Complete CMT Formula Cheat Sheet

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.

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.

Traditional thresholds are 70 for overbought and 30 for oversold, but trend regime matters.

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.

The 0.015 constant scales many observations inside the -100 to +100 range.

Measures trend strength without saying whether trend is up or down.

+DI and -DI come from smoothed directional movement divided by ATR.

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.

MFI can diverge from price when volume does not support the latest move.

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.

A strong market should show expanding new highs and limited new lows.

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.

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 ATR-based channels around a moving average.

Because ATR is range based, Keltner Channels often behave differently from Bollinger Bands.

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.

Measures volatility below a minimum acceptable return.

Sortino ratio uses downside deviation instead of total standard deviation.

Measures drawdown depth and duration.

Unlike standard deviation, it focuses on downside pain from prior peaks.

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.

Common extension ratios include 1.272, 1.618, and 2.618.

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.

Use the column specified by the chart method and direction of the breakout.

Projects a target from the width of an accumulation or distribution base.

Count the base columns consistently with the charting convention in the question.

Converts between cycle length and cycle frequency.

Keep units consistent: days, weeks, or months.

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%.

Calculates the simple average of observations.

Useful for expected one-period return, but it can overstate compound performance.

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.

Calculates weighted average portfolio return.

Weights should sum to 1 unless the portfolio includes leverage or cash treatment specified in the question.

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.

Drawdowns are often reported as negative percentages, but ratios usually use the absolute value.

Estimates loss at a confidence level under a normal-return assumption.

Check whether the question asks for daily, monthly, or annual VaR.

Measures expected loss beyond the VaR threshold.

Expected shortfall captures tail severity better than VaR alone.

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 share count for a long trade.

For short trades, use the absolute distance between entry and stop.

Estimates optimal fraction to wager based on edge and payoff.

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.

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.