CFA Level II Formula Sheet 2026

CFA® Program Level II FORMULA SHEET (2026) Version 1.0 Prepared by: Fabian Moa, CFA, FRM, CTP, FMVA, AFM, FSA Credential FOR REFERENCE ONLY (Note: Formula Sheet is not provided in the CFA exam) Follow us on: YouTube CFA Institute does not endorse, promote, or warrant the accuracy or quality of the products or services offered by Noesis Exed. CFA Institute, CFA® and Chartered Financial Analyst® are trademarks owned by CFA Institute. CFA Level 2 (2026) Formula Sheet by Fabian Moa Contents Setting Up the Texas BA II Plus Financial Calculator ............................................................................... 4 VOLUME 1: QUANTITATIVE METHODS ................................................................................................... 4 Learning Module 1 | Basics of Multiple Regression and Underlying Assumptions ............................ 4 Learning Module 2 | Evaluating Regression Model Fit and Interpreting Model Results ................... 4 Learning Module 3 | Model Misspecification ..................................................................................... 6 Learning Module 4 | Extensions of Multiple Regression .................................................................... 6 Learning Module 5 | Time-Series Analysis.......................................................................................... 7 Learning Module 6 | Machine Learning.............................................................................................. 8 Learning Module 7 | Big Data Projects ............................................................................................... 9 VOLUME 2: ECONOMICS ....................................................................................................................... 10 Learning Module 1 | Currency Exchange Rates: Understanding Equilibrium Value ........................ 10 Learning Module 2 | Economic Growth and the Investment Decision ............................................ 12 VOLUME 3: FINANCIAL STATEMENT ANALYSIS..................................................................................... 14 Learning Module 1 | Intercorporate Investments ............................................................................ 14 Learning Module 2 | Employee Compensation - Post-Employment and Share-Based .................... 15 Learning Module 3 | Multinational Operations................................................................................ 16 Learning Module 4 | Analysis of Financial Institutions ..................................................................... 17 Learning Module 5 | Evaluating Quality of Financial Reports .......................................................... 18 Learning Module 6 | Integration of Financial Statement Analysis Techniques ................................ 18 VOLUME 4: CORPORATE ISSUERS ......................................................................................................... 19 Learning Module 1 | Analysis of Dividends and Share Repurchases ................................................ 19 Learning Module 3 | Cost of Capital: Advanced Topics .................................................................... 20 Learning Module 4 | Corporate Restructuring ................................................................................. 23 VOLUME 5: EQUITY VALUATION ........................................................................................................... 24 Learning Module 1 | Equity Valuation Applications and Processes ................................................. 24 Learning Module 2 | Discounted Dividend Valuation ...................................................................... 24 Learning Module 3 | Free Cash Flow Valuation................................................................................ 25 Learning Module 4 | Market-Based Valuation Price and Enterprise Value Multiples...................... 27 Learning Module 5 | Residual Income Valuation ............................................................................. 29 Learning Module 6 | Private Company Valuation ............................................................................ 30 VOLUME 6: FIXED INCOME ................................................................................................................... 32 Learning Module 1 | The Term Structure and Interest Rate Dynamics............................................ 32 Learning Module 2 | The Arbitrage-Free Valuation Framework ...................................................... 33 Learning Module 3 | Valuation and Analysis - Bonds with Embedded Options ............................... 34 Learning Module 4 | Credit Analysis Models .................................................................................... 36 2 CFA Level 2 (2026) Formula Sheet by Fabian Moa Learning Module 5 | Credit Default Swaps....................................................................................... 37 VOLUME 7: DERIVATIVES ...................................................................................................................... 38 Learning Module 1 | Pricing and Valuation of Forward Commitments ........................................... 38 Learning Module 2 | Valuation of Contingent Claims ...................................................................... 42 VOLUME 8: ALTERNATIVE INVESTMENTS ............................................................................................. 46 Learning Module 1 | Introduction to Commodities and Commodity Derivatives ............................ 46 Learning Module 2 | Overview of Types of Real Estate Investment ................................................ 46 Learning Module 3 | Investments in Real Estate Through Publicly Traded Securities ..................... 48 Learning Module 4 | Hedge Fund Strategies .................................................................................... 49 VOLUME 9: PORTFOLIO MANAGEMENT ............................................................................................... 50 Learning Module 1 | Economics and Investment Markets............................................................... 50 Learning Module 2 | Analysis of Active Portfolio Management....................................................... 52 Learning Module 3 | Exchange-Traded Funds: Mechanics and Applications ................................... 53 Learning Module 4 | Using Multifactor Models ............................................................................... 54 Learning Module 5 | Measuring and Managing Market Risk ........................................................... 55 Learning Module 6 | Backtesting and Simulation............................................................................. 56 3 CFA Level 2 (2026) Formula Sheet by Fabian Moa CFA Level II – Formula Sheet (2026) Setting Up the Texas BA II Plus Financial Calculator Video: https://youtu.be/0MS8d8QOFmc VOLUME 1: QUANTITATIVE METHODS Learning Module 1 | Basics of Multiple Regression and Underlying Assumptions 𝑌𝑖 = 𝑏0 + 𝑏1 𝑋1𝑖 + 𝑏2 𝑋2𝑖 + ⋯ + +𝑏𝑘 𝑋𝑘𝑖 + 𝜀𝑖 𝑖 = 1, 2, 3, … , 𝑛 where: 𝑌 = dependent variable 𝑋 = independent variable 𝑏0 = intercept 𝑏1 , 𝑏2 , … , 𝑏𝑘 = slope coefficients 𝜀 = error term 𝑛 = number of observations 𝑘 = number of independent variables 𝑏0 , 𝑏1 , 𝑏2 , … , 𝑏𝑘 = regression coefficients 𝑛 𝑉𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑌 = ∑(𝑌𝑖 − 𝑌̅)2 𝑖=1 Learning Module 2 | Evaluating Regression Model Fit and Interpreting Model Results Coefficient of determination, 𝑅 2 𝑅2 = 𝑆𝑢𝑚 𝑜𝑓 𝑆𝑞𝑢𝑎𝑟𝑒𝑠 𝑅𝑒𝑔𝑟𝑒𝑠𝑠𝑖𝑜𝑛 𝑆𝑆𝑅 𝑆𝑆𝐸 = = 1− 𝑆𝑢𝑚 𝑜𝑓 𝑆𝑞𝑢𝑎𝑟𝑒𝑠 𝑇𝑜𝑡𝑎𝑙 𝑆𝑆𝑇 𝑆𝑆𝑇 𝑛 𝑆𝑢𝑚 𝑜𝑓 𝑆𝑞𝑢𝑎𝑟𝑒𝑠 𝑇𝑜𝑡𝑎𝑙, 𝑆𝑆𝑇 = ∑(𝑌𝑖 − 𝑌̅)2 𝑖=1 𝑆𝑢𝑚 𝑜𝑓 𝑆𝑞𝑢𝑎𝑟𝑒𝑠 𝑅𝑒𝑔𝑟𝑒𝑠𝑠𝑖𝑜𝑛, 2 𝑆𝑆𝑅 = ∑(𝑌̂𝑖 − 𝑌̅) 𝑛 𝑆𝑢𝑚 𝑜𝑓 𝑆𝑞𝑢𝑎𝑟𝑒𝑠 𝐸𝑟𝑟𝑜𝑟, 𝑛 𝑖=1 2 𝑆𝑆𝐸 = ∑(𝑌𝑖 − 𝑌̂𝑖 ) 𝑖=1 𝑆𝑆𝐸 ⁄(𝑛 − 𝑘 − 1) 𝑛−1 ) (1 − 𝑅 2 ) 𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑅 2 , 𝑅̅ 2 = 1 − [ ]=1−( 𝑆𝑆𝑇⁄(𝑛 − 1) 𝑛−𝑘−1 4 CFA Level 2 (2026) Formula Sheet by Fabian Moa Akaike’s information criterion (AIC) 𝑆𝑢𝑚 𝑜𝑓 𝑠𝑞𝑢𝑎𝑟𝑒𝑠 𝑒𝑟𝑟𝑜𝑟 ) + 2(𝑘 + 1) 𝐴𝐼𝐶 = 𝑛 ln ( 𝑛 where: 𝑛 = Sample size 𝑘 = Number of independent variables in the model Schwarz’s Bayesian information criterion (BIC of SBC) 𝑆𝑢𝑚 𝑜𝑓 𝑠𝑞𝑢𝑎𝑟𝑒𝑠 𝑒𝑟𝑟𝑜𝑟 ) + ln(𝑛) (𝑘 + 1) 𝐵𝐼𝐶 = 𝑛 ln ( 𝑛 F-distributed test statistic for jointly omitted variables 𝐹= (𝑆𝑢𝑚 𝑜𝑓 𝑠𝑞𝑢𝑎𝑟𝑒𝑠 𝑒𝑟𝑟𝑜𝑟 𝑟𝑒𝑠𝑡𝑟𝑖𝑐𝑡𝑒𝑑 𝑚𝑜𝑑𝑒𝑙 − 𝑆𝑢𝑚 𝑜𝑓 𝑠𝑞𝑢𝑎𝑟𝑒𝑠 𝑢𝑛𝑟𝑒𝑠𝑡𝑟𝑖𝑐𝑡𝑒𝑑)⁄𝑞 𝑆𝑢𝑚 𝑜𝑓 𝑠𝑞𝑢𝑎𝑟𝑒𝑠 𝑢𝑛𝑟𝑒𝑠𝑡𝑟𝑖𝑐𝑡𝑒𝑑 𝑚𝑜𝑑𝑒𝑙⁄(𝑛 − 𝑘 − 1) where: 𝑞 = Number of restrictions (i.e., number of variables omitted in the restricted model compared to the unrestricted model) 𝐻0 : 𝑏𝑚 = 𝑏𝑚+1 = ⋯ = 𝑏𝑚+𝑞−1 = 0 𝐻𝑎 : At least one of the 𝑞 slopes ≠ 0 F-test for joint test of slope coefficients ANOVA df SS MS Regression 𝑘 𝑆𝑆𝑅 𝑆𝑆𝑅 ⁄𝑘 Residual Total 𝐹 𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐 = 𝑛 − 𝑘 − 1 𝑆𝑆𝐸 𝑆𝑆𝐸 ⁄(𝑛 − 𝑘 − 1) 𝑛−1 𝑆𝑆𝑇 𝑀𝑒𝑎𝑛 𝑆𝑞𝑢𝑎𝑟𝑒 𝑅𝑒𝑔𝑟𝑒𝑠𝑠𝑖𝑜𝑛 𝑆𝑆𝑅 ⁄𝑘 = 𝑀𝑒𝑎𝑛 𝑆𝑞𝑢𝑎𝑟𝑒 𝐸𝑟𝑟𝑜𝑟 𝑆𝑆𝐸 ⁄(𝑛 − 𝑘 − 1) 𝐻0 : 𝑏1 = 𝑏2 = ⋯ = 𝑏𝑘 = 0 𝐻𝑎 : At least one 𝑏𝑗 ≠ 0 5 𝑭 𝑆𝑆𝑅 ⁄𝑘 𝑆𝑆𝐸 ⁄(𝑛 − 𝑘 − 1) CFA Level 2 (2026) Formula Sheet by Fabian Moa t-test statistic for slope coefficient 𝑡= 𝑏̂𝑗 − 𝐵𝑗 𝑠𝑏̂𝑗 where: 𝑏̂𝑗 = Regression estimate of 𝑏𝑗 𝐵𝑗 = Hypothesized value of coefficient 𝑗 𝑠𝑏̂ = Estimated standard error of 𝑏̂𝑗 𝑗 Video (Simple Linear Regression): https://youtu.be/uR_9im2JP18 Learning Module 3 | Model Misspecification Breusch-Pagan Test χ2𝐵𝑃,𝑘 = 𝑛𝑅 2 𝑇𝑒𝑠𝑡 𝑆𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐, where: 𝑅 2 = 𝑅-squared between squared residuals and independent variables Variance Inflation Factor (VIF) 𝑉𝐼𝐹𝑗 = 1 1 − 𝑅𝑗2 where: 𝑅𝑗2 = Variation in 𝑋𝑗 explained by the other 𝑘 − 1 independent variables Learning Module 4 | Extensions of Multiple Regression Detecting Influential Points Sum of individual leverages for all observations = 𝑘 + 1 If observation’s leverage > 3 ( 𝑘+1 𝑛 ) ⇒ Potentially influential observation Studentized Deleted Residual, 𝒕𝒊∗ 𝑒𝑖∗ 𝑒𝑖 𝑡𝑖 ∗ = = 𝑠𝑒 ∗ √𝑀𝑆𝐸(𝑖) (1 − ℎ𝑖𝑖 ) where: 𝑒𝑖∗ = The residual with the 𝑖th observation deleted 𝑠𝑒 ∗ = The standard deviation of the residuals 𝑘 = The number of independent variables 𝑀𝑆𝐸(𝑖) = Mean squared error of the regression model that deletes the 𝑖th observation ℎ𝑖𝑖 = The leverage value for the 𝑖th observation 6 CFA Level 2 (2026) Formula Sheet by Fabian Moa Logistic Regression (Logit) 𝑃 ) = 𝑏0 + 𝑏1 𝑋1 + 𝑏2 𝑋2 + ⋯ + 𝑏𝑘 𝑋𝑘 + 𝜀 ln ( 1−𝑃 𝑃= 1 1 + exp[−(𝑏0 + 𝑏1 𝑋1 + 𝑏2 𝑋2 + ⋯ + 𝑏𝑘 𝑋𝑘 )] 𝑃 ) = 𝐿𝑜𝑔 𝑜𝑑𝑑𝑠 ln ( 1−𝑃 𝑂𝑑𝑑𝑠 𝑟𝑎𝑡𝑖𝑜 = 𝑒 𝑏𝑖 Likelihood ratio (LR) test 𝐿𝑅 = −2(𝐿𝑜𝑔 𝑙𝑖𝑘𝑒𝑙𝑖ℎ𝑜𝑜𝑑 𝑟𝑒𝑠𝑡𝑟𝑖𝑐𝑡𝑒𝑑 𝑚𝑜𝑑𝑒𝑙 − 𝐿𝑜𝑔 𝑙𝑖𝑘𝑒𝑙𝑖ℎ𝑜𝑜𝑑 𝑢𝑛𝑟𝑒𝑠𝑡𝑟𝑖𝑐𝑡𝑒𝑑 𝑚𝑜𝑑𝑒𝑙) Learning Module 5 | Time-Series Analysis Linear Trend Models 𝑌𝑡 = 𝑏0 + 𝑏1 𝑡 + 𝜀𝑡 𝑡 = 1,2, … , 𝑇 𝑡 = time (independent variable) Log-Linear Trend Models 𝑌𝑡 = 𝑒 𝑏0+𝑏1𝑡 𝑡 = 1,2, … , 𝑇 ln 𝑌𝑡 = 𝑏0 + 𝑏1 𝑡 Growth rate of 𝑌 = 𝑒 𝑏1 − 1 p-th order autoregressive model, 𝑨𝑹(𝒑) 𝑥𝑡 = 𝑏0 + 𝑏1 𝑥𝑡−1 + 𝑏2 𝑥𝑡−2 + ⋯ + 𝑏𝑝 𝑥𝑡−𝑝 + 𝜀𝑡 Test statistic for autocorrelation of residuals 𝑡= 𝑅𝑒𝑠𝑖𝑑𝑢𝑎𝑙 𝑎𝑢𝑡𝑜𝑐𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 − 0 𝑅𝑒𝑠𝑖𝑑𝑢𝑎𝑙 𝑎𝑢𝑡𝑜𝑐𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 = 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑒𝑟𝑟𝑜𝑟 1⁄√𝑇 where: 𝐶𝑜𝑣(𝜀𝑡 , 𝜀𝑡−𝑘 ) 𝜌𝜀,𝑘 = = 𝑘 𝑡ℎ 𝑜𝑟𝑑𝑒𝑟 𝑎𝑢𝑡𝑜𝑐𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙 𝜎𝜀2 7 CFA Level 2 (2026) Formula Sheet by Fabian Moa Mean reverting level for AR(1) model 𝑥𝑡 = 𝑏0 1 − 𝑏1 Root Mean Squared Error 𝑅𝑀𝑆𝐸 = √ 𝑆𝑞𝑢𝑎𝑟𝑒𝑑 𝑒𝑟𝑟𝑜𝑟 𝑛 Dickey and Fuller Unit-Root Test 𝑥𝑡 − 𝑥𝑡−1 = 𝑏0 + 𝑔1 𝑥𝑡−1 + 𝜀𝑡 where: 𝑔1 = 𝑏1 − 1 n-Period Moving Average 𝑀𝐴𝑛 = 𝑥𝑡 + 𝑥𝑡−1 + ⋯ + 𝑥𝑡−(𝑛−1) 𝑛 qth-order Moving-Average, 𝑀𝐴(𝑞) 𝑥𝑡 = 𝜀𝑡 + 𝜃1 𝜀𝑡−1 + ⋯ + 𝜃𝑞 𝜀𝑡−𝑞 𝐸(𝜀) = 0, 𝐸(𝜀𝑡2 ) = 𝜎 2 , 𝑐𝑜𝑣(𝜀𝑡 , 𝜀𝑠 ) = 𝐸(𝜀𝑡 𝜀𝑠 ) = 0 𝑓𝑜𝑟 𝑡 ≠ 𝑠 Autoregressive Moving-Average (ARMA) Model, 𝑨𝑹𝑴𝑨(𝒑, 𝒒) 𝑥𝑡 = 𝑏0 + 𝑏1 𝑥𝑡−1 + 𝑏2 𝑥𝑡−2 + ⋯ + 𝑏𝑝 𝑥𝑡−𝑝 + 𝜀𝑡 + 𝜃1 𝜀𝑡−1 + ⋯ + 𝜃𝑞 𝜀𝑡−𝑞 𝐸(𝜀) = 0, 𝐸(𝜀𝑡2 ) = 𝜎 2 , 𝑐𝑜𝑣(𝜀𝑡 , 𝜀𝑠 ) = 𝐸(𝜀𝑡 𝜀𝑠 ) = 0 𝑓𝑜𝑟 𝑡 ≠ 𝑠 Autoregressive Conditional Heteroskedasticity (ARCH) Model ARCH(1): 2 𝜎̂𝑡+1 = 𝑎0 + 𝑎1 𝜖̂𝑡2 Learning Module 6 | Machine Learning Neural Networks 𝑃𝑎𝑟𝑡𝑖𝑎𝑙 𝑑𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑁𝑒𝑤 𝑛𝑒𝑡𝑤𝑜𝑟𝑘 = 𝑂𝑙𝑑 𝑤𝑒𝑖𝑔ℎ𝑡 − 𝐿𝑒𝑎𝑟𝑛𝑖𝑛𝑔 𝑟𝑎𝑡𝑒 × ( 𝑡𝑜𝑡𝑎𝑙 𝑒𝑟𝑟𝑜𝑟 𝑤𝑖𝑡ℎ 𝑟𝑒𝑠𝑝𝑒𝑐𝑡 ) 𝑤𝑒𝑖𝑔ℎ𝑡 𝑡𝑜 𝑡ℎ𝑒 𝑜𝑙𝑑 𝑤𝑒𝑖𝑔ℎ𝑡 8 CFA Level 2 (2026) Formula Sheet by Fabian Moa Learning Module 7 | Big Data Projects Normalization of variable X 𝑋𝑖 (𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑) = 𝑋𝑖 − 𝑋𝑚𝑖𝑛 𝑋𝑚𝑎𝑥 − 𝑋𝑚𝑖𝑛 Standardization of variable X 𝑋𝑖 (𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑𝑖𝑧𝑒𝑑) = 𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛, 𝑃 = 𝑅𝑒𝑐𝑎𝑙𝑙, 𝑅 = 𝑇𝑟𝑢𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑇𝑟𝑢𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 + 𝐹𝑎𝑙𝑠𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑇𝑟𝑢𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑇𝑟𝑢𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 + 𝐹𝑎𝑙𝑠𝑒 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝐴𝑐𝑐𝑢𝑟𝑎𝑐𝑦 = 𝐹1 𝑆𝑐𝑜𝑟𝑒 = 𝑋𝑖 − 𝜇 𝜎 𝑇𝑟𝑢𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 + 𝑇𝑟𝑢𝑒 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝑇𝑟𝑢𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 + 𝐹𝑎𝑙𝑠𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 + 𝑇𝑟𝑢𝑒 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒 + 𝐹𝑎𝑙𝑠𝑒 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒 2 × 𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 × 𝑅𝑒𝑐𝑎𝑙𝑙 𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 + 𝑅𝑒𝑐𝑎𝑙𝑙 𝐹𝑎𝑙𝑠𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑅𝑎𝑡𝑒, 𝐹𝑃𝑅 = 𝑇𝑟𝑢𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑅𝑎𝑡𝑒, 𝑇𝑃𝑅 = 𝐹𝑎𝑙𝑠𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑇𝑟𝑢𝑒 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒 + 𝐹𝑎𝑙𝑠𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑇𝑟𝑢𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑇𝑟𝑢𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 + 𝐹𝑎𝑙𝑠𝑒 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝐷𝑜𝑐𝑢𝑚𝑒𝑛𝑡 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦, 𝐷𝐹 = 𝑆𝑒𝑛𝑡𝑒𝑛𝑐𝑒 𝐶𝑜𝑢𝑛𝑡 𝑤𝑖𝑡ℎ 𝑊𝑜𝑟𝑑 𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑆𝑒𝑛𝑡𝑒𝑛𝑐𝑒𝑠 𝐼𝑛𝑣𝑒𝑟𝑠𝑒 𝐷𝑜𝑐𝑢𝑚𝑒𝑛𝑡 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦, 𝐼𝐷𝐹 = log ( 1 ) 𝐷𝐹 𝑇𝐹-𝐼𝐷𝐹 = 𝑇𝐹 × 𝐼𝐷𝐹 9 CFA Level 2 (2026) Formula Sheet by Fabian Moa VOLUME 2: ECONOMICS Learning Module 1 | Currency Exchange Rates: Understanding Equilibrium Value Cross Rates 𝐴 𝐶 𝐴 𝐴 𝐴 𝐵 𝐴 𝐴 𝐶 When given 𝐶 and 𝐵, then 𝐵 = 𝐶 × 𝐵 When given 𝐶 and 𝐶 , then 𝐵 = 𝐶 × 1 𝐵 ( ) 𝐶 Currency pair A/B B/A Bid Bid/Ask 𝑥 𝑦 1⁄𝑦 1⁄𝑥 Video: https://youtu.be/wyDKKPkPhzw Arbitrage Opportunities Between Dealers and Interbank Video: https://youtu.be/Lqo9UZ3yyEA Covered Interest Rate Parity 𝐹𝑓⁄𝑑 𝐴𝑐𝑡𝑢𝑎𝑙 1 + 𝑖𝑓 ( 360 ) = 𝑆𝑓⁄𝑑 [ ] 𝐴𝑐𝑡𝑢𝑎𝑙 1 + 𝑖𝑑 ( 360 ) 𝐴𝑐𝑡𝑢𝑎𝑙 𝐹𝑓⁄𝑑 − 𝑆𝑓⁄𝑑 (𝑖𝑓 − 𝑖𝑑 ) ( 360 ) = 𝐴𝑐𝑡𝑢𝑎𝑙 𝑆𝑓⁄𝑑 1 + 𝑖𝑑 ( 360 ) Video: https://youtu.be/9jOzFA9GuHU Mark-to-Market Value of a Forward Contract Original position: Long base currency d forward at forward rate 𝐹0,𝑓⁄𝑑 (Offer side) 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐿𝑜𝑛𝑔 𝐹𝑜𝑟𝑤𝑎𝑟𝑑 = (𝐹𝑡,𝑓⁄𝑑 − 𝐹0,𝑓⁄𝑑 ) × 𝐶𝑜𝑛𝑡𝑟𝑎𝑐𝑡 𝑆𝑖𝑧𝑒 𝑅𝑒𝑚𝑎𝑖𝑛𝑖𝑛𝑔 𝑑𝑎𝑦𝑠 𝑡𝑜 𝑚𝑎𝑡𝑢𝑟𝑖𝑡𝑦 ) 1 + 𝑖𝑓 ( 360 𝐹𝑡,𝑓⁄𝑑 = Forward rate at valuation date, t (Bid side) Video: https://youtu.be/wLqyZRrutAc 10 CFA Level 2 (2026) Formula Sheet by Fabian Moa Uncovered Interest Rate Parity 𝐴𝑐𝑡𝑢𝑎𝑙 1 + 𝑖𝑓 ( 360 ) 𝐸(𝑆𝑓⁄𝑑 ) = 𝑆𝑓⁄𝑑 [ ] 𝐴𝑐𝑡𝑢𝑎𝑙 1 + 𝑖𝑑 ( 360 ) %Δ𝑆𝑓𝑒⁄𝑑 𝐴𝑐𝑡𝑢𝑎𝑙 (𝑖𝑓 − 𝑖𝑑 ) ( 360 ) 𝐴𝑐𝑡𝑢𝑎𝑙 ) = ≈ (𝑖𝑓 − 𝑖𝑑 ) ( 𝐴𝑐𝑡𝑢𝑎𝑙 360 1 + 𝑖𝑑 ( 360 ) Video (Carry Trade): https://youtu.be/_26fG3Zvzyg Absolute PPP 𝑆𝑓⁄𝑑 = 𝑃𝑓 𝑃𝑑 Relative PPP %Δ𝑆𝑓⁄𝑑 𝐴𝑐𝑡𝑢𝑎𝑙 (𝜋𝑓 − 𝜋𝑑 ) ( 360 ) 𝐴𝑐𝑡𝑢𝑎𝑙 ) = ≈ (𝜋𝑓 − 𝜋𝑑 ) ( 𝐴𝑐𝑡𝑢𝑎𝑙 360 1 + 𝜋𝑑 ( 360 ) Ex ante PPP %Δ𝑆𝑓𝑒⁄𝑑 ≈ (𝜋𝑓𝑒 − 𝜋𝑑𝑒 ) ( 𝐴𝑐𝑡𝑢𝑎𝑙 ) 360 International Fisher Effect 𝑖𝑓 − 𝑖𝑑 = 𝜋𝑓𝑒 − 𝜋𝑑𝑒 where: 𝜋 𝑒 = Expected inflation rate 𝜋 = Actual inflation rate Mundell-Fleming Model Bonus Video: https://youtu.be/xNo3GpWYgKA 11 CFA Level 2 (2026) Formula Sheet by Fabian Moa Learning Module 2 | Economic Growth and the Investment Decision Grinold-Kroner Model 𝐸(𝑅𝑒 ) = 𝐷𝑌 + Δ(𝑃⁄𝐸 ) + 𝑖 + 𝑔 − Δ𝑆 where: 𝐸(𝑅𝑒 ) = Expected equity return 𝐷𝑌 = Dividend yield Δ(𝑃⁄𝐸 ) = Expected repricing 𝑖 = Expected inflation rate 𝑔 = Real economic growth rate Δ𝑆 = Change in shares outstanding Dilution effect Δ𝑆 = 𝑁𝑒𝑡 𝑏𝑢𝑦𝑏𝑎𝑐𝑘 + 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑑𝑦𝑛𝑎𝑚𝑖𝑠𝑚 Cobb-Douglas Production Function where a < 1 𝑌 = 𝑇𝐾 𝛼 𝐿1−𝛼 where: Y = Output 𝛼 = Share of output allocated to capital (𝐾) 1 − 𝛼 = share of output allocated to labor (𝐿) 𝑇 = total factor productivity (𝑇𝐹𝑃), represents technological progress of the economy 𝑌 𝐾 𝛼 𝐎𝐮𝐭𝐩𝐮𝐭 𝐩𝐞𝐫 𝐰𝐨𝐫𝐤𝐞𝐫 = = 𝑇 ( ) 𝐿 𝐿 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 = + 𝑙𝑎𝑏𝑜𝑟 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 𝑡𝑜𝑡𝑎𝑙 𝑓𝑎𝑐𝑡𝑜𝑟 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑑𝑒𝑒𝑝𝑒𝑛𝑖𝑛𝑔 Marginal product of capital, MPK 𝑌 𝑀𝑃𝐾 = 𝛼 ( ) 𝐾 Amount of output that is allocated to providers of capital, a 𝑟𝐾 𝛼= 𝑌 12 CFA Level 2 (2026) Formula Sheet by Fabian Moa Growth Accounting equation: ∆𝑌 ∆𝑇 ∆𝐾 ∆𝐿 = +𝛼 + (1 − 𝛼) 𝑌 𝑇 𝐾 𝐿 Growth rate in potential GDP = Long-term growth rate + Long-term growth rate of labor force in labor productivity 𝐿𝑎𝑏𝑜𝑟 𝑓𝑜𝑟𝑐𝑒 𝑝𝑎𝑟𝑡𝑖𝑐𝑖𝑝𝑎𝑡𝑖𝑜𝑛 = 𝐿𝑎𝑏𝑜𝑟 𝑓𝑜𝑟𝑐𝑒 𝑊𝑜𝑟𝑘𝑖𝑛𝑔 𝑎𝑔𝑒 𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 Sustainable growth rate of output per capita 𝜃 𝑔∗ = 1−𝛼 Sustainable growth rate of output (Steady state growth rate) 𝜃 𝐺∗ = +𝑛 1−𝛼 Equilibrium output-to-capital ratio (in steady state): 𝑌 1 𝜃 = [ + 𝑛 + 𝛿] 𝐾 𝑠 1−𝛼 where: 𝜃 = growth rate of TFP 𝛼 = elasticity of output with respect to capital 𝑠 = fraction of income (Y) that is saved 𝛿 = rate of depreciation of physical capital stock 𝑛 = labor supply growth = %∆𝐿 Endogeneous Growth Model Production function: 𝑦𝑒 = 𝑐𝑘𝑒 Growth rate of output per capita: Δ𝑦𝑒 Δ𝑘 = = 𝑠𝑐 − 𝛿 − 𝑛 𝑦𝑒 𝑘𝑒 where: 𝑦𝑒 = output per worker 𝑘𝑒 = capital per worker 𝑐 = marginal product of capital in the aggregate economy (constant) 13 CFA Level 2 (2026) Formula Sheet by Fabian Moa VOLUME 3: FINANCIAL STATEMENT ANALYSIS Learning Module 1 | Intercorporate Investments Investments in Associates (Equity Method) 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑆ℎ𝑎𝑟𝑒 𝑜𝑓 𝐴𝑚𝑜𝑟𝑡𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑒𝑥𝑐𝑒𝑠𝑠 𝐸𝑛𝑑𝑖𝑛𝑔 𝑆ℎ𝑎𝑟𝑒 𝑜𝑓 = + − 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑖𝑛 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑖𝑛 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 − 𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒 𝑝𝑟𝑖𝑐𝑒 𝑛𝑒𝑡 𝑖𝑛𝑐𝑜𝑚𝑒 𝑎𝑠𝑠𝑜𝑐𝑖𝑎𝑡𝑒𝑠 𝑎𝑠𝑠𝑜𝑐𝑖𝑎𝑡𝑒𝑠 𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑑 Impact on Investor’s Income Statement 𝐴𝑚𝑜𝑟𝑡𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑒𝑥𝑐𝑒𝑠𝑠 𝑆ℎ𝑎𝑟𝑒 𝑜𝑓 𝑈𝑛𝑟𝑒𝑎𝑙𝑖𝑧𝑒𝑑 𝑝𝑟𝑜𝑓𝑖𝑡 𝑓𝑟𝑜𝑚 𝑆ℎ𝑎𝑟𝑒 𝑜𝑓 = − − 𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒 𝑝𝑟𝑖𝑐𝑒 𝑑𝑜𝑤𝑛𝑠𝑡𝑟𝑒𝑎𝑚 𝑜𝑟 𝑢𝑝𝑠𝑡𝑟𝑒𝑎𝑚 𝑠𝑎𝑙𝑒 𝑛𝑒𝑡 𝑖𝑛𝑐𝑜𝑚𝑒 Business Combinations (Acquisition Method) Excess purchase price = Acquisition price – %Ownership × Book value of net identifiable assets Partial Goodwill = Acquisition price – (%Ownership × Fair value of identifiable net assets) = Acquisition price – (%Ownership × Book value of identifiable net assets) – (%Ownership × Excess purchase price attributable to identifiable net assets) 𝑁𝑜𝑛 𝑐𝑜𝑛𝑡𝑟𝑜𝑙𝑙𝑖𝑛𝑔 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 = %𝑁𝐶𝐼 × 𝐹𝑎𝑖𝑟 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑖𝑑𝑒𝑛𝑡𝑖𝑓𝑖𝑎𝑏𝑙𝑒 𝑛𝑒𝑡 𝑎𝑠𝑠𝑒𝑡𝑠 Full Goodwill = Fair value of entity – Fair value of net identifiable assets 𝑁𝑜𝑛 𝑐𝑜𝑛𝑡𝑟𝑜𝑙𝑙𝑖𝑛𝑔 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 = %𝑁𝐶𝐼 × 𝐹𝑎𝑖𝑟 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑒𝑛𝑡𝑖𝑡𝑦 Video: https://youtu.be/RgxmPbx4-0o IFRS 𝐶𝑎𝑟𝑟𝑦𝑖𝑛𝑔 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑅𝑒𝑐𝑜𝑣𝑒𝑟𝑎𝑏𝑙𝑒 𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝐼𝑚𝑝𝑎𝑖𝑟𝑚𝑒𝑛𝑡 = − 𝑐𝑎𝑠ℎ 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑢𝑛𝑖𝑡 𝑐𝑎𝑠ℎ 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑢𝑛𝑖𝑡 𝑙𝑜𝑠𝑠 US GAAP 𝐼𝑚𝑝𝑙𝑖𝑒𝑑 𝐹𝑎𝑖𝑟 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝐹𝑎𝑖𝑟 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑟𝑒𝑝𝑜𝑟𝑡𝑖𝑛𝑔 𝑢𝑛𝑖𝑡′𝑠 = − 𝑔𝑜𝑜𝑑𝑤𝑖𝑙𝑙 𝑟𝑒𝑝𝑜𝑟𝑡𝑖𝑛𝑔 𝑢𝑛𝑖𝑡 𝑖𝑑𝑒𝑛𝑡𝑖𝑓𝑖𝑎𝑏𝑙𝑒 𝑛𝑒𝑡 𝑎𝑠𝑠𝑒𝑡𝑠 𝐼𝑚𝑝𝑎𝑖𝑟𝑚𝑒𝑛𝑡 𝐶𝑎𝑟𝑟𝑦𝑖𝑛𝑔 𝑣𝑎𝑙𝑢𝑒 𝐼𝑚𝑝𝑙𝑖𝑒𝑑 = − 𝑜𝑓 𝑔𝑜𝑜𝑑𝑤𝑖𝑙𝑙 𝑔𝑜𝑜𝑑𝑤𝑖𝑙𝑙 𝑙𝑜𝑠𝑠 14 CFA Level 2 (2026) Formula Sheet by Fabian Moa Learning Module 2 | Employee Compensation - Post-Employment and Share-Based Share-Based Compensation Accounting Share Award 𝐶𝑜𝑚𝑝𝑒𝑛𝑠𝑎𝑡𝑖𝑜𝑛 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 = 𝐹𝑎𝑖𝑟 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑎𝑤𝑎𝑟𝑑 𝑜𝑛 𝑔𝑟𝑎𝑛𝑡 𝑑𝑎𝑡𝑒 𝑉𝑒𝑠𝑡𝑖𝑛𝑔 𝑝𝑒𝑟𝑖𝑜𝑑 Stock Options 𝐶𝑜𝑚𝑝𝑒𝑛𝑠𝑎𝑡𝑖𝑜𝑛 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 = 𝐹𝑎𝑖𝑟 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑜𝑝𝑡𝑖𝑜𝑛𝑠 𝑜𝑛 𝑔𝑟𝑎𝑛𝑡 𝑑𝑎𝑡𝑒 𝑉𝑒𝑠𝑡𝑖𝑛𝑔 𝑝𝑒𝑟𝑖𝑜𝑑 Treasury Stock Method 𝑃𝑟𝑜𝑐𝑒𝑒𝑑𝑠 𝑓𝑟𝑜𝑚 ( 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑜𝑟 𝑒𝑥𝑒𝑟𝑐𝑖𝑠𝑒 ) 𝐵𝑎𝑠𝑖𝑐 𝑆ℎ𝑎𝑟𝑒𝑠 𝑖𝑠𝑠𝑢𝑒𝑑 𝑓𝑟𝑜𝑚 𝐷𝑖𝑙𝑢𝑡𝑒𝑑 𝑜𝑓 𝑠ℎ𝑎𝑟𝑒 𝑏𝑎𝑠𝑒𝑑 𝑎𝑤𝑎𝑟𝑑𝑠 𝑠ℎ𝑎𝑟𝑒𝑠 𝑠ℎ𝑎𝑟𝑒𝑠 = + 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑜𝑟 𝑒𝑥𝑒𝑟𝑐𝑖𝑠𝑒 − 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑠ℎ𝑎𝑟𝑒 𝑝𝑟𝑖𝑐𝑒 𝑓𝑜𝑟 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 𝑜𝑓 𝑠ℎ𝑎𝑟𝑒 𝑏𝑎𝑠𝑒𝑑 𝑎𝑤𝑎𝑟𝑑𝑠 𝑡ℎ𝑒 𝑟𝑒𝑝𝑜𝑟𝑡𝑖𝑛𝑔 𝑝𝑒𝑟𝑖𝑜𝑑 𝐴𝑠𝑠𝑢𝑚𝑒𝑑 𝐶𝑎𝑠ℎ 𝑝𝑟𝑜𝑐𝑒𝑒𝑑𝑠 = + 𝑝𝑟𝑜𝑐𝑒𝑒𝑑𝑠 𝑓𝑟𝑜𝑚 𝑒𝑥𝑒𝑟𝑐𝑖𝑠𝑒 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑢𝑛𝑟𝑒𝑐𝑜𝑔𝑛𝑖𝑧𝑒𝑑 𝑠ℎ𝑎𝑟𝑒-𝑏𝑎𝑠𝑒𝑑 𝑐𝑜𝑚𝑝𝑒𝑛𝑠𝑎𝑡𝑖𝑜𝑛 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 where: 𝐶𝑎𝑠ℎ 𝑝𝑟𝑜𝑐𝑒𝑒𝑑𝑠 𝑓𝑟𝑜𝑚 𝑒𝑥𝑒𝑟𝑐𝑖𝑠𝑒 = { 𝑆𝑡𝑟𝑖𝑘𝑒 𝑝𝑟𝑖𝑐𝑒 × 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑝𝑡𝑖𝑜𝑛𝑠 0 𝐹𝑜𝑟 𝑜𝑝𝑡𝑖𝑜𝑛𝑠 𝐹𝑜𝑟 𝑅𝑆𝑈𝑠 𝑈𝑛𝑟𝑒𝑐𝑜𝑔𝑛𝑖𝑠𝑒𝑑 𝑠ℎ𝑎𝑟𝑒-𝑏𝑎𝑠𝑒𝑑 𝑈𝑛𝑣𝑒𝑠𝑡𝑒𝑑 𝐹𝑎𝑖𝑟 𝑣𝑎𝑙𝑢𝑒 𝑜𝑛 = × 𝑔𝑟𝑎𝑛𝑡 𝑑𝑎𝑡𝑒 𝑐𝑜𝑚𝑝𝑒𝑛𝑠𝑎𝑡𝑖𝑜𝑛 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 𝑎𝑤𝑎𝑟𝑑𝑠 Forecasting Shares Outstanding With Share-Based Awards 𝐵𝑎𝑠𝑖𝑐 𝑠ℎ𝑎𝑟𝑒𝑠 𝐵𝑎𝑠𝑖𝑐 𝑠ℎ𝑎𝑟𝑒𝑠 𝑆ℎ𝑎𝑟𝑒 𝑜𝑝𝑡𝑖𝑜𝑛𝑠 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔, = 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔, + 𝑅𝑆𝑈𝑠 𝑣𝑒𝑠𝑡𝑒𝑑 + 𝑒𝑥𝑒𝑟𝑐𝑖𝑠𝑒𝑑 𝑒𝑛𝑑 𝑜𝑓 𝑝𝑒𝑟𝑖𝑜𝑑 𝑏𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑜𝑓 𝑝𝑒𝑟𝑖𝑜𝑑 𝑆ℎ𝑎𝑟𝑒𝑠 𝑖𝑠𝑠𝑢𝑒𝑑 𝑓𝑟𝑜𝑚 𝑆ℎ𝑎𝑟𝑒 𝑠𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑖𝑒𝑠, + − 𝑟𝑒𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑠 𝑎𝑐𝑞𝑢𝑖𝑠𝑖𝑡𝑖𝑜𝑛𝑠, 𝑒𝑡𝑐. Defined Benefit Pension Plans 𝐹𝑢𝑛𝑑𝑒𝑑 𝑠𝑡𝑎𝑡𝑢𝑠 = 𝐹𝑎𝑖𝑟 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑝𝑙𝑎𝑛 𝑎𝑠𝑠𝑒𝑡𝑠 − 𝑃𝑒𝑛𝑠𝑖𝑜𝑛 𝑜𝑏𝑙𝑖𝑔𝑎𝑡𝑖𝑜𝑛 𝐸𝑛𝑑𝑖𝑛𝑔 𝑓𝑎𝑖𝑟 𝑣𝑎𝑙𝑢𝑒 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑓𝑎𝑖𝑟 𝑣𝑎𝑙𝑢𝑒 𝐴𝑐𝑡𝑢𝑎𝑙 𝑟𝑒𝑡𝑢𝑟𝑛 𝐵𝑒𝑛𝑒𝑓𝑖𝑡𝑠 = + 𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛𝑠 + − 𝑜𝑛 𝑝𝑙𝑎𝑛 𝑎𝑠𝑠𝑒𝑡𝑠 𝑜𝑓 𝑝𝑙𝑎𝑛 𝑎𝑠𝑠𝑒𝑡𝑠 𝑜𝑓 𝑝𝑙𝑎𝑛 𝑎𝑠𝑠𝑒𝑡𝑠 𝑝𝑎𝑖𝑑 15 CFA Level 2 (2026) Formula Sheet by Fabian Moa 𝐸𝑛𝑑𝑖𝑛𝑔 𝑝𝑒𝑛𝑠𝑖𝑜𝑛 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑝𝑒𝑛𝑠𝑖𝑜𝑛 𝑆𝑒𝑟𝑣𝑖𝑐𝑒 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝐵𝑒𝑛𝑒𝑓𝑖𝑡𝑠 𝐴𝑐𝑡𝑢𝑎𝑟𝑖𝑎𝑙 = + + + − 𝑙𝑜𝑠𝑠⁄(𝑔𝑎𝑖𝑛) 𝑜𝑏𝑙𝑖𝑔𝑎𝑡𝑖𝑜𝑛 𝑜𝑏𝑙𝑖𝑔𝑎𝑡𝑖𝑜𝑛 𝑝𝑎𝑖𝑑 𝑐𝑜𝑠𝑡𝑠 𝑐𝑜𝑠𝑡 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑐𝑜𝑠𝑡 = 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑝𝑒𝑛𝑠𝑖𝑜𝑛 𝑌𝑖𝑒𝑙𝑑 𝑜𝑛 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑔𝑟𝑎𝑑𝑒 × 𝑜𝑏𝑙𝑖𝑔𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑟𝑝𝑜𝑟𝑎𝑡𝑒 𝑏𝑜𝑛𝑑 IFRS Only In income statement, 𝑅𝑒𝑝𝑜𝑟𝑡𝑒𝑑 𝑝𝑒𝑛𝑠𝑖𝑜𝑛 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 = 𝑁𝑒𝑡 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑎𝑛𝑑 𝑝𝑎𝑠𝑡 + 𝑐𝑜𝑠𝑡⁄(𝑖𝑛𝑐𝑜𝑚𝑒) 𝑠𝑒𝑟𝑣𝑖𝑐𝑒 𝑐𝑜𝑠𝑡𝑠 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑝𝑒𝑛𝑠𝑖𝑜𝑛 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑓𝑎𝑖𝑟 𝑣𝑎𝑙𝑢𝑒 𝑁𝑒𝑡 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑌𝑖𝑒𝑙𝑑 𝑜𝑛 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 =( − )× 𝑐𝑜𝑠𝑡⁄(𝑖𝑛𝑐𝑜𝑚𝑒) 𝑔𝑟𝑎𝑑𝑒 𝑐𝑜𝑟𝑝𝑜𝑟𝑎𝑡𝑒 𝑏𝑜𝑛𝑑 𝑜𝑏𝑙𝑖𝑔𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑝𝑙𝑎𝑛 𝑎𝑠𝑠𝑒𝑡𝑠 Learning Module 3 | Multinational Operations Net assets = Total assets – Total liabilities Net monetary assets = Monetary assets – Monetary liabilities Current Rate Method Currency translation adjustment = Total assets of foreign subsidiary in parent currency terms − Total liabilities of foreign subsidiary in parent currency terms − Shareholder capital of foreign subsidiary in parent currency terms − Other equity items of foreign subsidiary in parent currency terms Hyperinflationary Environment IFRS 𝐸𝑛𝑑 𝑜𝑓 𝑝𝑒𝑟𝑖𝑜𝑑 𝑝𝑟𝑖𝑐𝑒 𝑖𝑛𝑑𝑒𝑥 𝑅𝑒𝑠𝑡𝑎𝑡𝑒𝑚𝑒𝑛𝑡 𝑓𝑎𝑐𝑡𝑜𝑟 𝑓𝑜𝑟 = 𝑚𝑜𝑛𝑒𝑡𝑎𝑟𝑦 𝑎𝑠𝑠𝑒𝑡𝑠 & 𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠 𝐸𝑛𝑑 𝑜𝑓 𝑝𝑒𝑟𝑖𝑜𝑑 𝑝𝑟𝑖𝑐𝑒 𝑖𝑛𝑑𝑒𝑥 𝐸𝑛𝑑 𝑜𝑓 𝑝𝑒𝑟𝑖𝑜𝑑 𝑝𝑟𝑖𝑐𝑒 𝑖𝑛𝑑𝑒𝑥 𝑅𝑒𝑠𝑡𝑎𝑡𝑒𝑚𝑒𝑛𝑡 𝑓𝑎𝑐𝑡𝑜𝑟 𝑓𝑜𝑟 = 𝑛𝑜𝑛-𝑚𝑜𝑛𝑒𝑡𝑎𝑟𝑦 𝑎𝑠𝑠𝑒𝑡𝑠 & 𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑜𝑓 𝑝𝑒𝑟𝑖𝑜𝑑 𝑝𝑟𝑖𝑐𝑒 𝑖𝑛𝑑𝑒𝑥 𝐸𝑛𝑑 𝑜𝑓 𝑝𝑒𝑟𝑖𝑜𝑑 𝑝𝑟𝑖𝑐𝑒 𝑖𝑛𝑑𝑒𝑥 𝑅𝑒𝑠𝑡𝑎𝑡𝑒𝑚𝑒𝑛𝑡 𝑓𝑎𝑐𝑡𝑜𝑟 𝑓𝑜𝑟 = 𝑖𝑛𝑐𝑜𝑚𝑒 𝑠𝑡𝑎𝑡𝑒𝑚𝑒𝑛𝑡 𝑖𝑡𝑒𝑚𝑠 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑝𝑟𝑖𝑐𝑒 𝑖𝑛𝑑𝑒𝑥 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑝𝑒𝑟𝑖𝑜𝑑 16 CFA Level 2 (2026) Formula Sheet by Fabian Moa Learning Module 4 | Analysis of Financial Institutions 𝑇𝑜𝑡𝑎𝑙 𝑇𝑖𝑒𝑟 1 𝐶𝑜𝑚𝑚𝑜𝑛 𝐸𝑞𝑢𝑖𝑡𝑦 𝐴𝑑𝑑𝑖𝑡𝑖𝑜𝑛𝑎𝑙 = + 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑇𝑖𝑒𝑟 1 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑇𝑖𝑒𝑟 1 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑇𝑜𝑡𝑎𝑙 𝑅𝑒𝑔𝑢𝑙𝑎𝑡𝑜𝑟𝑦 𝑇𝑜𝑡𝑎𝑙 𝑇𝑖𝑒𝑟 1 𝑇𝑜𝑡𝑎𝑙 𝑇𝑖𝑒𝑟 2 = + 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐶𝑜𝑚𝑚𝑜𝑛 𝐸𝑞𝑢𝑖𝑡𝑦 𝑇𝑖𝑒𝑟 1 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐶𝑜𝑚𝑚𝑜𝑛 𝐸𝑞𝑢𝑖𝑡𝑦 = ≥ 4.5% 𝑇𝑖𝑒𝑟 1 𝑅𝑎𝑡𝑖𝑜 𝑅𝑖𝑠𝑘 𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝐴𝑠𝑠𝑒𝑡𝑠 𝑇𝑜𝑡𝑎𝑙 𝑇𝑖𝑒𝑟 1 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑇𝑖𝑒𝑟 1 = ≥ 6.0% 𝑅𝑎𝑡𝑖𝑜 𝑅𝑖𝑠𝑘 𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝐴𝑠𝑠𝑒𝑡𝑠 𝑇𝑜𝑡𝑎𝑙 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑇𝑜𝑡𝑎𝑙 𝑅𝑒𝑔𝑢𝑙𝑎𝑡𝑜𝑟𝑦 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 = ≥ 8.0% 𝑅𝑎𝑡𝑖𝑜 𝑅𝑖𝑠𝑘 𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝐴𝑠𝑠𝑒𝑡𝑠 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 𝐶𝑜𝑣𝑒𝑟𝑎𝑔𝑒 𝐻𝑖𝑔ℎ 𝑄𝑢𝑎𝑙𝑖𝑡𝑦 𝐿𝑖𝑞𝑢𝑖𝑑 𝐴𝑠𝑠𝑒𝑡𝑠 = 𝑅𝑎𝑡𝑖𝑜, 𝐿𝐶𝑅 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑐𝑎𝑠ℎ 𝑜𝑢𝑡𝑓𝑙𝑜𝑤𝑠 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑎𝑦𝑠 𝑡ℎ𝑎𝑡 𝑏𝑎𝑛𝑘 𝑐𝑎𝑛 𝑤𝑖𝑡ℎ𝑠𝑡𝑎𝑛𝑑 = 𝐿𝐶𝑅 × 30 𝑎 𝑠𝑡𝑟𝑒𝑠𝑠 𝑙𝑒𝑣𝑒𝑙 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑐𝑎𝑠ℎ 𝑜𝑢𝑡𝑓𝑙𝑜𝑤𝑠 Number of days that bank can withstand a stress level volume of cash outflows for (𝐿𝐶𝑅 × 30) days. 𝑁𝑒𝑡 𝑆𝑡𝑎𝑏𝑙𝑒 𝐹𝑢𝑛𝑑𝑖𝑛𝑔 𝐴𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝑆𝑡𝑎𝑏𝑙𝑒 𝐹𝑢𝑛𝑑𝑖𝑛𝑔 = 𝑅𝑎𝑡𝑖𝑜, 𝑁𝑆𝐹𝑅 𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑆𝑡𝑎𝑏𝑙𝑒 𝐹𝑢𝑛𝑑𝑖𝑛𝑔 Property and Casualty Companies 𝐿𝑜𝑠𝑠 𝑎𝑛𝑑 𝑙𝑜𝑠𝑠 𝑎𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛𝑡 𝐿𝑜𝑠𝑠 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 + 𝐿𝑜𝑠𝑠 𝑎𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛𝑡 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 = 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 𝑟𝑎𝑡𝑖𝑜 𝑁𝑒𝑡 𝑝𝑟𝑒𝑚𝑖𝑢𝑚𝑠 𝑒𝑎𝑟𝑛𝑒𝑑 𝑈𝑛𝑑𝑒𝑟𝑤𝑟𝑖𝑡𝑖𝑛𝑔 𝑈𝑛𝑑𝑒𝑟𝑤𝑟𝑖𝑡𝑖𝑛𝑔 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 = 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 𝑟𝑎𝑡𝑖𝑜 𝑁𝑒𝑡 𝑝𝑟𝑒𝑚𝑖𝑢𝑚𝑠 𝑤𝑟𝑖𝑡𝑡𝑒𝑛 𝐶𝑜𝑚𝑏𝑖𝑛𝑒𝑑 𝐿𝑜𝑠𝑠 𝑎𝑛𝑑 𝑙𝑜𝑠𝑠 𝑎𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛𝑡 𝑈𝑛𝑑𝑒𝑟𝑤𝑟𝑖𝑡𝑖𝑛𝑔 = + 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 𝑟𝑎𝑡𝑖𝑜 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 𝑟𝑎𝑡𝑖𝑜 𝑟𝑎𝑡𝑖𝑜 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 𝑡𝑜 𝑝𝑜𝑙𝑖𝑐𝑦ℎ𝑜𝑙𝑑𝑒𝑟𝑠 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 𝑡𝑜 𝑝𝑜𝑙𝑖𝑐𝑦ℎ𝑜𝑙𝑑𝑒𝑟𝑠 (𝑠ℎ𝑎𝑟𝑒ℎ𝑜𝑙𝑑𝑒𝑟𝑠) = (𝑠ℎ𝑎𝑟𝑒ℎ𝑜𝑙𝑑𝑒𝑟𝑠) 𝑟𝑎𝑡𝑖𝑜 𝑁𝑒𝑡 𝑝𝑟𝑒𝑚𝑖𝑢𝑚𝑠 𝑒𝑎𝑟𝑛𝑒𝑑 𝐶𝑜𝑚𝑏𝑖𝑛𝑒𝑑 𝑟𝑎𝑡𝑖𝑜 𝐶𝑜𝑚𝑏𝑖𝑛𝑒𝑑 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 𝑡𝑜 𝑝𝑜𝑙𝑖𝑐𝑦ℎ𝑜𝑙𝑑𝑒𝑟𝑠 = + 𝒂𝒇𝒕𝒆𝒓 𝒅𝒊𝒗𝒊𝒅𝒆𝒏𝒅𝒔 (𝑠ℎ𝑎𝑟𝑒ℎ𝑜𝑙𝑑𝑒𝑟𝑠) 𝑟𝑎𝑡𝑖𝑜 𝑟𝑎𝑡𝑖𝑜 17 CFA Level 2 (2026) Formula Sheet by Fabian Moa Learning Module 5 | Evaluating Quality of Financial Reports Beneish Model 𝑀-𝑠𝑐𝑜𝑟𝑒 = − 4.84 + 0.920 (𝐷𝑆𝑅) + 0.528 (𝐺𝑀𝐼) + 0.404 (𝐴𝑄𝐼) + 0.892 (𝑆𝐺𝐼) + 0.115 (𝐷𝐸𝑃𝐼) − 0.172 (𝑆𝐺𝐴𝐼) + 4.670 (𝐴𝑐𝑐𝑟𝑢𝑎𝑙𝑠) − 0.327 (𝐿𝐸𝑉𝐼) where: DSR (day sales receivable index) = 𝑅𝑒𝑐𝑒𝑖𝑣𝑎𝑏𝑙𝑒𝑠𝑡 ⁄𝑆𝑎𝑙𝑒𝑠𝑡 𝑅𝑒𝑐𝑒𝑖𝑣𝑎𝑏𝑙𝑒𝑠𝑡−1⁄𝑆𝑎𝑙𝑒𝑠𝑡−1 𝐺𝑀𝑡−1 𝐺𝑀𝑡 [1 − (𝑃𝑃𝐸𝑡 + 𝐶𝐴𝑡 )/𝑇𝐴𝑡 ] AQI (asset quality index) = [1 − (𝑃𝑃𝐸𝑡−1 + 𝐶𝐴𝑡−1 )/𝑇𝐴𝑡−1 ] 𝑆𝑎𝑙𝑒𝑠𝑡 SGI (sales growth index) = 𝑆𝑎𝑙𝑒𝑠𝑡−1 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛𝑡−1 DEPI (depreciation index) = 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛𝑡 GMI (gross margin index) = 𝑆𝐺𝐴𝑡 /𝑆𝑎𝑙𝑒𝑠𝑡 𝑆𝐺𝐴𝑡−1 /𝑆𝑎𝑙𝑒𝑠𝑡−1 𝐼𝑛𝑐𝑜𝑚𝑒 𝑏𝑒𝑓𝑜𝑟𝑒 𝑒𝑥𝑡𝑟𝑎𝑜𝑟𝑑𝑖𝑛𝑎𝑟𝑦 𝑖𝑡𝑒𝑚𝑠 − 𝐶𝑎𝑠ℎ 𝑓𝑟𝑜𝑚 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑠 Accruals = 𝑇𝑜𝑡𝑎𝑙 𝑎𝑠𝑠𝑒𝑡𝑠 𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒𝑡 LEVI (leverage index) = 𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒𝑡−1 SGAI (sales, general, and administrative expenses index) = Earnings Persistence 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠𝑡+1 = 𝛼 + 𝛽(𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠𝑡 ) + 𝜀 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠𝑡+1 = 𝛼 + 𝛽1 (𝐶𝑎𝑠ℎ 𝑓𝑙𝑜𝑤𝑡 ) + 𝛽2 (𝐴𝑐𝑐𝑟𝑢𝑎𝑙𝑠𝑡 ) + 𝜀 Cash-flow-based accruals = NI – (CFO + CFI) Learning Module 6 | Integration of Financial Statement Analysis Techniques 𝑁𝑒𝑡 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 = − 𝐴𝑠𝑠𝑒𝑡𝑠 (𝑁𝑂𝐴) 𝐴𝑠𝑠𝑒𝑡𝑠 𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠 𝑇𝑜𝑡𝑎𝑙 𝐶𝑎𝑠ℎ 𝑎𝑛𝑑 𝑇𝑜𝑡𝑎𝑙 𝑇𝑜𝑡𝑎𝑙 =( − )−( − ) 𝐴𝑠𝑠𝑒𝑡𝑠 𝑆ℎ𝑜𝑟𝑡-𝑡𝑒𝑟𝑚 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡𝑠 𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠 𝐷𝑒𝑏𝑡 𝑁𝑂𝐴𝑡 − 𝑁𝑂𝐴𝑡−1 𝐵𝑎𝑙𝑎𝑛𝑐𝑒-𝑠ℎ𝑒𝑒𝑡-𝑏𝑎𝑠𝑒𝑑 = (𝑁𝑂𝐴𝑡 + 𝑁𝑂𝐴𝑡−1 )⁄2 𝑎𝑐𝑐𝑟𝑢𝑎𝑙𝑠 𝑟𝑎𝑡𝑖𝑜 𝐶𝑎𝑠ℎ-𝑓𝑙𝑜𝑤-𝑏𝑎𝑠𝑒𝑑 𝑁𝐼𝑡 − (𝐶𝐹𝑂𝑡 + 𝐶𝐹𝐼𝑡 ) = (𝑁𝑂𝐴𝑡 + 𝑁𝑂𝐴𝑡−1 )⁄2 𝑎𝑐𝑐𝑟𝑢𝑎𝑙𝑠 𝑟𝑎𝑡𝑖𝑜 18 CFA Level 2 (2026) Formula Sheet by Fabian Moa VOLUME 4: CORPORATE ISSUERS Learning Module 1 | Analysis of Dividends and Share Repurchases Dividend Payout Policies Target payout adjustment model (Lintner model) 𝐴𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛𝑡 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑇𝑎𝑟𝑔𝑒𝑡 𝑝𝑎𝑦𝑜𝑢𝑡 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝐿𝑎𝑠𝑡 𝐿𝑎𝑠𝑡 )× = +( × − 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑓𝑎𝑐𝑡𝑜𝑟 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑟𝑎𝑡𝑖𝑜 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 where: 𝐴𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛𝑡 𝑓𝑎𝑐𝑡𝑜𝑟 = 1 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑦𝑒𝑎𝑟𝑠 𝑓𝑜𝑟 𝑎𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛𝑡 𝑡𝑜 𝑡𝑎𝑘𝑒 𝑝𝑙𝑎𝑐𝑒 Constant dividend payout ratio policy 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 = × 𝑝𝑎𝑦𝑜𝑢𝑡 𝑟𝑎𝑡𝑖𝑜 𝑒𝑎𝑟𝑛𝑖𝑛𝑔𝑠 Video: https://youtu.be/hhcvNiTpZX4 EPS and BVPS After Share Repurchase 𝐸𝑃𝑆 𝑎𝑓𝑡𝑒𝑟 𝑏𝑢𝑦𝑏𝑎𝑐𝑘 = 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑏𝑒𝑓𝑜𝑟𝑒 𝑏𝑢𝑦𝑏𝑎𝑐𝑘 − 𝐴𝑓𝑡𝑒𝑟 𝑡𝑎𝑥 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑓𝑢𝑛𝑑𝑠 𝑆ℎ𝑎𝑟𝑒𝑠 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 𝑎𝑓𝑡𝑒𝑟 𝑏𝑢𝑦𝑏𝑎𝑐𝑘 Video: https://youtu.be/Pd0-QQF-VhQ 𝐵𝑉𝑃𝑆 𝑎𝑓𝑡𝑒𝑟 𝑏𝑢𝑦𝑏𝑎𝑐𝑘 = 𝐵𝑜𝑜𝑘 𝑉𝑎𝑙𝑢𝑒 𝑏𝑒𝑓𝑜𝑟𝑒 𝑏𝑢𝑦𝑏𝑎𝑐𝑘 − 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑠ℎ𝑎𝑟𝑒 𝑏𝑢𝑦𝑏𝑎𝑐𝑘 𝑆ℎ𝑎𝑟𝑒𝑠 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 𝑎𝑓𝑡𝑒𝑟 𝑏𝑢𝑦𝑏𝑎𝑐𝑘 Analysis of Dividend Safety 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑝𝑎𝑦𝑜𝑢𝑡 𝑟𝑎𝑡𝑖𝑜 = 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑐𝑜𝑣𝑒𝑟𝑎𝑔𝑒 𝑟𝑎𝑡𝑖𝑜 = 𝐹𝐶𝐹𝐸 𝑐𝑜𝑣𝑒𝑟𝑎𝑔𝑒 𝑟𝑎𝑡𝑖𝑜 = 𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 𝐹𝐶𝐹𝐸 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 + 𝑆ℎ𝑎𝑟𝑒 𝑟𝑒𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑠 19 CFA Level 2 (2026) Formula Sheet by Fabian Moa Learning Module 3 | Cost of Capital: Advanced Topics Weighted average cost of capital 𝑊𝐴𝐶𝐶 = 𝑤𝑑 𝑟𝑑 (1 − 𝑡) + 𝑤𝑝 𝑟𝑝 + 𝑤𝑒 𝑟𝑒 where: 𝑤𝑑 = Weight of debt in capital structure 𝑤𝑝 = Weight of preferred equity in capital structure 𝑤𝑒 = Weight of common equity in capital structure 𝑟𝑑 = Pre-tax cost of debt 𝑟𝑝 = Cost of preferred equity 𝑟𝑒 = Cost of common equity Cost of debt, 𝑟𝑑 = 𝑟𝑓 + 𝐶𝑟𝑒𝑑𝑖𝑡 𝑠𝑝𝑟𝑒𝑎𝑑 Cost of equity, 𝑟𝑒 = 𝑟𝑓 + 𝐸𝑅𝑃 + 𝐼𝑅𝑃 where: 𝐵𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 𝑖𝑛𝑑𝑒𝑥 𝑅𝑖𝑠𝑘 𝑓𝑟𝑒𝑒 − 𝑟𝑒𝑡𝑢𝑟𝑛 𝑟𝑎𝑡𝑒 𝐼𝑅𝑃 = Idiosyncratic risk premium 𝐸𝑅𝑃 = Equity risk premium = Leases 𝑃𝑟𝑒𝑠𝑒𝑛𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑃𝑟𝑒𝑠𝑒𝑛𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐹𝑎𝑖𝑟 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐿𝑒𝑠𝑠𝑜𝑟 ′ 𝑠 𝐷𝑖𝑟𝑒𝑐𝑡 + = + 𝐿𝑒𝑎𝑠𝑒 𝑃𝑎𝑦𝑚𝑒𝑛𝑡𝑠 𝑅𝑒𝑠𝑖𝑑𝑢𝑎𝑙 𝑉𝑎𝑙𝑢𝑒 𝑡𝑜 𝐿𝑒𝑎𝑠𝑒𝑑 𝐴𝑠𝑠𝑒𝑡 𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝐶𝑜𝑠𝑡𝑠 𝐿𝑒𝑠𝑠𝑜𝑟 Equity Risk Premium Historical Approach (Ex-Post) 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑏𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑟𝑖𝑠𝑘 𝐸𝑅𝑃 = − 𝑓𝑟𝑒𝑒 𝑟𝑎𝑡𝑒 𝑖𝑛𝑑𝑒𝑥 𝑟𝑒𝑡𝑢𝑟𝑛 Gordon Growth model 𝐸𝑅𝑃 = 𝐷1 + 𝑔 − 𝑟𝑓 𝑉0 20 CFA Level 2 (2026) Formula Sheet by Fabian Moa Grinold-Kroner Model 𝐸𝑅𝑃 = [𝐷𝑌 + Expected repricing + 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑔𝑟𝑜𝑤𝑡ℎ 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒] − 𝑟𝑓 𝐸𝑅𝑃 = [𝐷𝑌 + Δ(𝑃⁄𝐸 ) + 𝑖 + 𝑔 − Δ𝑆] − 𝑟𝑓 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑔𝑟𝑜𝑤𝑡ℎ 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 = 𝑖 + 𝑔 − Δ𝑆 where: 𝐷𝑌 = Dividend yield of market index Δ(𝑃⁄𝐸 ) = Expected growth rate in P/E 𝑖 = Expected inflation = 1+𝑌𝑇𝑀𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦 𝑏𝑜𝑛𝑑 1+𝑌𝑇𝑀𝑇𝐼𝑃𝑆 −1 𝑔 = Expected growth rate in real earnings per share Δ𝑆 = Expected change in shares outstanding (Δ𝑆 > 0 for share issuance; Δ𝑆 < 0 for share buyback) Cost of Equity Gordon Growth Model 𝑟𝑒 = 𝐷1 +𝑔 𝑃0 Two-Stage DDM 𝑛 𝑃0 = ∑ 𝑖=1 𝐷𝑡 𝑃𝑛 + (1 + 𝑟𝑒 )𝑡 (1 + 𝑟𝑒 )𝑛 Bond Yield Plus Risk Premium Approach (BYPRP) 𝑟𝑒 = 𝑟𝑑 + 𝑅𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 where 𝑟𝑑 = Cost of company’s long-term debt Capital Asset Pricing Model (CAPM) 𝑟𝑒 = 𝑟𝑓 + 𝛽 × 𝐸𝑅𝑃 21 CFA Level 2 (2026) Formula Sheet by Fabian Moa Fama-French model Three-factor model 𝑟𝑒 = 𝑟𝑓 + 𝛽1 𝐸𝑅𝑃 + 𝛽2 𝑆𝑀𝐵 + 𝛽3 𝐻𝑀𝐿 Five-factor model 𝑟𝑒 = 𝑟𝑓 + 𝛽1 𝐸𝑅𝑃 + 𝛽2 𝑆𝑀𝐵 + 𝛽3 𝐻𝑀𝐿 + 𝛽4 𝑅𝑀𝑊 + 𝛽5 𝐶𝑀𝐴 where: 𝑆𝑀𝐵 = Size premium 𝐻𝑀𝐿 = Value premium 𝑅𝑀𝑊 = Profitability premium 𝐶𝑀𝐴 = Investment premium Expanded CAPM 𝑟𝑒 = 𝑟𝑓 + 𝛽𝑝𝑒𝑒𝑟 (𝐸𝑅𝑃) + 𝑆𝑃 + 𝑆𝐶𝑅𝑃 Build-Up Approach 𝑟𝑒 = 𝑟𝑓 + 𝐸𝑅𝑃 + 𝑆𝑃 + 𝑆𝐶𝑅𝑃 + 𝐼𝑃 where: 𝑆𝑃 = Size premium (for smaller, privately held companies) 𝐼𝑃 = Industry risk premium 𝑆𝐶𝑅𝑃 = Company-specific risk premium Country Spread Model 𝐸𝑅𝑃 = 𝐸𝑅𝑃 𝑓𝑜𝑟 𝑎 + 𝜆 × 𝐶𝑜𝑢𝑛𝑡𝑟𝑦 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑 𝑚𝑎𝑟𝑘𝑒𝑡 where: 𝜆 = Level of exposure of the company in the local country 𝐶𝑜𝑢𝑛𝑡𝑟𝑦 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 = 𝑆𝑜𝑣𝑒𝑟𝑒𝑖𝑔𝑛 𝑦𝑖𝑒𝑙𝑑 𝑠𝑝𝑟𝑒𝑎𝑑 𝑌𝑖𝑒𝑙𝑑 𝑜𝑛 𝑒𝑚𝑒𝑟𝑔𝑖𝑛𝑔 𝑚𝑎𝑟𝑘𝑒𝑡 𝑏𝑜𝑛𝑑𝑠 𝑆𝑜𝑣𝑒𝑟𝑒𝑖𝑔𝑛 𝑦𝑖𝑒𝑙𝑑 𝑌𝑖𝑒𝑙𝑑 𝑜𝑛 𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑 𝑚𝑎𝑟𝑘𝑒𝑡 = (𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑒𝑑 𝑖𝑛 𝑡ℎ𝑒 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦 − 𝑔𝑜𝑣𝑒𝑟𝑛𝑚𝑒𝑛𝑡 𝑏𝑜𝑛𝑑𝑠 𝑠𝑝𝑟𝑒𝑎𝑑 𝑜𝑓 𝑡ℎ𝑒 𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑 𝑚𝑎𝑟𝑘𝑒𝑡) 22 CFA Level 2 (2026) Formula Sheet by Fabian Moa Aswath Damodaran’s CRP 𝐶𝑜𝑢𝑛𝑡𝑟𝑦 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 = 𝑆𝑜𝑣𝑒𝑟𝑒𝑖𝑔𝑛 𝑦𝑖𝑒𝑙𝑑 𝑠𝑝𝑟𝑒𝑎𝑑 × 𝜎𝐸𝑞𝑢𝑖𝑡𝑦 𝜎𝐵𝑜𝑛𝑑 where: 𝜎𝐸𝑞𝑢𝑖𝑡𝑦 = Volatility of the local country’s equity market 𝜎𝐵𝑜𝑛𝑑 = Volatility of the local country’s bond market International CAPM 𝐸(𝑟𝑒 ) = 𝑟𝑓 + 𝛽𝐺 [𝐸(𝑟𝑔𝑚 ) − 𝑟𝑓 ] + 𝛽𝐶 [𝐸(𝑟𝐶 ) − 𝑟𝑓 ] where: 𝐸(𝑟𝑔𝑚 ) − 𝑟𝑓 = Risk premium of a global index 𝑟𝐶 = Wealth-weighted foreign currency index return Learning Module 4 | Corporate Restructuring Evaluating Materiality Based on Size For Acquisition/Divestiture: 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡𝑟𝑎𝑛𝑠𝑎𝑐𝑡𝑖𝑜𝑛 𝐸𝑛𝑡𝑒𝑟𝑝𝑟𝑖𝑠𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑎𝑐𝑞𝑢𝑖𝑟𝑖𝑛𝑔 𝑐𝑜𝑚𝑝𝑎𝑛𝑦 For Cost Restructuring: 𝐶𝑜𝑠𝑡 𝑠𝑎𝑣𝑖𝑛𝑔𝑠 𝑆𝑎𝑙𝑒𝑠 Premium Paid Analysis 𝑇𝑎𝑘𝑒𝑜𝑣𝑒𝑟 𝑝𝑟𝑒𝑚𝑖𝑢𝑚, 𝑃𝑅𝑀 = 𝐷𝑃 − 𝑆𝑃 𝑆𝑃 where: 𝐷𝑃 = Deal price per share of the target company 𝑆𝑃 = Unaffected stock price of the target company (i.e., pre-announcement) 23 CFA Level 2 (2026) Formula Sheet by Fabian Moa VOLUME 5: EQUITY VALUATION Learning Module 1 | Equity Valuation Applications and Processes VE – P = (V – P) + (VE – V) where: 𝑉𝐸 = Estimated intrinsic value 𝑃 = Market price 𝑉 = Intrinsic value Conglomerate discount = Sum-of-the-parts value – Market value Learning Module 2 | Discounted Dividend Valuation Discounted Dividend Valuation 𝑛 𝑉0 = ∑ 𝑡=1 𝑉0 = 𝐶𝐹𝑡 (1 + 𝑟)𝑡 𝐷1 𝐷2 𝐷𝑛 𝑃𝑛 + + ⋯ + + (1 + 𝑟)1 (1 + 𝑟)2 (1 + 𝑟)𝑛 (1 + 𝑟)𝑛 Gordon Growth Model 𝐷1 𝐷0 (1 + 𝑔) 𝑉0 = = 𝑟−𝑔 𝑟−𝑔 Fixed-rate perpetual preferred stock 𝐷 𝑉0 = 𝑟 Value of stock = Value of a company + Present value of growth with zero-growth opportunities (PVGO) 𝐸1 𝑉0 = + 𝑃𝑉𝐺𝑂 𝑟 𝑉0 𝑃0 1 𝑃𝑉𝐺𝑂 = = + 𝐸1 𝐸1 𝑟 𝐸1 If dividend and earnings growth rate is constant, 𝐷1 𝑟= +𝑔 𝑃0 24 CFA Level 2 (2026) Formula Sheet by Fabian Moa Two-Stage Dividend Discount Model 𝑛 𝑉0 = ∑ 𝑡=1 𝐷0 (1 + 𝑔𝑠 )𝑡 𝐷0 (1 + 𝑔𝑠 )𝑛 (1 + 𝑔𝐿 ) + (1 + 𝑟)𝑡 (1 + 𝑟)𝑛 (𝑟 − 𝑔𝐿 ) Video: https://youtu.be/7vXWsTKiSPE The H-Model 𝑉0 = 𝐷0 (1 + 𝑔𝐿 ) + 𝐷0 𝐻(𝑔𝑆 − 𝑔𝐿 ) 𝑟 − 𝑔𝐿 where: 𝐻 = half-life in years of the high-growth period 𝑔𝑆 = Short-term growth-rate 𝑔𝐿 = Long-term growth rate Video: https://youtu.be/IAMFZXSPKOY PRAT model Sustainable growth rate, 𝑔 = 𝑏 × 𝑅𝑂𝐸 Video: https://youtu.be/MnfRRRhuGpA 𝑔= 𝑁𝐼 − 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 𝑁𝐼 𝑆𝑎𝑙𝑒𝑠 𝑇𝐴 × × × 𝑁𝐼 𝑆𝑎𝑙𝑒𝑠 𝑇𝐴 𝑇𝐸 Learning Module 3 | Free Cash Flow Valuation Free Cash Flow to the Firm (FCFF) Valuation Approach ∞ 𝐹𝑖𝑟𝑚 𝑉𝑎𝑙𝑢𝑒 = ∑ 𝑡=1 𝐹𝐶𝐹𝐹𝑡 (1 + 𝑊𝐴𝐶𝐶)𝑡 If non-operating assets = 0 Equity Value = Firm Value – Market Value of Debt FCFE Valuation Approach ∞ 𝐸𝑞𝑢𝑖𝑡𝑦 𝑉𝑎𝑙𝑢𝑒 = ∑ 𝑡=1 𝐹𝐶𝐹𝐸𝑡 (1 + 𝑟)𝑡 25 CFA Level 2 (2026) Formula Sheet by Fabian Moa Single-Stage (Constant Growth) FCFF and FCFE Model FCFF Valuation Approach 𝐹𝑖𝑟𝑚 𝑉𝑎𝑙𝑢𝑒 = 𝐹𝐶𝐹𝐹1 𝐹𝐶𝐹𝐹0 (1 + 𝑔) = 𝑊𝐴𝐶𝐶 − 𝑔 𝑊𝐴𝐶𝐶 − 𝑔 FCFE Valuation Approach 𝐸𝑞𝑢𝑖𝑡𝑦 𝑉𝑎𝑙𝑢𝑒 = 𝐹𝐶𝐹𝐸1 𝐹𝐶𝐹𝐸0 (1 + 𝑔) = 𝑟−𝑔 𝑟−𝑔 Free cash flow to the Firm, FCFF FCFF = NI + NCC + Int(1 – Tax Rate) – FCInv – WCInv = CFO + Int(1 – Tax Rate) – FCInv = EBIT(1 – Tax Rate) + Dep – FCInv – WCInv = EBITDA(1 – Tax Rate) + Dep(Tax Rate) – FCInv – WCInv where: NI = Net income available to common shareholders NCC = Net noncash charges (e.g. depreciation) Int = Interest expense FCInv = Fixed capital investments = Maintenance Capex + Growth Capex = Δ𝐺𝑟𝑜𝑠𝑠 𝑃𝑃𝐸 = Δ𝑁𝑒𝑡 𝑃𝑃𝐸 + 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 WCInv = Investment in working capital Free cash flow to the Equity, FCFE FCFE = FCFF – Int(1 – Tax Rate) + Net borrowing = 𝑁𝐼 + 𝑁𝐶𝐶 − 𝐹𝐶𝐼𝑛𝑣 − 𝑊𝐶𝐼𝑛𝑣 + 𝑁𝑒𝑡 𝑏𝑜𝑟𝑟𝑜𝑤𝑖𝑛𝑔 = CFO – FCInv + Net borrowing where: Net borrowing = Debt issued – Debt repaid Video: https://youtu.be/rtIvIy6Fl0A If (FCInv – Dep) and WCInv funded using Debt (based on debt ratio): FCFE = NI + Dep – FCInv – WCInv + Net borrowing where: Net borrowing = DR(FCInv – Dep) + DR(WCInv) 𝐷𝑒𝑏𝑡 𝐷𝑅 = 𝐷𝑒𝑏𝑡 𝑟𝑎𝑡𝑖𝑜 = 𝐴𝑠𝑠𝑒𝑡𝑠 26 CFA Level 2 (2026) Formula Sheet by Fabian Moa If company issues preferred shares: FCFF = CFO + Int(1 – Tax Rate) + Preferred dividends – FCInv Two-Stage Free Cash Flow Models 𝑛 𝐹𝑖𝑟𝑚 𝑣𝑎𝑙𝑢𝑒 = ∑ 𝑡=1 𝐹𝐶𝐹𝐹𝑡 𝐹𝐶𝐹𝐹𝑛+1 1 + [ ] 𝑡 (1 + 𝑊𝐴𝐶𝐶) (𝑊𝐴𝐶𝐶 − 𝑔) (1 + 𝑊𝐴𝐶𝐶)𝑛 𝑛 𝐸𝑞𝑢𝑖𝑡𝑦 𝑣𝑎𝑙𝑢𝑒 = ∑ 𝑡=1 𝐹𝐶𝐹𝐸𝑡 𝐹𝐶𝐹𝐸𝑛+1 1 + [ ] 𝑡 (1 + 𝑟) (𝑟 − 𝑔) (1 + 𝑟)𝑛 Value of Firm = Value of operating assets + Value of nonoperating assets (PV of FCFF) Learning Module 4 | Market-Based Valuation Price and Enterprise Value Multiples Enterprise value, EV = Market value of common stock + Market value of preferred equity + Market value of debt + Minority interest – Cash and Short-term investments Actual Justified Trailing P/E 𝑀𝑎𝑟𝑘𝑒𝑡 𝑝𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 𝐸𝑃𝑆 𝑜𝑣𝑒𝑟 𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠 12 𝑚𝑜𝑛𝑡ℎ𝑠 (1 − 𝑏)(1 + 𝑔) 𝑟−𝑔 Leading P/E 𝑀𝑎𝑟𝑘𝑒𝑡 𝑝𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 𝐹𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝑒𝑑 𝐸𝑃𝑆 𝑜𝑣𝑒𝑟 𝑛𝑒𝑥𝑡 12 𝑚𝑜𝑛𝑡ℎ𝑠 1−𝑏 𝑟−𝑔 P/B 𝑀𝑎𝑟𝑘𝑒𝑡 𝑝𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 𝐵𝑜𝑜𝑘 𝑣𝑎𝑙𝑢𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 𝑅𝑂𝐸 − 𝑔 𝑟−𝑔 Video: https://youtu.be/c0vmCUtDpZs 𝑉0 𝐸0 (1 − 𝑏)(1 + 𝑔) = × 𝑆0 𝑆0 𝑟−𝑔 P/S 𝑀𝑎𝑟𝑘𝑒𝑡 𝑝𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 𝑆𝑎𝑙𝑒𝑠 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 27 or 𝑉1 𝐸1 1 − 𝑏 = × 𝑆1 𝑆1 𝑟 − 𝑔 CFA Level 2 (2026) Formula Sheet by Fabian Moa Actual Justified 𝑟−𝑔 1+𝑔 Trailing D/P 4 × 𝑀𝑜𝑠𝑡 𝑟𝑒𝑐𝑒𝑛𝑡 𝑞𝑢𝑎𝑟𝑡𝑒𝑟𝑙𝑦 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑀𝑎𝑟𝑘𝑒𝑡 𝑝𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 Leading D/P 𝐹𝑜𝑟𝑒𝑐𝑎𝑠𝑡 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 𝑜𝑣𝑒𝑟 𝑡ℎ𝑒 𝑛𝑒𝑥𝑡 𝑦𝑒𝑎𝑟 𝑀𝑎𝑟𝑘𝑒𝑡 𝑝𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 𝑟−𝑔 𝐸𝑃𝑆 𝑃𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 𝑟−𝑔 (1 − 𝑏)(1 + 𝑔) Earnings yield Underlying Earnings = Net income – non recurring gains + non recurring loss Normalized Earnings Method 1: Average EPS Approach 𝑛 1 Normalized EPS = ∑ 𝐸𝑃𝑆𝑖 𝑛 𝑖=1 Method 2: Average ROE Approach 𝑛 1 Normalized EPS = ∑ 𝑅𝑂𝐸𝑖 × 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐵𝑜𝑜𝑘 𝑣𝑎𝑙𝑢𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 𝑛 𝑖=1 Price-to-Earnings Growth (PEG) Ratio 𝑃𝐸𝐺 𝑟𝑎𝑡𝑖𝑜 = 𝑃/𝐸 𝑟𝑎𝑡𝑖𝑜 𝑔 (𝑖𝑛 %) Momentum Indicators Earnings surprise = Reported EPS – Expected EPS 𝑺𝒄𝒂𝒍𝒆𝒅 𝒆𝒂𝒓𝒏𝒊𝒏𝒈𝒔 𝒔𝒖𝒓𝒑𝒓𝒊𝒔𝒆 = 𝑅𝑒𝑝𝑜𝑟𝑡𝑒𝑑 𝐸𝑃𝑆 − 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝐸𝑃𝑆 𝜎(𝐴𝑛𝑎𝑙𝑦𝑠𝑡 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡 𝐸𝑃𝑆) 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑆𝑢𝑟𝑝𝑟𝑖𝑠𝑒 Standardized unexpected earnings (SUE) = 𝜎(𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑆𝑢𝑟𝑝𝑟𝑖𝑠𝑒) Portfolio P/E 𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 ℎ𝑎𝑟𝑚𝑜𝑛𝑖𝑐 𝑚𝑒𝑎𝑛 = where: 𝑤𝑖 = Weight of stock i in portfolio 𝑋𝑖 = P/E of stock i 28 1 ∑𝑛𝑖=1 𝑤𝑖 𝑋𝑖 CFA Level 2 (2026) Formula Sheet by Fabian Moa Learning Module 5 | Residual Income Valuation Economic Value Added (EVA) 𝐸𝑉𝐴𝑡 = 𝐸𝐵𝐼𝑇𝑡 (1 − 𝑇) − (𝑊𝐴𝐶𝐶 × 𝐼𝑛𝑣𝑒𝑠𝑡𝑒𝑑 𝐶𝑎𝑝𝑖𝑡𝑎𝑙𝑡−1 ) Market Value Added (MVA) 𝑀𝑉𝐴𝑡 = 𝑀𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝐹𝑖𝑟𝑚𝑡 − 𝐼𝑛𝑣𝑒𝑠𝑡𝑒𝑑 𝐶𝑎𝑝𝑖𝑡𝑎𝑙𝑡 Residual Income, RI 𝑅𝐼𝑡 = 𝐸𝑡 − (𝑟 × 𝐵𝑡−1 ) = (𝑅𝑂𝐸 − 𝑟) × 𝐵𝑡−1 Residual Income Model 𝑅𝐼1 𝑅𝐼2 𝑅𝐼3 𝑉0 = 𝐵0 + [ + + +⋯] (1 + 𝑟)1 (1 + 𝑟)2 (1 + 𝑟)3 Video: https://youtu.be/O0KTBkEtP9M Single-stage residual income valuation model (𝑅𝑂𝐸 − 𝑟) × 𝐵0 𝑅𝐼1 𝑉0 = 𝐵0 + = 𝐵0 + 𝑟−𝑔 𝑟−𝑔 Video: https://youtu.be/82GJu5umrB0 Tobin’s Q 𝑇𝑜𝑏𝑖𝑛′ 𝑠 𝑄 = 𝑀𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑑𝑒𝑏𝑡 + 𝑀𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑒𝑞𝑢𝑖𝑡𝑦 𝑅𝑒𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑡𝑜𝑡𝑎𝑙 𝑎𝑠𝑠𝑒𝑡𝑠 Continuing Residual Income 𝑇−1 𝑉0 = 𝐵0 + ∑ 𝑡=1 𝑅𝐼𝑡 𝑅𝐼𝑇 + (1 + 𝑟)𝑡 (1 + 𝑟 − 𝜔)(1 + 𝑟)𝑇−1 0≤𝜔≤1 𝜔 = Persistence factor If RI declines to Long-run level in mature industry, with premium over book value 𝑇 𝑉0 = 𝐵0 + ∑ 𝑡=1 𝑅𝐼𝑡 𝑃𝑇 − 𝐵𝑇 + 𝑡 (1 + 𝑟) (1 + 𝑟)𝑇 Video: https://youtu.be/vhRW3q70E0w Clean surplus relationship: 𝐵𝑡 = 𝐵𝑡−1 + 𝐸𝑡 − 𝐷𝑖𝑣𝑡 29 CFA Level 2 (2026) Formula Sheet by Fabian Moa Learning Module 6 | Private Company Valuation Capitalized Cash Flow Method (CCM) 𝐹𝑖𝑟𝑚 𝑣𝑎𝑙𝑢𝑒 = 𝐹𝐶𝐹𝐹1 𝐹𝐶𝐹𝐹0 (1 + 𝑔) = → 𝑊𝐴𝐶𝐶 − 𝑔 𝑊𝐴𝐶𝐶 − 𝑔 𝐹𝑖𝑟𝑚 𝑣𝑎𝑙𝑢𝑒 = 𝐸𝐵𝐼𝑇1 (1 − 𝑡)(1 − 𝑅𝐼𝑅) 𝑊𝐴𝐶𝐶 − 𝑔 𝑅𝑒𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑟𝑎𝑡𝑒, 𝑅𝐼𝑅 = 𝐸𝑞𝑢𝑖𝑡𝑦 𝑣𝑎𝑙𝑢𝑒 = 𝐸𝑞𝑢𝑖𝑡𝑦 𝐹𝑖𝑟𝑚 𝑀𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 = − 𝑜𝑓 𝐷𝑒𝑏𝑡 𝑣𝑎𝑙𝑢𝑒 𝑣𝑎𝑙𝑢𝑒 𝑔 𝑊𝐴𝐶𝐶 𝐹𝐶𝐹𝐸0 (1 + 𝑔) 𝑟−𝑔 Excess Earnings Method (EEM) 𝑬𝒙𝒄𝒆𝒔𝒔 𝑁𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 = − (𝑊𝑜𝑟𝑘𝑖𝑛𝑔 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 × 𝑟𝑊𝐶 ) − (𝐹𝑖𝑥𝑒𝑑 𝐴𝑠𝑠𝑒𝑡𝑠 × 𝑟𝐹𝐴 ) 𝒆𝒂𝒓𝒏𝒊𝒏𝒈𝒔 𝑒𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑖𝑛𝑡𝑎𝑛𝑔𝑖𝑏𝑙𝑒 𝑎𝑠𝑠𝑒𝑡𝑠 (𝐸𝑥𝑐𝑒𝑠𝑠 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠)0 (1 + 𝑔) = (𝑅𝑒𝑠𝑖𝑑𝑢𝑎𝑙 𝑣𝑎𝑙𝑢𝑒) 𝑟𝑅𝐼 − 𝑔 Value of the firm = Working capital + Fixed assets + Intangible Assets where: 𝑔 = Growth of excess earnings 𝑟𝑅𝐼 = Required return on intangible assets Video: https://youtu.be/137ga1xgAbA Discount for Lack of Control and Marketability Discount for Lack of Control (DLOC) 𝐷𝐿𝑂𝐶 = 1 − 1 1 + 𝐶𝑜𝑛𝑡𝑟𝑜𝑙 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 Total discount = 1 – (1 – DLOC)(1 – DLOM) 𝐷𝐿𝑂𝑀 = 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐴𝑇𝑀 𝑜𝑝𝑡𝑖𝑜𝑛 𝑆ℎ𝑎𝑟𝑒 𝑝𝑟𝑖𝑐𝑒 where Strike price is based on forward price, 𝐹 = 𝑆0 𝑒 𝑟𝑓 ×𝑇 30 CFA Level 2 (2026) Formula Sheet by Fabian Moa Levered and Unlevered Beta Given the beta of a comparable company (𝛽𝑙𝑒𝑣𝑒𝑟𝑒𝑑 ), the unlevered beta: 𝛽𝑢𝑛𝑙𝑒𝑣𝑒𝑟𝑒𝑑 = 𝛽𝑙𝑒𝑣𝑒𝑟𝑒𝑑 𝐷𝑒𝑏𝑡𝑝𝑙𝑐 [1 + (1 − 𝑡𝑝𝑙𝑐 ) (𝐸𝑞𝑢𝑖𝑡𝑦 )] 𝑝𝑙𝑐 ∗ The beta of the private company (𝛽𝑙𝑒𝑣𝑒𝑟𝑒𝑑 ), 𝐷𝑒𝑏𝑡𝑝𝑣𝑡 ∗ 𝛽𝑙𝑒𝑣𝑒𝑟𝑒𝑑 = 𝛽𝑢𝑛𝑙𝑒𝑣𝑒𝑟𝑒𝑑 [1 + (1 − 𝑡𝑝𝑣𝑡 ) ( )] 𝐸𝑞𝑢𝑖𝑡𝑦𝑝𝑣𝑡 31 CFA Level 2 (2026) Formula Sheet by Fabian Moa VOLUME 6: FIXED INCOME Learning Module 1 | The Term Structure and Interest Rate Dynamics Forward Pricing Model 𝐷𝐹𝐵 = 𝐷𝐹𝐴 × 𝐹𝐴,𝐵−𝐴 where: 𝐷𝐹𝐵 = 1 (1 + 𝑧𝐵 )𝐵 𝐹𝐴,𝐵−𝐴 = 1 (1 + 𝑓𝐴,𝐵−𝐴 ) 𝐵−𝐴 Forward Rate Model (1 + 𝑧𝐵 )𝐵 = (1 + 𝑧𝐴 ) 𝐴 (1 + 𝑓𝐴,𝐵−𝐴 ) 𝐵−𝐴 where: 𝑧𝐵 = Spot rate for period 𝐵 𝑓𝐴,𝐵−𝐴 = (𝐵 − 𝐴) forward rate that starts in period 𝐴 Calculating spot rate from one-period forward rates 𝑧𝑇 = [(1 + 𝑧1 )(1 + 𝑓1,1 )(1 + 𝑓2,1 ) … (1 + 𝑓𝑇−1,1 )] 1⁄𝑇 −1 Boostrapping Spot Rates From Par Rates Video: https://youtu.be/-FnweFO172Q Fixed swap rate 𝑠𝑇 = 1 − 𝐷𝐹𝑇 1 − 𝐷𝑖𝑠𝑐𝑜𝑢𝑛𝑡 𝐹𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 𝐿𝑎𝑠𝑡 𝑃𝑎𝑦𝑚𝑒𝑛𝑡 = ∑𝑇𝑡=1 𝐷𝐹𝑡 𝑆𝑢𝑚 𝑜𝑓 𝐷𝑖𝑠𝑐𝑜𝑢𝑛𝑡 𝐹𝑎𝑐𝑡𝑜𝑟𝑠 Swap spread = YTM of swap rate – YTM of government bond (same maturity) TED spread = LIBOR – YTM of T-bill (same maturity) LIBOR-OIS spread = LIBOR – OIS Fixed rate 32 CFA Level 2 (2026) Formula Sheet by Fabian Moa For Parallel shifts in yield curve: %∆𝑃𝑉 = −𝑀𝑜𝑑𝐷𝑢𝑟 × ∆𝑌𝑇𝑀 ∆𝑃𝑉 = −𝑀𝑜𝑑𝐷𝑢𝑟 × ∆𝑌𝑇𝑀 × 𝑃𝑉0 %∆𝑃𝑉 = −𝐸𝑓𝑓𝐷𝑢𝑟 × ∆𝐶𝑢𝑟𝑣𝑒 ∆𝑃𝑉 = −𝐸𝑓𝑓𝐷𝑢𝑟 × ∆𝐶𝑢𝑟𝑣𝑒 × 𝑃𝑉0 Non-parallel shifts (i.e. change in slope or curvature): %∆𝑃𝑉 = −𝐾𝑒𝑦𝑅𝑎𝑡𝑒𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛 × ∆𝐾𝑒𝑦 𝑅𝑎𝑡𝑒 Bond Risk Premium 𝐵𝑜𝑛𝑑 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 = 𝑌𝑖𝑒𝑙𝑑 𝑜𝑓 𝑑𝑒𝑓𝑎𝑢𝑙𝑡 𝑓𝑟𝑒𝑒 𝑌𝑖𝑒𝑙𝑑 𝑜𝑓 𝑑𝑒𝑓𝑎𝑢𝑙𝑡 𝑓𝑟𝑒𝑒 − 𝑙𝑜𝑛𝑔 𝑡𝑒𝑟𝑚 𝑏𝑜𝑛𝑑 𝑠ℎ𝑜𝑟𝑡 𝑡𝑒𝑟𝑚 𝑏𝑜𝑛𝑑 Learning Module 2 | The Arbitrage-Free Valuation Framework Arbitrage-free Value of Bond 𝑉0 = 𝐶 𝐶 𝐹𝑉 + 𝐶 + + ⋯+ 1 2 (1 + 𝑧1 ) (1 + 𝑧2 ) (1 + 𝑧𝑛 )𝑛 where: 𝑧𝑛 = Spot rate for period n Backward Induction Valuation Methodology 𝐵𝑜𝑛𝑑 𝑣𝑎𝑙𝑢𝑒 𝑎𝑡 𝑎𝑛𝑦 𝑛𝑜𝑑𝑒 = (0.5 × 𝑉𝐻 + 0.5 × 𝑉𝐿 ) + 𝐶 1+𝑖 where: 𝑉𝐻 = bond’s value if the higher forward rate is realized one year hence 𝑉𝐿 = bond’s value if the lower forward rate is realized one year hence 𝐶 = coupon payment that is not dependent on interest rates Video (Backward Induction Valuation): https://youtu.be/DhAVQ3hIXlQ Video (Backward Induction with Financial Calculator): https://youtu.be/FycX2UwJxCM Video (Pathwise Valuation): https://youtu.be/3oM-220oi7o Binomial Interest Rate Tree 𝑖1,𝐻 = 𝑖1,𝐿 𝑒 2𝜎 𝑖2,𝐻𝐻 = 𝑖2,𝐿𝐿 𝑒 4𝜎 𝑖3,𝐻𝐻𝐻 = 𝑖3,𝐿𝐿𝐿 𝑒 6𝜎 𝑖2,𝐻𝐿 = 𝑖2,𝐿𝐿 𝑒 2𝜎 𝑖3,𝐻𝐻𝐿 = 𝑖3,𝐿𝐿𝐿 𝑒 4𝜎 33 𝑖3,𝐿𝐿𝐻 = 𝑖3,𝐿𝐿𝐿 𝑒 2𝜎 CFA Level 2 (2026) Formula Sheet by Fabian Moa Equilibrium Term Structure Models Cox-Ingersoll-Ross (CIR) Model 𝑑𝑟 = 𝑘(𝜃 − 𝑟𝑡 )𝑑𝑡 + 𝜎√𝑟𝑡 𝑑𝑧 Vasicek Model 𝑑𝑟 = 𝑘(𝜃 − 𝑟𝑡 )𝑑𝑡 + 𝜎𝑑𝑧 where: 𝑘 = Speed of reversion (> 0) 𝜃 = Long-run interest rate 𝜎 = Interest rate volatility Arbitrage Free Models Ho-Lee Model 𝑑𝑟𝑡 = 𝜃𝑡 𝑑𝑡 + 𝜎𝑑𝑧𝑡 Kalotay-Williams-Fabozzi (KWF) Model 𝑑(ln 𝑟𝑡 ) = 𝜃𝑡 𝑑𝑡 + 𝜎𝑑𝑧𝑡 where: 𝜃𝑡 = Time-dependent drift term Learning Module 3 | Valuation and Analysis - Bonds with Embedded Options Callable and Putable Bonds Value of callable bond = Value of straight bond – Value of issuer call option Value of putable bond = Value of straight bond + Value of investor put option Video (Valuing a callable bond): https://youtu.be/lWLSodiqZaM Video (Valuing a putable bond): https://youtu.be/qmUnAtpXIAg 𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 = (𝑃𝑉− ) − (𝑃𝑉+ ) 2 × (Δ𝐶𝑢𝑟𝑣𝑒) × 𝑃𝑉0 𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑐𝑜𝑛𝑣𝑒𝑥𝑖𝑡𝑦 = (𝑃𝑉− ) + (𝑃𝑉+ ) − 2 × 𝑃𝑉0 𝑃𝑉0 × (Δ𝐶𝑢𝑟𝑣𝑒)2 34 CFA Level 2 (2026) Formula Sheet by Fabian Moa Capped and Floored Floaters Value of capped floater = Value of straight floater – Value of cap Value of floored floater = Value of straight floater + Value of floor Video (Valuing a capped floater): https://youtu.be/d4LNMdXV9vU Video (Valuing a floored floater): https://youtu.be/YJZU0THHBNE Convertible Bonds 𝐶𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑈𝑛𝑑𝑒𝑟𝑙𝑦𝑖𝑛𝑔 𝐶𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 = × 𝑠ℎ𝑎𝑟𝑒 𝑝𝑟𝑖𝑐𝑒 𝑣𝑎𝑙𝑢𝑒 𝑟𝑎𝑡𝑖𝑜 𝑴𝒊𝒏𝒊𝒎𝒖𝒎 𝒗𝒂𝒍𝒖𝒆 𝐶𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑢𝑛𝑑𝑒𝑟𝑙𝑦𝑖𝑛𝑔 = 𝑴𝒂𝒙 [ , ] 𝑜𝑓 𝑐𝑜𝑛𝑣𝑒𝑟𝑡𝑖𝑏𝑙𝑒 𝑏𝑜𝑛𝑑 𝑆𝑡𝑟𝑎𝑖𝑔ℎ𝑡 𝑏𝑜𝑛𝑑 𝑣𝑎𝑙𝑢𝑒 𝑀𝑎𝑟𝑘𝑒𝑡 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝐶𝑜𝑛𝑣𝑒𝑟𝑡𝑖𝑏𝑙𝑒 𝑏𝑜𝑛𝑑 𝑝𝑟𝑖𝑐𝑒 = 𝑝𝑟𝑖𝑐𝑒 𝐶𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜 𝑀𝑎𝑟𝑘𝑒𝑡 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑀𝑎𝑟𝑘𝑒𝑡 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑈𝑛𝑑𝑒𝑟𝑙𝑦𝑖𝑛𝑔 𝑠ℎ𝑎𝑟𝑒 = − 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 𝑝𝑟𝑖𝑐𝑒 𝑝𝑟𝑖𝑐𝑒 𝑀𝑎𝑟𝑘𝑒𝑡 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑀𝑎𝑟𝑘𝑒𝑡 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 = 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝑟𝑎𝑡𝑖𝑜 𝑈𝑛𝑑𝑒𝑟𝑙𝑦𝑖𝑛𝑔 𝑠ℎ𝑎𝑟𝑒 𝑝𝑟𝑖𝑐𝑒 𝑃𝑟𝑒𝑚𝑖𝑢𝑚 𝑜𝑣𝑒𝑟 𝐶𝑜𝑛𝑣𝑒𝑟𝑡𝑖𝑏𝑙𝑒 𝑏𝑜𝑛𝑑 𝑝𝑟𝑖𝑐𝑒 = −1 𝑆𝑡𝑟𝑎𝑖𝑔ℎ𝑡 𝑣𝑎𝑙𝑢𝑒 𝑆𝑡𝑟𝑎𝑖𝑔ℎ𝑡 𝑣𝑎𝑙𝑢𝑒 Convertible Bond (With No Additional Options) 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑐𝑎𝑙𝑙 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 = + 𝑜𝑝𝑡𝑖𝑜𝑛 𝑜𝑛 𝑐𝑜𝑛𝑣𝑒𝑟𝑡𝑖𝑏𝑙𝑒 𝑏𝑜𝑛𝑑 𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡 𝑏𝑜𝑛𝑑 𝑖𝑠𝑠𝑢𝑒𝑟 ′ 𝑠 𝑠𝑡𝑜𝑐𝑘 Callable Convertible Bond 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 = + 𝑐𝑜𝑛𝑣𝑒𝑟𝑡𝑖𝑏𝑙𝑒 𝑏𝑜𝑛𝑑 𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡 𝑏𝑜𝑛𝑑 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑐𝑎𝑙𝑙 𝑜𝑝𝑡𝑖𝑜𝑛 𝑜𝑛 − 𝑖𝑠𝑠𝑢𝑒𝑟 𝑐𝑎𝑙𝑙 𝑜𝑝𝑡𝑖𝑜𝑛 𝑖𝑠𝑠𝑢𝑒𝑟 ′ 𝑠 𝑠𝑡𝑜𝑐𝑘 Putable Convertible Bond 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 = + 𝑐𝑜𝑛𝑣𝑒𝑟𝑡𝑖𝑏𝑙𝑒 𝑏𝑜𝑛𝑑 𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡 𝑏𝑜𝑛𝑑 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑐𝑎𝑙𝑙 𝑜𝑝𝑡𝑖𝑜𝑛 𝑜𝑛 + 𝑖𝑛𝑣𝑒𝑠𝑡𝑜𝑟 𝑝𝑢𝑡 𝑜𝑝𝑡𝑖𝑜𝑛 𝑖𝑠𝑠𝑢𝑒𝑟 ′ 𝑠 𝑠𝑡𝑜𝑐𝑘 35 CFA Level 2 (2026) Formula Sheet by Fabian Moa Learning Module 4 | Credit Analysis Models 𝐺-𝑠𝑝𝑟𝑒𝑎𝑑 = 𝑌𝑇𝑀 𝑜𝑓 𝐶𝑜𝑟𝑝𝑜𝑟𝑎𝑡𝑒 𝑏𝑜𝑛𝑑 − 𝑌𝑇𝑀 𝑜𝑓 𝐺𝑜𝑣𝑒𝑟𝑛𝑚𝑒𝑛𝑡 𝑏𝑜𝑛𝑑 𝐿𝑜𝑠𝑠 𝑔𝑖𝑣𝑒𝑛 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑅𝑒𝑐𝑜𝑣𝑒𝑟𝑦 = × (1 − ) 𝑒𝑥𝑝𝑜𝑠𝑢𝑟𝑒 𝑑𝑒𝑓𝑎𝑢𝑙𝑡 𝑟𝑎𝑡𝑒 𝐿𝑜𝑠𝑠 𝑅𝑒𝑐𝑜𝑣𝑒𝑟𝑦 =1− 𝑠𝑒𝑣𝑒𝑟𝑖𝑡𝑦 𝑟𝑎𝑡𝑒 Expected Loss = Probability of Default × Loss Given Default 𝐹𝑎𝑖𝑟 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑏𝑜𝑛𝑑 𝐹𝑎𝑖𝑟 𝑣𝑎𝑙𝑢𝑒 𝐶𝑟𝑒𝑑𝑖𝑡 𝑉𝑎𝑙𝑢𝑎𝑡𝑖𝑜𝑛 = − 𝑜𝑓 𝑐𝑟𝑒𝑑𝑖𝑡 𝑟𝑖𝑠𝑘𝑦 𝑏𝑜𝑛𝑑 𝑎𝑠𝑠𝑢𝑚𝑖𝑛𝑔 𝑛𝑜 𝑑𝑒𝑓𝑎𝑢𝑙𝑡 𝐴𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛𝑡 𝐶𝑟𝑒𝑑𝑖𝑡 𝑣𝑎𝑙𝑢𝑎𝑡𝑖𝑜𝑛 𝑎𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛𝑡, 𝑛 𝑛 𝑡=1 𝑡=1 𝐸𝐿𝑡 𝑃𝑂𝐷𝑡 × 𝐿𝐺𝐷𝑡 𝐶𝑉𝐴 = ∑ =∑ 𝑡 (1 + 𝑟𝑓𝑡 ) (1 + 𝑟𝑓𝑡 )𝑡 where: 𝐸𝐿𝑡 = Expected loss of bond at time t 𝑃𝑂𝐷𝑡 = Probability of default of bond at time t 𝐿𝐺𝐷𝑡 = Loss given default at time t = 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝐸𝑥𝑝𝑜𝑠𝑢𝑟𝑒𝑡 − 𝑅𝑒𝑐𝑜𝑣𝑒𝑟𝑦𝑡 𝑟𝑓𝑡 = Risk-free rate at time t 𝑛 = Bond’s remaining tenor 𝐸𝐿𝑡 𝑃𝑉 𝑜𝑓 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑙𝑜𝑠𝑠 𝑓𝑜𝑟 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡 = (1 + 𝑟𝑓𝑡 )𝑡 𝑃𝑂𝐷𝑡 = (1 − 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒)𝑡−1 × 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 Approximation of credit spread ≈ Annual hazard rate × (1 – Recovery rate) Video (Probability of Default): https://youtu.be/e7K4x48Eg4U Video (Valuing a Credit Risky Bond – Zero Interest Rate Volatility): https://youtu.be/2I9bgu-o7aI Video (YTM of Corporate Bonds – Default and Non-Default): https://youtu.be/K253Y7c2Yto Expected percentage price change of a corporate bond ∑ 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑐𝑟𝑒𝑑𝑖𝑡 𝑚𝑖𝑔𝑟𝑎𝑡𝑖𝑜𝑛 × %∆𝑃 where: %∆𝑃 = −𝑀𝑜𝑑𝐷𝑢𝑟 × ∆𝑐𝑟𝑒𝑑𝑖𝑡 𝑠𝑝𝑟𝑒𝑎𝑑 36 CFA Level 2 (2026) Formula Sheet by Fabian Moa Structural Model 𝐴𝑡 = 𝐷(𝑡, 𝑇) + 𝑆𝑡 In terms of… Call options Put options Equity 𝐸(𝑇) = 𝑀𝑎𝑥[𝐴(𝑇) − 𝐾, 0] 𝐸(𝑇) = 𝐴(𝑇) − 𝐾 + 𝑀𝑎𝑥[𝐾 − 𝐴(𝑇), 0] Debt 𝐷(𝑇) = 𝐴(𝑇) − 𝑀𝑎𝑥[𝐴(𝑇) − 𝐾, 0] 𝐷(𝑇) = 𝐾 − 𝑀𝑎𝑥[𝐾 − 𝐴(𝑇), 0] where: 𝑆𝑡 = 𝐸𝑞𝑢𝑖𝑡𝑦 𝑣𝑎𝑙𝑢𝑒 𝑎𝑡 𝑡𝑖𝑚𝑒 𝑡 𝐴𝑇 = 𝐴𝑠𝑠𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝑎𝑡 𝑡𝑖𝑚𝑒 𝑇 𝐾 = 𝐹𝑎𝑐𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑑𝑒𝑏𝑡 Learning Module 5 | Credit Default Swaps 𝐶𝐷𝑆 𝑠𝑝𝑟𝑒𝑎𝑑 ≈ (1 − 𝑅𝑒𝑐𝑜𝑣𝑒𝑟𝑦 𝑅𝑎𝑡𝑒) × 𝑃𝑂𝐷 CDS payout amount = Payout ratio × Notional = (1 − Recovery rate of CTD bond) × Notional Upfront payment = PV of protection leg – PV of premium leg 𝑃𝑉 𝑜𝑓 𝑃𝑉 𝑜𝑓 𝑈𝑝𝑓𝑟𝑜𝑛𝑡 = − 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝐶𝑟𝑒𝑑𝑖𝑡 𝑆𝑝𝑟𝑒𝑎𝑑 𝐹𝑖𝑥𝑒𝑑 𝐶𝑜𝑢𝑝𝑜𝑛 𝐶𝑟𝑒𝑑𝑖𝑡 𝐹𝑖𝑥𝑒𝑑 ) × 𝐶𝐷𝑆 𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛 ≈( − 𝑆𝑝𝑟𝑒𝑎𝑑 𝐶𝑜𝑢𝑝𝑜𝑛 𝑃𝑟𝑖𝑐𝑒 𝑜𝑓 𝐶𝐷𝑆 𝑝𝑒𝑟 100 𝑛𝑜𝑡𝑖𝑜𝑛𝑎𝑙 = 100 − 𝑈𝑝𝑓𝑟𝑜𝑛𝑡 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 % 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 = × 𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛 𝐶𝐷𝑆 𝑝𝑟𝑖𝑐𝑒 𝑠𝑝𝑟𝑒𝑎𝑑 𝑖𝑛 𝑏𝑝𝑠 37 CFA Level 2 (2026) Formula Sheet by Fabian Moa VOLUME 7: DERIVATIVES Learning Module 1 | Pricing and Valuation of Forward Commitments Forward Contracts Forward Pricing: 𝐹0 = 𝑆0 (1 + 𝑟)𝑇 𝐹0 = (𝑆0 + 𝐶𝐶0 − 𝐶𝐵0 )(1 + 𝑟)𝑇 𝐹0 = 𝑆0 𝑒 𝑟𝑐𝑇 𝐹0 = 𝑆0 𝑒 (𝑟𝑐+𝐶𝐶−𝐶𝐵)𝑇 where: 𝑆0 = Current spot price 𝐹0 = Forward price (set today) 𝑟 = Annually compounded risk-free rate 𝑟𝑐 = Continuously compounded risk-free rate 𝐶𝐶0 = PV of Carry cost 𝐶𝐵0 = PV of carry benefits 𝐶𝐶 = Continuously compounded cost of carry 𝐶𝐵 = Continuously compounded carry benefit Forward Valuation (Long Position): 𝑉0 = 0 𝑉𝑡 = 𝐹𝑡 − 𝐹0 𝐹0 = 𝑆𝑡 − 𝑇−𝑡 (1 + 𝑟) (1 + 𝑟)𝑇−𝑡 𝑉𝑇 = 𝑆𝑇 − 𝐹0 38 CFA Level 2 (2026) Formula Sheet by Fabian Moa Forward Rate Agreement (FRA) 𝑳𝒐𝒏𝒈 𝐹𝑅𝐴 𝑝𝑎𝑦𝑜𝑓𝑓 𝑎𝑡 𝒆𝒙𝒑𝒊𝒓𝒂𝒕𝒊𝒐𝒏 𝑜𝑓 𝐹𝑅𝐴 = 𝐹𝑅𝐴0 = ( 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙 × (𝐿𝑚 − 𝐹𝑅𝐴0 ) × 𝑡𝑚 1 + 𝐷𝑚 𝑡𝑚 1 + 𝐿 𝑇 𝑡𝑇 1 − 1) ( ) 1 + 𝐿ℎ 𝑡ℎ 𝑡𝑚 Valuation at time 𝑡 = 𝑔 (prior to FRA expiration): 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙 × (𝐹𝑅𝐴𝑔 − 𝐹𝑅𝐴0 ) × 𝑡𝑚 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐿𝑜𝑛𝑔 𝐹𝑅𝐴 𝑎𝑡 𝑔 = 1 + 𝐷𝑇−𝑔 𝑡𝑇−𝑔 where: 𝐷𝑚 = Discount rate for m periods at t = h ℎ = FRA tenor 𝑚 = Tenor of the underlying rate 𝑇 = ℎ + 𝑚 = Maturity of underlying instrument Video (Pricing an FRA): https://youtu.be/uBmAt_z9f3Y Video (Valuing an FRA): https://youtu.be/AYKRVdaYvxY Fixed Income Forwards and Futures Pricing: 𝑄𝑢𝑜𝑡𝑒𝑑 𝑓𝑢𝑡𝑢𝑟𝑒𝑠 𝐶𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝐹0 = × 𝑓𝑎𝑐𝑡𝑜𝑟 𝑝𝑟𝑖𝑐𝑒 = 𝐹𝑉(𝐵0 + 𝐴𝐼0 ) − 𝐴𝐼𝑇 − 𝐹𝑉𝐶𝐼 Valuation for fixed income forward contracts: 𝑉𝑡 = 𝑃𝑟𝑒𝑠𝑒𝑛𝑡 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑛 𝑓𝑜𝑟𝑤𝑎𝑟𝑑 𝑝𝑟𝑖𝑐𝑒𝑠 = 𝑃𝑉[𝐹𝑡 − 𝐹0 ] Valuation for fixed income futures contracts: 𝑉𝑡 = Price change since previous day’s settlement where: 𝐵0 = Quoted bond price 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑐𝑐𝑟𝑢𝑒𝑑 𝑑𝑎𝑦𝑠 𝑠𝑖𝑛𝑐𝑒 𝑙𝑎𝑠𝑡 𝑐𝑜𝑢𝑝𝑜𝑛 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 𝐴𝑛𝑛𝑢𝑎𝑙 𝑐𝑜𝑢𝑝𝑜𝑛 𝐴𝐼 = × 𝑇𝑜𝑡𝑎𝑙 𝑑𝑎𝑦𝑠 𝑑𝑢𝑟𝑖𝑛𝑔 𝑡ℎ𝑒 𝑐𝑜𝑢𝑝𝑜𝑛 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 𝑝𝑒𝑟𝑖𝑜𝑑 𝐶𝑜𝑢𝑝𝑜𝑛 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 39 CFA Level 2 (2026) Formula Sheet by Fabian Moa Interest Rate Swaps (IRS) Fixed Swap Rate 𝑟𝐹𝐼𝑋 = 1 − 𝑃𝑉𝑛 1 × 𝑛 ∑𝑖=1 𝑃𝑉𝑖 𝐴𝑃 where: 1 𝐷𝑎𝑦𝑠 𝑡𝑜 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦𝑖 1 + 𝑆𝑝𝑜𝑡 𝑟𝑎𝑡𝑒𝑖 ( ) 360 𝐴𝑃 = Accrual period (i.e., payment frequency of swap) 𝑃𝑉𝑖 = Fixed Swap Cash Flow 𝐹𝑆 = 𝐴𝑃 × 𝑟𝐹𝐼𝑋 Pay-fixed, receive-floating IRS 𝑛 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑆𝑤𝑎𝑝 = 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙 × (𝐹𝑆𝑡 − 𝑭𝑺𝟎 ) ∑ 𝑃𝑉𝑖 𝑖=1 Receive-fixed, pay-floating IRS 𝑛 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑆𝑤𝑎𝑝 = 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙 × (𝑭𝑺𝟎 − 𝐹𝑆𝑡 ) ∑ 𝑃𝑉𝑖 𝑖=1 Video (Pricing an Interest Rate Swap) : https://youtu.be/0QvtKZutr5E Video (Valuing an Interest Rate Swap): https://youtu.be/_A2a909etvg Currency Swap Pricing for fixed leg of currency swap in currency 𝑎 and 𝑏 1 − 𝑃𝑉𝑛,𝑎 1 𝑟𝑎 = 𝑛 × ∑𝑖=1 𝑃𝑉𝑖,𝑎 𝐴𝑃 𝑟𝑏 = 1 − 𝑃𝑉𝑛,𝑏 1 × 𝑛 ∑𝑖=1 𝑃𝑉𝑖,𝑏 𝐴𝑃 Fixed Cash Flows 𝐹𝑆𝑎 = 𝐴𝑃 × 𝑟𝑎 𝐹𝑆𝑏 = 𝐴𝑃 × 𝑟𝑏 40 CFA Level 2 (2026) Formula Sheet by Fabian Moa Value of a fixed-for-fixed currency swap (Receive currency 𝑎, Pay currency 𝑏) 𝑉𝐶𝑆 (𝑖𝑛 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦 𝑎) = 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙𝑎 × 𝑉𝑎 − 𝑆𝑡 × 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙𝑏 × 𝑉𝑏 𝑉𝐶𝑆 (𝑖𝑛 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦 𝑏) = 1 × 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙𝑎 × 𝑉𝑎 − 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙𝑏 × 𝑉𝑏 𝑆𝑡 Value of a fixed-for-fixed currency swap (Receive currency 𝑏, Pay currency 𝑎) 𝑉𝐶𝑆 (𝑖𝑛 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦 𝑎) = 𝑆𝑡 × 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙𝑏 × 𝑉𝑏 − 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙𝑎 × 𝑉𝑎 𝑉𝐶𝑆 (𝑖𝑛 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦 𝑏) = 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙𝑏 × 𝑉𝑏 − 1 × 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙𝑎 × 𝑉𝑎 𝑆𝑡 where: 𝑛 𝑉𝑎 = 𝐹𝑆𝑎 ∑ 𝑃𝑉𝑖,𝑎 + 𝑃𝑉𝑛,𝑎 × 𝑃𝑎𝑟𝑎 = 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦 𝑎 𝑙𝑒𝑔 𝑖=1 𝑛 𝑉𝑏 = 𝐹𝑆𝑏 ∑ 𝑃𝑉𝑖,𝑏 + 𝑃𝑉𝑛,𝑏 × 𝑃𝑎𝑟𝑏 = 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦 𝑏 𝑙𝑒𝑔 𝑖=1 𝑆𝑡 = Spot exchange rate at time 𝑡 (quoted as 𝑎⁄𝑏 ) Video (Pricing a currency swap): https://youtu.be/XZlxcVByc00 Video (Valuing a currency swap): https://youtu.be/3h4mElS48aA Equity Swap Value of equity swap (receive fixed-rate, pay equity return) 𝑆𝑡 𝑉𝐸𝑄,𝑡 = 𝑉𝐹𝐼𝑋 (𝐶0 ) − × 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙 − 𝑃𝑉𝑡 (𝑃𝑎𝑟 − 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙) 𝑆𝑡−1 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦 𝐿𝑒𝑔 = 𝑆𝑡 × 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙 𝑆𝑡−1 Cash flow for equity leg = 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙 × 𝑃𝑒𝑟𝑖𝑜𝑑𝑖𝑐 𝑒𝑞𝑢𝑖𝑡𝑦 𝑟𝑒𝑡𝑢𝑟𝑛 where: 𝑉𝐹𝐼𝑋 (𝐶0 ) = Value at time 𝑡 of a fixed-rate bond initiated with coupon 𝐶0 at Time 0 𝑆𝑡 = Current equity index level (on the valuation date) 𝑆𝑡−1 = Equity index level at last reset date 41 CFA Level 2 (2026) Formula Sheet by Fabian Moa Learning Module 2 | Valuation of Contingent Claims Hedge Ratio ℎ𝑐𝑎𝑙𝑙 𝑐+ − 𝑐− = + ≥0 𝑆 − 𝑆− ℎ𝑝𝑢𝑡 = 𝑝+ − 𝑝− ≤0 𝑆+ − 𝑆− No-arbitrage Approach: 𝑐 = ℎ𝑐𝑎𝑙𝑙 𝑆 + 𝑃𝑉(−ℎ𝑐𝑎𝑙𝑙 𝑆 + + 𝑐 + ) = ℎ𝑐𝑎𝑙𝑙 𝑆 + 𝑃𝑉(−ℎ𝑐𝑎𝑙𝑙 𝑆 − + 𝑐 − ) 𝑝 = ℎ𝑝𝑢𝑡 𝑆 + 𝑃𝑉(−ℎ𝑝𝑢𝑡 𝑆 + + 𝑝+ ) = ℎ𝑝𝑢𝑡 𝑆 + 𝑃𝑉(−ℎ𝑝𝑢𝑡 𝑆 − + 𝑝− ) Expectations Approach: 𝜋= (1 + 𝑟) − 𝑑 𝑢−𝑑 where: 𝑢 = Up factor 𝑑 = Down factor 𝑟 = Risk-free rate One-period Binomial Model 𝑐= 𝜋𝑐 + + (1 − 𝜋)𝑐 − 1+𝑟 𝜋𝑝+ + (1 − 𝜋)𝑝− 𝑝= 1+𝑟 where: 𝜋 = Risk-neutral probability of an up-move Note: For interest rate options, 𝜋 = 0.5 and discount expected option payoff using the 1-period forward rates. Video (Valuing interest rate options): https://youtu.be/X4R8j_cf8SA 42 CFA Level 2 (2026) Formula Sheet by Fabian Moa Two-period Binomial Model: 𝜋 2 𝑐 ++ + 2𝜋(1 − 𝜋)𝑐 +− + (1 − 𝜋)2 𝑐 −− 𝑐= (1 + 𝑟)2 𝜋 2 𝑝++ + 2𝜋(1 − 𝜋)𝑝+− + (1 − 𝜋)2 𝑝−− 𝑝= (1 + 𝑟)2 For 2-period American-styled call option with dividend in t = 1: 𝑆 + = 𝑢 × (𝑆 − 𝑃𝑉 𝑜𝑓 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 𝑎𝑡 𝑟𝑖𝑠𝑘 𝑓𝑟𝑒𝑒 𝑟𝑎𝑡𝑒) 𝑆 − = 𝑑 × (𝑆 − 𝑃𝑉 𝑜𝑓 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 𝑎𝑡 𝑟𝑖𝑠𝑘 𝑓𝑟𝑒𝑒 𝑟𝑎𝑡𝑒) Video: https://youtu.be/U_XkIZjJIAU Black-Scholes Option Pricing Model 𝑐 = 𝑆𝑁(𝑑1 ) − 𝑋𝑒 −𝑟𝑇 𝑁(𝑑2 ) 𝑝 = 𝑋𝑒 −𝑟𝑇 𝑁(−𝑑2 ) − 𝑆𝑁(−𝑑1 ) 𝑆 1 ln ( ) + (𝑟 + 𝜎 2 ) 𝑇 𝑋 2 𝑑1 = 𝜎√𝑇 𝑑2 = 𝑑1 − 𝜎√𝑇 Put-call parity: • • • • 𝑝 + 𝑆 = 𝑐 + 𝑋𝑒 −𝑟𝑇 Hedge ratio for calls = 𝑁(𝑑1 ) Probability that the call option expires in the money = 𝑁(𝑑2 ) = 𝑃𝑟𝑜𝑏(𝑆𝑇 > 𝑋) Hedge ratio for puts = 𝑁(𝑑1 ) − 1 = −𝑁(−𝑑1) Probability that the put option expires in the money = 1 − 𝑁(𝑑2 ) 𝑃𝑟𝑜𝑏(𝑆𝑇 < 𝑋) = 𝑁(−𝑑2 ) 43 CFA Level 2 (2026) Formula Sheet by Fabian Moa BSM model with carry benefits 𝑐 = 𝑆𝑒 −𝛾𝑇 𝑁(𝑑1 ) − 𝑋𝑒 −𝑟𝑇 𝑁(𝑑2 ) 𝑝 = 𝑋𝑒 −𝑟𝑇 𝑁(−𝑑2 ) − 𝑆𝑒 −𝛾𝑇 𝑁(−𝑑1 ) 𝑑1 = 𝑆 1 ln (𝑋) + (𝑟 − 𝛾 + 2 𝜎 2 ) 𝑇 𝜎√𝑇 𝑑2 = 𝑑1 − 𝜎√𝑇 Put-call parity: 𝑝 + 𝑆𝑒 −𝛾𝑇 = 𝑐 + 𝑋𝑒 −𝑟𝑇 Black Option Valuation Model European Options on Futures 𝑐 = 𝑒 −𝑟𝑇 [𝐹0 (𝑇) 𝑁(𝑑1 ) − 𝑋𝑁(𝑑2 )] 𝑐 = 𝑒 −𝑟𝑇 [𝑋𝑁(−𝑑2 ) − 𝐹0 (𝑇) 𝑁(−𝑑1 )] 𝐹 (𝑇) 1 ln [ 0𝑋 ] + 2 𝜎 2 𝑇 𝑑1 = 𝜎√𝑇 𝑑2 = 𝑑1 − 𝜎√𝑇 Put-call parity: 𝑐 = 𝑒 −𝑟𝑇 [𝐹0 (𝑇) − 𝑋] + 𝑝 Interest Rate Options 𝑐 = (𝐴𝑃)𝑒 −𝑟(𝑡𝑗−1 +𝑡𝑚) [𝐹𝑅𝐴(0, 𝑡𝑗−1 , 𝑡𝑚 )𝑁(𝑑1 ) − 𝑅𝑋 𝑒 −𝑟𝑇 𝑁(𝑑2 )] 𝑝 = (𝐴𝑃)𝑒 −𝑟(𝑡𝑗−1 +𝑡𝑚) [𝑅𝑋 𝑒 −𝑟𝑇 𝑁(−𝑑2 ) − 𝐹𝑅𝐴(0, 𝑡𝑗−1 , 𝑡𝑚 )𝑁(−𝑑1 )] 𝑑1 = 𝐹𝑅𝐴(0, 𝑡𝑗−1 , 𝑡𝑚 ) 1 ln [ ] + (2 𝜎 2 ) 𝑡𝑗−1 𝑋 𝜎√𝑡𝑗−1 𝑑2 = 𝑑1 − 𝜎√𝑡𝑗−1 44 CFA Level 2 (2026) Formula Sheet by Fabian Moa Payer Swaption 𝑛 𝑃𝐴𝑌𝑆𝑊𝑁 = 𝐴𝑃 × [𝑅𝐹𝐼𝑋 𝑁(𝑑1 ) − 𝑅𝑋 𝑁(𝑑2 )] × ∑ 𝑃𝑉𝑗 (1) 𝑗=1 Receiver Swaption 𝑛 𝑅𝐸𝐶𝑆𝑊𝑁 = 𝐴𝑃 × [𝑅𝑋 𝑁(−𝑑2 ) − 𝑅𝐹𝐼𝑋 𝑁(−𝑑1 )] × ∑ 𝑃𝑉𝑗 (1) 𝑗=1 𝑅 1 ln ( 𝑅𝐹𝐼𝑋 ) + (2 𝜎 2 ) 𝑇 𝑋 𝑑1 = 𝜎√𝑇 𝑑2 = 𝑑1 − 𝜎√𝑇 Video (Interest Rate Options & Swaptions Equivalences: https://youtu.be/uZQO50sEzso Optimal Number of Hedging Units (for Delta Hedging) 𝑁𝐻 = − 𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑑𝑒𝑙𝑡𝑎 𝐷𝑒𝑙𝑡𝑎𝐻 Video: https://youtu.be/v8RcvkQKFpw Option Greeks 𝐷𝑒𝑙𝑡𝑎𝑐𝑎𝑙𝑙 = 𝑒 −𝛿𝑇 𝑁(𝑑1 ) 𝐷𝑒𝑙𝑡𝑎𝑝𝑢𝑡 = −𝑒 −𝛿𝑇 𝑁(−𝑑1 ) where: 𝛿 = Continuously compounded dividend yield 𝐺𝑎𝑚𝑚𝑎𝑐𝑎𝑙𝑙 = 𝐺𝑎𝑚𝑚𝑎𝑝𝑢𝑡 = 𝑒 −𝛿𝑇 𝑆𝜎√𝑇 𝑁(𝑑1 ) 1 𝑐 = 𝑐0 + 𝐷𝑒𝑙𝑡𝑎𝑐𝑎𝑙𝑙 × 𝛥𝑆 + 𝐺𝑎𝑚𝑚𝑎𝑐𝑎𝑙𝑙 × (𝛥𝑆)2 2 1 𝑝 = 𝑝0 + 𝐷𝑒𝑙𝑡𝑎𝑝𝑢𝑡 × 𝛥𝑆 + 𝐺𝑎𝑚𝑚𝑎𝑝𝑢𝑡 × (𝛥𝑆)2 2 45 CFA Level 2 (2026) Formula Sheet by Fabian Moa VOLUME 8: ALTERNATIVE INVESTMENTS Learning Module 1 | Introduction to Commodities and Commodity Derivatives 𝑆𝑝𝑜𝑡 𝑝𝑟𝑖𝑐𝑒 𝑜𝑓 𝐹𝑢𝑡𝑢𝑟𝑒𝑠 𝑆𝑡𝑜𝑟𝑎𝑔𝑒 𝐶𝑜𝑛𝑣𝑒𝑛𝑖𝑒𝑛𝑐𝑒 = + − 𝑝𝑟𝑖𝑐𝑒 𝑦𝑖𝑒𝑙𝑑 𝑝ℎ𝑦𝑠𝑖𝑐𝑎𝑙 𝑐𝑜𝑚𝑚𝑜𝑑𝑖𝑡𝑦 𝑐𝑜𝑠𝑡𝑠 𝐿𝑜𝑛𝑔𝑒𝑟 𝑡𝑒𝑟𝑚 𝑁𝑒𝑎𝑟 𝑡𝑒𝑟𝑚 𝐶𝑎𝑙𝑒𝑛𝑑𝑎𝑟 = 𝑓𝑢𝑡𝑢𝑟𝑒𝑠 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 − 𝑓𝑢𝑡𝑢𝑟𝑒𝑠 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 𝑠𝑝𝑟𝑒𝑎𝑑 𝑐𝑙𝑜𝑠𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒 𝑐𝑙𝑜𝑠𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒 𝑃𝑟𝑖𝑐𝑒 𝑟𝑒𝑡𝑢𝑟𝑛 = 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑝𝑟𝑖𝑐𝑒 − 𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠 𝑝𝑟𝑖𝑐𝑒 𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠 𝑝𝑟𝑖𝑐𝑒 𝐿𝑜𝑛𝑔𝑒𝑟 𝑡𝑒𝑟𝑚 𝑁𝑒𝑎𝑟 𝑡𝑒𝑟𝑚 (𝑓𝑢𝑡𝑢𝑟𝑒𝑠 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 − 𝑓𝑢𝑡𝑢𝑟𝑒𝑠 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡) 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑐𝑙𝑜𝑠𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒 𝑐𝑙𝑜𝑠𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒 𝑅𝑜𝑙𝑙 𝑟𝑒𝑡𝑢𝑟𝑛 = × 𝑖𝑛 𝑡ℎ𝑒 𝑓𝑢𝑡𝑢𝑟𝑒𝑠 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 𝑁𝑒𝑎𝑟 𝑡𝑒𝑟𝑚 𝑏𝑒𝑖𝑛𝑔 𝑟𝑜𝑙𝑙𝑒𝑑 𝑓𝑢𝑡𝑢𝑟𝑒𝑠 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 𝑐𝑙𝑜𝑠𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒 𝑅𝑒𝑏𝑎𝑙𝑎𝑛𝑐𝑖𝑛𝑔 𝑃𝑟𝑖𝑐𝑒 𝑇𝑜𝑡𝑎𝑙 𝑅𝑜𝑙𝑙 𝐶𝑜𝑙𝑙𝑎𝑡𝑒𝑟𝑎𝑙 = + + + 𝑟𝑒𝑡𝑢𝑟𝑛 (𝑓𝑜𝑟 𝑖𝑛𝑑𝑒𝑥 𝑜𝑛𝑙𝑦) 𝑟𝑒𝑡𝑢𝑟𝑛 𝑟𝑒𝑡𝑢𝑟𝑛 𝑟𝑒𝑡𝑢𝑟𝑛 𝑟𝑒𝑡𝑢𝑟𝑛 Learning Module 2 | Overview of Types of Real Estate Investment Net Operating Income 𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑔𝑟𝑜𝑠𝑠 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑃𝑟𝑜𝑝𝑒𝑟𝑡𝑦 𝑚𝑎𝑖𝑛𝑡𝑒𝑛𝑎𝑛𝑐𝑒 𝑁𝑂𝐼 = − − 𝑒𝑥𝑝𝑒𝑛𝑠𝑒𝑠 𝑖𝑛𝑐𝑜𝑚𝑒 𝑎𝑙𝑙𝑜𝑤𝑎𝑛𝑐𝑒 𝐺𝑟𝑜𝑠𝑠 𝑟𝑒𝑛𝑡 = 𝐵𝑎𝑠𝑒 𝑟𝑒𝑛𝑡 × 𝑅𝑒𝑛𝑡𝑎𝑏𝑙𝑒 𝑎𝑟𝑒𝑎 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 𝑟𝑒𝑐𝑜𝑣𝑒𝑟𝑦 = 𝑅𝑒𝑐𝑜𝑣𝑒𝑟𝑦 × 𝑅𝑒𝑛𝑡𝑎𝑏𝑙𝑒 𝑎𝑟𝑒𝑎 Loan-to-value ratio 𝐿𝑇𝑉 = 𝐷𝑒𝑏𝑡 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 𝑃𝑟𝑜𝑝𝑒𝑟𝑡𝑦 𝑣𝑎𝑙𝑢𝑒 Debt service coverage ratio 𝐷𝑆𝐶 = 𝐸𝑞𝑢𝑖𝑡𝑦 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑟𝑎𝑡𝑒 = 𝑁𝑒𝑡 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑖𝑛𝑐𝑜𝑚𝑒 𝐷𝑒𝑏𝑡 𝑠𝑒𝑟𝑣𝑖𝑐𝑒 𝑃𝑟𝑒𝑡𝑎𝑥 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤 𝑃𝑟𝑜𝑝𝑒𝑟𝑡𝑦 𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒 𝑝𝑟𝑖𝑐𝑒 − 𝑀𝑜𝑟𝑡𝑔𝑎𝑔𝑒 𝑙𝑜𝑎𝑛 46 CFA Level 2 (2026) Formula Sheet by Fabian Moa 𝑃𝑟𝑒𝑡𝑎𝑥 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤 = 𝑁𝑒𝑡 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑖𝑛𝑐𝑜𝑚𝑒 − 𝐷𝑒𝑏𝑡 𝑠𝑒𝑟𝑣𝑖𝑐𝑒 𝐴𝑓𝑡𝑒𝑟 𝑡𝑎𝑥 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤 = 𝑃𝑟𝑒𝑡𝑎𝑥 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤 − 𝑇𝑎𝑥𝑒𝑠 Where: 𝑇𝑎𝑥𝑒𝑠 = 𝑡 × (𝑁𝑂𝐼 − 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 − 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝑒𝑥𝑝𝑒𝑛𝑠𝑒) Funds from Operations 𝐹𝐹𝑂 = 𝑁𝑒𝑡 𝑖𝑛𝑐𝑜𝑚𝑒 + 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 + 𝐴𝑚𝑜𝑟𝑡𝑖𝑧𝑎𝑡𝑖𝑜𝑛 − 𝑁𝑒𝑡 𝑔𝑎𝑖𝑛𝑠 𝑓𝑟𝑜𝑚 𝑝𝑟𝑜𝑝𝑒𝑟𝑡𝑦 𝑠𝑎𝑙𝑒𝑠 Gross potential rental income 𝐺𝑃𝑅𝐼 = 𝑀𝑎𝑟𝑘𝑒𝑡 𝑟𝑒𝑛𝑡 × 𝑅𝑒𝑛𝑡𝑎𝑏𝑙𝑒 𝑠𝑝𝑎𝑐𝑒 Income Approach Direct Capitalization method 𝑃𝑟𝑜𝑝𝑒𝑟𝑡𝑦 𝑣𝑎𝑙𝑢𝑒 = where: 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑁𝑂𝐼 𝐶𝑎𝑝𝑖𝑡𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 𝐶𝑎𝑝𝑖𝑡𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 = 𝑟 − 𝑔 𝑟 = Required return on similar properties 𝑔 = Constant growth rate Discounted Cash Flow (DCF) Methodology 𝑛 𝑃𝑟𝑜𝑝𝑒𝑟𝑡𝑦 𝑣𝑎𝑙𝑢𝑒 = ∑ 𝑡=1 𝑁𝑂𝐼𝑡 𝑇𝑒𝑟𝑚𝑖𝑛𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 + 𝑡 (1 + 𝑟) (1 + 𝑟)𝑛 𝑇𝑒𝑟𝑚𝑖𝑛𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 = 𝑁𝑂𝐼𝑛 (1 + 𝑔) 𝑟−𝑔 Appraisal-based index 𝑁𝑂𝐼 − 𝑅𝑒𝑡𝑢𝑟𝑛 = 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝐸𝑛𝑑𝑖𝑛𝑔 +( − ) 𝐸𝑥𝑝𝑒𝑛𝑑𝑖𝑡𝑢𝑟𝑒𝑠 𝑚𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝑚𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑚𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 Adjustment for Appraisal Lag 𝑅𝑡∗ 1−𝑎 ∗ ) 𝑅𝑡−1 𝑅𝑡 = −( 𝑎 𝑎 where: 𝑅𝑡 = Actual index return 𝑅𝑡∗ = Appraisal index return ∗ 𝑅𝑡−1 = Prior period’s appraisal index return 𝑎 = Speed at which actual returns are reflected in appraisal-based returns (0 ≤ 𝑎 ≤ 1) 47 CFA Level 2 (2026) Formula Sheet by Fabian Moa Learning Module 3 | Investments in Real Estate Through Publicly Traded Securities Net Asset Value Approach 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑇𝑜𝑡𝑎𝑙 𝑑𝑒𝑏𝑡 + − 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑒𝑠𝑡𝑎𝑡𝑒 𝑜𝑡ℎ𝑒𝑟 𝑎𝑠𝑠𝑒𝑡𝑠 𝑎𝑛𝑑 𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠 𝑁𝐴𝑉 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠ℎ𝑎𝑟𝑒𝑠 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 If valuation of operating real estate is not provided: 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑒𝑠𝑡𝑎𝑡𝑒 = 𝑁𝑂𝐼1 𝐶𝑎𝑝 𝑟𝑎𝑡𝑒 Video: https://youtu.be/WncC3BZmfs8 𝑁𝑂𝐼 = 𝐺𝑟𝑜𝑠𝑠 𝑟𝑒𝑛𝑡𝑎𝑙 𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑣𝑎𝑐𝑎𝑛𝑐𝑦 𝑎𝑛𝑑 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 − − 𝑒𝑥𝑝𝑒𝑛𝑠𝑒𝑠 𝑟𝑒𝑣𝑒𝑛𝑢𝑒 𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑖𝑜𝑛𝑠 𝑙𝑜𝑠𝑠 Relative Value Approach Funds from Operations: 𝐹𝐹𝑂 = 𝑁𝑒𝑡 𝑖𝑛𝑐𝑜𝑚𝑒 + 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 + 𝐴𝑚𝑜𝑟𝑡𝑖𝑧𝑎𝑡𝑖𝑜𝑛 − 𝑁𝑒𝑡 𝑔𝑎𝑖𝑛𝑠 𝑓𝑟𝑜𝑚 𝑝𝑟𝑜𝑝𝑒𝑟𝑡𝑦 𝑠𝑎𝑙𝑒𝑠 Adjusted Funds from Operations: 𝐴𝐹𝐹𝑂 = 𝐹𝐹𝑂 − 𝑁𝑜𝑛 𝑐𝑎𝑠ℎ 𝑅𝑒𝑐𝑢𝑟𝑟𝑖𝑛𝑔 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 − 𝑒𝑥𝑝𝑒𝑛𝑑𝑖𝑡𝑢𝑟𝑒 𝑟𝑒𝑛𝑡 Two-Stage Dividend Discount Model 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑎 𝑅𝐸𝐼𝑇 𝑠ℎ𝑎𝑟𝑒 = 𝑃𝑉 𝑜𝑓 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 + 𝑃𝑉 𝑜𝑓 𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 48 CFA Level 2 (2026) Formula Sheet by Fabian Moa Learning Module 4 | Hedge Fund Strategies Equity Market Neutral Pairs Trading 𝐵𝑒𝑡𝑎 𝑜𝑓 𝑢𝑛𝑑𝑒𝑟𝑣𝑎𝑙𝑢𝑒𝑑 𝑠𝑡𝑜𝑐𝑘 × 𝐴𝑚𝑜𝑢𝑛𝑡 𝐼𝑛𝑣𝑒𝑠𝑡𝑒𝑑 𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑆ℎ𝑜𝑟𝑡 𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛 =− 𝐵𝑒𝑡𝑎 𝑜𝑓 𝑜𝑣𝑒𝑟𝑣𝑎𝑙𝑢𝑒𝑑 𝑠𝑡𝑜𝑐𝑘 𝑖𝑛 𝑂𝑣𝑒𝑟𝑣𝑎𝑙𝑢𝑒𝑑 𝑆𝑡𝑜𝑐𝑘 Merger Arbitrage Strategy For a stock-for-stock deal: 𝑃𝑎𝑦𝑜𝑓𝑓 𝑖𝑓 𝑚𝑒𝑟𝑔𝑒𝑟 𝑖𝑠 𝑠𝑢𝑐𝑐𝑒𝑠𝑠𝑓𝑢𝑙 = (𝑁𝐴 × 𝑃𝐴 ) − (𝑁𝑇 × 𝑃𝑇 ) where: 𝑁𝐴 = Number of acquirer’s shares to short sell 𝑃𝐴 = Share price of acquirer post announcement 𝑁𝑇 = Number of target’s shares to buy 𝑃𝑇 = Share price of target post announcement Convertible Arbitrage Strategy 𝐶𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑝𝑟𝑖𝑐𝑒 = 𝐶𝑜𝑛𝑣𝑒𝑟𝑡𝑖𝑏𝑙𝑒 𝑏𝑜𝑛𝑑 𝑝𝑟𝑖𝑐𝑒 𝐶𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜 𝐶𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑣𝑎𝑙𝑢𝑒 = 𝑆ℎ𝑎𝑟𝑒 𝑝𝑟𝑖𝑐𝑒 × 𝐶𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜 Conditional Factor Risk Model 𝑅𝑖,𝑡 = 𝛼𝑖 + 𝛽𝑖,1 (𝐹𝑎𝑐𝑡𝑜𝑟 1)𝑡 + 𝛽𝑖,2 (𝐹𝑎𝑐𝑡𝑜𝑟 2)𝑡 + ⋯ + 𝛽𝑖,𝐾 (𝐹𝑎𝑐𝑡𝑜𝑟 𝐾)𝑡 + +𝐷𝑡 𝛽𝑖,1 (𝐹𝑎𝑐𝑡𝑜𝑟 1)𝑡 + 𝐷𝑡 𝛽𝑖,2 (𝐹𝑎𝑐𝑡𝑜𝑟 2)𝑡 + ⋯ + 𝐷𝑡 𝛽𝑖,𝐾 (𝐹𝑎𝑐𝑡𝑜𝑟 𝐾)𝑡 + (𝑒𝑟𝑟𝑜𝑟)𝑖,𝑡 where: 𝑅𝑖,𝑡 = Return of hedge fund 𝑖 in period 𝑡 𝛽𝑖,𝐾 (𝐹𝑎𝑐𝑡𝑜𝑟 𝐾)𝑡 = Exposure to risk factor 𝐾 for hedge fund 𝑖 in period 𝑡 during normal times 𝐷𝑡 𝛽𝑖,𝐾 (𝐹𝑎𝑐𝑡𝑜𝑟 𝐾)𝑡 = Incremental exposure to risk factor 𝐾 for hedge fund 𝑖 in period 𝑡 during financial crisis periods 𝐷𝑡 = Dummy variable that equals 1 during financial crisis periods (0 otherwise) 𝛼𝑖 = Intercept for hedge fund 𝑖 (𝑒𝑟𝑟𝑜𝑟)𝑖,𝑡 = Random error with zero mean and standard deviation 𝜎𝑖 49 CFA Level 2 (2026) Formula Sheet by Fabian Moa VOLUME 9: PORTFOLIO MANAGEMENT Learning Module 1 | Economics and Investment Markets One-period real-risk free rate: 𝑙𝑡,1 = 1 𝐸𝑡 [𝑚 ̃ 𝑡,1 ] −1 where: 𝐸𝑡 [𝑚 ̃ 𝑡,1 ] = Inter-temporal rate of substitution 𝑃𝑟𝑖𝑐𝑒 𝑜𝑓 𝑟𝑖𝑠𝑘𝑦 𝑎𝑠𝑠𝑒𝑡 = 𝐸[𝑃̃𝑡+1,𝑠−1 ] + 𝑐𝑜𝑣𝑡 [𝑃̃𝑡+1,𝑠−1 , 𝑚 ̃ 𝑡,1 ] 1 + 𝑙𝑡,1 where: 𝐸[𝑃̃𝑡+1,𝑠−1 ] 1+𝑙𝑡,1 = risk neutral present value 𝑐𝑜𝑣𝑡 [𝑃̃𝑡+1,𝑠−1 , 𝑚 ̃ 𝑡,1 ] = covariance between investor’s inter-temporal rate of substitution and the random future price the investment at t + 1, based on the information available to investor today. 𝑠 = time to maturity of investment Default-free nominal coupon-paying bond 𝑁 𝑃𝑡𝑖 =∑ 𝑠=1 𝑖 𝐶𝐹𝑡+𝑠 (1 + 𝑙𝑡,𝑠 + 𝜃𝑡,𝑠 + 𝜋𝑡,𝑠 )𝑠 where: 𝑙𝑡,𝑠 = Real-risk free rate 𝜃𝑡,𝑠 = Expected inflation rate 𝜋𝑡,𝑠 = Uncertainty in future inflation rate 𝜃𝑡,𝑠 + 𝜋𝑡,𝑠 = Breakeven rate of inflaton Short-dated nominal zero-coupon government bonds (e.g., T-bills) 𝑃𝑡𝑖 𝑖 𝐶𝐹𝑡+𝑠 = (1 + 𝑙𝑡,𝑠 + 𝜃𝑡,𝑠 )𝑠 50 CFA Level 2 (2026) Formula Sheet by Fabian Moa Taylor Rule 𝑝𝑟𝑡 = 𝐼𝑡 + 𝜋𝑡 + 0.5(𝜋𝑡 − 𝜋𝑡∗ ) + 0.5(𝑌𝑡 − 𝑌𝑡∗ ) where: 𝑝𝑟𝑡 = policy rate at time t 𝐼𝑡 = level of real short-term interest rates that balance long-term savings and borrowing in the economy 𝜋𝑡 = rate of inflation 𝜋𝑡∗ = target rate of inflation 𝑌𝑡 = logarithmic level of actual GDP 𝑌𝑡∗ = logarithmic level of potential real GDP 𝑌𝑡 − 𝑌𝑡∗ = output gap Corporate bond 𝑁 𝑃𝑡𝑖 =∑ 𝑠=1 𝑖 ̃𝑡+𝑠 𝐸𝑡 [𝐶𝐹 ] (1 + 𝑙𝑡,𝑠 + 𝜃𝑡,𝑠 + 𝜋𝑡,𝑠 + 𝛾𝑡,𝑠 )𝑠 where: 𝛾𝑡,𝑠 = Credit premium Equity ∞ 𝑃𝑡𝑖 =∑ 𝑠=1 𝑃𝑡𝑖 𝑖 ̃𝑡+𝑠 𝐸𝑡 [𝐶𝐹 ] (1 + 𝑙𝑡,𝑠 + 𝜃𝑡,𝑠 + 𝜋𝑡,𝑠 + 𝛾𝑡,𝑠 + 𝜅𝑡,𝑠 )𝑠 ∞ =∑ 𝑠=1 𝑖 ̃𝑡+𝑠 𝐸𝑡 [𝐶𝐹 ] (1 + 𝑙𝑡,𝑠 + 𝜃𝑡,𝑠 + 𝜋𝑡,𝑠 + 𝜆𝑡,𝑠 )𝑠 where: 𝜅𝑡,𝑠 = Equity premium relative to risky bonds 𝜆𝑡,𝑠 = 𝛾𝑡,𝑠 + 𝜅𝑡,𝑠 = Equity risk premium Commercial Real Estate 𝑁 𝑃𝑡𝑖 =∑ 𝑠=1 𝑖 ̃𝑡+𝑠 𝐸𝑡 [𝐶𝐹 ] (1 + 𝑙𝑡,𝑠 + 𝜃𝑡,𝑠 + 𝜋𝑡,𝑠 + 𝛾𝑡,𝑠 + 𝜅𝑡,𝑠 + 𝜙𝑡,𝑠 )𝑠 where: 𝜙𝑡,𝑠 = liquidity risk premium 51 CFA Level 2 (2026) Formula Sheet by Fabian Moa Learning Module 2 | Analysis of Active Portfolio Management Active return, 𝑅𝐴 = 𝑅𝑃 − 𝑅𝐵 𝐴𝑙𝑝ℎ𝑎, 𝛼𝑝 = 𝑅𝑝 − 𝛽𝑝 𝑅𝐵 𝑀 𝑉𝑎𝑙𝑢𝑒 𝑎𝑑𝑑𝑒𝑑, 𝑀 𝑅𝐴 = ∑ ∆𝑤𝑗 𝑅𝐵,𝑗 + ∑ 𝑤𝑃,𝑗 𝑅𝐴,𝑗 𝑗=1 𝑗=1 𝑆𝑅𝑃2 = 𝑆𝑅𝐵2 + 𝐼𝑅 2 𝜎 2 (𝑅𝑃 ) = 𝜎 2 (𝑅𝐵 ) + 𝜎 2 (𝑅𝐴 ) For optimal Sharpe ratio, 𝜎(𝑅𝐴 ) = 𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡, 𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡, 𝐼𝑅 𝜎 (𝑅𝐵 ) 𝑆𝑅𝐵 𝜇𝑖 𝑇𝐶 = 𝐶𝑜𝑟𝑟 ( , ∆𝑤𝑖 𝜎𝑖 ) 𝜎𝑖 𝑅𝐴𝑖 𝜇𝑖 𝐼𝐶 = 𝐶𝑜𝑟𝑟 ( , ) 𝜎𝑖 𝜎𝑖 𝐼𝐶 ≈ 2(𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑟𝑖𝑔ℎ𝑡 𝑐𝑎𝑙𝑙) − 1 Forecasted active return, 𝜇𝑖 = 𝐼𝐶 × 𝜎𝑖 × 𝑆𝑖 where: 𝑆𝑖 is set of standardized forecasts of expected returns across securities Mean-variance optimal weights ∆𝑤𝑖∗ = 𝜇𝑖 𝜎𝐴 2 𝜎𝑖 𝐼𝐶√𝐵𝑅 Full Fundamental Law 𝐸(𝑅𝐴 ) = 𝑇𝐶 × 𝐼𝐶√𝐵𝑅𝜎𝐴 𝐼𝑅 = 𝑇𝐶 × 𝐼𝐶√𝐵𝑅 𝐼𝑅 ∗ 𝜎 (𝑅𝐴 ) = 𝑇𝐶 × 𝜎 (𝑅𝐵 ) 𝑆𝑅𝐵 𝑆𝑅𝑃2 = 𝑆𝑅𝐵2 + (𝑇𝐶)2 (𝐼𝑅∗ )2 52 CFA Level 2 (2026) Formula Sheet by Fabian Moa Performance Measurement 𝑅𝐴 = 𝐸(𝑅𝐴 |𝐼𝐶𝑅 ) + 𝑁𝑜𝑖𝑠𝑒 𝑇𝐶 2 = Proportion of variation in realized performance attributed to realized information coefficient where: 𝐼𝐶𝑅 = realized information coefficient Ex-ante measurement of skill 𝐸(𝑅𝐴 ) = 𝐼𝐶 𝜎 𝜎𝐼𝐶 𝐴 Independence of Investment Decision 𝐵𝑅 = 𝑁 1 + (𝑁 − 1)𝜌 Learning Module 3 | Exchange-Traded Funds: Mechanics and Applications End-of-day ETF premium or discount (%) 𝐸𝑇𝐹 𝑝𝑟𝑖𝑐𝑒 − 𝑁𝐴𝑉 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 𝑁𝐴𝑉 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 Intraday ETF premium or discount (%) 𝐸𝑇𝐹 𝑝𝑟𝑖𝑐𝑒 − 𝐼𝑛𝑑𝑖𝑐𝑎𝑡𝑒𝑑 𝑁𝐴𝑉 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 𝐼𝑛𝑑𝑖𝑐𝑎𝑡𝑒𝑑 𝑁𝐴𝑉 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 𝐻𝑜𝑙𝑑𝑖𝑛𝑔 𝑝𝑒𝑟𝑖𝑜𝑑 𝑐𝑜𝑠𝑡 (%) = 𝑅𝑜𝑢𝑛𝑑 𝑡𝑟𝑖𝑝 𝑡𝑟𝑎𝑑𝑒 𝑐𝑜𝑠𝑡 (%) + 𝑀𝑎𝑛𝑎𝑔𝑒𝑚𝑒𝑛𝑡 𝑓𝑒𝑒 (%) 𝑅𝑜𝑢𝑛𝑑 𝑡𝑟𝑖𝑝 𝑡𝑟𝑎𝑑𝑒 𝑐𝑜𝑠𝑡 % = 𝑂𝑛𝑒 𝑤𝑎𝑦 𝑐𝑜𝑚𝑚𝑖𝑠𝑠𝑖𝑜𝑛 % × 2 + 𝐵𝑖𝑑 𝑎𝑠𝑘 𝑠𝑝𝑟𝑒𝑎𝑑 % 53 CFA Level 2 (2026) Formula Sheet by Fabian Moa Learning Module 4 | Using Multifactor Models Arbitrage Pricing Theory (APT) 𝐸(𝑅𝑝 ) = 𝑅𝐹 + 𝜆1 𝛽𝑝,1 + ⋯ + 𝜆𝐾 𝛽𝑝,𝐾 where: 𝐸(𝑅𝑝 ) = the expected return to portfolio p 𝑅𝐹 = the risk-free rate 𝛽𝑝,𝑗 = the sensitivity of the portfolio to factor j 𝜆𝑗 = the expected reward for bearing the risk of factor j 𝐾 = the number of factors Carhart Four-Factor Model 𝐸(𝑅𝑝 ) = 𝑅𝐹 + 𝛽𝑝,1 𝑅𝑀𝑅𝐹 + 𝛽𝑝,2 𝑆𝑀𝐵 + 𝛽𝑝,3 𝐻𝑀𝐿 + 𝛽𝑝,4 𝑊𝑀𝐿 where: 𝑅𝑀𝑅𝐹 = Return on a value-weighted equity index minus one-month T-bill rate SMB = small minus big; average return on three small-cap portfolios minus the average return on three large-cap portfolios HML = high minus low; average return on two high book-to-market portfolios minus average return on two low book-to-market portfolios WML = winners minus losers, a momentum factor; return on a portfolio of past year’s winners minus return on a portfolio of past year’s losers. Macroeconomic Factor Model 𝑅𝑖 = 𝑎𝑖 + 𝑏𝑖1 𝐹1 + 𝑏𝑖2 𝐹2 + ⋯ + 𝑏𝑖𝐾 𝐹𝐾 + 𝜀𝑖 where: 𝐹𝑘 = the surprise in the factor k 𝑏𝑖𝑘 = the sensitivity of the return on asset i to a surprise in factor k, k = 1, 2, …, 𝑎𝑖 = Expected return on the portfolio Fundamental Factor Model 𝑏𝑖𝑘 = Value of attribute 𝑘 for asset 𝑖 − Average value of attribute 𝑘 𝜎(Values of attribute 𝑘) 54 CFA Level 2 (2026) Formula Sheet by Fabian Moa Return Attribution 𝐴𝑐𝑡𝑖𝑣𝑒 𝑟𝑒𝑡𝑢𝑟𝑛 = 𝑅𝑃 − 𝑅𝐵 𝐾 𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝐵𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 𝑆𝑒𝑐𝑢𝑟𝑖𝑡𝑦 𝐹𝑎𝑐𝑡𝑜𝑟 ) −( ) ]×( = ∑ [( ) + 𝑠𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 𝑘 𝑠𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 𝑘 𝑟𝑒𝑡𝑢𝑟𝑛 𝑘 𝑠𝑒𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑘=1 𝑇𝑟𝑎𝑐𝑘𝑖𝑛𝑔 𝑒𝑟𝑟𝑜𝑟, 𝑇𝐸 = 𝑠(𝑅𝑃 − 𝑅𝐵 ) 𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜, 𝐼𝑅 = 𝑅̅𝑃 − 𝑅̅𝐵 𝑠(𝑅𝑃 − 𝑅𝐵 ) Active risk squared = Active factor risk + Active specific risk Learning Module 5 | Measuring and Managing Market Risk Parametric VaR (Using Normal Distribution) 𝑉𝑎𝑙𝑢𝑒 𝑎𝑡 𝑅𝑖𝑠𝑘, 𝑉𝑎𝑅 = −[𝐸(𝑅𝑝 ) − 𝑧 × 𝜎𝑝 ] × 𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑉𝑎𝑙𝑢𝑒 where: 𝐸(𝑅𝑝 ) = Portfolio expected return 𝜎𝑝 = Portfolio standard deviation Two-asset portfolio: 𝐸(𝑅𝑝 ) = 𝑤1 𝐸(𝑅1 ) + 𝑤2 𝐸(𝑅2 ) 𝜎𝑝2 = 𝑤12 𝜎12 + 𝑤22 𝜎22 + 2𝑤1 𝑤2 𝜌1,2 𝜎1 𝜎2 Scaling from daily returns to annual returns (Assuming 1 year = 250 trading days): 𝑅𝑑𝑎𝑖𝑙𝑦 × 250 𝑡𝑟𝑎𝑑𝑖𝑛𝑔 𝑑𝑎𝑦𝑠 Scaling from daily standard deviation to annual standard deviaton: 𝜎𝑑𝑎𝑖𝑙𝑦 × √250 𝐼𝑛𝑐𝑟𝑒𝑚𝑒𝑛𝑡𝑎𝑙 𝑉𝑎𝑅 (𝐼𝑉𝑎𝑅) = 𝑉𝑎𝑅 𝑎𝑓𝑡𝑒𝑟 𝑐ℎ𝑎𝑛𝑔𝑒 − 𝑉𝑎𝑅 𝑏𝑒𝑓𝑜𝑟𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 Percentage change in bond price: ΔB Δ𝑦 1 Δy 2 ) ≈ −𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛 + 𝐶𝑜𝑛𝑣𝑒𝑥𝑖𝑡𝑦 ( 𝐵 1+𝑦 2 1+𝑦 55 CFA Level 2 (2026) Formula Sheet by Fabian Moa 1 New call price: 𝑐 + Δ𝑐 ≈ 𝑐 + Delta𝑐 (Δ𝑆) + 2 Gamma𝑐 (Δ𝑆)2 + 𝑉𝑒𝑔𝑎𝑐 (Δ𝜎) 1 New put price: 𝑝 + Δ𝑝 ≈ 𝑝 + Delta𝑝 (Δ𝑆) + 2 Gamma𝑝 (Δ𝑆)2 + 𝑉𝑒𝑔𝑎𝑝 (Δ𝜎) Learning Module 6 | Backtesting and Simulation No formula. 56