Review core formulas tied to the published 2026 learning objectives, plus a few clearly labeled supplemental practitioner measures. Always follow the convention stated in a question.
Reviewed . Original study reference; not an official exam formula handout.
Check the official 2026 CMT Program GuideTry each calculation before opening the answer. Use decimals for returns (5% = 0.05), match time horizons, and follow the smoothing convention stated in the question.
A $50,000 account risks 1% on a long trade entered at $100 with a $96 stop. Ignore costs and assume the stop fills at its stated price. What is the maximum whole-share position?
125 shares. The stop distance is $4 per share, so planned loss is $500. Position value is $12,500, not $500. Slippage, gaps, fees, and leverage constraints can require a smaller position; a stop does not guarantee the realized loss.
Practice this topic →A portfolio moves from $100,000 to $120,000, falls to $90,000, and then recovers to $110,000. What is its maximum drawdown?
25%. Divide the $30,000 fall by the preceding $120,000 peak, not the initial account value or the trough. A 33.33% gain from the $90,000 trough would restore the peak; a 25% gain would not.
Practice this topic →With VIX at 20 and the index at 5,000, estimate a 30-calendar-day volatility range using a 365-day year and constant volatility.
Approximately ±5.73%, or ±287 index points. This is a rough one-standard-deviation range under the stated assumptions, not a directional target or a guaranteed probability interval. The one-twelfth-year shortcut gives ±5.77%; do not mix calendar and trading-day conventions.
Practice this topic →For a 14-period RSI, yesterday’s smoothed average gain and loss were 1.2 and 0.8. Today the close rises by 0.7. What is the updated RSI?
Approximately 61.05. Today’s gain is 0.7 and loss is zero, but the smoothed average loss remains positive. Replacing the smoothed loss with zero would incorrectly force RSI to 100. Initialize the first averages from the first 14 price changes.
Practice this topic →Use these formulas to identify trend direction, trend strength, overbought or oversold conditions, and momentum confirmation.
Smooths price over a fixed lookback window.
Every observation has equal weight. Shorter windows react faster but produce more whipsaws.
Gives more weight to recent prices.
The smoothing factor increases as the lookback period gets shorter.
Weights the newest observation most heavily, then reduces weight linearly.
The newest price receives weight n and the oldest receives weight 1.
Measures the absolute price change over n periods.
Positive momentum confirms upside pressure; negative momentum confirms downside pressure.
Converts momentum into a percentage oscillator.
ROC is easier to compare across securities than raw price momentum.
Flags momentum extremes and failure swings.
After the initial seed, average gain and loss use Wilder smoothing (alpha = 1/n). Traditional 70/30 thresholds remain context dependent.
Compares fast and slow trend measures.
The histogram equals MACD minus Signal and often turns before the lines cross.
Compares the close with the recent high-low range.
Best used in ranges or as a divergence tool; strong trends can stay pinned near extremes.
Shows where the close sits inside the recent range.
Values near 0 are stronger; values near -100 are weaker.
Measures how far typical price deviates from its average.
MD is the mean absolute deviation of typical price. The 0.015 constant scales many observations inside the -100 to +100 range.
Measures trend strength without saying whether trend is up or down.
Standard ADX uses Wilder smoothing, commonly with n = 14. DI+ and DI- come from smoothed directional movement divided by ATR.
Use volume and breadth formulas to test whether price movement is supported by participation across securities and volume.
Accumulates volume based on up closes and down closes.
OBV divergence can warn that price movement lacks volume confirmation.
Shows the average transaction price weighted by volume.
Intraday traders use VWAP as an execution and mean-reversion reference.
Combines typical price and volume into an RSI-style oscillator.
Positive and negative flows are classified by whether typical price rises or falls. MFI can diverge when volume does not support price.
Measures whether volume closes nearer the high or low of the period.
If H equals L, the money flow multiplier is normally treated as zero.
Normalizes accumulation and distribution over a lookback window.
Positive CMF supports accumulation; negative CMF supports distribution.
Tracks cumulative market participation.
A rising index with a falling A-D line is a classic bearish breadth divergence.
Compares the count of advancing stocks with declining stocks.
Use with the absolute A-D spread to avoid overreading small denominators.
Combines issue breadth and volume breadth.
Readings above 1 often show downside pressure; readings below 1 often show upside pressure.
Measures breadth momentum using the net advances series.
The McClellan Summation Index is the cumulative total of the oscillator.
Measures leadership quality through new highs and new lows.
The conventional High-Low Index smooths the daily new-high percentage with a 10-day SMA.
Shows how broad a trend is across a market universe.
Extreme readings can be trend confirmation or exhaustion depending on context.
Measures option-market sentiment.
High readings often indicate fear; low readings often indicate optimism.
Compares outstanding short positions with normal trading liquidity.
A high ratio indicates heavy short interest and more days needed to cover; interpret it with trend and sentiment context.
These formulas define volatility, price envelopes, and range-based tools that help separate normal fluctuation from breakout risk.
Measures dispersion around the sample mean.
Use n minus 1 for a sample estimate; use n for a full population.
Converts variance back into the original unit.
Many risk and band formulas use standard deviation as the volatility input.
Creates volatility-adjusted bands around a moving average.
The common default is n equals 20 and k equals 2.
Shows where price sits inside or outside the bands.
Values above 1 are above the upper band; values below 0 are below the lower band.
Measures volatility expansion and contraction.
Low bandwidth can precede breakouts but does not forecast direction by itself.
Captures intraperiod range and overnight gaps.
True Range is the input used to calculate ATR.
Smooths true range into a volatility measure.
This is Wilder smoothing; some charting packages use EMA variants.
Builds range-based channels around a moving average.
Keltner’s original method uses typical price and high-low range. Modern platforms often use EMA_n plus or minus m times ATR_n; state the convention.
Tracks breakout boundaries using recent highs and lows.
Turtle-style systems often use Donchian breakouts for entries and exits.
Annualizes daily return volatility.
Use N equals 252 for trading days unless a question specifies another convention.
Scales annualized implied volatility into an approximate horizon move and price range.
For N trading days. A VIX of 20 implies about 5.77% over 30 calendar days (roughly 21 trading days). This is a volatility range, not a directional forecast.
Measures volatility below a minimum acceptable return.
This common convention divides by all n observations, with upside deviations counted as zero. Use a specified alternative convention when a question supplies one.
Measures drawdown depth and duration.
Supplemental: not named in the published 2026 LOS. Unlike standard deviation, it focuses on downside pain from prior peaks.
These formulas translate chart structure into retracement levels, price objectives, and cycle measurements.
Forms the basis for common Fibonacci ratios.
Common retracements include 23.6%, 38.2%, 50%, 61.8%, and 78.6%.
Projects pullback levels after an upward swing.
For a 61.8% retracement, Ratio equals 0.618.
Projects rally levels after a downward swing.
Always define the swing high and swing low before applying the ratio.
Projects continuation targets beyond the prior swing.
Define the anchor explicitly—typically the retracement low in an uptrend or retracement high in a downtrend. Common ratios include 1.272 and 1.618.
Creates a central reference level from the prior period.
Floor-trader support and resistance levels are derived from this pivot.
Projects near-term support and resistance from the pivot.
Use prior-period high, low, and close unless a question states otherwise.
Projects the price objective from a classical chart pattern.
Add height for upside breakouts and subtract height for downside breakouts.
Projects a target from the height of the relevant P&F column.
Fixed-box vertical-count convention: B is box size and M is the specified projection multiplier (often the reversal amount; some bearish methods use a different multiplier). Anchor at the selected count column low for a bullish count or high for a bearish count, not automatically at the breakout price. Follow the count method supplied in the question.
Projects a target from the width of an accumulation or distribution base.
This fixed-box convention anchors at the base low for a bullish count and the base high for a bearish count. B is box size; M is the specified multiplier. Horizontal-count methods differ in count line, boundaries, anchor, and multiplier, so use the question’s convention. Percentage box scaling requires its own method.
Converts between cycle length and cycle frequency.
Keep units consistent: days, weeks, or months.
Compares a 3% price filter with a volatility-scaled ATR filter.
R is resistance, S is support, and k is the chosen ATR multiplier. Apply the threshold in the intended breakout direction. The two filters can disagree; neither guarantees continuation. Use the rule specified in the question.
Centers a smoothing window on the cycle midpoint and places percentage bands around it.
The formula shows an odd-length window; even-length moving averages require a second centering step. Centering uses future observations and is not a real-time signal.
Measures continuously compounded return.
Log returns add across time more cleanly than simple returns.
Shows how much return is needed to recover from a drawdown.
After a 25% loss, the required gain is 0.25 divided by 0.75, or 33.3%.
These formulas support CMT questions on return distributions, regression, correlation, beta, and hypothesis testing basics.
Calculates the simple average of observations.
Useful for expected one-period return, but it can overstate compound performance.
Fits a least-squares line with one predictor and an intercept.
The fitted line passes through the sample means. X must have nonzero variance. Use consistent sample or population conventions in covariance and variance; R-squared measures fit, not causation.
Flags observations outside quartile-based screening fences.
Use the quartile convention specified by the dataset or question. A flagged observation is not automatically an error and should not be deleted without investigation.
Measures compound average growth.
Geometric mean is usually lower than arithmetic mean when returns are volatile.
Measures how two variables move together.
Positive covariance means variables tend to move in the same direction.
Standardizes covariance between -1 and +1.
Correlation shows direction and strength, not slope size.
Measures sensitivity to market returns.
Beta above 1 means higher market sensitivity; beta below 1 means lower market sensitivity.
Estimates required return for systematic risk.
The market risk premium is expected market return minus risk-free rate.
Measures return above or below CAPM expectation.
Positive alpha means the return exceeded the beta-adjusted benchmark expectation.
Shows explained variance in a single-factor regression.
In simple regression, R-squared is the square of correlation.
Measures uncertainty around a sample mean.
Standard error falls as sample size increases.
Standardizes an observation against a known population mean and standard deviation.
A z-score shows how many standard deviations an observation is from the mean.
Tests a sample mean when population standard deviation is unknown.
Use t-distribution degrees of freedom n minus 1.
Compares risk per unit of mean return.
Lower CV indicates less dispersion per unit of average return.
Use these formulas for portfolio return, risk attribution, benchmark comparison, and risk-adjusted performance.
Calculates weighted average portfolio return.
Weights should sum to 1 unless the portfolio includes leverage or cash treatment specified in the question.
Tracks relative performance against a selected benchmark.
A rising ratio indicates outperformance, even when both prices fall. Compare aligned dates and consistent currency and dividend conventions. This ratio is not RSI, and its raw level is not comparable across arbitrary price scales.
Distinguishes price-weighted, capitalization-weighted, and equal-weighted construction.
D denotes the index divisor, adjusted for relevant corporate actions. S denotes eligible shares (free-float adjusted where required). Equal weights apply at rebalancing and drift as prices change; index return depends on constituent weights and returns.
Measures risk for a two-asset portfolio.
Diversification benefit increases as correlation falls.
Measures excess return per unit of total volatility.
Best suited when total risk is the relevant risk measure.
Measures excess return per unit of downside volatility.
MAR means minimum acceptable return.
Measures excess return per unit of systematic risk.
Most relevant for diversified portfolios where beta risk dominates.
Measures active return per unit of active risk.
Higher IR indicates more efficient benchmark-relative performance.
Measures volatility of active return versus a benchmark.
Benchmark-relative managers often focus on tracking error and information ratio together.
Measures realized portfolio return above CAPM expectation.
Jensen alpha is beta-adjusted performance.
Compares return with maximum drawdown.
Use maximum drawdown as a positive number in the denominator.
Measures the largest peak-to-trough loss as a positive magnitude.
A drawdown series may be plotted as negative returns, but Calmar and similar ratios use positive maximum-drawdown magnitude.
Estimates loss at a confidence level under a normal-return assumption.
This is absolute VaR with positive z alpha (for example 1.645 at 95%). Relative VaR omits mean return. Match return, volatility, and horizon units.
Measures expected loss beyond the VaR threshold.
Expected shortfall captures tail severity better than VaR alone.
Links price with fundamentals, valuation, and sentiment in the Level III fusion framework.
This is a conceptual relationship rather than a calibrated pricing equation: price strength reflects the combined effect of fundamentals, valuation change, and sentiment.
These formulas turn signal quality into capital allocation, trade risk, and repeatable system evaluation.
Defines the dollar amount that can be lost if the stop is hit.
This should be set before calculating number of shares or contracts.
Converts account risk into shares or contracts for either trade direction.
For shares, PointValue is normally 1. Include contract multipliers, fees, and slippage when the question specifies them.
Compares planned profit distance with initial loss distance before entry.
Use directionally valid targets and stops; a 3-to-1 setup has three units of planned reward for each unit of risk.
Estimates optimal fraction to wager based on edge and payoff.
Supplemental: not named in the published 2026 LOS. Many practitioners use fractional Kelly because full Kelly can be volatile.
Measures expected profit or loss per trade.
A system can be profitable with a low win rate if payoff ratio is high enough.
Compares total winning trade profit with total losing trade loss.
Use gross loss as a positive number in the denominator.
Compares average winning trade size with average losing trade size.
Pair payoff ratio with win rate; neither tells the full story alone.
Finds the win rate needed to break even before costs.
Transaction costs raise the required breakeven win rate.
Normalizes trade result by initial risk for a long trade.
Use absolute risk distance and reverse the price signs for short trades.
Evaluates trade distribution quality using R-multiples.
Supplemental: not named in the published 2026 LOS. SQN improves when average R rises, dispersion falls, or sample size grows.
Measures annualized compound return.
CAGR smooths the path and does not show drawdown or volatility by itself.
Memorizing formulas is only half the work. Practice the exhibit-based questions where these calculations appear with charts, volume tables, risk metrics, and portfolio scenarios.