Formulas

Annualized Volatility Formula

The annualized volatility formula scales per-period return standard deviation by the square root of periods per year. Root-time scaling explained.

4 VARIABLES

Beta Formula

The beta formula: covariance of asset and market returns over market variance. The CAPM regression slope measuring systematic risk, with an example.

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Calmar Ratio Formula

The Calmar ratio formula: annualized return divided by maximum drawdown over the period. A drawdown-based risk-adjusted return with a worked example.

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CAPM Formula

The CAPM formula: expected return equals the risk-free rate plus beta times the market risk premium. The basis for pricing systematic risk.

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Correlation Formula

The Pearson correlation formula: covariance of two return series over the product of their standard deviations. The key diversification input.

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CVaR / Expected Shortfall Formula

The CVaR formula: the average loss in the worst tail beyond VaR. Expected shortfall, a coherent risk measure favored by Basel, with a worked example.

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Downside Deviation Formula

The downside deviation formula: root mean square of returns below a target, over total observations. The risk term inside the Sortino ratio.

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Fractional Kelly Formula

The fractional Kelly formula stakes a fixed multiple of full Kelly to cut volatility for a small growth cost. Why half-Kelly is popular.

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Historical VaR Formula

The historical VaR formula: the empirical quantile of past returns at a confidence level. A distribution-free Value-at-Risk method, with an example.

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Information Ratio Formula

The information ratio formula: active return over a benchmark divided by tracking error. Measures the consistency of excess return, with an example.

5 VARIABLES

Jensen's Alpha Formula

Jensen's alpha formula: realized return minus the CAPM-expected return given beta. The excess return a manager earns beyond market risk.

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Kelly Criterion Formula

The Kelly criterion formula: the bet fraction maximizing long-run log growth from win probability and payoff odds. The optimal sizing rule.

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Kurtosis Formula

The kurtosis formula: the fourth standardized moment of returns. Measures tail heaviness, with excess kurtosis relative to the normal, and an example.

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M-Squared (M2) Formula

The M-squared formula: the return a portfolio earns if levered to market volatility. Modigliani risk-adjusted performance in return units.

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Maximum Drawdown Formula

The maximum drawdown formula: the largest peak-to-trough decline in an equity curve. The worst loss from a prior high, with a worked example.

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Omega Ratio Formula

The Omega ratio formula: probability-weighted gains above a threshold over losses below it. Uses the whole return distribution, with a worked example.

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Parametric VaR Formula

The parametric VaR formula: Value-at-Risk from the mean, volatility, and a normal z-score. The variance-covariance method, with a worked example.

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R-Squared Formula

The R-squared formula: the share of a portfolio's return variance explained by its benchmark. The squared correlation behind beta and alpha.

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Sharpe Ratio Formula

The Sharpe ratio formula: excess return over the risk-free rate divided by return volatility, then annualized. Every variable defined, with a worked example.

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Skewness Formula

The skewness formula: the third standardized moment of returns. Measures asymmetry, the tilt toward large gains or losses, with a worked example.

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Sortino Ratio Formula

The Sortino ratio formula: excess return over a target divided by downside deviation, so only harmful volatility is penalized. With a worked example.

5 VARIABLES

Sterling Ratio Formula

The Sterling ratio formula: annualized return over average annual drawdown plus a 10% penalty. A stricter drawdown-adjusted return, with an example.

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Tracking Error Formula

The tracking error formula: the standard deviation of a portfolio's active return versus its benchmark. How tightly a fund tracks its index.

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Treynor Ratio Formula

The Treynor ratio formula: excess return over the risk-free rate divided by beta. Reward per unit of systematic market risk, with a worked example.

3 VARIABLES

Ulcer Index Formula

The Ulcer Index formula: the root mean square of percentage drawdowns from running highs. Measures depth and duration of losses, with an example.

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CAGR Formula

The CAGR formula: the constant annual rate growing a beginning value to an ending value over n years. The true geometric return, with a worked example.

3 VARIABLES

Deflated Sharpe Ratio Formula

The deflated Sharpe ratio formula: the probability a strategy's Sharpe is real after correcting for the number of trials, return skew, kurtosis, and sample length.

7 VARIABLES

Expectancy Formula

The expectancy formula: win rate times average win minus loss rate times average loss. The expected profit per trade in R-multiples, with an example.

5 VARIABLES

Fundamental Law of Active Management Formula

The fundamental law of active management: information ratio equals information coefficient times the square root of breadth. With an example.

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Gain-to-Pain Ratio Formula

The gain-to-pain ratio formula: sum of returns over the absolute sum of losing periods. A robust Schwager measure of return per unit of pain.

3 VARIABLES

Information Coefficient Formula

The information coefficient formula: correlation between forecast and realized returns. How to measure quant forecasting skill, with a worked example.

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Probabilistic Sharpe Ratio Formula

The probabilistic Sharpe ratio formula: the chance a true Sharpe beats a benchmark, adjusting for skew, kurtosis, and sample length, with an example.

6 VARIABLES

Probability of Backtest Overfitting (PBO) Formula

The PBO formula: the probability the best in-sample strategy lands below median out-of-sample, via combinatorial cross-validation. With an example.

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Profit Factor Formula

The profit factor formula: gross profit divided by gross loss. A single number summarizing a strategy's edge, what values mean, with a worked example.

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Win Rate Formula

The win rate formula: winning trades divided by total trades. Why win rate alone is meaningless without the payoff ratio, with a breakeven example.

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Cost Per 1K Tokens Formula

The cost-per-1K-tokens formula: input tokens times input price plus output tokens times output price. Why output dominates LLM cost, with an example.

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Cost Per Validated Trade Formula

The cost-per-validated-trade formula: total LLM spend over trades that pass validation. The real unit economics of an AI trading agent.

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Prompt Cache Break-Even Formula

The prompt-cache break-even formula: how many reuses of a cached prefix repay its write premium. When caching pays off for LLM workloads.

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Portfolio Turnover Formula

The portfolio turnover formula: the lesser of purchases or sales over average assets. How turnover drives transaction costs and tax drag.

4 VARIABLES