, because trades are closed outwhen prices are moving in the profitable direction.• It is not necessary to reverse a position from long or short, or short tolong, in many cases. Smaller orders mean a better execution price.
2512.56Profit-Taking Level (Percent)
3
Figure 5-2. Hang Seng reward/risk chart. No profit-taking occurred atthe 50% or 100% levels, but improvements can be seen in a predictablepattern at lower percentages. Longer-term trends were improved with larger profit-taking objectives, while faster trends were consistently betterusing smaller targets.
Profit-Taking
81
• The more profit-taking, the less exposure to market uncertainty andfewer equity swings. The risk declines because you are not in themarket as much, thus avoiding unnecessary volatility and an occasional price shock.• The extra profits that may be gained at the end of a move tend to havemuch higher volatility associated with marginal returns.• The larger investment needed to wait for and then hold a longer,more volatile trade downgrades the total performance. Because riskis lower using profit-taking, your investment can be smaller.• Setting a smaller profit-taking level means that the system does notdepend on a few large profits, but on regular price movement.Closing out a trade with profits is not only personally satisfying butis sensible. As with other rules, it must be done properly. In a trend-following program, there are more losses than profits; therefore, the profits must be larger than the losses; Liquidating a trade as soon as you seea profit will not result in a successful trading program. You must firsttest your system for a selection of profit-taking levels to see how thereturn/risk ratio changes. Then you have the basis for adding profittaking to your plan.
Profit Objectivesversus TimeThe first part of this chapter showed that taking profits improves trendfollowing systems of all speeds. Longer trends develop larger profits;therefore they were helped by larger profit-taking objectives. Fastertrends needed smaller goals. Using a small profit-taking objective in along-term system causes small profits and relatively larger losses; alarge profit objective in a fast trending system was rarely reached.The relationship between the time interval (the speed of the trend orthe length of the trade) and the size of the profit-taking objective is similar to the pattern of volatility over time (see Figure 5-3). As the periodof evaluation becomes longer, the potential for profits levels off. This isthe result of the maximum price move that would normally occur during that time period.Taking Profits at Only One PointIt is easiest to think of taking profits at one price for each trade. This isoften a fixed value or a percentage of the entry price. For example, buying
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Using Old and New Trading Tools for Reasonable Objectives
Fast TrendSlow TrendFigure 5-3. Size of profit-taking objectives forvarying trend speeds. Profit-taking objectivesIncrease in size as the trend period increases. This pattern is very similar to risk or volatility over time.
IBM shares at $60 using a medium-speed trend might have a profit-takinggoal of $5 (about 8.3 percent). A foreign exchange trader might look for aprofit of .0075 in the British pound, equal to .5 percent (one-half of 1 percent). Using a percentage to specify the size of profits is a little more adaptable than using fixed values.Simple profit-taking goals are easy to test and simple to trade. Theentire position goes on and off at the same time. But it is not as good asusing multiple exit points, which give you more chances to succeed andreduce risk.Problems of Using OneProfit-Taking ObjectiveSingle price objectives are impractical and often frustrating. If GM isbought at 30, with an objective of 33, what do you do if prices stop at3234, or at 32%? When are you close enough to your objective so that thefew extra points are not important?A single profit-taking level is usually a number that worked "onaverage" over some historic period, whether it was a few weeks ormany years. "On average" may have been very good in 1990 and verybad in 1994. Even clever profit-taking schemes, which adjust to volatility, may be out-of-phase for long time periods.
Profit-Taking
83
Benefits of Using MoreThan One Profit ObjectiveThe greatest benefit of profit-taking is the reduced risk gained by beingout of the market. It follows that the sooner you begin to take profits, the fasteryour risk exposure will drop. To make this work, you need to trade a position large enough to close it out in at least two parts, but preferably fourparts. Two basic profit-taking strategies are shown in Figures 5-4 and 5-5.In both cases, a long position is taken at the same point—50.00—and amove of 2 percent is expected.Because price movement looks very similar to a random distribution,prices will move back and forth by 1 percent more than twice as often asthey will reach 2 percent, and they will move 0.5 percent more than fourtimes as often as they move 2 percent. This is important information whensetting profit objectives. If, for every ten trades, you capture a profit of 2percent only once, then you should have reached a 1 percent profit twice,and a profit of 0.5 percent four times. If the market was more volatile andyou captured profits of 2 percent twice in ten trades, then you should havereached a 1 percent profit four times and a 0.5 percent profit eight times.
Figure 5-4. Two equally spaced profit objectives. Using two profit objectives, each for an equal part of thetrade, greatly Increases your chancesof reaching one of the goals. Once partof the trade has been removed successfully, half the risk Is gone.
Figure 5-5. Three or four profitobjectives are ideal. They should bespaced farther apart as profits getlarger. This pattern takes advantageof market noise. The average profit, ifall objects are reached, should be thesame as the result of a single profitobjective used for the entire position.
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Using Old and New Trading Tools for Reasonable Objectives
It is important that we start by knowing how many times you reachedthe profit goal in your trading strategy. That gives us a way to knowhow often smaller profit objectives would be reached. This approachseparates theory from reality. Look again at the number of times theprofit levels would have been reached:If a profit goal of 2% was reached twice in ten trades, then:Number TimesReached
ProfitLevel
TotalProfits
248
2%1%0.5%0.5%
4%4%4%4%
(known from testing)(2 extra)(4 extra)
First, we see that the total profits remain the same. When you divide theprofit objective by 2, you double the number of times you will reach thatlevel. That is an important feature of a normal distribution. Of course,when profit-taking objectives are small and frequent, the transactioncosts will be proportionately larger. That makes very small, frequentprofit-taking unrealistic for real trading.Second, the four times that the 1 percent objective was reached includethe two times that the price also reached the 2 percent level. Then there areonly two additional times that prices reached the 1 percent level and didnot reach the 2 percent level. Similarly, there were only four times thatprices reached the 0.5 percent level without reaching the 1 percent level.Remember that the disadvantage is the added transaction costs due tomore trades.Example. Two Profit Levels. Let us apply this to trading. Instead oftaking a position with only 1 contract, 100 snares, or $1 million, take a position of 2 contracts, 200 shares, or $2 million. Compare the result of using asingle profit objective of 2 percent with two different objectives of 2 percent and 1 percent, each for half of the position. At first we will look onlyat the profits that are taken:Case 1. Profit-Taking with Oneand Two TargetsUnits
No. ofTimes
EachProfit
UnitTotal
Total
With one profit-taking level of 2%:222%2%8%8%With two profit-taking levels (2% and 1%):122%2%4%8%141%4%1%
Profit-Taking
85
From this, it would appear that setting more than one profit objectiveis the same as setting a single larger one, therefore, why not use the smallest ones? For two reasons:1. You must still achieve an average profit of about the same size. Because thesize of the losses remain the same, the average profit objective mustalso be similar. If you have not increased the number of systemtrades, you will get worse performance when you replace big profitswith small ones and keep the same losses.2. The transaction costs become too high. The size of the profits can becometoo small to make up for the transaction costs, which remain aboutthe same. Every trade pays a combination of brokerage fees and slippage. These transaction costs are relatively fixed, that is, they arebased on position size rather than frequency of trading. Taking profits at smaller levels makes these fixed transaction costs reduce profits by a larger percentage, while adding the same amount to losses.As long as you can be profitable using smaller profit-taking levels,you have the following advantages:• The execution price is better.• More (unit) trades are profitable. For example, you will have taken someprofits on 8 out of 10 trades, rather than all profits on 2 of 10 trades.• Results are more consistent. Because market noise helps price reachsome profit levels, you are out of the market more and not as subjectto random market patterns.• You don't have to worry as much about missing the profit-taking level by afew points.• Overall risk is lower. Most important is that risk is reduced by beingout of the market. The more profits taken, the less you are subject tounexpected and unpleasant price moves. The only restriction is thattransaction costs eat up small profits.Adding Risk to the PictureWe have discussed how the normal distribution of prices causes a clearpattern of how many times you can reach a preset target. Now let's lookat the risk.It is safe to say that when prices move up 0.5 percent, they also movedown 0.5 percent during the same time period. It would be especially correct if we did not have a very good timing strategy, or we selected an arbitrary period of price movement. In our 10-trade example, we assumed that,for each profit level reached, there was an equal risk. Looking at the tradingprofile for a trend-following system, there are 10 losses and only 2 profits:
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Using Old and New Trading Tools for Reasonable Objectives
Case 2. No Profit-TakingUnits
No. ofTimes
Profit(Loss)
UnitTotal
With one profit-takinglevel of 2%:Profits generated:222%8%Risk taken:210(2%)(40%)Return/risk ratio: 8/40= 20
Total
8%(40%)
Note that the 10 trades each have a risk of 2 percent, because no profittaking is used. In the next case, where profits are taken at two levels, therisk is always 2 percent unless profits are taken at a lower level, then therisk is equal to that level. For two profit-taking levels, the results are:Case 3. Two Profit-Taking LevelsUnits
No. ofTimes
Profit(Loss)
UnitTotal
Total
With two profit-taking levels (2% and 1%):Profits generated:122%4%144%1%8%Risk taken:110(2%)(20%)141(1%)(4%)16J(12%)(36%)(2%)Return/risk ratio: 8/36= .22
Note that the bracket shows the 4 trades where profits were taken atthe 1 percent level, and the remaining 6 trades where profits were nottaken (where a full 2 percent loss is posted). This is the worst possiblecase, yet the return/risk ratio improved by 10 percent. This gain is theresult of reducing the risk to 1 percent on a few units, rather than beingexposed to a 2 percent risk on all trades.A 10 percent improvement in the reward/risk ratio is the same asadding 10 percent to your profits (with the same investment and samerisk), or reducing the risk by 10 percent.With a Better Trading Strategy...What we have done is to look at profit-taking based on the number of profitlevels reached in your current trading strategy. We have assumed that, whenprofits were not reached, prices were just as volatile in the wrong direction.
87
Profit-Taking
A good trading strategy may only hold a trade for a short time. Ifprofits are not reached within a preset number of days, the trade isended. Therefore, if the market becomes less volatile and does not reachthe 1 percent profit level, the trade can be closed out with a small profit or loss—and never show a 2 percent risk. This would improve thereward/risk ratio significantly.Stop-LossesA stop-loss that is smaller than the largest profit-taking level (e.g., 2percent) can prevent you from reaching that profit level in 50 percent ofthe situations. Stops that are half the size of the largest profit level willcause the trade to be stopped out 75 percent of the time. This is simplybased on the equal chance of a price move caused by market noise.Stop-losses must be used carefully, otherwise they interfere with performance. If your trading strategy is good, prices move in a profitabledirection more often and do not reach the stop. If the entry timing is not asgood, the stop-loss will be hit and prevent you from reaching your goal.More Profit-TakingIf your trading program was able to take profits 4 times out of 10 trades,rather than the 2 times used in the example, the results of using profittaking would be even better:Case 4. Using Profit-Taking witha Better System Performance
Units
No. ofUnitsReached
Profit(Loss)
UnitTotal
Total
With one profit-taking of 2%:Profits generated:242%16%Risk taken:210(2%)(48%)Return/risk ratio: 16/48 = .33With two profit-taking levels of 2% and 1%:Profits generated:142%8%181%8%Risk taken:110(2%)(20%)18(1%)(8%)12(2%)(4%)Return/risk ratio: 16/32 = .50
16%(48%)
16%
(32%)
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Using Old and New Trading Tools for Reasonable Objectives
The ratio improved 50 percent from .33 to .50 using a strategy thatwas able to take profits 4 out of 10 trades. That is a substantial improvement, but it can only be realized by frequent profit-taking. It would belimited to a professional trading group with the ability to watch themarket closely.
SummaryProfit-taking reduces risk, and more frequent profit-taking at differentlevels reduces risk more. In addition:• Transaction costs limit small profits.• Spreading profit levels over a broad range gives the most improvement; grouping them closely together allows only a small improvement.• Using a stop-loss that is smaller than the biggest profit-taking levelwill prevent prices from reaching the profit objectives.• Limiting the time that you hold a trade reduces the trading risk bybeing out of the market; therefore, the more often you take profits,the lower your risk.To find out how to get the profit-taking levels, you first need to testyour own strategy assuming one profit point. That gives you the average of all profit objectives. You can then combine profit levels and position size to identify a simple pattern in the way profits should be taken.The most common plan is to have more targets at lower profit levels andspread them out further as profit targets become larger. The reductionin risk due to being out of the market may allow profit goals to be setmuch lower and still net very good returns with a better trading profile.
6The Mixed Roleof Stops forControlling RiskKeeping losses small, which can mean using a closely placed Stop order,has always been considered sensible risk control, but it may presentmore problems than it solves. A series of losses from short-term tradescan be greater than a single, large loss caused by a longer-term position.In addition, when you get stopped out but the trend remainsunchanged, how do you decide when to reenter the market?A stop-loss order is a mixed blessing. It is not the order itself, because theact of monitoring the market and using Limit orders to carefully liquidate atrade has the same result. Large stop-losses offer some protection against catastrophic events and price shocks; however, attempts to keep risk very smallcauses larger losses and a worse risk profile. Small risk limits are often activated by market noise; there is little relationship between getting stopped outand the direction—or change of direction—of price movement.Historically, there is some level of risk protection that would havebenefited a portfolio. Close inspection of lengthy test results show thatthe reason for improved performance is a single, adverse price jumpthat would have been reduced by using a stop-loss. But it is not clearthat such a situation would occur again, and if it occurred, that the stoploss order could have been executed profitably.In some cases, a poor trading strategy is improved by using stops. Butthen, it would also be improved by not trading. There are occasionalimprovements in the return/risk ratio of performance using systematicrisk control. When the program has no position, after the risk limit hasbeen reached, the equity is not subject to the ups and downs of price89
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Using Old and New Trading Tools for Reasonable Objectives
movement. If a large loss is averted during this time, overall performance improves. The alternative which is to trade a smaller portfolio, isoften the better choice for risk reduction.
Need for Risk ControlIdeally, a Stop order that has been entered into the market is expected toautomatically get you out of a position when prices move against you. Itforces you to decide, in advance, how much you can afford to lose, so thatyour trading risk is under control. It avoids last-minute decisions and thetemptation to hold a losing position with the hope that prices will recover.Stops are normally "resting orders" held by the floor broker to be executed when the price is reached. For our purpose, we will include anytrader who intends to limit losses to a fixed amount, whether or not theorder is placed in advance as a Stop order.
Risk Protection orFalse Hope?The use of stops, or the intent to limit losses to a predetermined fixedamount, may give a false sense of security (shown in Table 6-1). Forexample, a Stop order that is reached during an illiquid or quiet marketwill result in large slippage; during a fast market, or a price jump, it willoften get the worst fill. Large traders cannot enter stops because theymove the market and cause substantial slippage.Setting Stops Based on What TonCan Afford to LoseStops are set for two main reasons:• They can trigger a change in market direction, or• They can limit losses to a preset amount.Table 6-1. Using a Stop-LossExpectationsLimits losses to preset levels
Reality
Slippage and price shocks increase the size of theloss substantiallyLosses will be much smaller than profits Individual losses may be smaller, but a series oflosses can be very largeThere can still be more frequent profitable Market noise causes more losses than profitstrades than losing onesunless the trader has a very good strategy
The Mixed Role Stops for Controlling Risks
91
Stops that react to market direction are not primarily intended to limitmarket risk, but do so as a secondary benefit. A foreign exchange trader who gets a moving average trend signal to be long the dollar againstthe yen at 100.50 places a stop at 99.50, assuming that new lows in thedollar mean renewed weakness. The stop-loss combines an acceptablerisk level with a perceived change of direction.Stops placed to limit the size of losses are more common and moredifficult to evaluate. The use of a small risk control can be intended toproduce a particular performance profile, as in Case 1.Case 1. A different foreign exchange trader buying 10 million$/marks expects to iiold the trade for a US$20,000, or 0.20 percentprofit, based on a 1-day volatility strategy. To show proper risk control, the trader would like to keep losses under US$10,000, giving a2:1 ratio of average profits to average losses. The trader would alsolike to have at least half of the trades profitable over a long-term performance record. The total picture would show a steady profitability and reasonably small losses—a very pleasing performance.But the market does not work this way. It is not possible to control boththe return/risk ratio and the number of profitable trades.Interference from Market Noise"Noise" is the term given to unpredictable price movements. Normallynoise is associated with small price changes, but in reality it includeslarge price shocks. Noise is caused by traders entering and exiting themarket with different objectives and different time frames. An institution adds positions because of new investment funds; Russia sells goldto pay for a wheat purchase; or an auto company liquidates part of itsstock portfolio to cover foreign exchange losses. Although each event isunique, the total picture of this noise creates a very predictable randomdistribution with some very special properties. Figure 6-1 shows the general rule that erratic prices (noise) which are twice as large occur half as often.The S&P price changes appear to fall exactly on the random distribution line in Figure 6-1 (a), while the bonds and Deutsche marks haveabout twice as many moves of 1 percent and 4 percent than a randomoccurrence. It is important to note, however, that the number of occurrences of bonds and Deutsche marks still decline by 50 percent as thesize of the move increases in steps of 0.5 percent.When we look closely at the larger moves (called the "tail" of the distribution) in Figure 6-1 (b), the S&P has more extreme changes thaneither of the other markets and much more than if it were a random distribution. These large moves are caused by price shocks.
92
Using Old and New Trading Tools for Reasonable Objectives
3.00
4.50
6.00
Size of M o v e (Percent)(a)
Figure 6 - 1 . Random distribution of noise, (a) The frequency of price movements is plotted against the size of those movements. A random distribution hasa unique property: doubling the size of the price moves reduces the number ofoccurrences by half. For every increment of 0.5%, the frequency drops by onehalf. More than 10 years of data, totaling 3,375 days, were used to compare-theS&P, U.S. Treasury bonds, and Deutsche marks against a random distribution(shown as the heavy solid line). The extent to which prices do not keep to thispattern is the way its nonrandom pattern is measured.
Total Losses Are the SameThe interesting phenomenon concerning the size and frequency of erratic price noise is that the number of occurrences times the size of the move isalways the same. Although the bonds and Deutsche marks varied from arandom distribution, they still conformed very closely to the same rule.Specifying the Performance Profile. Based on the normal distribution of prices shown in Figure 6-1 and Table 6-2, the foreign exchange trading example, Case 1, could not work. If a trader targets a US$20,000 profitwith losses one-half the size, then there should be twice as many losses. Asthe size of the profits increases compared with the average loss, the num jber of small losses must also increase. If a naive trading model gives fourprofits averaging US$20,000 and eight losses of US$10,000, then a goodstrategy must capture higher profits, reduce the losses, or turn one or twolosses into small profits.
The Mixed Role Stops for Controlling Risks
93
Size of Move (Percent)(b)
Figure 6 - 1 . (Continued) Random distribution of noise, (b) Magnification of {a)at the extreme right of the distribution. All three markets have much larger pricemoves than the comparable random curve. These could occur because of priceshocks.
ExpectationsIn these cases, the real prices are so similar to random movement thatyou could not tell the difference without a careful mathematical study.We can assume that decreasing the size of a stop-loss will cause a predictable additional number of trades to be stopped out, always conforming to Table 6-2, with the possible exception of large stops.. Our expectations of improved performance using a small stop shouldbe low. As the stop-loss gets smaller, the number of trades that arestopped out gets larger. Each time a stop-loss is activated, there is addiTable 6-2. Size versus Frequency of Stop(If Random Price Movement)Size of Stop
No. of Occurrences
Size of Loss
5 points10 points20 points
20105
100 points + slippage100 points + slippage100 points + slippage
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Using Old and New Trading Tools for Reasonable Objectives
tional slippage because the order forces an execution in the direction ofmarket movement.The larger stops may be different. If prices are exceptionally volatile,then a stop-loss might save some of that loss. If you plan to get out whena price shock hits, then a stop-loss could not make things worse—andmight make it better by acting as a major risk control. Large stops onlywork with longer-term trading; a fast trend will always give a reversalat the same time a larger stop would have been reached. Therefore,small stops will generally be ineffective, but larger stops will sometimesimprove performance.Capitalizing on Distribution. A successful system will need to capture larger than normal profits, or cut losses. The use of a stop-loss is theplace to start. If a few of the unusually large price moves shown in Figure6-1 (b) can be controlled when they generate losses and captured whenthey produced profits, the overall system performance will improve.
Testing a System witha Stop-LossA simple trend-following system was tested on daily data using stoplosses to see whether they helped profits and controlled risk. The system included the following main features:• An exponential moving average, @ Exp_MA, was used for the trend.• A buy signal was given when the trendline turned up,@ Exp_MA > @ Exp_MA[1 ].• A sell signal was given when the trendline turned down,@Exp_MA< @Exp_MA[1].• The trade was exited if the loss, at the close, exceeded a preset percentage level (the stop-loss), or when a reverse buy or sell signal occurred.• All orders were executed on the close of the local trading day.• There were no commissions or slippage charged to any trade.• Risk was defined as 1 standard deviation of equity.In actual trading, the more active systems will show additional lossesdue to relatively larger transaction costs. Because all trades are executed in the direction of the price movement, individual estimates of costcan be subtracted from the profits per trade. Without costs, the resultsof this test will still give a reasonable comparison of the use of differentstop-loss limits.
The Mixed Role Stops for Controlling Risks
95
Test ResultsTable 6-3 shows a 10-year optimization of trend speed versus percentagestop-loss for Chrysler, Siemens (for only 5 years), the Deutsche mark,and Eurodollars, ending June 1993. Only the adjusted rate of return isshown to allow comparisons (see in Chapter 4, "Choosing Between theCurrency and Bond Portfolios," for an explanation of adjusted rate ofreturn). The far right column in Table 6-3, marked "None," shows theresults of the trend system without any stop-loss. The far left column,marked ".02," shows a very small .02 percent stop-loss.The conclusion is that improvements are inconsistent. The best resultsfor this test set seem to be Siemens, which has higher adjusted returnsfor trends below 100 days, and scattered improvement in the middle ofthe table, centered near a stop-loss of .50 percent.Because the major currencies are said to have more trends, we expected a stop-loss in the Deutsche mark to produce better results. Prices thatreach the stop-loss level in the D-mark should continue in the samedirection until it activates a new, reverse trend signal. That did not happen. The results from the smallest stops were uniformly worse than theuse of no stops in the 10-year test. Improvement occurs in a small areain the center of the table.Larger stops, or no stop, show a more uniform result. When using anoptimization test to select the best trading rules, it is preferable to seesmooth, consistent results, rather than alternating profits and losses.Both Chrysler and the D-mark have poor returns in the bottom left corner of the tables.Another View with a ShorterTest PeriodTable 6-4 compares the cash returns with risk-adjusted returns for theDeutsche mark and Eurodollars over the 4 years ending November1992, using comparable stops. The Deutsche mark cash returns appearmuch better than Eurodollars but have higher, inconsistent risk. Whenadjusted for risk, the Eurodollar returns are clearly better.Contour Map of Eurodollar Stop-Loss Tests. Figure 6-2 shows acontour map of the Eurodollar tests. The white areas have the highestprofits and the black parts the worst losses. As in the 10-year tests, theuse of small stops, seen at the left edge of the figure, is inconsistent, alternating between light and dark, with neither the best or worst results. Asstops become larger toward the right, performance is more uniform andpredictable. We can conclude that small stops are sensitive to specificprice patterns and noise; therefore they are erratic.
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Using Old and New Trading Tools for Reasonable Objectives
Table 6-3. Stop-Losses: Results of Longer Term TestsValues are annualized rate of return, adjusted to a 25% maximumdrawdown.a. Chrysler Motors: 2329 Days (1/05/84 to 3/18/93)Stop-Loss in Whole PercentDays .02
.05
.10
.15
.25
.50
1.00
2.00
4.00
7.00
10.00 NONE
510255075100150200250300
-2.8-2.8-2.8-2.6-1.2-1.55.72.2-2.53.6
-2.7-2.8-2.8-2.6-1.2-1.55.72.2-2.53.4
-2.7-2.8-2.7-2.6-1.4-1.65.31.9-2.53.4
-2.7-2.8-2.8-2.6-1.4-1.75.41.7-2.53.2
-2.8-2.8-2.8-2.6-1.5-1.94.91.6-2.53.1
-2.8-2.8-2.6-2.2-1.5-.64.51.4-2.53.0
-2.7-2.8-2.6-2.3-1.6-.74.02.8-.42.5
-2.8-2.8-2.6-2.2-1.4-.53.62.7-.12.4
-2.8-2.8-2.6-2.2-1.5-.63.52.72.02.4
-2.8-2.8-2.6-2.2-1.5-.63.52.72.02.4
-2.8-2.8-2.8-2.6-1.2-1.55.82.2-2.53.6
-2.8-2.8-2.6-2.2-1.5-.63.52.72.02.4
b. Siemens: 1452 Days (2/3/87 to 11/23/92)Days .02
.05
.10
.15
.25
.50
1.00
2.00
4.00
7.00
10.00 NON
5102550751001502002