FRM Formula Sheet




GARP FRM Formulas

Our comprehensive FRM formula booklet has been updated and, as a show of commitment to the industry and its students, we have made our content downloadable at absolutely no charge. We thank you for your continued support and look forward to serving you even more for the future. In our free formula guide, we discuss many different formulas that are all segmented into their relevant sections;

IMPORTANT: Please note that ALL our content, free and paid, feature:

  • Unlimited Printing
  • Unlimited Downloads
  • Password-free Direct-Download Links
  • Universal PDF Formatting


  • There are no time-restrictions on your downloaded files
  • We do not use third-party software to control the usage of our e-books
  • There is no software to download or install in order to use our materials
  • We do not ‘device-lock’ our files. We allow file-copying of our e-books across multiple devices owned by the user
  • We fundamentally believe that all students have the right to use the content that they have paid for, as long as they desire and without any restrictions
  • We do not use or support subscription-based service models. With us, you only pay once

Level 1 Formulas  

Level 1, Segment 1: Foundations of Risk Management

  • Correlation coefficient between two Securities, Variance of Two Securities
  • Perfect Positive Correlation, Perfect Negative Correlation
  • Standard Deviation, Risk Adjusted Ranking
  • Sharpe Ratio, Sortino Ratio, Treynor Measure, Jenson’s Alpha
  • Information Ratio, Portfolio beta, Portfolio Expected Return
  • Expected Return, Capital Asset Pricing Model, Adjusted Exposure
  • Expected Loss, Adjusted Exposure, Probability of Default, Loss Given Default
  • Basis, Futures price of contract, Market Coefficient of Variation
  • Market Expected Return, Standard Deviation of Market, Covariance
  • Correlation Coefficient, Standard deviation of a two-stock portfolio
  • Total Risk, Market Risk, Firm Specific Risk, Systematic Risk, Unsystematic Risk
  • Un-diversifiable risk, Expected Return, Stock’s Alpha, Risk Free Rate
  • Excess Return, Beta, Value at Risk, Portfolio Value at Risk
  • Initial Portfolio Value, Capital Markets Line, Expected Residual Return
  • Residual Risk, Covariance for Markets A and B, Equation of a Straight Line


Level 1, Segment 2: Quantitative Analysis

  • Exceptions, Confidence Interval, Portfolio’s Value-at-Risk, Semi-annual comparable yield
  • YTM for Annual Pay Bond, Standard Deviation, Volatility Estimate, Combinations
  • Standard Error, Standard Error of a Mean, Standard Deviation of Returns
  • Basis, Bayes’ Theorem, Expectations, Value of the z-statistic
  • Hypothesized Mean, Standard Deviation of Population, Sample Mean
  • Sample Size, Sample Variance, Sample Standard Deviation, General Regression Equation
  • Total Variation, Unexplained Variation, Coefficient of Determination
  • Standard Error, Correlation Coefficient, F-Statistic, MSR, MSE, RSS, SSE
  • Kurtosis, Variance, Slope Coefficient, Regression, Sum Total of Squares
  • Standard Error of the Estimate, Population Regression, The Vasicek model
  • Chi Square Test, F Test, Bond Survival Rate, Total Variation
  • Sum of Squares Error, Residual Sum of Squares, Explained Sum of Squares
  • Risk-Adjusted Return, Business Line RAROC


Level 1, Segment 3: Financial Markets and Products

  • Price of a Bond, Present Value of Coupon Payments, Time to Maturity
  • Forward Pricing, Spot Price, Value of a Long Forward, Price of Delivery
  • Time of Payoff, Continuous return, Total Asset Price, Maximum Bond Values
  • Minimum Bond Values, American Call, American Put, European Call
  • European Put, Value of a Swap, Present Value of Payments, Present Value of Par Values
  • Accrued Interest, Forward Rate Agreement, Settlement Rate, Dollar Default Rate
  • Par Value of defaulted bonds, Required Rate of Return, Beta
  • Market Risk Premium, Cheapest to Deliver, Current Futures Price
  • Conversion Factor, Riskless Pure Discount, The KMV model
  • Weighted Debt, Convexity, Interest Rate Parity, The theoretical contract price
  • Interest Rate Parity for Currencies, Foreign Currency Rate
  • Interest Earned between Dates, Fair Value of a Futures Contract
  • No-Arbitrage Forward Price, Put-Call Parity Formula, PV of the strike
  • The Optimal Hedge Ratio for a Fund, The Value of the Fixed Payment
  • Fixed Rate Coupon, Notional value, Annual fixed rate, Cost of Carry
  • Storage Cost, Convenience Yield for a Consumption Asset, Issuer Default Rate, Key Rate Duration, Dollar Default Rate


Level 1, Segment 4: Valuation and Risk Models

  • Put Option’s Value, Call Option’s Value, Down Volatility, Up Volatility
  • Put-call parity relationship, Call Premium, Put Premium, Annual Interest Rate
  • Value at Risk, Z-Score, Price Change Standard Deviation, Annual Standard Deviation
  • Daily Standard Deviation, Convexity Adjustment, Synthetic Call Price
  • Covered Call, Short Call, Unexpected Loss, loss rate, exposure amount
  • Implied 1‐Yr Forward Rate, Risk Neutral Probability, Dirty Price
  • Daily Delta Normal VaR, Mean Loss Rate, Sample-Mean, Portfolio’s Beta



Level 2 Formulas

Level 2, Segment 1: Market Risk Measurement and Management

  • Value at Risk, Sharpe Ratio, Sortino Ratio, Treynor Measure, Portfolio beta
  • Information Ratio, Jenson’s Alpha, Minimum Accepted Return
  • Return on Portfolio, Standard Deviation of Returns, CAPM predicted Return
  • Tracking Error, Benchmark Return, Hedging Relationships, Correlation coefficient
  • Covariance, The Vasicek Model, Binomial Distribution, Binomial Distribution of Exceedances
  • Forward Pricing


Level 2, Segment 2: Credit Risk Measurement and Management

  • Firm Value, Netting Factor, Expected Loss, Debt Value
  • Value of Risk Free Debt, Value of Put Option, Credit Spread, Conditional Prepayment Rate
  • Credit Valuation Adjustment, Average Life
  • Discount Factor, Probability of Default, Recovery Rate, Exposure at Default
  • Loan Equivalent Ratio


Level 2, Segment 3: Operational Risk and Resiliency

  • Risk-adjusted return on capital
  • Risk Adjusted Capital
  • Expected Losses
  • Adjusted RAROC
  • Market Return
  • Probability of Default
  • Recovery Rate
  • Worst Case Default Rate
  • Default Correction
  • Liquidity Cost


Level 2, Segment 4: Liquidity and Treasury Risk Measurement

  • Liquidity Risk Ratios
  • Leverage Indicators
  • Portfolio Pricing
  • Return on Portfolio
  • Portfolio Standard Deviation


Level 2, Segment 5: Risk Management and Investment Management

  • Risk Aversion
  • Sharpe Ratio
  • Sortino Ratio
  • Minimum Accepted Return
  • Return on Portfolio
  • Portfolio Standard Deviation of Return
  • Treynor Measure
  • Jenson’s Alpha
  • Information Ratio
  • Information Ratio
  • Marginal Contribution to Value Added
  • Marginal Contribution to Active Risk