 19-26) is the moving average of the50-minute highs, used as a Buy Stop, or the moving average of the 50-minute lows,used as a Sell Stop.
3. The 10-minute Gann swings, based on 1line shows when the Gann swing representswhen it shows a downtrend.
‘The interpretation of these techniques relies on the faster response provided by the10-minute bars, combined with the direction given by the longer time frames.
1. Based on the 10-minute Gann swings, the trend turned from up to down at about121-00, while the daily Gann swings place the trend change much later, near 120-00.2. The slope of the daily Gann swing, measured from point X to point Y on both
charts, was down, defining the dominant trend. Short trades can be entered using
the downtrend of the 10-minute time frame. The process of coordinating the trendof the higher time period'with that of the lower time period, and acting in only thatdirection, seems to be the most advantageous approach. The low of each 10-minuteswing, marked £, F G, H, and [on the 10-minute bar chart, provides opportunitiesto add to the original position.
3, At the top left of the 10-minute chart, the 10-minute close falls below the Sell Stopof the 50-minute HiLo Activator at point K (about 120-06). The Buy Stop then ap-plies and follows declining prices for 3 days. These changes occur in the same areawhere the Gann swing indicates a trend change from up to down.
4, The 50-minute moving average of the highs, shown in a step formation on the 10-minute chart, tracks the highs of the market rallies on days 1, 3, and 4. The dailymoving average of the highs (the Daily Hilo Activator) remained level on day 2 andturned down on day 3. The trend can only change to up when the Daily HiLo Acti-
vator turns up again. ‘
O-minute bars (in Figure 19-26). The solidan upward trend, and the broken line
A COMMENT ON MULTIPLE TIME FRAMES
In thinking out the use of multiple time frames it is necessary to understand that you can-not substitute a 10-period moving average of 1-hour bars with a 40-period moving averageof 15-minute bars. Similarly, you cannot substitute a 10-week average with a 50-day aver-age. It seems natural to think that any two trends covering the same time span will give thesame result, but that is not the case. Although we can average many data points, we cannotget rid of all the noise; fewer data points over the same time span will always yield anoother result. Therefore, the use of hourly, daily, and weekly time periods—multipletime frames—gives a much different picture of the market than simply using three differ-ent moving averages based on the same data. It is much easier to see the major trend usingSeekly data, find the short-term direction based on daily data, and time your entry using
hourly bars.
> This chart analysis was provided by Robert Krausz.
20
Advanced Techniques
 
stop-loss points and point-and-figure box sizes. But volatility is more uniform than¥ its short-term measurement would imply; it is a more predictable component of aprice series than the trend. Volatility is usually the main ingredient in risk; the more volatilethe market, the greater the risk. As systematic programs mature, there seems to be agreater, justifiable concentration on how to manage volatility. .
Vives is an essential ingredient in many calculations, from Wilder's RSI to variables
MEASURING VOLATILITY.
In general, the volatility of most price series, whether stocks, financial markets, commodi-ies, or the spread between two series, is directly proportional to the increase and decreasein the price level. This price-volatility relationship has been described as lognormal in thestock market and is very similar to a percentage-growth relationship. In Chapter 11 (“Point-and-Figure Charting”), it was shown that soybeans increased in volatility at an average rateof 2.38% relative to price, very much the same as a logarithmic increase.
(a-day volatility) V(r) = X In (Proday — Prase)where V() is the n-day volatilityPrday is today's price
Prac is the base price of the commodity, somewhere below the cost of productioncis a scaling factor, near 1
This shows that, beginning at its base price, the volatility of a market increases in propor-tion to its price increase. To express this relationship for interest rate markets, it is neces-sary to use yield rather than price. In addition, as we have discussed from time to timethroughout this book, that currency volatility cannot be expressed this way because it hasno base price; instead, it has a point of equilibrium. Prices become more volatile as theymove away from equilibrium in either direction.
Shifting the Volatility Base
It follows that prices are more volatile at higher levels and that most trading systems mustcope with this change by adjusting their parameters. For example, a stop-loss in gold mightbe $2 per ounce when the price is under $350 per ounce, $4 per ounce at about $400, and$10 per ounce at $500. A point-and-figure box size might vary in the same way as the stop-loss; as prices become higher, it requires a larger box size to maintain the same frequencyof trend changes and signals. Similarly, a swing chart will need a larger reversal criterion.
__ Using the stop-loss as an example, most traders are willing to take a fixed amount oftisk (for example, $500), regardless of whether this risk is too large or too small for marketconditions; for many traders, it is only a matter of how much they can afford to lose. A stop-loss that is based on margin offers some improvement because margins are set accordingto market risk and contract size; however, the lag time needed for the exchange to changethe margin is far too long to keep this relationship current. A percentage stop is a popular
  
 
 
 
 
 
Y
Posse
-i
‘an ADVANCED TECHNIQUES
 
solution for analysts wha realize that volatility increases with price, but it falls far behindduring major bull and bear markets. A reasonable representation of long-term or underly:ing risk is the adjusted, lognormal price-volatility relationship. Although volatility may varygreatly at any price level, this relationship establishes a foundation for the normal level.
Base Price
The volatility relationship must include the price level at which volatility is essentially zero.Of course, we cannot find that level on a chart because no trading would have occurred.‘Although we do not know the price now, we call the level at which volatility is zero the baseprice. All interest rates, stock indices, and commodities have a base price. Certainly, if Trea-sury bills were to decline to a point at which the yield was near zero, most investors wouldchoose to place their money elsewhere, causing activity (and volatility) to disappear. Simi-larly, when the price of corn falls to $1.75 per bushel, below the cost of production, farm-cas ine not inclined to sell; they will wait until prices rise. This waitand-see approachreduces volatility.
Figure 20-12 shows that the base price can be found by detrending the data and for-mulating the volatility based on the detrended values. Although Figure 20-1b does not indi-tate a time period, volatility only makes sense when measured over some interval. Oncedetrended, a scatter diagram of price versus volatility should show a relationship similar toFigure 20-16. Figure 20-1¢ is a reminder that the magnitude of the volatility, and the prits-volatility relationship, is directly proportional to the time interval over which the volatilityis measured.
Considering the price-volatiliey relationship of gold since 1976 gives a typical exampleof how to find the base price. Figure 20-2a is a scatter diagram of monthly gold prices ver-sus the monthly change in price, taken as positive numbers. A more sophisticated studywould look at the price range over the month, rather than the net price change. The rangewill approach zero a little more slowly than the price change. Note that there is a cluster ofdots in the price range from $100 to $175 per ounce and then at $300 to $450 per ounce.The lower values can be related to the pre-1980 price levels, while the higher groupingshows low volatility during periods of higher prices since 1980. Again, the use of monthlyprice changes can yield a value of zero even if there was significant volatility during thesronth, simply because prices ended at the same place at they began. Using a price rangewill show a smoother pattern of price versus volatility. N
Detrending the price of gold using the Consumer Price Index, a technique applied to.gold in Chapter 3, improves the uniformity of the results, seen in Figure 20-25. Instead oftwo separate clusters of dots at low-volatility levels, there is only one cluster in the rangefrom $110 to $250 per ounce. A curved line has been drawn to represent the pattern ofdeclining volatility in relationship to declining price. This line could be straight if priceswere further adjusted using a log or exponential function. According to this curve, volatil-ity approaches zero at a slower rate as prices drop below $200 per ounce.
‘The time period over which volatility is measured is also a significant factor in theprice-volatility relationship. Longer measurement periods give higher volatility values.Regardless of the number of days used to determine yolatiliry, volatility will increase asprice increases. This direct relationship will be very uniform for exchange-traded marketsexcept when prices are very high. Exchange rules may limit trading when prices move 00quickly; therefore, charts of real marker peices will show that volatility stops expandingwhen it collides with these artificial constraints.
‘The magnitude of price movement will also increase as the period of measurementgets longer. During a volatite interval, prices will move farther in one direction during 3 or
@ days than they will in 1 or 2 days. As this interval gets very long, the volatility does norkeep increasing at the same rate; it tends to slow, as shown in Figure 20-1¢, The flattening
MEASURING VOLATILITY
FIGURE 20- it ili i
FIGURE 20- vomneasuring yolatliy from a relative base price. (a) Prices become less volatilet rt  (detrending line). (b) Volatility as a function of th
price. (c) Change in volatility relative to the interval over which it is measured. Getrended
  
Price —me-
Detrending line
Time—>
(a)
 
 
' |11t [L-—— Detrending line1a3 I! ys 1'itI'Price——(0)2s20 40 ~(OO. —Time interval (days){c)
————$—
473 
 
[ADVANCED TECHNIQUES4T4
FIGURE 20-2 Finding the base price where volatility is zero, gold 1976-1993. (a) Volatilityversus price. (b) Volatility versus deflated prices.
 
 
   
160 °
140
120 |-2SL2S 100+2 r °2 Bor= r More recent2 60 lows °
+ °= gol. Previous o gee °lows: ° ° oO ° oo OF
 
 
Gold (US$ per ounce) .(a)
 
160
140 /-
420
8T
Monthly price change8
 
 
Gold (US$ per ounce)(b)
5 i A iceof the curve occurs at the point equal to the duration of the maximum sustained pric
move.
Alternate Measures
The three most used measures of volatility all satisfy the previous lognormal relationshipsit i ices rise. The one dis
that is, they all expand at an increasing rate as price: s s
been net. spvice change over time. This is equivalent to a momentum calculation @abs(P;
P._.,), where volatility is calculated over 7 days. This measure is most useful for estab-
lishing the probability of a price change at different levels.
 
MEASURING VOLATILITY 47s
Markets that do not have a significant price change may also be volatile. Many systemsuse the daily or weekly high-low range to define risk and volatility. This technique canwork, although it does not always capture a full measure of activity. The sum of the
absolute price changes is a more descriptive value. Using Figure 20-3, the three measurescan be shown as:
1. Price change over time interval 7:Vi=Pi—Prenst
2. The maximum fluctuation during the interval n:V, = max (Py Prn1)— min (P, Prone)
3. The sum of the absolute price changes over the interval 7:
v= > [PH Peal
  
In (1), the volatility is entirely dependent on the value of the two endpoints P, and Py nv 1,regardless of the price activity that occurred during the days between them. Over longertime periods, a predictable change can be expected, but in the short term this approach isnot as good as either (2) or (3).
The maximum range (2) corrects for the dependence on only two points and will pro-duce a more consistent measure of volatility, which may be used as an estimate of risk. Thismethod may be effective as the basis for a stop-loss, because it defines the extent of theprice fluctuation at each price level. Because prices end near where they began in Figure20-28, the close-to-close method (1) would show little or no volatility.
The sum of the absolute price changes (3) is the most descriptive measurement ofvolatility, although it is nondirectional. It clearly shows that prices are more or less activein cases that are not apparent to either (1) or (2). A price sequence that moves from highsto lows alternately éach day is much more volatile than one in which prices move slowly tothe highs and then back to the lows only once during the same time period. This measureis useful for indicating a change in market character, an increase or decrease in activity.
Ratio Measurements
Bookstaber! presents a volatility measurement Y, which is a ratio of successive closingprices, the high and low, or a combination of the two as follows,
where CG; is the closing price on day ¢H,, is the high price on day tL, is the low on day tV, is the volatility on day ¢
(a) Close-to-close volatilityG
   
and
leA wey Re
1 Richard Bookstabes, The Complete Investment Book (Scott, Foresman, Glenview, IL, 1985, p. 349).416 ADVANCED TECHNIQUES,
NNFIGURE 20-3 Three ways of measuring volatility.
PB
1, Close-to-close
 
2, High-to-jow range
3. Sum ofpositivechanges
 
   
-1
andy,=VVi(b) High-low volatility601 < ?v= 7S 1n 2" (4)
 
 
(©) High-low-close volatility- AY Cc, \os ALY _ 39 ip (Ge- S}=.51n zn) 39in()LS - a=D .v= Vi
Note that the current ¢ may be a time interval rather than a single day. Then, C, is the lastprice of the period, and H, and L, aft the highest and lowest prices of the interval.
In the close-to-close estimation, the volatility V, is the standard deviation of the closingprice ratios. Bookstaber states that this measurement will follow a 7° distribution and that
 
 
 
 
MEASURING VOLATILITY aqT
 
the actual volatility during the current period t can be set within the error bounds definedby the distribution.
Volatility SystemThe daily volatility can be used in a trading strategy, presented by Bookstaber,? as follows:
leVid) = 5 > Dress
mm
where D, is the maximum of:
a. |Hi-C.-1|b. H.-L,ce. [L- Cal
and His the high on day ¢Z, is the low on day ¢C, is the close on day ¢
Note that D, is the extended range (“true range”) concept that appears in many otherworks. V, is the average extended range over the 7-day interval. The trading strategy pre-sented with this is
Buy if the close C,,1 rises by more than k * V,(n) from the previous close C,.
Sell if the close C,,, falls by more than.& * V,(n) from the previous close C,.
‘The volatility constant & is given as approximately 3, but it can be varied higher or lower tomake the trading signals less or more frequent, respectively.
Volatility Filters
High volatility is clearly related to greater risk, but low volatility may also mean that thereis no chance of profits. This is especially true for trend-following systems. The followingare reasonable expectations for selecting trades based on volatility:
Entering on very high volatility will increase risk. It may be best to simply avoid thosetrades.
Entering on low volatility seems safe, but prices often have no direction and producelosses. Waiting for an increase in activity before entering might improve returns.Exiting a position when prices become very volatile should reduce both profits andrisk, but may come after-the-fact. This is an issue best resolved by testing.
Filter or Delay
Whenever a high- or low-volatility situation occurs at the time of an entry signal, there aretwo choices. The trade can be completely eliminated by filtering, or it can be delayed untilthe high volatility drops or the low volatility increases to an acceptable level. If the tradeends during the waiting period, the trade is eliminated. Both of these cases have been stud-ied and the results follow.
Constructing a Volatility FilterCalculating the volatility is simple to program using any spreadsheet or strategy-testingsoftware. The following steps were used here: -
7 Ibid., pp. 224-236, 
 
 
478 ADVANCED TECHNIQUES:
_ Calculate a moving average trend.2. Calculate the volatility, using any one of the methods described early in this chapter,
but not including the volatility of the current day.3, Enter a new trade if the volatility is (a) above the low-filter level or (b) below thehigh-filter level.4, Exit a current position if the volatility is above the high-filter level and (a) the cur-rent price change is a profit or (©) the current price change is a loss.To give these choices a chance to show which are robust, five different markets weretested, each for more than 10 years ending in 1993: Eurodollars, Japanese yen, crude oil,IBM, and the S&P 500. Futures market prices were gap-adjusted and indexed, using thenearest delivery month. Results from these tests are shown as percentage changes; IBMwas quoted in share price. The trend speed (a simple moving average) was the same as theperiod over which the volatility was calculated. Periods of 35 days and 10 days were theonly ones tested; 35 days was arbitrarily chosen as about ‘one-eighth of a trading year. The10-day period (2 weeks) was included as a short-term contrast,
_
Standard Deviation MeasurementA standard deviation was used to determine the volatility threshold level. For example, fora high-volatility filter, a 1-standard deviation threshold means that no trades were takenif the volatility was above the average volatility plus 1 standard deviation, the top 16%. A2-standard deviation threshold puts volatility in the top 2.5%, and a 3-standard devia-tion threshold means the top .5%. AO standard deviation would filter all trades above theaverage volatility. Because only 35 days are used, actual volatility can jump well beyond the“normal 3-standard deviation maximum. Filter values above 3 standard deviations (up to 7standard deviations in these tests) must be used to isolate the most extreme volatile price
movements.
Entry Filter ResultsTable 20-1 shows the results for both high- and low-volatility entry options, expressed asnate of return based on maximum drawdown. The case where the standard deviation valuesaecro indicates no filtering; tests were run for a calculation period of 35 days, In part (@),the high-volatility filter causes a delay until volatility drops below the designated standard“eviation level; in part (®), volatility must increase to be above the standard deviation level.Results for the high-volatility filter are not impressive. The Eurodollar improves forlower levels while the Japanese yen and crude oil do not. Both IBM and the S&P improveby waiting for lower volatility, but both have underlying losing strategies; therefore, omit-ting trades is likely to improve results. Because these results are a function of both returnsand risk, the elimination of high volatility does not clearly improve either component of
performance.‘The low-volatility filter is much clearer. In all cases except the S&P, taking only those
trades that occur with conditions of higher volatility shows improvements for all markets.Because of the few cases that would have occurred with volatility greater than 6.0 standarddeviations, the large return shown by IBM is not realistic. A standard deviation between—1 and +1, indicating the practical elimination of 16% to 84% of all trades, shows the most
consistency.
High-Volatility Exits: Distinguishing a Volatile Good Move from a Bad One
it may be that exiting due to high volatility is acting after-the-fact; then, it would be inef-fective for reducing risk. Ifa market is noisy then price jumps are short-lived, in which caseyou should close out positions when a volatile move is profitable because profits will soondisappear. Or, if the volatile move is an immediate loss, then waiting should recover at least
 
 
MEASURING VOLATILITY479
 
 
 
 
 
 
TABLE 20-1 High- and Low-Volatility Filter Results*
SDev Euros Yen Crude IBM S&P(a) High-Volauilty Entry Filter with Delayed Entry
none 35 340 218 13-66.0 886 340 182 7 45.0 876 340 193 9 44.0 884 361 183 {8 43.0 932 399 176 19 -172.0 948 401 197 12 -I71.0 988 410 198 20 -2° 923 425 323 -35 -27
(6) Low-Volatlity Entry Filter with Trade Elimination
6.0 109 266 139 3,1815. 4040 457 47 94 308 5520 1,172 8s, ~20 B16 85° 491 340 83 214 -95-1.0 860 337 156 -19 ~6720 882 320 219 19 ~36none 835 320 84 13 -36
 
* Thirty-five days’ calculation period, rate of return based on maximum drawdown,
part of the loss. The opposite is true for a trendiending market. A good price mofollowed by more profits, and a bad move by further losses. Beee? we should befests of exit filters were separated into positive a agatit iTe : : ind negative price moves. Whe:eeees a option was elected, exits occurred when the high-volatility level was ached and,enerated a profit for the day. When the negative was used,Brices generated 2 pro ga used, prices must have pro-y. For the Eurodollar, returns improve whi aril iare liquidated, and returns decline whe: : Sr ea We cont conde, ‘n profitable moves are closed out. We can conclud; .that the Eurodollar is a trending market, and cutting a trade short due to increased volatil-ity is por ta good pee That is not true with the S&P which has a high degree of noisetiods. It was also not the case for the yen, which has erratic pri
c 3 . tic price behav-ior. Both of these markets improved when profits were taken on a positive move, “ters Because shorterterm analysis operates in an environment of greater noise, the exit fil-
ss i gene ly be an improvement. For markets-with significant long-term trends andsysi ms that are intended to capitalize on those trends, exiting a trade for almost any rea-son, other than a change of trend, is going to adversely affect the performance.
Creating Your Own Filters ~
A volatility filter is a simple calculation. Deciding which volatility filter to use is more cplex because it requires a number of different testing programs. The following Omega pro.gram and the spreadsheet program (Table 20-2) combine all of these features into onetesting program. An option is used to select each feature. meOMEGA Easy Language Code
{High and Low-Volatility FiltersCopyright 1994-1998, P.J. Kaufman. All rights reserved.
Do not enter trades on high volatilit iv y and price in trend di x iand price change of direction option end aiection. Enis on nigh voles ittyADVANCED TECHNIQUESTABLE 20-2 Spreadsheet Sample :Corel Quattro Spreadsheet Code
 
 
  
 
Begin
Col Description Row Calculations
i [Constant]
13 __Low-filter limit factor t
M3 High-filter limit factor [Constant]
A Date 5 [Input]
B-D Open, High, Low prices 5 [Input]
E Closing price 5 novel
FG Vol, Oplint data
H Positive value of price changes & @ABS(ES.ES)
! 35-day moving average 39 @AVG(ES..E39)
J ‘Average volatility 39 @AVG(H5..H39)
K Standard deviation of volatility 39 @sTOtHs 99)
L Low-flter limit 39 238-1 59°699
N eel 7 Bir dsoet39 -1,1)
N Position Ay
© —_Low-volatility indicator 40 GIF H40< 59.1.0)
¢ Ce ow er 2 SireNeont #AND#NG9=1,
Q Buy/sell with low filter SES bya
@IF(SN40=-1#AND#NS9=1,~ @IF(SH40>$L39,"sell”,“c/o"),” "))R Buy/sell with low delay 40 @ IEGSNAO @ FISH 4Or S199, Puy- @IF(SH40>$.39,"sell”,@IF(GN39=1,"c/0","")),""))i 40 @IF(N40=1#AND#$N39=-1,s Buy/sell with high filter BNA buy" °00). @IF(SN40=-1 #AND#P30=1,@IF($H40<$M33,"sell”,“c/0"),""))T Buy/sell with high del 40 @IF(SN40=1, @IF(SH40<$M39,"buy”,
@IFISN39=-1,"c/0"."")),@IF(GN40=-1,eirier40csh139 "sel" @IF(SN39=1,"c/0","”)),""))Exit on high volatility @IF($H40>$M39,"c/o”,"")
 
Option 0 = No entry or exit fiiterOption 1 = Entry filter only ;Option 2 = Exit filter only - no price direction _Option 3 = Exit filter only - profitable move+ contrary moveOption 4= Exit filter only - con!Option § = Both entry and exit filters (options 1 and 22)
0), Xfactor(1.0), prndate0);vars ae ea eee prtanecO) soph Tai, Sivgioy, srortO), aeltapi(0>,vee ta) ratiot 0). position(0), variance(0), change(0), ELuplimit(o);{Volatility ~ average + standard deviation of price changes.Calculate average and sd before new prices}change = @AabsValue(close ~ close(1});vavg = @Average(changell),tength);vsd = @Stddev(changeli], length);
{extreme volatility limits}Jowlimit = vavg - vsdiEuplimit = vavg + 2*Efactor*vsd;
 
 
MEASURING VOLATILITY 481
ELuplimit = vavg + 2*ELfactor*vsd;Kuplimit = vavg * 2*xfactortvsd;
{System rules dased on moving average trend!
mavg = @average(close, length) ;
if mavg>mavgl1] and position = -1 then position = 0;if mavg<mavgl1) and position = 1 then position = 0;
(enter on new trend signals below high volatility:
Efilter or new trend signals above low volatility: ELfilterl
if option=l or option=5 then begin
{High volatility delay)
{ if mavg>mavg(i] and position <> I and change<Euplimit then begins{Low volatility filter!
{ if mavg>mavg(1] and mavgl1]<emavg{2] and change<Euplimit and change>€Luplimit then begin!(Low volatility delay)
if mavg>mavgl1] and position <> 1 and change<Eupiimit and change>£Luplimit then beginbuy on close;position = 1;end;(High volatility delay)(if mavgémavg(1] and position <> -1 and change<Euplimit then begin)flow volatility filterh{if mavgémavgl1] and mavgfl]>=mavgl2) and chenge<Euplimit and changerELupl init then begin!(Low volatility delay}if mavgémavgli] and position <> -1 and change<Euplimit and change>ELuplimit then beginsell on close;position = -1;end;end; ,
(Normal entry only once in the same direction}if optiong>1 and option<>S then beginif mavg>mavgl1] and position <> 1 then beginbuy on close;position = 1;end;if mavg>mavgll] and position <> -1 then beginsell on close;position = -1;end;end;
{Don't reenter after high volatility exit)if option>1: then begin
if mavg>mavgC1] and change<Xuplimit and position <>1 then begin
buy on close;
position = 1;end; -mavgémavgl1] and change<Xuplimit and position <> -1 then beginsel] on close; ~position = -1; 7end;end; -
if
