Apply technical evidence to entries, exits, portfolio choices, and risk with 20 original multiple-choice questions and 60 worked concepts. Coverage follows the supplied 2026 CMT Program Guide as of October 16, 2026: Theory and History 7%, Classical Techniques 40%, Advanced Techniques 40%, Application of Technical Analysis 10%, and Ethics 3%. This representative preview uses 1/8/8/2/1 questions and 4/24/24/6/2 concepts; these are editorial allocations, not official item counts. The guide emphasizes interpretation, calculations, model limitations, and ethical communication. Citations establish syllabus relevance rather than independently verifying every technical explanation. Level II is one examination within the CMT program.
What this guide covers
Apply CMT Level II methods with 20 original practice questions, worked solutions and 60 focused study concepts.
Theory and History
1. Dow Theory: confirmation and trend persistence
Dow Theory developed from observations of broad market averages and distinguishes primary trends from secondary reactions and shorter fluctuations. A central interpretive rule is confirmation: related averages should provide compatible evidence before an analyst declares a broad trend change. A trend remains the working hypothesis until sufficient contrary evidence appears. This approach favors confirmation over picking exact turning points and therefore accepts some delay. Modern applications should specify which benchmarks are economically relevant and how swing highs and lows establish confirmation; historical principles do not supply a universal trading algorithm.
Worked example: An industrial benchmark exceeds its previous major high while a transportation benchmark remains below its corresponding high. The analyst records incomplete confirmation and waits for the second benchmark or clearer contrary price evidence before upgrading the broad trend assessment.
Common mistake: Assuming one average’s new high automatically confirms the entire market ignores the distinction between an isolated signal and broad confirmation.
Official syllabus reference: [1]
2. Weak-form efficiency and testable technical edges
Weak-form market efficiency holds that past market information is already reflected in prices sufficiently to prevent reliable abnormal profits from that information alone. Technical analysis can challenge this proposition through testable claims about trends, reversals, or participation. A visually compelling pattern is insufficient evidence: its incremental return must survive realistic costs, risk adjustment, selection effects, and independent testing. Efficiency is therefore a useful benchmark for evaluating an alleged edge. Evidence of predictability also differs from evidence of economic profitability, especially when turnover, capacity, or execution frictions absorb the forecast advantage.
Worked example: A moving-average rule predicts next-day direction slightly better than chance, but frequent trading consumes its gross gains. The analyst distinguishes statistical predictability from a usable investment edge and compares net results with a risk-matched benchmark.
Common mistake: Treating any predictable price movement as proof of profitable market inefficiency overlooks costs, risk exposure, and the reliability of the evidence.
Official syllabus reference: [1]
3. Prospect theory and the disposition effect
Prospect theory describes decisions relative to a reference point, with losses often felt more intensely than comparable gains and risk preferences changing across gains and losses. One trading manifestation is the disposition effect: realizing winners readily while retaining losers to avoid recognizing a loss. The purchase price can become psychologically important even when it has little relevance to the security’s current opportunity. A technical process counters this by defining invalidation and exit criteria prospectively. These tendencies describe behavioral patterns rather than rules that every investor follows or profitable signals that automatically transfer to every market.
Worked example: A trader sells a rising position after a small gain but keeps a larger losing position after its support breaks, hoping to return to the purchase price. A predefined support-based exit would evaluate current evidence rather than the emotional appeal of breaking even.
Common mistake: Believing a loss becomes economically meaningful only when sold confuses accounting realization with the decline already suffered in current wealth.
Official syllabus reference: [1]
4. Availability versus anchoring in market forecasts
Availability bias arises when memorable or easily recalled observations dominate probability judgments. Anchoring arises when a reference value exerts excessive influence on subsequent estimates, even after relevant evidence changes. The distinction matters because remedies differ: broader historical sampling challenges availability, while independently rebuilding an estimate helps challenge anchoring. Both can distort technical interpretation without changing the underlying chart. An analyst should ask whether a forecast follows reproducible evidence or merely a vivid recent event or familiar price. Neither bias is established solely because a forecast ultimately proves wrong.
Worked example: After a dramatic crash, an analyst assigns unusually high probability to another immediate crash without examining comparable periods. A colleague instead insists that a stock must revisit its former $100 peak. The first judgment suggests availability; the second suggests anchoring.
Common mistake: Calling every mistaken forecast anchoring obscures whether the actual problem was a fixed reference point, selective memory, or a defensible estimate.
Official syllabus reference: [1]
Classical Techniques
5. Adjusted OHLC data and corporate-action gaps
An OHLC bar records the opening, highest, lowest, and closing prices for its interval. Corporate actions can create apparent discontinuities that do not represent ordinary buying or selling pressure. A split-adjusted series places historical prices on a consistent share basis; dividend adjustment depends on whether the analysis seeks price behavior or total return. Adjustment methods must remain internally consistent across open, high, low, close, and volume where relevant. Otherwise indicators and patterns may react to data transformations. Investigate large discontinuities before interpreting them as breakouts, exhaustion gaps, or volatility shocks.
Worked example: A two-for-one split changes a stock’s quoted price from roughly $80 to $40. An unadjusted chart appears to show a collapse. Adjusting earlier prices to the new share basis removes the artificial break before trend and range calculations are evaluated.
Common mistake: Interpreting every large price discontinuity as a trading gap can turn a routine corporate action into a false technical signal.
Official syllabus reference: [1]
6. Logarithmic scales preserve proportional moves
A linear chart assigns equal vertical distance to equal currency changes, while a logarithmic chart assigns equal distance to equal proportional changes. On a log scale, a move from $20 to $40 occupies the same vertical distance as a move from $40 to $80. This is useful when comparing long histories or securities with large cumulative appreciation. Trendline geometry can change materially with scale, so the scale is part of the analytical specification. Logarithmic price axes require positive values and should not be applied mechanically to series containing zero or negative observations.
Worked example: A stock rises from $25 to $50 and later from $50 to $100. A linear chart makes the later advance look twice as tall. A logarithmic chart displays both advances equally because each represents a 100% gain.
Common mistake: Comparing trendline steepness across charts without checking their scales can mistake a display choice for a change in economic momentum.
Official syllabus reference: [1]
7. Point-and-figure box size and reversal rules
Point-and-figure charts emphasize price movement rather than equal time intervals. Columns of Xs represent advances and columns of Os represent declines, with a new opposite column requiring the specified reversal. Box size controls the minimum plotted price increment, while reversal size controls how much countertrend movement changes columns. Larger settings filter more noise but recognize turns later. Construction also depends on whether the method uses closes or intraday highs and lows. State those conventions before comparing signals, because different construction choices can produce different patterns from the same market history.
Worked example: Using $1 boxes and a three-box reversal, an X column reaches $47. A decline to $45 is insufficient to reverse the column. A decline to $44 meets the three-box condition, beginning an O column under the stated construction rule.
Common mistake: Assuming each new point-and-figure column represents one day confuses price-event construction with the fixed time spacing used in bar charts.
Official syllabus reference: [1]
8. Candlestick bodies, shadows, and location
A candlestick separates the open-to-close body from the full high-low range shown by its shadows. A long lower shadow indicates that price traded lower and recovered before the close, but its significance depends on the preceding move and nearby support. The same geometry can carry different implications after a decline, after an advance, or inside a narrow range. Candlestick analysis becomes more useful when combined with swing structure, volume, and a defined invalidation level. A named candle is a description of intraperiod behavior, not an independent guarantee of the next period’s direction.
Worked example: After several declining sessions, a stock touches established support, trades sharply lower, and closes near its opening price with a long lower shadow. The analyst watches for subsequent buying and uses the candle’s low as a candidate invalidation reference.
Common mistake: Buying every long lower shadow overlooks whether the candle appears at meaningful support or merely within ordinary intraday noise.
Official syllabus reference: [1]
9. Swing highs and lows define trend structure
An uptrend is commonly identified by a sequence of higher swing highs and higher swing lows; a downtrend uses lower highs and lower lows. The swing definition must match the decision horizon, because a daily correction can occur within a weekly uptrend. One broken minor swing does not necessarily reverse the larger structure. Analysts should distinguish an interruption, a range, and a confirmed opposing sequence. Swing points identified with future bars also create recognition delay, which must be respected in testing so that a strategy does not trade a pivot before it became observable.
Worked example: Weekly lows rise from $62 to $67 to $71 while weekly highs also advance. A daily pullback below a minor two-day low weakens the short-term structure, but the analyst does not declare the weekly trend reversed without relevant weekly evidence.
Common mistake: Mixing intraday swing breaks with weekly trend labels creates contradictory conclusions because the signals describe different time horizons.
Official syllabus reference: [1]
10. Trendlines and parallel price channels
An ascending trendline connects relevant rising lows, while a descending trendline connects falling highs. A parallel line through an opposing swing can define a channel and help describe the trend’s range and rate of advance. More independent touches may increase the line’s descriptive importance, but repeated redrawing can make the analysis unfalsifiable. A line break signals a change in the previous trajectory, not necessarily a full trend reversal. Channel boundaries can support trade planning when combined with structural invalidation, liquidity, and the distinction between normal overshoots and sustained acceptance beyond the boundary.
Worked example: A stock repeatedly rebounds from a rising lower channel boundary. It later closes below that boundary but remains above its last major swing low. The analyst recognizes a broken rate of ascent while waiting for further evidence about the broader trend.
Common mistake: Equating every trendline break with a completed reversal ignores the possibility of sideways consolidation or a slower continuation trend.
Official syllabus reference: [1]
11. Support-resistance zones and polarity
Support and resistance are price areas where prior transactions, expectations, and positioning may influence future supply and demand. They are usually better treated as zones than exact immutable prices. After a sustained break, former resistance may become support because late buyers and previously frustrated participants respond differently on a retest. This role change is called polarity. A zone’s usefulness depends on the trading horizon, the quality of the break, and subsequent behavior. A brief penetration can reflect noise, so confirmation rules should be specified before interpreting a test.
Worked example: Several rallies stall between $48 and $49. Price later closes at $51 and pulls back to $49 before renewed buying appears. The analyst treats the old ceiling as a candidate support zone and defines failure using a sustained return below it.
Common mistake: Treating support as a guaranteed floor overlooks that it represents a conditional concentration of demand which can be overwhelmed.
Official syllabus reference: [1]
12. SMA and EMA weighting create different lag
A simple moving average gives equal weight to observations within its window. An exponential moving average updates recursively as EMA today = α × price today + (1 − α) × EMA yesterday, commonly using α = 2 / (n + 1). The EMA places greater weight on recent observations while retaining declining influence from older data. Both smooth prices and lag changes. Faster averages can recognize shifts sooner but are more vulnerable to whipsaws. Compare methods using the same implementation conventions, because initialization and lookback choices can affect early values and signal timing.
Worked example: With a prior EMA of $100, a current close of $104, and α of 0.20, the updated EMA is $100.80. Only part of the new price move enters immediately, illustrating why greater responsiveness still does not eliminate lag.
Common mistake: Calling an EMA lag-free because it emphasizes recent prices confuses faster adjustment with knowledge of a turning point before it occurs.
Official syllabus reference: [1]
13. ADX measures strength while directional indicators compare direction
The directional movement system compares upward and downward movement through positive and negative directional indicators, commonly written +DI and −DI. ADX smooths their normalized separation to describe trend strength rather than trend direction. Rising ADX can accompany either a strong advance or a strong decline. A directional crossover may suggest a change in control, while ADX provides context about whether directional separation is strengthening. Particular cutoff values are conventions requiring calibration, not universal laws. Use price structure to distinguish a newly emerging trend from a late-stage trend that already contains substantial extension.
Worked example: A market falls steadily, −DI remains above +DI, and ADX rises. The combined reading describes strengthening downward directional movement. Interpreting the rising ADX itself as bullish would reverse the role of a measure that has no directional sign.
Common mistake: Reading rising ADX as a buy signal confuses increasing trend strength with the separate question of whether that trend points upward.
Official syllabus reference: [1]
14. Head-and-shoulders completion requires neckline evidence
A head-and-shoulders top contains a peak, a higher central peak, and a lower final peak after an advance. The neckline connects the intervening reaction lows and can slope. Until price breaks it under the chosen confirmation rule, the formation remains a candidate rather than a completed reversal. A conventional objective projects the head-to-neckline height downward from the break area, with care when the neckline slopes. Volume can provide supporting context but does not replace price confirmation. Pattern failure is possible, so objective selection and invalidation should be distinct decisions.
Worked example: A stock forms peaks at $66, $74, and $67, with intervening lows near $61. A confirmed break below $61 completes the candidate under the trader’s rule. The $13 height suggests an approximate $48 objective, while risk still requires a separate stop decision.
Common mistake: Selling solely because three peaks are visible can anticipate a reversal before the neckline provides the required evidence of completion.
Official syllabus reference: [1]
15. Triangles describe compression before resolution
Triangles form when successive swings converge, indicating compression of the trading range. An ascending triangle combines relatively level resistance with rising lows; a descending triangle combines relatively level support with falling highs; a symmetrical triangle has converging upper and lower boundaries. Their shapes suggest changing pressure but do not ensure breakout direction. A conventional projection uses the formation’s widest height, while entry requires an explicit breakout rule. Declining volume during compression and expansion during resolution may support interpretation. Late or weak breaks deserve particular scrutiny because compression can resolve through drift rather than decisive expansion.
Worked example: Price repeatedly stalls near $90 while reaction lows rise from $81 to $85 to $88. This is an ascending-triangle candidate. The analyst waits for the specified resistance break rather than assuming that rising lows alone establish a completed upside breakout.
Common mistake: Treating a triangle’s descriptive name as a directional guarantee ignores that the eventual break can contradict the formation’s usual tendency.
Official syllabus reference: [1]
16. Flags and pennants need a preceding impulse
A flag or pennant is typically interpreted as a short consolidation following a strong directional move. Flags often resemble small parallel channels, while pennants have converging boundaries. The preceding impulse distinguishes these formations from ordinary ranges and standalone triangles. A continuation interpretation becomes stronger when the consolidation shows reduced activity and price subsequently resolves in the impulse direction. A measured projection may use the preceding move, but this is a conditional estimate. If the consolidation expands, lasts disproportionately long, or breaks against the impulse, the original classification may no longer be useful.
Worked example: A stock surges from $30 to $38, then drifts between narrowing boundaries for several sessions on reduced volume. An upside break restores the impulse direction. The analyst evaluates a pennant continuation while retaining an exit if price returns decisively into the consolidation.
Common mistake: Labeling any small sideways range a flag overlooks the preceding directional impulse that gives the continuation interpretation its meaning.
Official syllabus reference: [1]
17. Breakaway, continuation, and exhaustion gaps
A price gap leaves an interval between trading ranges with no observed transactions in that interval. A breakaway gap emerges from an established range, a continuation gap appears within an active trend, and an exhaustion gap occurs near a trend’s termination. These categories depend on context and later evidence; a gap’s appearance alone cannot reliably distinguish them. Volume, location, extension, and subsequent follow-through help interpretation. Corporate actions and data errors must first be excluded. The belief that all gaps must fill has no useful universal timing rule and can create poorly bounded trades.
Worked example: After weeks beneath $45 resistance, a stock opens above $47 on heavy activity and holds the new area. The gap supports a breakaway interpretation. A similar gap after a prolonged vertical rise would require greater scrutiny for exhaustion and failed follow-through.
Common mistake: Assuming every gap will promptly close substitutes a market saying for evidence about location, participation, and the prevailing trend.
Official syllabus reference: [1]
18. Wyckoff springs and tests of supply
Wyckoff analysis interprets price and volume as evidence of the interaction between supply and demand within trading ranges and trends. A spring is a move below established range support followed by recovery into the range, potentially indicating that available supply has been absorbed. A subsequent test with reduced selling pressure can strengthen that interpretation. It is not enough to label every undercut a spring: persistent weakness below support may instead indicate distribution or renewed markdown. The analytical task is to compare effort, result, location, and follow-through rather than infer hidden intentions with certainty.
Worked example: A stock briefly trades below a multiweek range, recovers above support, and later revisits the area on lower volume without making a new low. The analyst interprets the sequence as a possible spring and test, contingent on subsequent demand.
Common mistake: Calling every support break a spring ignores the recovery and successful test that distinguish potential absorption from sustained selling pressure.
Official syllabus reference: [1]
19. Elliott impulse rules constrain wave counts
A conventional Elliott impulse contains five waves, with waves one, three, and five moving in the larger trend direction and waves two and four correcting. Core constraints include wave two not retracing beyond the start of wave one, wave three not being the shortest motive wave, and wave four not entering wave one’s price territory in a standard impulse. Diagonal structures have different characteristics. These constraints invalidate certain counts but do not make the remaining count uniquely correct. Alternate interpretations should remain explicit because retrospective labeling can otherwise hide uncertainty.
Worked example: An analyst labels a rising sequence as a standard five-wave impulse. The proposed fourth wave then falls into the first wave’s price territory. That observation invalidates the standard impulse count and requires reconsideration rather than simply moving the labels.
Common mistake: Using Fibonacci proportions to preserve a count that violates a core impulse rule confuses optional guidelines with structural constraints.
Official syllabus reference: [1]
20. Fibonacci retracements locate conditional reaction zones
A retracement measures how much of a prior move has been reversed. Fibonacci-based analysis applies commonly used proportions, such as 38.2% and 61.8%, to a clearly defined swing; 50% is also widely plotted although it is not a Fibonacci ratio. In an advance, subtract the chosen fraction of the swing height from the high. These levels are reference zones rather than demonstrated barriers. Their usefulness depends on independent evidence such as prior support, price response, and an explicit invalidation rule. Changing swing endpoints after observing the result undermines reproducibility.
Worked example: A stock advances from $50 to $70, a $20 move. A 38.2% retracement lies near $62.36 because $70 minus 0.382 times $20 equals $62.36. The analyst watches price behavior there rather than assuming an automatic rebound.
Common mistake: Treating a retracement level as compulsory support mistakes a geometric reference for evidence that buyers will actually defend that price.
Official syllabus reference: [1]
21. RSI compares smoothed gains with losses
Relative strength index transforms the ratio of smoothed gains to smoothed losses into a bounded oscillator: RSI = 100 − 100 / (1 + RS). It measures a security’s own recent momentum, not its performance against a benchmark. Elevated readings can persist during strong uptrends, while depressed readings can persist during strong declines. Divergence compares oscillator extremes with corresponding price extremes and is a warning rather than automatic reversal confirmation. Calculation conventions, especially smoothing and initialization, matter when reproducing values. Trend regime influences how oscillator ranges and midpoint behavior should be interpreted.
Worked example: If average gain is $1.50 and average loss is $0.50, RS equals 3 and RSI equals 75. That reading reflects gains dominating recent losses. It does not establish that the stock outperformed an index or must decline next.
Common mistake: Confusing RSI with a stock-to-index ratio merges an internal momentum oscillator with a separate measure of relative market performance.
Official syllabus reference: [1]
22. MACD line, signal line, and histogram
MACD is the difference between a faster and slower exponential moving average. A signal line smooths that difference, and the histogram subtracts the signal line from MACD. A positive MACD indicates that the faster average exceeds the slower average; a rising histogram indicates that MACD is improving relative to its signal line. These are related but distinct observations. Histogram improvement can occur while MACD remains negative. Because MACD is derived from price averages, it lags and can whipsaw in ranges. Its raw magnitude is also price-dependent, complicating direct comparisons across differently priced securities.
Worked example: MACD rises from −1.2 to −0.8 while its signal line remains at −1.0. The histogram becomes positive even though MACD remains below zero. The analyst distinguishes improving short-term momentum from a completed positive faster-versus-slower average relationship.
Common mistake: Assuming a positive MACD histogram means MACD itself is above zero confuses the signal-line comparison with the zero-line comparison.
Official syllabus reference: [1]
23. Stochastic oscillators locate closes within ranges
The stochastic oscillator compares the current close with the recent high-low range. A basic %K calculation is 100 × (close − lowest low) / (highest high − lowest low), with smoothing producing commonly used variants and signal lines. It therefore measures the close’s location inside the lookback range rather than the size of a close-to-close return. Readings near the upper boundary can persist in an advance. Crossovers need context, especially in trending markets. A zero high-low denominator requires an explicit software convention rather than an improvised arithmetic result.
Worked example: Over the chosen window, the highest high is $60 and the lowest low is $50. A $58 close produces raw %K of 80. The reading places the close near the range’s top without independently predicting the next session’s direction.
Common mistake: Reading a stochastic value of 80 as an 80% price gain confuses normalized range position with an investment return.
Official syllabus reference: [1]
24. On-balance volume tracks signed participation
On-balance volume adds the session’s volume when the close rises, subtracts it when the close falls, and typically leaves the total unchanged when the close is unchanged. Its absolute starting value is arbitrary; the path and relationship to price are what matter. OBV can support an advance when both make new highs or warn when participation fails to confirm price. It assigns all session volume using the close’s direction, so it is an approximation rather than a transaction-by-transaction classification of buying and selling. Reliable, consistently defined volume data are essential.
Worked example: Starting from an arbitrary OBV of zero, an up-close session with 200,000 shares adds 200,000. A down-close session with 120,000 shares leaves OBV at 80,000. The analyst then compares its trajectory with price rather than interpreting the level as money invested.
Common mistake: Treating OBV as actual net cash entering a security overlooks that it signs total share volume using only the closing-price change.
Official syllabus reference: [1]
25. Advance-decline lines reveal concentration
An advance-decline line cumulatively adds advancing issues minus declining issues within a specified universe. It describes participation rather than capitalization-weighted performance. An index can rise while its advance-decline line weakens if a smaller group of heavily weighted constituents leads. That divergence warns of concentration but does not precisely time a market reversal. Universe composition matters: exchange-wide breadth can include securities that differ from the benchmark’s constituents. Corporate listings, delistings, and methodological changes can also affect long histories, so breadth comparisons should use clearly identified and reasonably compatible datasets.
Worked example: A capitalization-weighted index reaches a new high while only 180 of its 500 constituents advance and its cumulative breadth line remains below its prior peak. The analyst notes narrowing participation rather than treating the index high as uniformly broad strength.
Common mistake: Assuming an index high means most constituents are rising ignores the difference between capitalization weighting and counting each issue equally.
Official syllabus reference: [1]
26. TRIN normalizes issue breadth by volume breadth
TRIN divides the advancing-to-declining issue ratio by the advancing-to-declining volume ratio. Algebraically, it compares average volume per declining issue with average volume per advancing issue. A value below one means advancing issues carry greater average volume; a value above one means declining issues do. This direct interpretation differs from contrarian uses of unusually extreme readings. Extremes require a defined historical reference and often smoothing because daily values can be unstable. Zero counts or zero volume make ordinary ratio calculations problematic and require explicit handling rather than casual substitution.
Worked example: There are 900 advancing and 600 declining issues, with 270 million advancing shares and 90 million declining shares. TRIN is 1.5 divided by 3, or 0.50, reflecting greater average volume among advancing issues during that session.
Common mistake: Reading TRIN below one as proof of an imminent decline confuses its direct volume-breadth meaning with a conditional contrarian interpretation.
Official syllabus reference: [1]
27. Put-call ratios need participant and regime context
A put-call ratio divides put activity by call activity, using a specified measure such as volume or open interest. Higher values can indicate greater demand for downside exposure or protection, but hedging, institutional activity, and contract selection affect interpretation. Equity-only and index-option ratios need not convey the same sentiment. Contrarian analysis asks whether positioning is unusually one-sided relative to an appropriate history and whether price confirms a shift. A fixed numerical reading is not universally bullish or bearish. Keep measurement definitions consistent when comparing observations or testing sentiment rules.
Worked example: An index put-call volume ratio jumps as institutions purchase portfolio protection, while an equity-only ratio changes little. The analyst avoids treating the aggregate change as pure speculative pessimism and compares each series with its own historical distribution.
Common mistake: Applying one universal put-call cutoff across index options, individual equities, volume, and open interest ignores materially different participant motives and measurements.
Official syllabus reference: [1]
28. Cycle period, amplitude, phase, and harmonics
A cycle’s period is the interval between equivalent points, frequency is its reciprocal, amplitude measures vertical displacement from the midpoint, and phase locates the cycle relative to a reference. Harmonics have frequencies that are integer multiples of a base frequency. Combining components can strengthen or offset observed movement depending on phase. Market cycles are approximate and can drift in period and amplitude, so calendar projections need price-based confirmation. A cycle estimate describes timing structure rather than a complete forecast of direction, magnitude, or the location of support and resistance.
Worked example: An estimated 30-session cycle and a 15-session harmonic approach troughs together. The analyst treats this alignment as a timing window, then looks for price stabilization. If support continues failing, the calendar estimate alone does not justify a long entry.
Common mistake: Confusing phase with period makes a shifted cycle appear slower even when the interval between its own successive troughs is unchanged.
Official syllabus reference: [1]
Advanced Techniques
29. Simple returns compound while log returns add
A simple return is ending price divided by beginning price minus one. A log return is the natural logarithm of that price ratio. Across periods, simple gross returns multiply, whereas log returns add exactly. This distinction matters for aggregation, volatility analysis, and interpreting average returns. An arithmetic average of periodic simple returns generally differs from the compound growth rate because gains and losses interact multiplicatively. Log returns require positive price ratios and should not be treated as directly additive across portfolio holdings; portfolio aggregation follows the holdings and weights.
Worked example: A price rises from $100 to $110 and then returns to $100. The simple returns are 10% and approximately −9.09%, yet total return is zero. The two log returns sum to zero, matching the unchanged ending wealth.
Common mistake: Adding periodic simple returns to calculate exact multi-period growth ignores compounding and can report a gain when wealth has merely returned to its start.
Official syllabus reference: [1]
30. Sample variance and estimation uncertainty
Sample variance measures dispersion around the sample mean, commonly dividing squared deviations by n − 1 when estimating an unknown population variance under standard sampling assumptions. Standard deviation is its square root and has the original return units. A volatility estimate from a short sample is uncertain even when calculated correctly. Standard error of the mean answers a different question: uncertainty about average return rather than variability of individual returns. Financial observations can violate independence and stable-distribution assumptions, making textbook uncertainty estimates optimistic unless dependence and changing regimes are addressed.
Worked example: Three returns are −1%, 0%, and 1%, with mean zero. Their squared deviations sum to two squared percentage points. Dividing by two gives sample variance of one squared percentage point and sample standard deviation of one percentage point.
Common mistake: Using standard error as a forecast of daily return variability confuses uncertainty in an estimated mean with dispersion of the underlying observations.
Official syllabus reference: [1]
31. Regression beta separates sensitivity from fit
In a linear return regression, beta estimates the change in the dependent return associated with a one-unit change in the explanatory return. The intercept captures the fitted value when the explanatory return is zero, while residuals represent unexplained variation. R-squared describes the fraction of sample variation explained by the model, not the magnitude of beta or proof of causation. A high beta can coexist with a weak fit. Interpretation depends on return frequency, sample choice, and stability. Residual patterns and outliers matter because a simple fitted line can conceal changing relationships.
Worked example: A stock regression has beta 1.4 but R-squared of 0.20. The estimated market sensitivity is relatively large, yet the market explains only one-fifth of sample return variation. The analyst does not infer that most stock-specific risk has disappeared.
Common mistake: Interpreting beta of 1.4 as 140% explained variation confuses a regression slope with the separate goodness-of-fit statistic.
Official syllabus reference: [1]
32. P-values address a null model, not profitability
A p-value measures how incompatible the observed result is with a specified null model, using the probability of a result at least as extreme under that model. It is not the probability that the null is true or that a strategy will lose money. A significance level controls a procedure’s false-rejection rate under its assumptions. Practical importance requires effect size, uncertainty, costs, and implementation analysis. Financial tests also need appropriate treatment of dependence and non-normality. Statistical significance can coexist with an economically trivial or unstable trading advantage.
Worked example: A strategy’s estimated gross edge is two basis points per trade with a small p-value. Expected round-trip costs are five basis points. The analyst recognizes statistical evidence about the modeled mean while rejecting a claim of positive net economic value.
Common mistake: Calling a p-value of 0.03 a 97% probability of future profitability gives a null-model statistic a predictive meaning it does not possess.
Official syllabus reference: [1]
33. Autocorrelation changes effective information
Autocorrelation measures association between observations separated by a specified lag. Positive return autocorrelation can indicate persistence, while negative autocorrelation can indicate short-horizon reversal, although market microstructure and data construction can also generate such patterns. Dependence means that a long observation count may contain less independent information than it appears to contain. Overlapping multi-period returns are mechanically dependent because adjacent observations share underlying periods. Testing and resampling should preserve relevant dependence. A statistically detected relationship must still survive costs, changing regimes, and the timing constraints of an executable strategy.
Worked example: A researcher calculates a new 20-day return every day and treats 500 observations as independent. Neighboring returns share 19 daily changes. The analyst uses dependence-aware inference or nonoverlapping observations rather than accepting the nominal sample size at face value.
Common mistake: Assuming daily recording makes overlapping monthly returns independent ignores the shared price changes embedded in adjacent observations.
Official syllabus reference: [1]
34. Multiple comparisons create selection bias
When many indicators, parameters, markets, or entry rules are tested, the strongest historical result benefits from selection even if none has a genuine edge. Under true nulls, repeated tests generate false positives at a rate related to the chosen significance procedure. Research discipline includes recording the search space, distinguishing exploration from confirmation, and using multiplicity-aware methods or untouched validation. A holdout repeatedly inspected during revisions becomes part of the search. The relevant unit is the entire research process, not merely the final attractive strategy that survives it.
Worked example: An analyst tests 200 variations and advertises the one with the highest Sharpe ratio. Before implementation, the research team asks how the other 199 performed and evaluates the selected rule on a later period that did not influence its design.
Common mistake: Reporting only the winning parameter set hides the search process that can make an ordinary chance outcome look unusually convincing.
Official syllabus reference: [1]
35. ATR incorporates gaps but does not indicate direction
True range is the maximum of the current high-low range, the absolute high-to-previous-close distance, and the absolute low-to-previous-close distance. Average true range smooths these observations to estimate price-range volatility. Including the previous close captures gaps that a high-low measure misses. ATR is expressed in price units, so direct comparisons across differently priced securities need normalization, such as ATR divided by price. Rising ATR means greater range activity, not necessarily falling prices. ATR-based stops and sizing should use data available at the decision time and retain allowance for execution risk.
Worked example: A stock previously closes at $70, then trades between $73 and $76. The session range is $3, but true range is $6 because the previous close-to-high distance includes the gap. A smoothed ATR incorporates that larger observation.
Common mistake: Treating rising ATR as inherently bearish confuses the magnitude of price movement with its direction and can misread volatile advances.
Official syllabus reference: [1]
36. Bollinger Band width and directional uncertainty
Bollinger Bands place upper and lower boundaries around a moving average using a multiple of rolling standard deviation. Narrowing bands indicate reduced recent dispersion under the chosen calculation; widening bands indicate increased dispersion. A squeeze identifies compression but does not determine the direction of the eventual move. Price can remain near or beyond a band during a strong trend, so band contact is not automatically a reversal signal. Band width and price location answer different questions. The familiar standard-deviation construction also does not guarantee fixed probability coverage for non-normal, dependent market prices.
Worked example: A stock’s bands narrow during a quiet consolidation. The analyst prepares conditional breakout plans in both directions and waits for price confirmation. Buying solely because the bands are tight would add a directional assumption that the volatility measure does not contain.
Common mistake: Assuming every upper-band touch must reverse applies a range-trading interpretation even when price is persistently trending along the band.
Official syllabus reference: [1]
37. Implied volatility and horizon scaling
Implied volatility is the volatility input consistent with an option’s price under a specified pricing model. It reflects option-market pricing of uncertainty and risk compensation rather than a guaranteed physical forecast. Under an explicit square-root-of-time approximation, horizon volatility equals annualized volatility multiplied by the square root of the year fraction. Calendar-day and trading-day conventions must not be mixed. The result describes a scale of movement rather than direction or a maximum loss. Jumps, skew, term structure, and changing variance limit simple symmetric interpretations.
Worked example: An option-based estimate is 24% annualized. Using an explicitly assumed 252-trading-day year, approximate one-day volatility is 24% divided by the square root of 252, or about 1.51%. The estimate does not predict whether the next move is upward or downward.
Common mistake: Treating implied volatility as a guaranteed future realized range ignores pricing assumptions, risk premiums, and the possibility of moves beyond a modeled scale.
Official syllabus reference: [1]
38. Historical volatility responds to window and weighting
Historical return volatility is commonly estimated as the standard deviation of returns over a specified window and then annualized under stated assumptions. A short window responds quickly but can be noisy; a long window is smoother but slower to reflect regime changes. Equal weighting can create abrupt changes when an old shock exits the window. Exponentially weighted methods reduce older observations’ influence gradually and respond more strongly to recent squared returns. Neither method eliminates estimation risk. Price-level standard deviation and return volatility are different quantities and should not be substituted without a clear purpose.
Worked example: A large shock remains inside a 20-day equal-weight volatility window for several weeks, then drops out and causes the estimate to fall abruptly. An exponentially weighted estimate decays more gradually as the shock becomes older, illustrating a methodological rather than new-market difference.
Common mistake: Comparing annualized volatilities without checking return frequency, window, and weighting can attribute calculation differences to genuine changes in market risk.
Official syllabus reference: [1]
39. Trend-following and mean-reversion models require different payoffs
Trend-following models seek persistence after directional movement, while mean-reversion models seek a return toward a reference after deviation. Their entries can therefore oppose each other at the same price. Trend systems often tolerate frequent small losses in exchange for occasional large gains; mean-reversion systems may win frequently while carrying adverse tail exposure when a deviation becomes a sustained trend. These are tendencies rather than mandatory statistics. Evaluate each model using its mechanism, exit logic, regime sensitivity, costs, and loss distribution instead of selecting solely by win rate.
Worked example: After a sharp upside break, a trend model buys continuation while a mean-reversion model considers selling an extension. The research team tests each with its own exit and risk structure rather than assuming that one entry direction must be universally correct.
Common mistake: Choosing a model solely because it wins more often ignores payoff asymmetry and the possibility that infrequent losses dominate its economics.
Official syllabus reference: [1]
40. Trigger, filter, and value rules have separate jobs
A trigger specifies the event that initiates action, such as a breakout. A filter restricts when a trigger is allowed, such as requiring a favorable longer-term trend. A value rule specifies a condition or level used by the model to assess attractiveness or implement the decision. Terminology can vary by system, so operational definitions should be explicit. Separating these functions makes testing interpretable: an apparent improvement may come from fewer trades, altered exposure, or genuine selection. Every rule must use information available when the trade is decided.
Worked example: A strategy buys when price crosses above its 20-day high, but only while the 100-day average rises. The breakout is the trigger and the rising average is the filter. A predefined acceptable entry-price condition can supply a separate value constraint.
Common mistake: Testing a trigger and filter as an inseparable package makes it difficult to identify which rule changes expectancy, turnover, or exposure.
Official syllabus reference: [1]
41. Look-ahead and survivorship bias distort backtests
Look-ahead bias uses information that was unavailable at the historical decision time, such as a completed day’s high before the close. Survivorship bias excludes securities that disappeared, often removing failures from the tested universe. Both can materially inflate results while leaving the strategy’s code apparently sensible. Point-in-time datasets, historically accurate constituents, realistic publication delays, and explicit signal timestamps help prevent these errors. Revised economic data and retroactively adjusted classifications also need attention. A backtest should reconstruct what the strategy could have known and traded at each moment.
Worked example: A researcher tests a stock-selection rule over ten years using only today’s index members. Companies removed after severe declines never enter the simulation. Reconstructing historical membership and delisting outcomes may materially reduce the reported return and improve the test’s credibility.
Common mistake: Assuming a clean current database is automatically suitable for historical testing overlooks missing failures and information that arrived only later.
Official syllabus reference: [1]
42. Walk-forward testing and parameter plateaus
Walk-forward testing repeatedly calibrates a model on an earlier training window and evaluates the frozen result on a subsequent window. Combining those subsequent results approximates a sequence of decisions made without future information. Parameter robustness is stronger when nearby settings produce reasonably similar behavior than when one narrow optimum dominates. A plateau does not prove future profitability, but an isolated spike raises concern about sample-specific fitting. Window lengths, recalibration frequency, costs, and the entire selection process must be specified beforehand or included in the development burden.
Worked example: A breakout model performs similarly with lookbacks from 35 to 50 sessions but poorly outside that region. The team selects a defensible setting within the plateau, freezes it, and evaluates the next period before recalibrating under the predetermined schedule.
Common mistake: Calling the highest historical return robust ignores whether neighboring parameters, later periods, and realistic execution produce comparable behavior.
Official syllabus reference: [1]
43. Expectancy and profit factor answer different questions
Trade expectancy is the probability-weighted average payoff, commonly win probability times average win minus loss probability times average loss, with costs included consistently. Profit factor divides gross winning profits by the absolute total of losing profits. Expectancy is an amount per trade, while profit factor is a ratio over the sample. Neither statistic alone describes drawdown, capital usage, tail risk, or uncertainty. A small number of unusually large wins can dominate both. Check whether trade sizes and cost treatment are comparable before interpreting differences between models.
Worked example: A system wins 30 trades at $500 each and loses 20 trades at $400 each. Gross profit is $15,000, gross loss is $8,000, profit factor is 1.875, and gross expectancy across 50 trades is $140 per trade.
Common mistake: Interpreting profit factor as average dollars earned per trade confuses a dimensionless aggregate ratio with the expectancy calculation.
Official syllabus reference: [1]
44. CAGR and maximum drawdown describe different paths
Compound annual growth rate is (ending wealth / beginning wealth) raised to the reciprocal of years, minus one. It describes a constant annual growth rate connecting endpoints, not the actual sequence of annual returns. Maximum drawdown measures the largest peak-to-subsequent-trough decline in an equity curve. Two strategies can have identical CAGR but substantially different drawdowns and recovery periods. The sampling frequency matters because monthly equity observations can miss intramonth troughs. Cash flows, leverage, and valuation conventions must be handled consistently before comparing growth and path-dependent risk.
Worked example: An account grows from $100,000 to $121,000 over two years, giving a 10% CAGR. If it first peaks at $110,000 and falls to $88,000, that segment contains a 20% drawdown despite the attractive final compound growth.
Common mistake: Assuming a 10% CAGR means the account earned 10% each year overlooks the potentially uneven and stressful path between endpoints.
Official syllabus reference: [1]
45. Sharpe, Sortino, information, and Calmar denominators
The Sharpe ratio compares excess return over a risk-free reference with total return volatility. Sortino uses downside deviation relative to a specified target. The information ratio compares active return against a benchmark with tracking error. Calmar commonly compares annualized compound growth with the magnitude of maximum drawdown over a defined period. These measures reward different properties, so rankings can diverge. Return frequency, annualization, target definitions, and sample windows must align. None fully captures liquidity or tail risk, and estimated ratios can be unstable when samples are short or returns are dependent.
Worked example: Two funds earn the same average return, but one frequently differs from its benchmark. Its information ratio may be lower because tracking error is larger, even if its Sharpe ratio is similar. The relevant denominator depends on the investor’s objective.
Common mistake: Using tracking error in a Sharpe calculation confuses benchmark-relative variability with the total volatility of excess returns.
Official syllabus reference: [1]
46. MAE and MFE connect trade paths to exits
Maximum adverse excursion measures the largest unrealized loss reached during a trade, while maximum favorable excursion measures the largest unrealized gain. These trade-level path measures differ from realized profit and portfolio drawdown. Studying their distributions can help evaluate initial stops, trailing exits, and whether profitable trades typically require substantial room. Use executable prices and consistent intrabar assumptions. Optimizing stops against the same excursion history can overfit, especially when bar data do not reveal the order of highs and lows. Validate any resulting exit rule independently.
Worked example: A long entry at $50 falls to $47, rises to $58, and exits at $55. Ignoring costs, MAE is $3 per share, MFE is $8, and realized profit is $5. Each statistic describes a different aspect of the trade.
Common mistake: Calling the final $5 profit the maximum favorable excursion overlooks the larger unrealized gain reached before the exit.
Official syllabus reference: [1]
47. Relative-strength ratios separate leadership from direction
A relative-strength ratio divides an asset’s price by a benchmark’s price or compares consistently constructed total-return indices. A rising ratio indicates outperformance, which can occur while both investments decline. Its trend therefore describes leadership rather than an absolute buy signal. Currency, distributions, and return conventions should match when comparing assets. Combining relative strength with absolute trend filters can distinguish leaders in healthy markets from merely defensive performers in weak markets. Ratio changes also differ mathematically from simple return differences, although the two can be close for small moves.
Worked example: Asset A loses 2% while its benchmark loses 8%. The relative ratio changes by 0.98 divided by 0.92 minus one, approximately 6.52%. Asset A demonstrates leadership during the decline, but an unhedged investor still experiences a loss.
Common mistake: Treating relative outperformance as proof of positive absolute returns ignores that the benchmark may simply have declined more severely.
Official syllabus reference: [1]
48. Bond duration links yields to cross-asset behavior
For a conventional fixed-rate bond, price generally moves inversely to yield. Modified duration approximates the percentage price change for a small yield change: percentage change is roughly negative duration times the yield change in decimal form. Convexity and larger moves limit the linear approximation. This mechanism helps interpret cross-asset signals involving bonds, rates, equities, and currencies, but broader correlations depend on the economic regime. Rising yields caused by stronger growth can accompany different equity behavior from rising yields caused by inflation or a changing risk premium.
Worked example: A bond portfolio has modified duration of six years. A 0.25-percentage-point yield increase implies an approximate 1.5% price decline before convexity effects. The analyst distinguishes this mechanical sensitivity from the separate question of how equities will react to the same news.
Common mistake: Assuming bonds and equities must always move oppositely replaces regime-dependent economic relationships with an unsupported fixed correlation rule.
Official syllabus reference: [1]
49. Covariance determines diversification benefit
Portfolio variance depends on individual variances, portfolio weights, and covariances between holdings. For two assets, the covariance contribution is twice the product of their weights, volatilities, and correlation. Diversification can reduce volatility when correlation is below perfect positive correlation, but owning many securities does not ensure diverse risk exposures. Correlations estimated in calm periods can rise during stress, and liquidity exposures can align unexpectedly. Portfolio construction should examine underlying factors and plausible stress scenarios rather than relying only on historical pairwise averages.
Worked example: Two equally weighted assets each have 10% volatility. With zero correlation, portfolio volatility is about 7.07%; with perfect positive correlation, it is 10%. Adding a second holding helps only to the extent that its risk is not fully redundant.
Common mistake: Equating a large number of positions with diversification ignores common factor exposures that can cause apparently different holdings to decline together.
Official syllabus reference: [1]
50. Position size links stop distance to account risk
A basic risk-budget position size divides the permitted monetary loss by the planned loss per unit, including relevant contract multipliers and costs. A wider stop therefore permits fewer units when the risk budget is fixed. Additional constraints can cap notional exposure, leverage, concentration, or liquidity. Planned stop risk is not a guaranteed maximum because gaps, slippage, and market disruption can prevent execution at the assumed level. Leverage increases sensitivity to price changes and can create financing or margin demands. Evaluate those exposures separately from the arithmetic of the initial stop.
Worked example: An account allocates $600 of planned risk to a stock with a $2 entry-to-stop distance. Ignoring costs, the risk-based size is 300 shares. If an exposure cap permits only 240 shares, the smaller limit controls the actual position.
Common mistake: Assuming a stop order makes leveraged losses precisely bounded overlooks gaps and execution conditions that can exceed the planned per-unit loss.
Official syllabus reference: [1]
51. VaR marks a quantile while expected shortfall measures severity
Value at risk is a loss quantile for a specified horizon, confidence level, and model. It identifies a boundary in the modeled loss distribution rather than the maximum possible loss. Expected shortfall averages losses in the designated tail beyond that boundary, subject to the method’s treatment of discrete observations and ties. It therefore provides information about tail severity that VaR alone omits. Historical, parametric, and simulation methods can produce different estimates. Both measures remain sensitive to data, dependence, liquidity, and distributional assumptions, especially when the available tail sample is small.
Worked example: A model reports one-day VaR of $80,000 and expected shortfall of $130,000 at the same confidence level. The analyst interprets the latter as average modeled tail severity, while recognizing that neither number caps what a severe future event can cost.
Common mistake: Describing VaR as the worst possible daily loss mistakes a modeled quantile for a hard limit on future outcomes.
Official syllabus reference: [1]
52. Loss clustering and drawdown recovery mathematics
Loss sequences affect capital survival even when average trade expectancy is positive. With fixed fractional risk, successive proportional losses compound, reducing exposure as equity falls. Correlated or clustered losses can be more damaging than an independent-trade model suggests. Recovery is asymmetric: after a fractional drawdown d, the gain needed to return to the original peak is d / (1 − d). This arithmetic supports conservative risk allocation and stress testing of losing sequences. A positive historical expectancy alone does not establish an acceptable probability of avoiding a specified ruin or drawdown boundary.
Worked example: After a 25% drawdown, an account retains 75% of its former value and needs a 33.33% gain to recover. A trader evaluates clusters of losses rather than assuming that the next few trades will offset the decline merely because long-run expectancy is positive.
Common mistake: Assuming a 25% loss requires only a 25% gain to recover applies the gain to the wrong, smaller capital base.
Official syllabus reference: [1]
Application of Technical Analysis
53. Higher-timeframe regime and lower-timeframe execution
Multiple-timeframe analysis assigns different jobs to different charts. A higher timeframe can define the prevailing regime and major support, while a lower timeframe identifies an executable trigger and nearby invalidation. This avoids treating every short-term countertrend move as a change in the investment thesis. The hierarchy must be explicit: a short-term entry cannot automatically override a broken higher-timeframe premise. Indicators derived from the same prices are also related evidence, so agreement across several charts is not equivalent to several independent confirmations. Position management should follow the stated holding horizon.
Worked example: A weekly chart shows rising major lows, while a daily chart pulls back toward weekly support. The trader waits for a daily reversal trigger and defines a daily execution stop, while separately identifying the weekly level that would undermine the larger thesis.
Common mistake: Switching to a longer timeframe only after a short-term trade fails changes the original risk premise rather than applying a consistent analytical hierarchy.
Official syllabus reference: [1]
54. Measured objectives and reward-to-risk screening
A trade plan combines an entry, a technical invalidation level, and a defensible objective. For a long trade, planned reward-to-risk is (objective − entry) / (entry − stop), with costs incorporated consistently. A favorable ratio does not imply positive expectancy because the probability of reaching the objective also matters. Objectives derived from chart height are estimates, and nearby opposing structure may justify a more conservative target. The stop should reflect invalidation rather than being moved artificially close merely to improve the ratio. Execution assumptions can materially change the practical result.
Worked example: A planned entry is $80, the structural stop is $76, and nearby resistance offers an $88 objective. Planned reward-to-risk is two. Raising the objective to $96 improves the arithmetic but requires evidence that the more distant target is plausible.
Common mistake: Selecting whichever target produces the desired ratio reverses the planning process and can conceal weak evidence for the expected reward.
Official syllabus reference: [1]
55. Failed breakouts require acceptance back inside the range
A failed breakout occurs when price moves beyond a recognized boundary but cannot sustain the new area and returns into the prior range under the chosen failure rule. This can trap traders positioned for continuation and create pressure in the opposite direction. A normal retest differs because the broken boundary holds and price resumes outward. Define acceptance, confirmation, and execution in advance rather than labeling failure after the move is obvious. Reversing a position is a separate decision requiring its own entry, invalidation, liquidity assessment, and risk budget.
Worked example: A stock closes above a range ceiling, then spends two sessions back below it and breaks the breakout session’s low. Under a rule requiring sustained recovery failure, the trader exits the long thesis and evaluates a separate short setup rather than automatically doubling exposure.
Common mistake: Calling the first pullback a failed breakout overlooks the possibility of a successful polarity retest before the trend continues.
Official syllabus reference: [1]
56. Model implementation depends on costs and capacity
A model is suitable for implementation only when its apparent edge remains credible under executable timing, realistic costs, capital constraints, and the intended mandate. Turnover, spread, slippage, market impact, borrow availability, and financing can change performance substantially. Capacity is the amount of capital a strategy can absorb before implementation frictions materially weaken results. A strong backtest in small positions does not imply scalability. Compare independent evidence, parameter stability, drawdown behavior, and operational requirements, then define observable criteria for reducing or suspending deployment if assumptions deteriorate.
Worked example: A model earns eight basis points per trade before costs. Estimated small-order costs are three basis points, but the proposed fund size raises expected impact to ten. The analyst rejects scaling the original return estimate directly to the larger capital base.
Common mistake: Multiplying a small-account backtest’s profit by the proposed capital increase ignores the nonlinear execution costs that often limit strategy capacity.
Official syllabus reference: [1]
57. Eligibility filters precede portfolio score normalization
A technical allocation process can first define eligibility through absolute trend or momentum conditions and then distribute capital using relative-strength scores among eligible assets. Separating the stages prevents a strong relative score from admitting an asset that fails a required absolute condition. Weights proportional to scores divide each eligible positive score by their sum, subject to concentration and risk constraints. If no asset qualifies, the fallback allocation must be defined. Ranking strength and sizing risk are distinct: a high-scoring asset may still need a reduced weight because of volatility or correlated exposure.
Worked example: Three assets have positive scores of six, three, and one, but the last fails the trend filter. The remaining scores sum to nine, producing provisional weights of two-thirds and one-third before concentration limits or volatility adjustments are applied.
Common mistake: Normalizing every score before enforcing eligibility can allocate capital to securities that the strategy’s own trend rules exclude.
Official syllabus reference: [1]
58. Volatility-based trailing exits should respect ratchet rules
A volatility-based trailing stop adjusts its distance using a measure such as ATR while anchoring to a favorable price reference. For a long position, a candidate stop might be the highest price since entry minus a specified ATR multiple. If the strategy requires a ratchet, the effective stop is the greater of the previous stop and the new candidate, preventing increased volatility from loosening protection. The multiplier, reference price, update timing, and execution assumptions must be explicit. A volatility trail manages exposure conditionally and cannot guarantee capture of a specified share of gains.
Worked example: A long trade’s highest price is $120 and ATR is $3. A three-ATR candidate stop is $111. If ATR later rises to $4 without a new high, the candidate falls to $108, but a ratcheting rule retains the previous $111 stop.
Common mistake: Recalculating a long trailing stop downward after volatility rises can quietly expand risk when the intended rule permits tightening only.
Official syllabus reference: [1]
Ethics
59. Reasonable basis and honest performance presentation
Ethical technical research requires diligence, a reasonable analytical basis, and communication that accurately represents methods and limitations. Backtested performance should be identified as simulated, with material assumptions about costs, selection, and implementation explained sufficiently for readers to assess it. Omitting failed versions or presenting an optimized history as live results can mislead even when individual numbers are arithmetically correct. The supplied guide establishes adoption of the CFA Institute Code and Standards; it does not reproduce all current provisions. Apply the relevant current text rather than importing wording from an older handbook.
Worked example: An analyst presents a ten-year simulation and clearly distinguishes it from six months of live trading. The report explains that parameters were selected using part of the historical period and shows results after stated costs, allowing readers to evaluate the evidence appropriately.
Common mistake: Believing accurate calculations justify any presentation overlooks how omitted assumptions and misleading labels can distort a reader’s understanding of performance.
Official syllabus reference: [1]
60. Conflict disclosure and fair dissemination
Conflicts arise when personal holdings, compensation arrangements, or other interests could reasonably affect professional judgment. Meaningful disclosure identifies relevant interests clearly and prominently while controls protect analytical independence. Disclosure alone does not excuse biased research or improper handling of recommendations. Fair dealing also requires a defensible dissemination process so selected recipients do not receive an unjustified advantage. Exact obligations depend on the applicable current Code and Standards and circumstances. A technical method does not remove these duties because conflicts concern professional conduct, not whether the analysis uses charts or financial statements.
Worked example: Before distributing a favorable note, an analyst identifies a material personal holding and the employer’s paid relationship with the issuer. The firm includes understandable disclosures, applies its independent-review controls, and releases the recommendation through its established process for the relevant client audience.
Common mistake: Assuming a generic statement that conflicts may exist adequately explains known material interests leaves readers unable to assess the actual relationship.
Official syllabus reference: [1]