ast thefuture. You only know that the future is going to be different.The assumption made by rigid systems, such as trend-following,fixed cycles, or patterns, that the current state of affairs will continue,contradicts reality. We are only passing through the current state. Atrend-follower can only hope that unexpected changes do not causeextreme volatility that results in unreasonable losses. It is not the forecasting attributes of a trending system that allow profits, it is the riskcontrols.
Assessing Market Reality
29
To forecast successfully is to accept the inevitability of change andthe risks associated with it. You cannot assume that the future will bethe same as the past, that the risks and profits and patterns will repeatthemselves. We can only try to develop systems that recognize thepossibility of change and are flexible enough to profit from it.
3
ReasonableExpectations GiveAchievable ResultsThe combination of technology, optimism, and the success of somehighly visible traders can easily lead to unrealistic expectations. We seethe profits before the risks, then we attack and eliminate the risks without questioning the validity of the profits. When developing a tradingstrategy, the failure to understand what is most likely to happen canwaste time and effort, as well as cost a great deal of money.
Trade-OffsEvery profit opportunity has risk. Larger profits have larger risk. Eachsystematic approach to trading has its own risk and reward trade-offs.And a trade-off is always an unpleasant compromise. It is a mistake tothink that you can find a trading strategy that has no losses, or an arbitrage that will absorb unlimited funds.A pure trend-following method has smaller losses and larger profits. Itis classified as a "conservation of capital" approach. To keep lossessmall, it is necessary to close out trades quickly. The system continually tries to fmd a trend but exits as soon as prices move in the wrongdirection. Therefore, there are more losing trades than winning ones. Ifyou increase your tolerance for risk, by using a slower trend or largerstop-loss, the system will have a larger percentage of winning tradesbut larger losses and equity swings. Make the trend very slow and thestop-loss far away and you have a passive portfolio of one open trade.•
31
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How Changing Markets and Technology Affect Results
Countertrend strategies typically allow more risk to achieve frequent,small profits. When the strategy errs, there are large losses. Its trade-offshave the same, continuous relationship as a trend-following method,but in reverse. As the targeted profits get smaller, they are more frequent. In exchange, the fewer losses get larger.Trend and countertrend traders have similar choices: smaller lossesor smaller profits more often, offset by larger profits or smaller lossesless often.Commodity arbitrageurs compete for "riskless" opportunities, such as alocation arbitrage. Profits can be made when the differential between thesame product selling in separate locations is greater than the cost oftransportation, insurance, and other carrying charges. Competition canbe so keen that the arbitrageur accepts both small profits arid small volume, a situation that, at some minimum, is not worth the effort.There is no secret way to produce constant trading profits. Somemethods are better than others, but none of them are immune fromthese trade-offs. It is important to identify and understand the alternatives before making a final choice (see Table 3-1).Risk and RewardWe all know that there is higher risk with higher profits and that theonly system that doesn't have losses is the one that doesn't trade. Whenyou sit in front of a powerful computer with sophisticated tools, however, you tend to forget that these limitations still apply.Profits seems to stand out when you look at the trading results of hundreds of strategies. The high leverage of options and futures pushesmany of the test returns well above 100 percent per year. These areexceptionally high compared with most investment returns and can beintoxicating at first. But presented in a more traditional risk-adjustedform, with adequate capitalization to insure safety, results are scaled
Table 3-1. Trade-Offs
Trend-followingCountertrend
For Every Positive
There Is a Negative
Large profitsSmall lossesMany profitsOnly a few losses
Many small lossesMore losses than profitsEach one smallEach one largeFew opportunitiesVery competitiveSmall profits
{
ArbitrageAll systems
High profits
High risk
Reasonable Expectations Give Achievable Results
33
down to a more sensible range of 5 percent to 25 percent annually. Thisis discussed in Chapters 4 and 11. You may discover that the risk-adjusted returns of a very profitable trading method are no better than a conservative bond fund.Be Wary of UnreasonablyGood ResultsDeveloping a trading method is hard work. The main idea can be theresult of years of watching market patterns, or the formation of precisemathematical relationships. The process of testing and verifying is alsodifficult. Each calculation needs to be checked and entry and exit pricesmust be reviewed. It can be so tedious that, at some point, you wouldwillingly accept good test results and stop looking for errors. You beginto look at larger individual losses without also reviewing the largerprofits. But errors cause both good and bad results, and a program is notvalid until it is error free.A trading strategy that returns more than 20 percent annually, with areward/risk ratio greater than 3.0, is an enviable achievement. If youadd a stop-loss to a system to reduce its risk, you find that the returnsalso drop; or, by selecting specific trades with better opportunities, youreduce the frequency of trading so that each trade must generate largerprofits to reach the original rate of return. Each day that you are out ofthe market, waiting for an entry signal, reduces the rate of return.In the end, all systems must conform to the expected trade-offs. Ifthey don't, you have reason to be suspicious. A system with no losses, areward/risk ratio over 5.0, or annualized returns over 50 percent for 10years must have compensating limitations for these benefits. You cannot accept their results at face value; you must find and understandtheir problems. There is no room for careless optimism.
Giving the ComputerFree ReinComputers excel in the manipulation of data. Great advances in technology are the result of the ability to consolidate massive amounts ofinformation and produce solutions. What better application than solving a price-forecasting problem?It is a simple task to input fundamental and economic data necessary forthe interpretation of stock prices. Or information about supply anddemand, which are the primary factors affecting the price of food, energy,and other commodities. It is also possible to add to the database less obvious influences (e.g. financial data, such as money supply, unemployment,
34
How Changing Markets and Technology Affect Results
and per capita income) that when combined with other events, will causeprices to shift.The computer can be given sophisticated tools for finding relationships in the data that explain price movement. The most popular hasbeen a form of multiple regression—finding constant relationships overtime between numerous factors. More recently, neural networks arereplacing regression analysis as the favorite method. For example,when crude oil stocks decline more than 10 percent below the average,prices rise. And, when OPEC calls an emergency meeting, prices rise.When the two happen at the same time, the prices rise higher.Fundamentals provide a reasonable, classic approach to predictingprice movement.In the past, the speed limitations of computers curtailed the amount ofdata that could be matched against each other. Calculations werelengthy and the results showed a clear relationship, but large variability.Because not all the price movement could be "explained," the predictivequality also had uncertainty. Newer, faster computers can analyze muchmore data. They should be able to reduce the variance and improve forecasting. Entering as much data as possible and letting the computer findthe relationships is a simple extension of the same problem.But the solution usually is not improved. Many choices of statistics, incombination, can "explain" the price movement. Which combination isthe right one? Or are any of them correct? With enough data, countlesspatterns are produced. The power of the computer can find them all,without having any way to identify the right ones.Recognizing Reliable PatternsA common use of computer analysis is pattern recognition. In an attemptto find relationships not yet clear to others, the computer can scan, forexample, unemployment data and find that a drop greater than 3 percent in November was followed by a rally of at least 4 percent in housing starts during the following May, for all of the 18 years available.Is that a perfect solution or a coincidence? It depends on how muchdata the computer scanned. If you started with the premise that unemployment affects housing, and that more people working means morehome sales, then you needed to scan only those two data series to confirm the relationship that you already believed to be true.If you began with the entire database of U.S. statistics spanning thepast 50 years, looking for a perfect relationship, this would have beenone of many that you found. Another one may have been the infestationof gypsy moths relating perfectly to the import of Chilean grapes.Employment and housing sound right, but how do you know it is any
Reasonable Expectations Give Achievable Results
35
more significant than moths and grapes? You can only know if youapplied a logical argument, determined before testing, then validatedthe theory using the computer. Because we never would have thoughtof a trading program using gypsy moths, even the most astoundingresult must be ignored. Box 3-1 shows how to calculate when a relationship is "significant."
Throwing Microchips at ItBig companies have more choices than individuals. When they need tosolve a more complicated problem, they can buy a bigger computer andget more crunching power. They also get a very impressive computercenter and a higher electric bill.Some solutions require long calculations. Finding meaningful relationships among thousands of data series can require hours of computing time even on large machines. Yet, figuring out the navigationalsequences and landing instructions for putting a space team on themoon takes a small computer only a few minutes. Why is the differenceso great? The computer that guides explorers to the moon has bothobjectives and well-defined physical relationships. The effects of planetary motion and gravity are precise, although intricate. Specify the timeand everything else can be solved.Although forecasting a price can be stated as a clear objective, thesolution is not clear. The answer may not even be hidden in all the datastored in the computer. The method used to scrutinize the informationmay not be the way the market works.You do not necessarily get a better solution by using more computerpower, you just get a faster one. Power can overwhelm reason. No matter how big or fast, the computer only solves problems the way it is told.It does not claim to solve a problem that has no answer.Oversimplifying a SolutionIndicators have been given credit for correctly signaling major pricemoves in stocks and financial markets. On-balance volume, short-interest, customer margin debt, "insider" trading, percentage of cash holdings of mutual funds, oscillators, contrary opinion, and countless othersclaim accurate forecasting ability. It is true that they have produced buyand sell signals at key points. But at other times, they signal the wrongmoves or no move at all.A indicator is an optimistic, oversimplification of a solution. It is anattempt to find a single, orderly solution to a complex problem.
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How Changing Markets and Technology Affect Results
Box 3-1. WHEN DOES 18 OUT OF 18BECOME SIGNIFICANT?You would think that finding a perfect pattern over 18 years is animpressive discovery. But not if the computer finds it by scanning alarge database. For example, with 5 years of data, there are 2A5 = 32possible up-down patterns:1
Patterns
32
1
UUUUUUUUUUUUUUUUDDDDDDDDDDDDDDDD
2Year 345
UUUUUUUUDDDDDDDDUUUUUUUUDDDDDDDDUUUUDDDDUUUUDDDDUUUUDDDDUUUUDDDDUUDDUUDDUUDDUUDDUUDDUUDDUUDDUUDDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUDUD
If you scan 33 series of 5-year up-down patterns, two of those seriesmust be identical although that doesn't prove they have anything incommon. There is only a 1 in 32 chance that any two series will be identical. Therefore, if you were to take only two series that you thoughtdepended on one another, and they proved to be identical, you wouldsucceed with a 3.1 percent probability. If you were able to match 6years, there would be a 1 in 64 chance, or 1.5 percent.Rating the ResultsStatistics say that there has to be less than a 5 percent chance of occurrence before an event is called probably significant. But thaf s of minimumCombining multiple indicators does not seem to eliminate the bad signals, as you would want. Instead, the new composite indicator has thesame erratic properties as its components.This disappointing inconsistency is not the fault of the indicator, butof the user. Indicators are constructed to emphasize a particular marketfeature. On-balance volume will confirm a trend if there is one; stochastics and contrary opinion will show when a market is overbought oroversold, but not whether it's a good time to buy or sell.A reliable strategy is one that uses relevant information or specific indicators only when they are important. At other times, these indicators have novalue; forcing them to say something all the time is a misdirectedapproach to analysis. The market does not always have something to say.Standard econometric analysis, often based on multiple regressionanalysis, tries to form continuous relations between the data. Thatrequires all data to interact in the same way throughout history, even
Reasonable Expectations Give Achievable Results
37
Box 3-1. (Continued)interest. It needs to have less than a 1 percent chance (1/100) of occurring to be called significant, and less than .1 percent (1/1000) to be highly significant.When Is 18 Out of 18 Significant?Finding the importance of a pattern of results requires only a few simple steps:Step 1: How many different combinations are there in a series of 18 ups anddowns?There are 2 possibilities (up or down) for every one of the 18 items inthe series. Then there are 2 X 2 X 2 x ... x 2 (18 times), or 262,144 totalcombinations.Step 2: What are the chances of having two identical series?If you entered one more than the total combinations, or 262,145, seriesof 18 years into the computer, one of those series must be a duplicate.When half the data (131,072 series) have been tested, there is a 50 percent chance that one of them is a duplicate.Step 3: When is there a "significant" 1 percent chance?When you compare only two data series of 18 items, there is only a 1 in262,144 chance of them being the same (which is very small). There is a1 percent chance of finding two identical patterns in 2,622 series.Selected at random, statistics states that it is not likely to be coincidence.
when markets are being driven by different forces, or by nothing at all.That technique is similar to forcing a relationship. This problem can nowbe avoided by using a neural network for threshold analysis to isolate different market scenarios. A single event, or combination of events, willtrigger the use of a selected set of information applying only to that situation. For example, an unusually large jump in inflation will turn thefocus to interest rates, and begin monitoring the Producer Price Index, theGoldman Sachs Commodity Index, the yield curve, and the U.S. dollar,looking for confirmation. More about this can be found in Chapter 9.Data GrowsAn interesting feature common to price charts and system testing is thatmany of the patterns depend on the length of the chart. You cannot find
38
How Changing Markets and Technology Affect Results
a head-and^shoulders formation with only one week of daily data, or amajor bull market with one year. Performance expectations are also distorted by using too little data, or selected data. It is not necessarily theprofile of the profitable trades that change as you look at more priceexamples, but the risk. A sustained sideways market and an exceptionally volatile period will create prolonged large losses not seen in asmaller test.The more data you use, the more patterns you see. A test of 500 daysof data will have longer sustained moves than a test of 250 days; 1000days is that much better than 500 days. More data means more of everyprice pattern and their combinations. There will be more new highs andnew lows, whipsaw periods, and price shocks. In total, the risk getsgreater as you use more data, and the profits rarely keep pace withthem.When you begin trading, you are adding the current data to your datahistory. After a year, you have increased a 1000-day test to 1250 days.The combined periods will contain new or more extreme patterns, justas though you had tested 1250 days, and as the data grows, so does thetrading risk. As a result, when you begin trading, the risk may be larger than is seen in testing.
The Use of SystemsComputers and systems have added valuable structure to both individualand institutional trading. Arbitrage, strips, multiple decision-making programs, and expert systems would not be possible without current technology. It has also contributed to risk control and dynamic asset allocation. It allows theories to be tested without real losses.The use of computerized strategies is not the "easy" answer. It is really a more disciplined and limited form than traditional trading. Itrequires users to carefully review their procedures and decision making,and put them in an orderly form. In doing this, many traders questionwhat they have been doing. Discretionary trading—the ability to applyinstinct and select outside factors—is what makes a great trader. A computer is not going to make an exception. For those traders who consistently benefit from their market judgment, a computerized programoften serves as a guideline. It can tell them the trend direction, show keyprice levels, and give them an idea of how others are positioned.Some successful traders already use systems as a basis for trading.They are able to select which trades have more potential, enter at a better price, or exit before profits disappear. You might find that theyattribute much of their success to the system, while a careful, systematic
Reasonable Expectations Give Achievable Results
39
test of the method will show that it does not produce net profits at all.The traders' skill is what actually makes it work. Yet these traders swearto the system's success.Many traders are unsure whether computerized strategies improvetheir performance or only contribute to their peace of mind. It is saidthat, because life is a struggle against disorder, some traders wouldrather use a bad system than no system at all. Systems are good becausethey are definitive and can be validated by testing. Not all systems worksimply because they are clear. This book is intended to help you understand systems and improve your trading performance.Right Position, Wrong ReasonWhen a market technician holds a position supported by fundamentals,expectations of success increase. But the rules of most systematic trading are not compatible with the equity fluctuations needed to maintaina trade based on government policy, supply and demand, or corporateexpectations.The reason for technical analysis is to cope with the unpredictableway that prices react to fundamentals, the difficulty in assessing objectives, and the need to control risk. In exchange for improving controlover an investment, it is necessary to sacrifice what seems to be an"obvious" bull move because prices retrace from their recent highs andexceed preset risk levels.A technical system grinds out profits, alternating with losing trades.It may take a big loss on a short position during a bull move. Althoughtraders can claim that they "know the system was wrong," it is the discipline of the program that ultimately succeeds.Technical trading is not glamorous. It will never let you say that youbought at the lows and took profits at the top. But trading should be abusiness, and a systematic program is a plan to profit over time, ratherfrom a single trade.Why Does Everyone KnowExcept Ton?If you can keep your head, when all about youare losing theirs, then maybe you haven't,heard the news.H. L. MENCKEN
Conversations with other traders can lead you to believe that they knewmore than you did about a surprising market move. You lost and theyprofited. However, if the move was a price shock, then no one could
4rO
How Changing Markets and Technology Affect Results
have known it was going to happen. They were probably caught on theright side of the market while you were on the wrong side.Newspapers highlight the big winners or those newsletters that gavethe right advice. Considering the number of reports published, somemust have been short before the October 1987 stock market crash. Theiradvice could have been mediocre before that and worse, but you alwaysfind out who was right after a price shock. You can always assume thathalf the traders you know were right about a move, and those are theones most likely to talk about it.
ExpectationsHigh expectations are essential to success, but unrealistic ones justwaste time. Computers do not tell you how to profit in the market, theycan only verify your own ideas. Using a computer to develop tradingprograms is a sensible, conservative approach. As with other tools, itrequires skill, which comes from study and practice. As you becomemore proficient, you will learn more.Because it is only a tool, results of system testing must be comparedfairly with all other investments. Returns should be risk adjusted, andinvestments must be properly capitalized.Be suspicious of unrealistic results, even when they are profitable.Strategies are trade-offs between many features. With more complextools, there are many more chances for error. Check the details carefully before accepting the results. There is no substitution for careful work.Use new technology cautiously. Increased computer power takes thepressure off the individual's need to conceive a profitable strategybefore testing. Many of the new methods discussed later can be a greatasset or a crutch; their benefits are entirely in the hands of the user.Researching and developing trading programs are unique activitiesamong businesses. There is no assurance that some problems have asolution. Other times, successful plans and opportunities are shortlived; even market patterns that have been reliable for many years candisappear. Part of developing a program is identifying when it nolonger works.
4Risk andReturnAmateur traders first look at profits while professionals first look atrisk. It is far more interesting to search for a profitable system than toconcentrate on losses, but an understanding of risk is essential to everyaspect of trading. Otherwise, it is only a matter of time before a priceshock forces you out of the market, or a series of losses become enoughof a worry to stop your trading. In this book, you will find that sometrading methods are considered better than others. This chapter willexplain how those choices were made. The preferred methods are basedon sound rules that incorporate both risk and return. These techniquescan be applied to any trading method.Figure 4-1 shows two equity plots for the same time period. The left one(a) shows much higher profits, but more risk. The price fluctuations aboveand below the straight line (the rate of return) are clearly larger than in theright plot (b). Which is better, the one with higher profits, or the returnswith lower risk? Is it investor "risk preference" that decides the answer?The "best" performance is not based on whether the investor is conservative or risk-seeking. It is entirely a function of which performancegives the highest returns for the lowest risk, which in turn will translateback into higher profits. In Figure 4-1, it is difficult to decide which isbetter without being given the exact risk and return for each chart.
Risk PreferenceRisk preference is the investor's willingness to accept more or less risk inexchange for profits. When two systems have the same returns, rationalinvestors will choose the system with the lowest risk. Similarly, when41
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How Changing Markets and Technology Affect Results
(a) Currency Portfolio
(b) Bond Portfolio
Figure 4 - 1 . Which equity pattern is better? (a) High returns and highrisk. A currency futures portfolio shows a 50% return and a 20% risk, (b)Low returns and low risk. A bond portfolio with an 8% return and a 2% risk.
two systems have the same risk, investors would choose the one withthe highest returns. Among programs with the best combination of riskand reward, it is necessary to accept proportionately higher risk toincrease returns by a small amount.
Standardizing Riskand ReturnBefore comparing the currency and bond portfolios in Figure 4-1, thereturns and risk must be represented in a standard, convenient form.This allows different test periods to be compared equally with oneanother. The most popular approach is used extensively by equities andfinancial analysts:• Return is the annualized, compounded rate of return.• Risk is the annualized standard deviation of the equity changes.Compounded Rate of ReturnA compounded rate of return means that the accumulated funds are reinvested. In the case of a simple interest-bearing savings account, "daily
Risk and Return
43
compounding" means that the interest earned each day is added to thetotal savings and earns interest starting the next day.Using annualized compounding, you may earn, for example, 5 percenton an investment, leaving the interest to accumulate. Because the interest is posted only once each year, a $1,000 investment is worth $1,050 atthe end of the first year. At the end of the second year, the $1,050 hasgrown by another 5 percent to $1,102.50, and after the third year to$1,157,625. The same result can be found by multiplying the initialinvestment of $1,000 by the rate of interest raised to the number of yearsthat the funds were invested.This technique is useful for system evaluation when you have thestarting and ending value of an investment and you want to find thecompounded rate of return that would give those values. The calculation can simply be reversed, as shown in Box 4-1.Annualized Standard DeviationThe annualized standard deviation measures risk. It is simply the standard deviation of the annual increase or decrease in equity (compoundedreturns). Therefore, if the annualized return is only one value each of 20years, the annualized standard deviation uses only those 20 values. Youmay use monthly changes in equity to get more accuracy. The next fewsections will compare risk and return evaluated over different timeperiods, and show that they are not easily interchanged.Using a Standard Deviation toDetermine the Chance of LossThe standard deviation is the classic measurement of distribution. Itshows how data is clustered around the average value. It assumes thatthe pattern of results is symmetrical. For example, a chart of tradingperformance is shown in Figure 4-2(a). The rate of return is the solidangled line drawn upward through the center of the equity. The standard deviation of the monthly profits and losses (subtracting last month's equity, or accumulated profits and losses, from this month's value)will show how the returns are clustered above and below the rate-ofreturn line.It is easier to see the distribution of equity changes in Figure 4-2(b). Bysubtracting the equity value of each month from the previous month,the equity has been detrended. Fluctuations are centered above andbelow a zero line, rather than an upward regression line, as in Figure 42(a). The standard deviation is useful because it puts a value on thechance of loss. In Figure 4-2(b) bands are drawn parallel to the straight-
Box 4-1. CALCULATING THE RISK A N D RETURNMost market analysts have standardized their way of representingboth risk and return. This book will adopt the same notation.Returns are the annualized, compounded rate of return. This is givenasCROR = (Ending_Equity/lnvestment)A(1/Period) - 1
where CROR is the compounded rate of returnEnding_Equity is the last account valueInvestment is the starting account valuePeriod is the number of years (for annualized returns)The Period, or number of years, is expressed as a decimal fraction(e.g., 8V2 years is 8.5). Therefore, if your $1,000 investment is worth$1,300 after 41/2 years, you have earned a compounded rate of returnequal to 6.00 percent:CROR = (1300/1000)A(1/4.5) - 1= 1.0600-1.00= 6.00% per annum
For a monthly compounded rate of return, the period would be 54.0months, or .487 percent per month.Risk is the annualized standard deviation of the equity, which wewill take as the standard deviation of the annual returns. ThenASD = @SUM(Yearly_ReturnsA2)/Period
where ASD is the annualized standard deviation@SUM is the program function that adds a list of valuesYearly_Returns is a list of yearly changes in returnsPeriod is the number of years (for annualized returns)• Spreadsheet. This calculation is readily available on spreadsheetprograms as a built-in function. In Quattro, it is simply specifiedas @STD(B4..B20) in order to find one standard deviation of thevalues in column B, rows 4 through 20.• TeleTrac and System Writer. Both testing software programs have similar built-in standard deviation functions, Std_Dv(series,period) inTeleTrac and @StdDev(series,period) for System Writer. Each calculatesand returns the value of one standard deviation.
44
Risk and Return
45
(a)
(b)
Figure 4 - 2 . Standard deviation of equity and equity changes, (a) Thestandard deviation of the equity shows the chance of a total profit or lossswing with respect to the straight line approximation of the rate of return, (b)The standard deviation of monthly equity changes shows the likelihood ofprofit or loss during any one month.line, detrended rate of return (0). These lines show the grouping of 1, 2,and 3 standard deviations, as follows:68% of all data falls between ± standard deviation(the band from A to - A )95% of all data falls between ± 2 standard deviation(the band from B to - B )
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How Changing Markets and Technology Affect Results
99% of all data falls between ± 3 standard deviations(the band from C to -C)
Because we are only interested in the risk of loss, we need to know thechance of equity falling below —A, - B , and - C . If 68 percent of the datafalls between +A and -A then 32 percent falls outside. One half of the 32percent will be above + A and the other half below - A . Therefore, there isonly a 16 percent chance that losses will exceed 1 standard deviation, a 2.5percent chance they will exceed 2 standard deviations, and a .5 percentchance they will exceed 3 standard deviations.
Choosing Between theCurrency and BondPortfoliosOnce the returns and risk are in uniform notation, the comparisonbetween the currency and bond portfolios becomes simple. The portfolios are risk-adjusted by dividing the larger risk (20 percent in the currency portfolio) by the smaller risk of the bond portfolio, giving 20/2 =10. If the currency risk is reduced by a factor of 10, then the currencyprofit of 50 percent must also be divided by 10. The result is that the currency portfolio returns only 5 percent, compared with 8 percent forbonds, when they are both at the 2 percent risk level. The bond portfolio (Figure 4-lb) is 60 percent better.LeverageThe risk-adjusted return is a better measurement of performancebecause it is the simplest way of getting the most portfolio diversification, especially when futures or options programs allow leverage. Thebond portfolio, with 8 percent returns, could have been leveraged ashigh as 20 times using the futures markets, returning 160 percent with a40 percent risk.Options and other derivatives allow the investor considerable flexibilityin varying leverage. Portfolios that deleyerage by holding cash reserves alsohave latitude for varying the investments based on risk and reward. Onlythe fully invested account (which can assume more risk than either the currency or bond portfolios) may choose the highest profits.Actual System Test for Findingthe Best ChoiceA trend-following system was tested on two years of the Bombay stockindex, the SENSEX. Table 