## 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.

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In our free formula guide, we discuss many different formulas that are all segmented into their relevant sections;

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**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