CMT Level III cheat sheet

Trend structure: an uptrend prints higher highs and higher lows; a downtrend prints lower highs and lower lows. A break of the last swing low is the first structural warning for an uptrend.

Moving average crossover rule: a fast MA crossing above a slow MA signals trend shift; whipsaw frequency rises as the two lookback lengths converge, so spread lengths (e.g., 20 vs 50) to reduce false signals.

Relative Strength Index: RSI = 100 − 100/(1 + RS), where RS = average gain / average loss over N periods (Wilder smoothing, default N = 14). Range is 0–100; readings above 70 or below 30 flag stretched conditions, not automatic reversals.

MACD: MACD line = EMA(12) − EMA(26); signal line = EMA(9) of the MACD line; histogram = MACD line − signal line. Crossings mark momentum shifts; zero-line crosses mark trend alignment.

Bollinger Bands: middle = N-period SMA (default 20); upper/lower = middle ± k standard deviations (default k = 2). Band width contraction (squeeze) precedes expansion; close outside a band is not a standalone sell/buy.

Volume confirmation: an upside breakout is more reliable when volume exceeds its recent average; a breakout on contracting volume has elevated failure risk. Volume precedes price at major turns in Dow Theory.

Dow Theory tenets: the averages discount everything; three trend classes (primary, secondary, minor); three phases (accumulation, public participation, distribution); a trend persists until a clear reversal; confirmation requires both averages.

Candlestick and chart-pattern signals require context: a doji or hammer at support after a decline carries more information than the same shape mid-range. Measure a pattern's target as the height of the formation projected from the breakout point.

Oscillator divergence: price making a higher high while RSI or MACD makes a lower high is bearish divergence; it flags weakening momentum but needs a price-structure break to become actionable.

Volatility: σ = sqrt( Σ (r_i − r̄)² / (n − 1) ) for a sample; annualize daily σ by multiplying by sqrt(252) for daily data. Volatility is symmetric and treats upside and downside moves alike.

Sharpe ratio = (R_p − R_f) / σ_p; Sortino ratio replaces total σ with downside deviation, so it does not penalize upside volatility. Both are excess-return-per-unit-of-risk measures.

Beta = Cov(R_p, R_b) / Var(R_b); it measures sensitivity to the benchmark, not standalone risk. R² from the same regression gives the share of variance explained by the benchmark.

Maximum drawdown = (trough value − prior peak value) / prior peak value; report it with recovery length, since two portfolios with equal drawdowns can differ greatly in time underwater.

Value at Risk at confidence c over horizon h estimates the loss not exceeded with probability c. It says nothing about the size of losses beyond the threshold; expected shortfall (CVaR) averages those tail losses.

Correlation drives diversification: portfolio variance = w₁²σ₁² + w₂²σ₂² + 2w₁w₂ρσ₁σ₂. At ρ = 1 no risk reduction is possible; lower ρ shrinks the variance term contributed by covariance.

Position sizing by risk: shares = (account equity × risk per trade %) / (entry price − stop price). This ties exposure to the stop distance rather than to a fixed dollar amount.

Risk of ruin rises with the product of trade frequency, per-trade risk fraction, and negative edge; even a positive-expectancy system can be ruined by oversized positions during a drawdown sequence.

Tracking error = standard deviation of the difference between portfolio and benchmark returns; information ratio = active return / tracking error. Both are relevant only against a defined benchmark.