CMT cheat sheet

Dow Theory: a primary trend persists until a confirmed reversal; confirmation requires Dow Industrials and Dow Transportation to move together.

Trend identification: higher highs and higher lows define an uptrend; lower highs and lower lows define a downtrend.

Moving average signal: price above a rising MA favors longs; a shorter MA crossing below a longer MA is bearish.

RSI(14) above 70 is commonly overbought and below 30 oversold; price-RSI divergence can precede reversal.

MACD line = 12-period EMA minus 26-period EMA; signal line = 9-period EMA of MACD; histogram = MACD minus signal.

Fibonacci retracement levels are 23.6%, 38.2%, 50%, 61.8%, and 78.6% of a prior swing; 61.8% is the golden-ratio retracement.

Volume confirmation: breakouts on above-average volume are more reliable than low-volume breakouts, which often fail.

Support and resistance: prior swing highs and lows and round numbers act as reaction levels; broken resistance often becomes support.

Head-and-shoulders measured move: project the head-to-neckline height from the neckline breakout to estimate a target.

Prospect theory: losses loom larger than equivalent gains; the value function is concave for gains and convex for losses.

Loss aversion is commonly estimated near 2, meaning a loss feels about twice as painful as an equal-sized gain.

Disposition effect: investors tend to sell winners too early and hold losers too long to avoid realizing a loss.

Anchoring: forecasts and fair-value estimates are biased toward an initial reference price or prior forecast.

Confirmation bias: analysts overweight evidence supporting an existing view and discount contradictory data.

Overconfidence: excessive confidence in forecasts raises trading frequency and can reduce net returns after costs.

Herding: investors follow the crowd rather than private information, amplifying momentum and bubbles.

Mental accounting: treating money differently by source or purpose violates fungibility and can distort risk decisions.

Regret aversion: fear of making a wrong decision can cause inertia or holding a suboptimal portfolio.

Position size = (account equity × risk per trade %) ÷ (entry price − stop price).

Risk of ruin rises with larger per-trade risk and lower win rate; small per-trade risk reduces compounding drag.

Value at Risk (VaR) estimates the loss threshold not exceeded with a given confidence over a horizon; it ignores tail losses beyond that threshold.

Sharpe ratio = (portfolio return − risk-free rate) ÷ standard deviation of returns; it measures excess return per unit of total risk.

Sortino ratio uses downside deviation instead of total standard deviation, penalizing only harmful volatility.

Maximum drawdown = (peak value − trough value) ÷ peak value; it measures the worst peak-to-trough decline.

Correlation diversification: combining assets with correlation below +1 reduces portfolio volatility when weights are positive.

Stop-loss placement should be based on volatility or market structure, not arbitrary fixed dollar amounts; wider stops require smaller position size.

Kelly fraction f* = edge ÷ odds; fractional Kelly such as half-Kelly is used to reduce estimation error and drawdowns.

Backtest overfitting: testing many rules on one dataset inflates the best result; use out-of-sample and walk-forward tests.

Look-ahead bias uses information not available at the decision time; it overstates backtest performance.

Survivorship bias excludes delisted or failed securities and overstates historical returns.

Data snooping bias arises from repeated testing until a pattern appears significant; adjust for multiple comparisons.

Transaction costs, slippage, and market impact must be modeled; high-turnover strategies are most sensitive to them.

Momentum strategy: buy past winners and sell past losers; returns can reverse during crises or when crowding unwinds.

Mean-reversion strategy: assume prices return to a moving average or equilibrium; it performs poorly in strong trends.

Factor model: return = alpha + beta × factor return + error; multi-factor models decompose risk into style and market exposures.

Monte Carlo simulation resamples returns or trades to estimate a distribution of outcomes rather than relying on one historical path.