continuously trading those markets in var-ious groups that are likely to reflect fundamental changes. This avoids the need toidentify which market will perform the best.
3. Offset unexpected losses caused by a system failing to perform in the current mar-ket, or a single trade that generates a large loss. It may be only bad luck that one sys-tem gave a short signal in coffee the day before the freeze that moved prices limit-upfor 21 days, but another system might have given an offsetting buy signal.
4. Reduce exposure in any one market or related group by having funds distributedover many groups. If there are 10 unique asset classes, then an equal allocation onlyrisks one-tenth of the portfolio. The more groups, the less the risk.
Diversification is accomplished by applying as many of the following techniques aspossible:
1. Selecting individual markets from different groups. Trying to trade those productswith as little interrelationship (low covariance or correlation, discussed in Chapter3, “Regression”) as possible. Traditionally, futures markets have been categorizedinto sectors of interest rates, currencies, index, grains, livestock, metals (industrialand precious), foods, and miscellaneous. The last group accounts for fibers, woods,oil, and other products with little relationship to other markets.
There is a larger category called financials, which encompasses interest rates,currencies, and index markets. While these sectors tend to move on their own mostdays, they are known to have very sympathetic, correlated reactions to unexpectedeconomic news. This overriding similarity must be considered when allocating as-sets within a portfolio.
Even without the close economic ties ‘shown by the financials, there is consid-erable interaction between all of these groups. Without special news, agriculturalmarkets have little to do with metals and each moves according to their own funda-DIVERSIFICATION - 599
 
mentals; however, a radical change in the value of the U.S. dollar or interest ratescould move all prices in the same direction. For example, rising interest rates arebad for commodities that must be stored, because it increases those costs. In rurn,investors will sell gold and farmers will sell soybeans rather than pay a larger carry-ing charge.
Slow changes in the value of the U.S. dollar will affect export markets; changesin interest rates will directly impact the stock index. A crisis in the potato market,however, has little effect on other areas of the economy. When selecting those mar-kets to be used in a diversified portfolio, it is necessary to check the historical simi-larity of equity patterns as well as consider the major forces that currently drive themarket—both historic and predictive sides of the problem. When properly selected,diversification will reduce risk, as shown in Figure 23-6.
2. Multiple systems. Using more than one system will reduce risk, provided the sys-tems are not similar. Techniques may appear different and yet be highly correlated.A moving average system, ARIMA model, and point-and-figure are very differentmethods, but all are trend-following. If the sensitivity of all three systems is similar(as determined by the number of trades per year), the equity patterns will also besimilar. For system diversification, it is best to select strategies with different func-tional attributes. For example, the following list gives systems that are likely to beless correlated and techniques within each method that tend to be different.
a. Trend-following (moving averages or point-and-figure)
b, Countertrend (stochastic or contrary opinion)
c. Spreading (interdelivery, intercommodity, arbitrage, product)d. Fundamental
All four techniques are very different. Fundamentals may be trending in naturebut should have a longer time_perspective. The four types of spreads all offer excel-.lent diversification. .
3. Balanced risk. Equalizing risk is necessary if the selection of different commoditiesand systems is to offer proper diversification. Traditionally, price volatility or marketvalue is used to equate risk; however, this method tends to concentrate trading inthose products that are least active—and less likely to be profitable, For example, inearly 1986, corn was trading at $3 per bushel and the S&P 500 Index at 200, mak-ing their contract values $15,000 and $100,000, respectively. Equalizing contract
 
FIGURE 23-6 Effect of diversification on risk.
Risk (o)
oo
Number of markets (different futures categories}
 600 RISK CONTROL
 
values would mean trading seven corn to one S&P even though the likelihood ofprofiting in corn is far less than that of the S&P.
Equalizing risk must account for the way the trading model performs i in the se-lected markets; most systems do best in volatile periods. Because the most prof-itable strategies require some substantial price move, they concentrate on marketsthat have greater volatility. Therefore, it is both easier and better to diversify by dis.tributing the investment among different systems and evaluating only the correla-tions in equity. A dynamic capital allocation will be necessary as one systembecomes successful and its contribution to both profits and risk becomes dispro-portionately large. Withdrawing trading capital from the more successful systems atsuch times will maintain equal risk among systems and stabilize equity patterns.
These three justifications for diversification have their negative side as well. Diversifi-cation can mean lower profits. If there are equal returns from trading all markets and allsystems, the diversified returns reduce risk and leave profits at the same high level. How-ever, this never happens. It is not likely that silver and soybeans will be profitable at thesame rate, nor is it to be expected that two systems will parallel themselves in performanceusing two distinctly different techniques.
A classic example is the use of a system that actually loses money but has such a nega-tively correlated performance to one with a high return that the results of using them.together are obviously better than either of them alone, (Figure 23-7). Because system Breturns only a small loss, it does little to affect the profitability of System A. It will, however,sharply reduce the equity drops by being profitable during periods when System A is losing.
Portfolio Calculations
Deciding which systems and markets should be traded at the same time, in an effort toreduce risk through diversification, is an entire field of expertise called portfolio manage-ment, While markets have always changed, reflecting economic policy and the growth ofparticipation, more recent years of globalization have made portfolio management muchmore difficult: As more institutions trade international markets as they do their own, theycause a higher correlation of price movements throughout the world. This increase in cor-relation between previously unrelated areas makes it more difficult to reduce risk throughdiversification, and makes previous asset allocations obsolete. One answer to‘this problemis simply to rebalance the portfolios more often, regrouping assets by their similar pricemovements,
 
FIGURE 23-7 Stabilizing eq
 
using negatively correlated systems.
  
System A
  
P/t
System B0 | Moan Lo,DIVERSIFICATION - 601
 
Traditionally, the analyst builds up a portfolio from the expectations of the individualitems to be traded. Even more sophisticated portfolios are constructed by selecting mar-kets from groups that have been chosen, in advance, after performing a correlation analy-sis. Those that show different performance patterns qualify as potential assets in theportfolio, Once selected, the expected return of the portfolio is the weighted average ofthe expected returns on the individual components of the portfolio,® assuming each com-ponent is invested with the same percentage of the total.
E(R) = w,E(R,) + w2E(Rz) + 7° WaERn)
= > wER)
i=
The worth of a portfolio is not only its return, but its risk; therefore, the variance of theportfolio becomes an important criterion in deciding which combination of assets createthe best results:
OR= > who? t+ DD) wiwjCyi fetj=rwhere 6? is the variance of the returns of market i, and C,, is the covariance between thereturns of market 7 and the returns of market 7 The covariance, C, between two markets isthe product of their standard deviations times the correlation coefficient (corr) betweenthe same two markets:
Cy = Cory SG;Given two portfolios with the same returns, the one with the smaller variance is more
desirable; when the variances are the same, the portfolio with the highest return is best. Fora portfolio of only two assets, the calculations needed for expected return and variance are:E(R) = wy,E(R1) + WER) |Of = wio? + wo} + 2w,w,Cy,
It is important to compare portfolios using this basic comparison of return and risk;however, it is not the entire picture. When evaluating the relationship between a largenumber of data points, there may be only one case in which an extreme price movementwould have caused a fatal loss of equity. That one case can be lost in the statistics, becausethe large number of normal cases overwhelm one extreme. For safety, it is necessary to alsolook at the maximum portfolio loss. In addition, we must assume that the largest historicloss will be exceeded sometime in the future, if only by chance (consider the number ofheads or tails in a row based only on the number of coin flips). Ideally, we should try toimagine the worst-case scenario, in which globalization increases the correlations, and thePast events are not fully representative of future events.
Spreadsheet Approach
A practical way of evaluating a portfolio without requiring special mathematical knowledgeor expensive software is to use a spreadsheet program. Using a classic stock and bond mix,Table 23-2 shows the monthly returns of the S&P 500 (S&P) and the Lehman Brothers Trea-sury Index (LBTI) combined into a portfolio of 60% stocks and 40% bonds. Columns B andC show the monthly percentage returns of these two inputs and columns E and F have thecorresponding cumulative returns. At the bottom of columns B and C are some basic cal-culations that describe the performance. The S&P has an annualized return of 16.41% witha monthly standard deviation of 3.32%; bonds have a7.65% return with a 2.61% standard
* Peter L. Bernstein, The Portable MBA in Investment (John Wiley & Sons, 1995, p. 252).TABLE 23-2 Portfolio Evaluation of Stocks and Bonds Using a Spreadsheet
 
 
 
Pertentage Change Cumulative Values(A) (B) S&P (G tat! (D) Stk + Bad (E) S&P (F) L8TI (G) Stk + Bond
Jan 94 3.40 2.44 3.02 3.40 2.44 3.02Feb 94 -2.71 4.03 3.24 0.69 ~159 0.22Mar 94 4.00 4.22 4.09 ~331 ~5.81 431Apr 94 1.28 =1.36 0.22 ~2.03 ~217 4.09May 94 1.64 -0.61 0.74 ~0.39 -7.78 3.35Jun 94 -2.45 -0.09 -151 ~2.84 ~787 4.85Jul 94 3.60 3.03 3.37 0.76 ~4.84 -1.48Aug 94 4.10 -0.53 2.25 4,86 ~5.37 077Sep 94 ~2.45 -3.09 -271 241 8.46 1,94Oct 94 2.25 -0.43 118 4.66 ~8.89 -0.76Nov 94 -3.64 0.48 -1.99 1.02 -8.41 -275Dec 94 1.48 242 1.86 2.50 ~5.99 -0.90jan 95 2.59 2.68 2.63 5,09 ~3.31 1,73Feb 95 3.90 2.88 3.49 8.99 ~0.43 5.22Mar 95 2.95 O64. 2.03 11.94 0.21 7.25Apr 95 2.94 78 2.48 14.88 1,99 9.72May 95 4.00 7.90 5.56 18.88 9.89 15,28Jun 95 2.32 106 1.82 21.20 10.95 I710 4Jul 95 3.32 1.64 134 24.52 9.31 18.44Aug 95 0.25 2.13 1.00 24.77 1144 19.44Sep 95 4.22 1.73 . 3.22 28,99 (3.17 22.66Oct 95 0.36 2.93 0.96 28.63 16.10 23.62Nov 95 439 257 3.66 33.02 18.67 27.28Dec 95 1,93 2670 2.23 34.95 21.34 29.51Jan 96 3.26 -0.02 1.95 38.21 21.32 31.45Feb 96 0.69 4.82 151 38,90 16,50 29.94Mar 96 0.79 =1.85 0.27 39.69 14.65 29.68Apr 96 1.34 -1.72 0.12 41.03 12.93 29.79May 96 2.28 -0.04 1.35 43,32 12.89 3115Jun 96 0.22 2.10 0.97 43.54 14.99 32.12jul 96 4.57 0.00 -2.74 38.97 14.99 29.38Aug 96 241 1.34 0.73 41.08 13.65 S301Sep 96 5.63 2.74 447 4671 16,39 34.58Oct 96 2.76 3.94 3.23 49.47 20.33 37.81Nov 96 7.56 3.32 5.86 57.03 23.65 43.68Dec 96 -1.98 -2.34 -2.12 55.05 20.34 AL5SJan 97 6.25 0.84 34 64.30 20.47 44,97Feb 97 0.78 -0.01 0.46 62.08 20.46 45.43Mar 97 4.10 -2.44 -3.44 57.98 18.02 42,00Apr 97 5.97 2.34 452 63.95 — 20.36 4651May 97 6.09 - ila. 4ly 70.04 21.50 50.62jun 97 4.48 1.94 3.46 7452 23.44 54.09jul 97 7.96 589. 743 82.48 29.33 64.22Aug 97 5.60 -2.87 451 76.88 26.46 56.71Sep 97 5.48 2.84 442 82.36 29.30 ~ 6114Oct 97 -3.34 3.34 ~0.67 79.02 32.64 60.47Cum 7902. 32.64 60.47
AROR 1641 7.65 13.43
StDev 3.32 261 271
Ratio 494 293 4.84
602INDIVIDUAL TRADE RISK. 603
 
deviation. The ratio of AROR to standard deviation shows that the stock market has beenreturning a much better reward to risk ratio during these 4 years.
Using the standard 60% stock and 40% bond portfolio, column D (row 5) becomes+B5*.6 + C5*.4 and column G becomes the cumulative value of that portfolio. When thesame statistics are calculated for the mix, the AROR is 13.13% with a standard deviation of2.71%. As expected, the return of 13.13% is about 60% of the difference between the bondand S&P returns; however, the standard deviation has increased only 14% (rather than40%) of the difference between the two initial standard deviations. The ratio of 4.84 is veryclose to the S&P ratio, reflecting the sharp drop in risk due to combining these two assets.This easy method allows us to look for maximum drawdown, plot the original assets andfinal portfolio, and even apply a strategy to the new equity stream.
INDIVIDUAL TRADE RISK
The first line of defense in controlling risk is the individual trade, alchough sequences oftrades are also an important consideration. Trades can be viewed as one continuous eventfor the purpose of assigning risk; alternately, a strategy may consider separating the tradeinto two or more parts, for example (1) from the time of entry until the trade becomesprofitable, and (2) from the time it is profitable until the end of the trade.
Risk on Initial Positions
We associate the entry point of a trade with a period of greatest uncertainty. Depending onhow quickly you anticipate the new trade, prices are either about to change direction orhave just changed. Each type of trading method has its own intrinsic risk associated withinitial entries. The trend philosophy will take small, frequent losses and reenter the tradeas many times as necessary; the breakout technique will only limit losses by the size of thecurrent trading range. It is not clear that the accumulated sequential losses of the trendmethod is less than a single loss in the breakout approach; and, in exchange for these twodistinct approaches, the profit profile is also different.
Additional Risk Control
Most traders prefer specific risk controls added to the one that occurs naturally when thetrading method reverses position. These are generally considered stops, because they areconverted to price levels and subsequently into orders that will force the exit for a currentposition. Three of the more general approaches to determining the level of individualtrade risk are:
1. An estimate based on initial margin, for example, 50% to 70% of initial margin.This is loosely related to long-term volatility and lags considerably.’ An estimate oflong-term volatility may be a more satisfactory alternative.
2, A percentage of the portfolio, for example, 1.0% to 2.5%. This concept of equalizingrisk (and perhaps reward) across all markets is very popular; however, it is not sensi-
~ tive to individual markets, and as with many stops, imposes artificial overrides. If thevolatility becomes very high, as in the case of the S&P then this risk level could bereached on every trade causing consistent losses. It is, therefore, necessary to deter-mine when a market with exceptional volatility should be removed from the portfolio.
3. The maximum adverse excursion determined by historic evaluation.” A stop isplaced just beyond the maximum adverse excursion for each trade, or 2.5%,whichever is smaller.
° Tushar Chandé and Stanley Kroll, The New Technical Trader (John Wiley & Sons, 1994). ”® John Sweeney, Campaign Trading (John Wiley & Sons, New York, 1997).604 RISK CONTROLSa ONTROL
Stops
Stop orders provide the ability to control risk most of the time. The reason it is not “all thetime” is that exchange-traded markets can gap open, leaving your stop far behind. Whenstops are placed very close to the market, they are hit with a frequency resembling a ran.dom distribution; this is not particularly helpful to performance unless you only want toremain with a trade if ic performs properly from the beginning. When stops are placedmuch farther from the current price levels, they can serve to protect you from extremelosses, but not always. When a price shock occurs, stops are often filled far from theirintended level and can actually be filled at the worst point of the move. A system shouldnot be profitable because of stops, but must work before stops are introduced.
If stops are to work, they must be based on values other than an arbitrary financiallimit. Some worthwhile possibilities that change with the market are:
1. Advance the stop by a percentage of price, as in Wilder’s parabolic system,
2. Use a swing high or low point, based on a percentage minimum swing.
3. Use the highest high or lowest low of the recent periods,
4. Apply a method such as Kaufman’s Adaptive Moving Average (KAMA) as a Stop.5. Adjust the stop by the volatility, such as three times a 10-day average true range,
Standard Deviation Stop '
As a sound statistical measurement of risk, the standard deviation can be used to deter-mine stop-loss levels.’? In a method called the Dev-stop, Cynthia Kase uses the followingsteps to create stop-loss levels for both long and short positions:
1, Calculate the true range (7R) of the past 2 trading days using the highest high andlowest low of the 2-day period.
2. Calculate the moving average A7R of 7R (in step 1), using 30 periods for intradaycharts and 20 periods for daily charts.
3. Calculate the standard deviation of the true ranges in step 1 using the same periodas in step 2.
4. The stop-loss values are DDEV = ATR + (f*SDEV), where f= 1, 2.06 to 2.25, and 3.20to 3.50, and where the Jarger values of the pairs correct for skew and the largernumbers allow for larger risk.
5. The dev-stop for long positions is Trade high — DDEV: the dev-stop for short posi-tions is 7rade low + DDEV.
This method adjusts for volatility using standard statistical measurement and is applied tothe extreme profit of a trade to prevent unnecessary loss of equity.
Kaufman on Stops
As with many techniques, the use of stops has both good and bad features. The goodaspects are summarized in the increased control of risk—in particular, the unexpected,extremely large risk. It is an added assurance that volatility will not cause losses that are outof proportion tc system performance and expected returns.
Ideally, a Stop order entered into the market is expected+to automatically get you outof a position when prices move against you. It has the advantage of forcing the trader todecide, in advance, the size of the maximum loss, so that risk is under control. It avoids
"! Chande and Krol (see footnote 9). ="2 Cynthia Kase, “Redefining Volatility and Position Risk,” Technical Analysis of Stocks & Commodities (Octo-ber 1993).INDIVIDUALTRADE RISK 605
 
last-minute decisions and the temptation to hold a losing position with the hope thatPrices will recover.
Stops are normally resting orders; that is, they are held by the floor broker to be exe-cuted when the price is reached. For the purposes of discussion, a stop will be any form ofan order that is intended to limit losses to a fixed amount, whether the order is placed inadvance or monitored real-time.
Risk Protection or False Hope?
The use of stops, or the intent to limit losses to a predetermined, fixed amount may give afalse sense of security. For example, a Stop order that is reached during an illiquid or quietmarket will result in large slippage; during a fast market, or a price jump, it will often resultin the worst fill. Large traders cannot enter stops because they will move the market andguarantee substantial slippage.
Market Noise and the Frequency of Stops
The use of small stops, or the trading practice of exiting a trade with a small loss, causes thetotal performance of a trend strategy to be worse. Small losses occur frequently due to mar-ket noise and are not an indication that the trading strategy, or the trend direction, is wrong.
Larger stop-losses offer some benefit for longer-term trading, when high volatility hascaused the natural system stop to be very far away. Large stops may help reduce the risk ofa price shock, but not always. Stops may reduce the performance volatility of a portfoliosimply by causing more time out of the market.
Theoretically, the purpose of using a stop-loss order is to limit each loss to a controlledamount, and generate a performance profile with a reasonable ratio of average profits toaverage losses (for example, 2 : 1). In addition, a trader would like to have at least one-halfof all trades profitable. Unfortunately, the market does not work this way. It is not possibleto control both the reward/risk ratio and the percentage of profitable trades.
Noise is the term given to erratic and unpredictable price movements. It is most oftenassociated with relatively small moves, but can actually be any size. Noise is caused bytraders entering and exiting the market with different objectives and different time hori-zons, For example, an institutional investor adds positions because of new funds from itsclients; Russia sells gold to pay for a wheat purchase; or, an auto company liquidates partof its stock portfolio to cover foreign exchange losses. Because each event is unrelated tothe other, and there are so many of them, the total picture of this noise creates a randomdistribution. This pattern has many of the properties of a random number distribution, inparticular, erratic prices (noise) that are twice as large occur half as often.
Total Losses Are Constant
If noise is very similar to a random distribution, then the number of occurrences times thesize of the move will be very close to a constant value. The following is a typical result ofsetting stops of different sizes:
 
 
Size of Stop No. of Occurrences Size of Loss5 pips 20 100 pips + slippage10 pips 10 100 pips + slippage20 pips 5 {00 pips + slippage
 
 
In reality, this pattern may vary slighty from market to market, however, the cost ofslippage will usually be large enough to cause the net losses to be similar. In addition, the606 RISK CONTROL—_— eemore frequent trades must also have additional transaction costs, with a chance of largerslippage from time to time; therefore, the strategy that uses smaller stop-losses should per-form worse than the strategy with larger stops.
A Stop-Loss Can Conflict with the Trading Strategy
Combining a small stop-loss with a trend-following system is very likely to conflict in pur-pose. If a trending system gives one new trend signal each month, but the stop-loss is sosmall that it would be reached once each week, it would be very difficult to stay with a sys.tem position. Once stopped-out, if the market turns and moves in the direction of thetrend, the system is proved right but you have no position, It is necessary to create a reen-try strategy that can be unnecessarily complex.
If every time you are stopped out of a trade, the price continues in the same directionuntil a reverse position is signaled, then it follows that the selection of the trend period istoo slow. Rather than exit the trade when the stop is reached, the system should be revers-ing its position. By shortening the trend calculation period, the need for a stop is elimi-nated.
Testing Stops over Ten Years
Table 23-3 gives the pattern of performance for a simple moving average trading systemwith calculation periods from 5 to 300 days and stops from .02% to 10%. Four major mar-kets were selected, two stocks and two futures markets. The smallest stop-loss of 2%appears on the left, and the largest of 10% and no stop (“NONE”) appear on the far right.Overall, the performance of the trend program without a stop is most consistent for therange of trend periods, although specific stops can be better for some intervals, It may benoted that there ‘is a pattern in Siemens, in which the best performance runs diagonallyfrom the upper left toward the bottom right, indicating that the size of the optimum stop-loss may be related to the speed of the trend, but this pattern is not the same for the othermarkets tested and, therefore, it may be the result of a single trade, such as the crash of1987, and not a robust relationship. Table 23-4 shows the same results for theDeutschemark and Eurodollars in terms of risk-adjusted returns, in which the returns aredivided by one standard deviation of the equity changes. In general, these results were the
same as the unadjusted ones in Table 23-3.\
Managing Risk with and without Stops
Despite the conclusion that the placement of fixed-level stops causes a trade to be stoppedout arbitrarily, it is difficult to trade without a clear idea of risk. For longer-term positions, afixed stop-loss may help in the case of catastrophic risk. Before a stop-loss is used, it shouldbe tested and compared with system performance that does not use a stop. Careful selec-tion of the trading strategy may provide adequate risk control with a separate stop-loss.
While fixed stops do not seem to enhance a trading program, a stop based on supportand resistance levels may be quite different. It is already known that a breakout system,‘which enters on a new high and reverses on a new low, assumes the risk of the rangedefined by the difference between the high and low. This is analogous to the size of asupport-resistance range. Because this range varies with market volatility and offers a viewof risk that contrasts with a trend system, the combination of the two may improve net per-formance.
The safest way to reduce risk is simply by reducing the size of your positions. Tradinga smailer portfolio, a lower margin to equity ratio, is the simplest approach to risk reduc-tion and does not conflict with the underlying trading strategy. In tle final analysis, the onewho can profit by trading the smallest amount will be hurt the least when a price shock hitsthe market.TABLE 23-3 Results of Tests Comparing Trend Period and Size of Fixed Stops*Annualized Rate of Return (Adjusted for 25% Drawdown)
Stop-Loss in Whole Percent02 05 10 AS 25 50 100 2.00 400 7.00 10.00 NONEa. Chrysler Motors: 2,329 Days (1/05/84 to 3/18/93)
5  -28 -28 -27 -27 -27  -28 -28 -27 -