CFA level 2 formula

CFA® Program Level II FORMULA SHEET (2022) Version 1.0 Prepared by: Fabian Moa, CFA, FRM, FMVA, AFM FOR REFERENCE ONLY (Note: Formula Sheet is not provided in the CFA exam) Follow us on: Facebook (Malaysia) Facebook (Singapore) Facebook (Vietnam) LinkedIn Instagram YouTube NOESIS EXED SDN BHD Block VO2, Level 5, Unit 8, Lingkaran SV, Sunway Velocity, 55100 Kuala Lumpur, Malaysia Website: www.noesis.edu.sg 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. Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed CFA Level 2 – Formula Sheet (2022) QUANTITATIVE METHODS Reading 1: Introduction to Linear Regression 𝑌 𝑏 𝑏𝑋 𝜀 𝑖 1, 2, 3, … , 𝑛 where: 𝑌 dependent variable 𝑋 independent variable intercept 𝑏 𝑏 slope coefficient 𝜀 error term 𝑛 number of observations Linear least squares ∑ 𝐶𝑜𝑣 𝑋, 𝑌 𝑋 𝑋 𝑌 𝑏 𝑉𝑎𝑟 𝑋 ∑ 𝑋 𝑋 𝑏 𝑌 𝑌 𝑏𝑋 1 𝐶𝑜𝑣 𝑋, 𝑌 𝑛 1 𝑉𝑎𝑟 𝑋 𝑛 1 𝑋 𝑌 𝑋 1 𝑋 𝑌 𝑋 𝐶𝑜𝑣 𝑋, 𝑌 𝐶𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑉𝑎𝑟 𝑋 𝑉𝑎𝑟 𝑌 Note: Correlation coefficient is labelled as Multiple R in regression output. Coefficient of Determination, R2 𝑆𝑢𝑚 𝑜𝑓 𝑆𝑞𝑢𝑎𝑟𝑒𝑠 𝑅𝑒𝑔𝑟𝑒𝑠𝑠𝑖𝑜𝑛 𝑅 𝑆𝑢𝑚 𝑜𝑓 𝑆𝑞𝑢𝑎𝑟𝑒𝑠 𝑇𝑜𝑡𝑎𝑙 𝑅 1 𝑆𝑆𝐸 𝑆𝑆𝑇 𝐶𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑆𝑢𝑚 𝑜𝑓 𝑆𝑞𝑢𝑎𝑟𝑒𝑠 𝑇𝑜𝑡𝑎𝑙 𝑆𝑆𝑇 𝑆𝑢𝑚 𝑜𝑓 𝑆𝑞𝑢𝑎𝑟𝑒𝑠 𝑅𝑒𝑔𝑟𝑒𝑠𝑠𝑖𝑜𝑛 𝑆𝑆𝑅 𝑌 𝑌 𝑅𝑆𝑆 𝑌 2 𝑌 𝑆𝑆𝐸 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed 𝑆𝑢𝑚 𝑜𝑓 𝑆𝑞𝑢𝑎𝑟𝑒𝑠 𝐸𝑟𝑟𝑜𝑟 𝑆𝑆𝐸 𝑌 𝑌 Confidence interval for slope coefficient: 𝑡 𝑠 𝑏 𝑏 𝑡 𝑠 Slope coefficient (using linear regression) critical t value (degrees of freedom 𝑛 2) standard error of slope coefficient 𝐹 𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐 𝐹 𝑀𝑒𝑎𝑛 𝑆𝑞𝑢𝑎𝑟𝑒 𝑅𝑒𝑔𝑟𝑒𝑠𝑠𝑖𝑜𝑛 𝑀𝑒𝑎𝑛 𝑆𝑞𝑢𝑎𝑟𝑒 𝐸𝑟𝑟𝑜𝑟 𝑆𝑆𝑅 ⁄1 𝑆𝑆𝐸 ⁄ 𝑛 2 𝑡 𝑠𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐 𝑓𝑜𝑟 𝑏 ANOVA df SS MSS Regression 1 𝑆𝑆𝑅 𝑆𝑆𝑅⁄1 Residual Total 2 𝑆𝑆𝐸 𝑆𝑆𝐸 ⁄ 𝑛 1 𝑆𝑆𝑇 𝑛 𝑛 F 𝑆𝑆𝑅⁄1 𝑆𝑆𝐸 ⁄ 𝑛 2 2 Standard error of the estimate (𝑠 ) 𝑠 𝑆𝑆𝐸 𝑛 2 √𝑀𝑆𝐸 Test statistic for Slope Coefficient: 𝑡 𝐵 𝑠 𝑏 𝐵 𝑠 Hypothesized slope coefficient (in null and alternative hypotheses) 𝑠 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑒𝑟𝑟𝑜𝑟 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑙𝑜𝑝𝑒 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 ∑ 𝑋 𝑋 Test statistic for Correlation Coefficient: 𝑡 𝑛 2 𝐻 :𝜌 𝑟√𝑛 √1 Degrees of freedom 0 versus 𝐻 : 𝜌 0 3 2 𝑟 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Test statistic for the Intercept: 𝑏 𝑡 𝐵 𝑠 𝛽 𝑠 Hypothesized intercept (in null and alternative hypotheses) 1 𝑛 𝑋 𝑋 ∑ 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑒𝑟𝑟𝑜𝑟 𝑜𝑓 𝑡ℎ𝑒 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 𝑋 Prediction Interval for 𝒀𝒇 𝑌 𝑡 ⁄ 𝑠 Variance of prediction error 𝑠 𝑠 1 1 𝑛 𝑋 1 𝑠 𝑋 𝑛 𝑠 1 𝑛 1 𝑋 𝑋 ∑ 𝑋 𝑋 Log‐Lin Model ln 𝑌 𝑏 𝑏𝑋 Lin‐Log Model 𝑌 𝑏 𝑏 ln 𝑋 Lin‐Log Model ln 𝑌 𝑏 𝑏 ln 𝑋 Reading 2: Multiple Regression 𝑌 𝑏 𝑏𝑋 𝑏 𝑋 ⋯ 𝑏 𝑋 where: 𝑌 dependent variable 𝑋 independent variable intercept 𝑏 slope coefficients 𝑏 ,𝑏 ,…,𝑏 𝜀 error term 𝑛 number of observations 𝑘 number of independent variables 𝑏 ,𝑏 ,𝑏 ,…,𝑏 regression coefficients 4 𝜀 𝑖 1, 2, 3, … , 𝑛 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Test statistic for coefficient 𝑗 𝑡 𝑏 𝑏 𝑠 𝑏 𝑏 𝑠 Regression estimate of 𝑏 Hypothesized value of coefficient 𝑗 Estimated standard error of 𝑏 ANOVA df SS MSS Regression 𝑘 𝑆𝑆𝑅 𝑆𝑆𝑅⁄𝑘 Residual Total 𝑛 𝑘 𝑛 1 1 𝑆𝑆𝐸 𝑆𝑆𝐸 ⁄ 𝑛 𝑆𝑆𝑇 Adjusted R2 𝑅 𝑛 1 𝑛 1 𝑘 1 F 𝑆𝑆𝑅⁄1 𝑆𝑆𝐸 ⁄ 𝑛 𝑘 𝑘 1 1 𝑅 1 Breusch‐Pagan Test 𝑇𝑒𝑠𝑡 𝑆𝑡𝑎𝑡𝑖𝑠𝑡𝑖𝑐, 𝑅 χ 𝑛𝑅 R‐squared between squared residuals on independent variables Durbin Watson test ∑ 𝐷𝑊 𝜀̂ ∑ 𝜀̂ 𝜀̂ 2 1 𝑟 If sample is very large, 𝐷𝑊 where 𝑟 sample correlation between regression residuals from one period and those from the previous period Logistic Regression (Logit Model) ln where 𝑝 𝑝 1 𝑝 𝑏𝑋 𝑏 𝑏 𝑋 𝑏 𝑋 probability that event of interest happens Odds of an event happening 𝑝 1 exp 𝑏 1 𝑏𝑋 5 𝑏 𝑋 𝑏 𝑋 𝜀 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Reading 3: Time‐Series Analysis Linear Trend Models 𝑌 𝑡 𝑏 𝑏𝑡 𝜀 𝑡 1,2, … , 𝑇 time (independent variable) Log‐Linear Trend Models 𝑒 𝑌 Growth rate of 𝑦 𝑒 𝑡 1,2, … , 𝑇 1 p-th order autoregressive model, AR(p): 𝑥 𝑏 𝑏𝑥 𝑏 𝑥 Test statistic for autocorrelation of residuals: 𝑅𝑒𝑠𝑖𝑑𝑢𝑎𝑙 𝑎𝑢𝑡𝑜𝑐𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 𝑡 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑒𝑟𝑟𝑜𝑟 𝑏 𝑥 1⁄√𝑇 𝑏 1 𝑏 Root Mean Squared Error: 𝑅𝑀𝑆𝐸 𝑆𝑞𝑢𝑎𝑟𝑒𝑑 𝑒𝑟𝑟𝑜𝑟 𝑛 ARCH(1): 𝜎 𝑎 𝑎 𝜖̂ Reading 5: Big Data Projects Normalization of variable X 𝑋 𝑋 𝑋 Standardization of variable X 𝑋 𝑋 𝑋 𝑋 𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛, 𝑃 𝜖 𝑅𝑒𝑠𝑖𝑑𝑢𝑎𝑙 𝑎𝑢𝑡𝑜𝑐𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 0 Mean reverting level for AR(1) model: 𝑥 ⋯ 𝜇 𝜎 𝑇𝑟𝑢𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑇𝑟𝑢𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝐹𝑎𝑙𝑠𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 6 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed 𝑅𝑒𝑐𝑎𝑙𝑙, 𝑅 𝐴𝑐𝑐𝑢𝑟𝑎𝑐𝑦 𝐹1 𝑆𝑐𝑜𝑟𝑒 𝑇𝑟𝑢𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑇𝑟𝑢𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝐹𝑎𝑙𝑠𝑒 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝑇𝑟𝑢𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 2 𝑇𝑟𝑢𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑇𝑟𝑢𝑒 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝐹𝑎𝑙𝑠𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑇𝑟𝑢𝑒 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝐹𝑎𝑙𝑠𝑒 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 𝑅𝑒𝑐𝑎𝑙𝑙 𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 𝑅𝑒𝑐𝑎𝑙𝑙 𝐹𝑎𝑙𝑠𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑅𝑎𝑡𝑒, 𝐹𝑃𝑅 𝑇𝑟𝑢𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑅𝑎𝑡𝑒, 𝑇𝑃𝑅 𝐹𝑎𝑙𝑠𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑇𝑟𝑢𝑒 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝐹𝑎𝑙𝑠𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑇𝑟𝑢𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑇𝑟𝑢𝑒 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝐹𝑎𝑙𝑠𝑒 𝑁𝑒𝑔𝑎𝑡𝑖𝑣𝑒 𝑇𝑒𝑟𝑚 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝐶𝑜𝑙𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝐿𝑒𝑣𝑒𝑙 𝑇𝑒𝑟𝑚 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑆𝑒𝑛𝑡𝑒𝑛𝑐𝑒 𝐿𝑒𝑣𝑒𝑙 𝐷𝑜𝑐𝑢𝑚𝑒𝑛𝑡 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦, 𝐷𝐹 𝑇𝐹 𝑊𝑜𝑟𝑑 𝐶𝑜𝑢𝑛𝑡 𝑖𝑛 𝑆𝑒𝑛𝑡𝑒𝑛𝑐𝑒 𝑇𝑜𝑡𝑎𝑙 𝑊𝑜𝑟𝑑𝑠 𝑖𝑛 𝑆𝑒𝑛𝑡𝑒𝑛𝑐𝑒 𝑆𝑒𝑛𝑡𝑒𝑛𝑐𝑒 𝐶𝑜𝑢𝑛𝑡 𝑤𝑖𝑡ℎ 𝑊𝑜𝑟𝑑 𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑆𝑒𝑛𝑡𝑒𝑛𝑐𝑒𝑠 𝐼𝑛𝑣𝑒𝑟𝑠𝑒 𝐷𝑜𝑐𝑢𝑚𝑒𝑛𝑡 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦, 𝐼𝐷𝐹 𝑇𝐹-𝐼𝐷𝐹 𝑇𝑜𝑡𝑎𝑙 𝑊𝑜𝑟𝑑 𝐶𝑜𝑢𝑛𝑡 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑜𝑟𝑑𝑠 𝑖𝑛 𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑖𝑜𝑛 log 1 𝐷𝐹 𝐼𝐷𝐹 7 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed ECONOMICS Reading 6: Currency Exchange Rates: Understanding Equilibrium Value Currency pair A/B B/A Bid Bid/Ask 𝑥 𝑦 1⁄𝑦 1⁄𝑥 Covered Interest Rate Parity 𝐹 𝐹 𝑆 ⁄ 𝑆 ⁄ 𝑆 ⁄ 1 𝑖 1 𝑖 ⁄ ⁄ 𝐴𝑐𝑡𝑢𝑎𝑙 360 𝐴𝑐𝑡𝑢𝑎𝑙 360 𝑖 𝑖 1 𝑖 𝐴𝑐𝑡𝑢𝑎𝑙 360 𝐴𝑐𝑡𝑢𝑎𝑙 360 Mark‐to‐Market Value of a Forward Contract Original position: Long base currency d forward at forward rate 𝐹 , 𝐹, 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐿𝑜𝑛𝑔 𝐹𝑜𝑟𝑤𝑎𝑟𝑑 1 𝐹, ⁄ ⁄ 𝑖 ⁄ (Offer side) 𝐹, ⁄ 𝐶𝑜𝑛𝑡𝑟𝑎𝑐𝑡 𝑆𝑖𝑧𝑒 𝑅𝑒𝑚𝑎𝑖𝑛𝑖𝑛𝑔 𝑑𝑎𝑦𝑠 𝑚𝑎𝑡𝑢𝑟𝑖𝑡𝑦 360 Forward rate at valuation date, t (Bid side) Uncovered Interest Rate Parity 𝐸 𝑆 %Δ𝑆 ⁄ 𝑆 ⁄ 𝑖 𝑖 1 𝑖 ⁄ 1 𝑖 1 𝑖 𝐴𝑐𝑡𝑢𝑎𝑙 360 𝐴𝑐𝑡𝑢𝑎𝑙 360 Absolute PPP 𝑆 𝑃 𝑃 ⁄ 8 𝐴𝑐𝑡𝑢𝑎𝑙 360 𝐴𝑐𝑡𝑢𝑎𝑙 360 𝑖 𝑖 𝐴𝑐𝑡𝑢𝑎𝑙 360 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Relative PPP %Δ𝑆 𝜋 𝜋 1 𝜋 %Δ𝑆 ⁄ ⁄ 𝐴𝑐𝑡𝑢𝑎𝑙 360 𝐴𝑐𝑡𝑢𝑎𝑙 360 𝜋 𝐴𝑐𝑡𝑢𝑎𝑙 360 𝜋 Ex ante PPP 𝜋 𝐴𝑐𝑡𝑢𝑎𝑙 360 𝜋 International Fisher Effect 𝑖 𝜋 𝜋 𝑖 𝜋 𝜋 Expected inflation rate Actual inflation rate Reading 7: Economic Growth and the Investment Decision 𝑃 𝐺𝐷𝑃 𝐸 𝐺𝐷𝑃 Return on aggregate equity market %∆𝑃 𝑃 𝐸 %∆𝐺𝐷𝑃 %∆ 𝑃 𝐸 𝐸 𝐺𝐷𝑃 %∆ 𝑃 𝐸 aggregate value of equities aggregate earnings Cobb-Douglas Production Function 𝑌 𝑇𝐾 𝐿 where a < 1 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 𝐎𝐮𝐭𝐩𝐮𝐭 𝐩𝐞𝐫 𝐰𝐨𝐫𝐤𝐞𝐫 𝑌 𝐿 𝑇 𝐾 𝐿 Marginal product of capital, MPK 𝑀𝑃𝐾 𝛼 𝑌 𝐾 Amount of output that is allocated to providers of capital, a 𝑟𝐾 𝛼 𝑌 9 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Growth Accounting equation: ∆𝑇 𝑇 ∆𝑌 𝑌 𝛼 ∆𝐾 𝐾 1 𝛼 ∆𝐿 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 𝑔∗ 𝜃 1 Sustainable growth rate of output 𝛼 𝜃 𝐺∗ 1 𝑛 𝛼 Equilibrium output-to-capital ratio (Steady state): 𝑌 1 𝜃 𝑛 𝐾 𝑠 1 𝛼 𝜃 𝛼 𝑠 𝛿 𝑛 𝛿 growth rate of TFP elasticity of output with respect to capital fraction of income (Y) that is saved rate of depreciation of physical capital stock labor supply growth %∆𝐿 Endogeneous Growth Model Production function: 𝑦 𝑐𝑘 Δ𝑘 𝑘 𝑠𝑐 Growth rate of output per capita: Δ𝑦 𝑦 𝑦 𝑘 𝑐 𝛿 𝑛 output per worker capital per worker marginal product of capital in the aggregate economy (constant) 10 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed FINANCIAL REPORTING AND ANALYSIS Reading 9: Intercorporate Investments Financial Assets Amortized Cost 𝐸𝑛𝑑𝑖𝑛𝑔 𝐷𝑒𝑏𝑡 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝐷𝑒𝑏𝑡 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑅𝑒𝑎𝑙𝑖𝑧𝑒𝑑 𝐺𝑎𝑖𝑛 𝑜𝑟 𝐿𝑜𝑠𝑠 𝑆𝑎𝑙𝑒𝑠 𝑝𝑟𝑜𝑐𝑒𝑒𝑑𝑠 FVOCI or FVPL 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝐼𝑛𝑐𝑜𝑚𝑒 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑑 𝐶𝑎𝑟𝑟𝑦𝑖𝑛𝑔 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝐹𝑖𝑛𝑎𝑛𝑐𝑖𝑎𝑙 𝐴𝑠𝑠𝑒𝑡 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝐹𝑎𝑖𝑟 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝐹𝑖𝑛𝑎𝑛𝑐𝑖𝑎𝑙 𝐴𝑠𝑠𝑒𝑡 𝑈𝑛𝑟𝑒𝑎𝑙𝑖𝑧𝑒𝑑 𝐺𝑎𝑖𝑛 𝑜𝑟 𝐿𝑜𝑠𝑠 Investments in Associates 𝐸𝑛𝑑𝑖𝑛𝑔 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑖𝑛 𝑎𝑠𝑠𝑜𝑐𝑖𝑎𝑡𝑒𝑠 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑖𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡 𝑖𝑛 𝑎𝑠𝑠𝑜𝑐𝑖𝑎𝑡𝑒𝑠 𝑆ℎ𝑎𝑟𝑒 𝑜𝑓 𝑛𝑒𝑡 𝑖𝑛𝑐𝑜𝑚𝑒 Impact on Investor’s Income Statement 𝐴𝑚𝑜𝑟𝑡𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑒𝑥𝑐𝑒𝑠𝑠 𝑆ℎ𝑎𝑟𝑒 𝑜𝑓 𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒 𝑝𝑟𝑖𝑐𝑒 𝑛𝑒𝑡 𝑖𝑛𝑐𝑜𝑚𝑒 𝑆ℎ𝑎𝑟𝑒 𝑜𝑓 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑑 𝐴𝑚𝑜𝑟𝑡𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑒𝑥𝑐𝑒𝑠𝑠 𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒 𝑝𝑟𝑖𝑐𝑒 𝑆ℎ𝑎𝑟𝑒 𝑜𝑓 𝑈𝑛𝑟𝑒𝑎𝑙𝑖𝑧𝑒𝑑 𝑝𝑟𝑜𝑓𝑖𝑡 𝑓𝑟𝑜𝑚 𝑑𝑜𝑤𝑛𝑠𝑡𝑟𝑒𝑎𝑚 𝑜𝑟 𝑢𝑝𝑠𝑡𝑟𝑒𝑎𝑚 𝑠𝑎𝑙𝑒 Acquisition Method Excess purchase price = Acquisition price – %Ownership × Book value of net identifiable assets Partial Goodwill = Acquisition price – (%Ownership × Fair value of net identifiable assets) = Acquisition price – %Ownership × Book value of identifiable net assets – %Ownership × Excess purchase price attributable to net identifiable 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 IFRS 𝐼𝑚𝑝𝑎𝑖𝑟𝑚𝑒𝑛𝑡 𝑙𝑜𝑠𝑠 %𝑁𝐶𝐼 𝐹𝑎𝑖𝑟 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑒𝑛𝑡𝑖𝑡𝑦 𝐶𝑎𝑟𝑟𝑦𝑖𝑛𝑔 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑐𝑎𝑠ℎ 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑢𝑛𝑖𝑡 𝑅𝑒𝑐𝑜𝑣𝑒𝑟𝑎𝑏𝑙𝑒 𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑐𝑎𝑠ℎ 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑢𝑛𝑖𝑡 11 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed US GAAP 𝐼𝑚𝑝𝑙𝑖𝑒𝑑 𝐹𝑎𝑖𝑟 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑔𝑜𝑜𝑑𝑤𝑖𝑙𝑙 𝑟𝑒𝑝𝑜𝑟𝑡𝑖𝑛𝑔 𝑢𝑛𝑖𝑡 𝐼𝑚𝑝𝑎𝑖𝑟𝑚𝑒𝑛𝑡 𝑙𝑜𝑠𝑠 𝐹𝑎𝑖𝑟 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑟𝑒𝑝𝑜𝑟𝑡𝑖𝑛𝑔 𝑢𝑛𝑖𝑡′𝑠 𝑖𝑑𝑒𝑛𝑡𝑖𝑓𝑖𝑎𝑏𝑙𝑒 𝑛𝑒𝑡 𝑎𝑠𝑠𝑒𝑡𝑠 𝐶𝑎𝑟𝑟𝑦𝑖𝑛𝑔 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑔𝑜𝑜𝑑𝑤𝑖𝑙𝑙 𝐼𝑚𝑝𝑙𝑖𝑒𝑑 𝑔𝑜𝑜𝑑𝑤𝑖𝑙𝑙 Reading 10: Employee Compensation - Post-Employment and Share-Based 𝐹𝑢𝑛𝑑𝑒𝑑 𝑠𝑡𝑎𝑡𝑢𝑠 𝐹𝑎𝑖𝑟 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑝𝑙𝑎𝑛 𝑎𝑠𝑠𝑒𝑡𝑠 𝑁𝑒𝑡 𝑃𝑒𝑛𝑠𝑖𝑜𝑛 𝐴𝑠𝑠𝑒𝑡 𝑃𝑒𝑟𝑖𝑜𝑑𝑖𝑐 𝑝𝑒𝑛𝑠𝑖𝑜𝑛 𝑐𝑜𝑠𝑡 𝑀𝑖𝑛 𝑃𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝐹𝑢𝑛𝑑𝑒𝑑 𝑆𝑡𝑎𝑡𝑢𝑠, 𝐴𝑠𝑠𝑒𝑡 𝐶𝑒𝑖𝑙𝑖𝑛𝑔 𝑩𝒆𝒈𝒊𝒏𝒏𝒊𝒏𝒈 𝑬𝒏𝒅𝒊𝒏𝒈 𝐸𝑚𝑝𝑙𝑜𝑦𝑒𝑟 𝑓𝑢𝑛𝑑𝑒𝑑 𝑠𝑡𝑎𝑡𝑢𝑠 𝑓𝑢𝑛𝑑𝑒𝑑 𝑠𝑡𝑎𝑡𝑢𝑠 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛𝑠 𝑃𝑎𝑠𝑡 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝐴𝑐𝑡𝑢𝑎𝑙 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝐴𝑐𝑡𝑢𝑎𝑟𝑖𝑎𝑙 𝑠𝑒𝑟𝑣𝑖𝑐𝑒 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 𝑠𝑒𝑟𝑣𝑖𝑐𝑒 𝑙𝑜𝑠𝑠 𝑔𝑎𝑖𝑛 𝑝𝑙𝑎𝑛 𝑎𝑠𝑠𝑒𝑡𝑠 𝑐𝑜𝑠𝑡𝑠 𝑐𝑜𝑠𝑡𝑠 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑏𝑒𝑛𝑒𝑓𝑖𝑡 𝑜𝑏𝑙𝑖𝑔𝑎𝑡𝑖𝑜𝑛 𝐸𝑛𝑑𝑖𝑛𝑔 𝑏𝑒𝑛𝑒𝑓𝑖𝑡 𝑜𝑏𝑙𝑖𝑔𝑎𝑡𝑖𝑜𝑛 𝐸𝑛𝑑𝑖𝑛𝑔 𝑓𝑎𝑖𝑟 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑝𝑙𝑎𝑛 𝑎𝑠𝑠𝑒𝑡𝑠 𝑃𝑉 𝑜𝑓 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑏𝑒𝑛𝑒𝑓𝑖𝑡 𝑜𝑏𝑙𝑖𝑔𝑎𝑡𝑖𝑜𝑛 𝑆𝑒𝑟𝑣𝑖𝑐𝑒 𝑐𝑜𝑠𝑡 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑓𝑎𝑖𝑟 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑝𝑙𝑎𝑛 𝑎𝑠𝑠𝑒𝑡𝑠 𝐵𝑒𝑛𝑒𝑓𝑖𝑡𝑠 𝑝𝑎𝑖𝑑 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑐𝑜𝑠𝑡 𝐴𝑐𝑡𝑢𝑎𝑙 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑝𝑙𝑎𝑛 𝑎𝑠𝑠𝑒𝑡𝑠 𝐴𝑐𝑡𝑢𝑎𝑟𝑖𝑎𝑙 𝑙𝑜𝑠𝑠/ 𝑔𝑎𝑖𝑛 𝐸𝑚𝑝𝑙𝑜𝑦𝑒𝑟′𝑠 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝐵𝑒𝑛𝑒𝑓𝑖𝑡𝑠 𝑝𝑎𝑖𝑑 IFRS 𝑃𝑒𝑟𝑖𝑜𝑑𝑖𝑐 𝑝𝑒𝑛𝑠𝑖𝑜𝑛 𝑐𝑜𝑠𝑡 𝑖𝑛 𝒊𝒏𝒄𝒐𝒎𝒆 𝒔𝒕𝒂𝒕𝒆𝒎𝒆𝒏𝒕 𝑁𝑒𝑡 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑒𝑥𝑝𝑒𝑛𝑠𝑒⁄ 𝑖𝑛𝑐𝑜𝑚𝑒 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑠𝑒𝑟𝑣𝑖𝑐𝑒 𝑐𝑜𝑠𝑡𝑠 𝐷𝑖𝑠𝑐𝑜𝑢𝑛𝑡 𝑟𝑎𝑡𝑒 𝑃𝑎𝑠𝑡 𝑠𝑒𝑟𝑣𝑖𝑐𝑒 𝑐𝑜𝑠𝑡𝑠 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑃𝐵𝑂 𝑁𝑒𝑡 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑒𝑥𝑝𝑒𝑛𝑠𝑒/ 𝑖𝑛𝑐𝑜𝑚𝑒 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑃𝑙𝑎𝑛 𝐴𝑠𝑠𝑒𝑡𝑠 US GAAP 𝑃𝑒𝑟𝑖𝑜𝑑𝑖𝑐 𝑝𝑒𝑛𝑠𝑖𝑜𝑛 𝑐𝑜𝑠𝑡 𝑖𝑛 𝒊𝒏𝒄𝒐𝒎𝒆 𝒔𝒕𝒂𝒕𝒆𝒎𝒆𝒏𝒕 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 𝐷𝑖𝑠𝑐𝑜𝑢𝑛𝑡 𝑟𝑎𝑡𝑒 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑝𝑙𝑎𝑛 𝑎𝑠𝑠𝑒𝑡𝑠 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐴𝑚𝑜𝑟𝑡𝑖𝑧𝑒𝑑 𝑝𝑎𝑠𝑡 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 𝑠𝑒𝑟𝑣𝑖𝑐𝑒 𝑐𝑜𝑠𝑡𝑠 𝑠𝑒𝑟𝑣𝑖𝑐𝑒 𝑐𝑜𝑠𝑡𝑠 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 𝐴𝑚𝑜𝑟𝑡𝑖𝑧𝑒𝑑 𝐴𝑐𝑡𝑢𝑎𝑟𝑖𝑎𝑙 𝑙𝑜𝑠𝑠/ 𝑔𝑎𝑖𝑛 𝑜𝑛 𝑝𝑙𝑎𝑛 𝑎𝑠𝑠𝑒𝑡𝑠 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑃𝐵𝑂 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑟𝑛 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑃𝑙𝑎𝑛 𝐴𝑠𝑠𝑒𝑡𝑠 12 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Reading 12: Analysis of Financial Institutions 𝐶𝑜𝑚𝑚𝑜𝑛 𝐸𝑞𝑢𝑖𝑡𝑦 𝑇𝑖𝑒𝑟 1 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑇𝑜𝑡𝑎𝑙 𝑇𝑖𝑒𝑟 1 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑇𝑜𝑡𝑎𝑙 𝑅𝑒𝑔𝑢𝑙𝑎𝑡𝑜𝑟𝑦 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑇𝑜𝑡𝑎𝑙 𝑇𝑖𝑒𝑟 1 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑅𝑖𝑠𝑘 𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝐴𝑠𝑠𝑒𝑡𝑠 𝑇𝑜𝑡𝑎𝑙 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑅𝑎𝑡𝑖𝑜 𝑇𝑜𝑡𝑎𝑙 𝑇𝑖𝑒𝑟 2 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐶𝑜𝑚𝑚𝑜𝑛 𝐸𝑞𝑢𝑖𝑡𝑦 𝑇𝑖𝑒𝑟 1 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑅𝑖𝑠𝑘 𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝐴𝑠𝑠𝑒𝑡𝑠 𝐶𝑜𝑚𝑚𝑜𝑛 𝐸𝑞𝑢𝑖𝑡𝑦 𝑇𝑖𝑒𝑟 1 𝑅𝑎𝑡𝑖𝑜 𝑇𝑖𝑒𝑟 1 𝑅𝑎𝑡𝑖𝑜 𝑇𝑜𝑡𝑎𝑙 𝑇𝑖𝑒𝑟 1 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐴𝑑𝑑𝑖𝑡𝑖𝑜𝑛𝑎𝑙 𝑇𝑖𝑒𝑟 1 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 6.0% 𝑇𝑜𝑡𝑎𝑙 𝑅𝑒𝑔𝑢𝑙𝑎𝑡𝑜𝑟𝑦 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑅𝑖𝑠𝑘 𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝐴𝑠𝑠𝑒𝑡𝑠 𝐿𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦 𝐶𝑜𝑣𝑒𝑟𝑎𝑔𝑒 𝑅𝑎𝑡𝑖𝑜, 𝐿𝐶𝑅 4.5% 8.0% 𝐻𝑖𝑔ℎ 𝑄𝑢𝑎𝑙𝑖𝑡𝑦 𝐿𝑖𝑞𝑢𝑖𝑑 𝐴𝑠𝑠𝑒𝑡𝑠 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑐𝑎𝑠ℎ 𝑜𝑢𝑡𝑓𝑙𝑜𝑤𝑠 Bank can withstand a stress level volume of cash outflows for (𝐿𝐶𝑅 𝑁𝑒𝑡 𝑆𝑡𝑎𝑏𝑙𝑒 𝐹𝑢𝑛𝑑𝑖𝑛𝑔 𝑅𝑎𝑡𝑖𝑜, 𝑁𝑆𝐹𝑅 30 days. 𝐴𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒 𝑆𝑡𝑎𝑏𝑙𝑒 𝐹𝑢𝑛𝑑𝑖𝑛𝑔 𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑆𝑡𝑎𝑏𝑙𝑒 𝐹𝑢𝑛𝑑𝑖𝑛𝑔 Property and Casualty Companies 𝐿𝑜𝑠𝑠 𝑎𝑛𝑑 𝑙𝑜𝑠𝑠 𝑎𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛𝑡 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 𝑟𝑎𝑡𝑖𝑜 𝑈𝑛𝑑𝑒𝑟𝑤𝑟𝑖𝑡𝑖𝑛𝑔 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 𝑟𝑎𝑡𝑖𝑜 𝐶𝑜𝑚𝑏𝑖𝑛𝑒𝑑 𝑟𝑎𝑡𝑖𝑜 𝐿𝑜𝑠𝑠 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 𝐿𝑜𝑠𝑠 𝑎𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛𝑡 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 𝑁𝑒𝑡 𝑝𝑟𝑒𝑚𝑖𝑢𝑚𝑠 𝑒𝑎𝑟𝑛𝑒𝑑 𝑈𝑛𝑑𝑒𝑟𝑤𝑟𝑖𝑡𝑖𝑛𝑔 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 𝑁𝑒𝑡 𝑝𝑟𝑒𝑚𝑖𝑢𝑚𝑠 𝑤𝑟𝑖𝑡𝑡𝑒𝑛 𝐿𝑜𝑠𝑠 𝑎𝑛𝑑 𝑙𝑜𝑠𝑠 𝑎𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛𝑡 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 𝑟𝑎𝑡𝑖𝑜 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 𝑡𝑜 𝑝𝑜𝑙𝑖𝑐𝑦ℎ𝑜𝑙𝑑𝑒𝑟𝑠 𝑠ℎ𝑎𝑟𝑒ℎ𝑜𝑙𝑑𝑒𝑟𝑠 𝑟𝑎𝑡𝑖𝑜 𝐶𝑜𝑚𝑏𝑖𝑛𝑒𝑑 𝑟𝑎𝑡𝑖𝑜 𝒂𝒇𝒕𝒆𝒓 𝒅𝒊𝒗𝒊𝒅𝒆𝒏𝒅𝒔 𝑈𝑛𝑑𝑒𝑟𝑤𝑟𝑖𝑡𝑖𝑛𝑔 𝑒𝑥𝑝𝑒𝑛𝑠𝑒 𝑟𝑎𝑡𝑖𝑜 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 𝑡𝑜 𝑝𝑜𝑙𝑖𝑐𝑦ℎ𝑜𝑙𝑑𝑒𝑟𝑠 𝑠ℎ𝑎𝑟𝑒ℎ𝑜𝑙𝑑𝑒𝑟𝑠 𝑁𝑒𝑡 𝑝𝑟𝑒𝑚𝑖𝑢𝑚𝑠 𝑒𝑎𝑟𝑛𝑒𝑑 𝐶𝑜𝑚𝑏𝑖𝑛𝑒𝑑 𝑟𝑎𝑡𝑖𝑜 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 𝑡𝑜 𝑝𝑜𝑙𝑖𝑐𝑦ℎ𝑜𝑙𝑑𝑒𝑟𝑠 𝑠ℎ𝑎𝑟𝑒ℎ𝑜𝑙𝑑𝑒𝑟𝑠 𝑟𝑎𝑡𝑖𝑜 13 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Reading 13: 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 DSR day sales receivable index GMI gross margin index AQI asset quality index SGI sales growth index DEPI depreciation index 𝑅𝑒𝑐𝑒𝑖𝑣𝑎𝑏𝑙𝑒𝑠 ⁄𝑆𝑎𝑙𝑒𝑠 𝑅𝑒𝑐𝑒𝑖𝑣𝑎𝑏𝑙𝑒𝑠 ⁄𝑆𝑎𝑙𝑒𝑠 𝐺𝑀 𝐺𝑀 𝐶𝐴 /𝑇𝐴 1 𝑃𝑃𝐸 1 𝑃𝑃𝐸 𝐶𝐴 /𝑇𝐴 𝑆𝑎𝑙𝑒𝑠 𝑆𝑎𝑙𝑒𝑠 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝑆𝐺𝐴 /𝑆𝑎𝑙𝑒𝑠 𝑆𝐺𝐴 /𝑆𝑎𝑙𝑒𝑠 𝐶𝑎𝑠ℎ 𝑓𝑟𝑜𝑚 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛𝑠 SGAI sales, general, and administrative expenses index 𝐼𝑛𝑐𝑜𝑚𝑒 𝑏𝑒𝑓𝑜𝑟𝑒 𝑒𝑥𝑡𝑟𝑎𝑜𝑟𝑑𝑖𝑛𝑎𝑟𝑦 𝑖𝑡𝑒𝑚𝑠 𝑇𝑜𝑡𝑎𝑙 𝑎𝑠𝑠𝑒𝑡𝑠 𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒 LEVI leverage index 𝐿𝑒𝑣𝑒𝑟𝑎𝑔𝑒 Accruals Reading 14: Integration of Financial Statement Analysis Techniques 𝑁𝑒𝑡 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝐴𝑠𝑠𝑒𝑡𝑠 𝑁𝑂𝐴 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝐴𝑠𝑠𝑒𝑡𝑠 𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠 𝑇𝑜𝑡𝑎𝑙 𝐶𝑎𝑠ℎ 𝑎𝑛𝑑 𝐴𝑠𝑠𝑒𝑡𝑠 𝑆ℎ𝑜𝑟𝑡-𝑡𝑒𝑟𝑚 𝐼𝑛𝑣𝑒𝑠𝑡𝑚𝑒𝑛𝑡𝑠 𝐵𝑎𝑙𝑎𝑛𝑐𝑒-𝑠ℎ𝑒𝑒𝑡-𝑏𝑎𝑠𝑒𝑑 𝑎𝑐𝑐𝑟𝑢𝑎𝑙𝑠 𝑟𝑎𝑡𝑖𝑜 𝐶𝑎𝑠ℎ-𝑓𝑙𝑜𝑤-𝑏𝑎𝑠𝑒𝑑 𝑎𝑐𝑐𝑟𝑢𝑎𝑙𝑠 𝑟𝑎𝑡𝑖𝑜 𝑁𝑂𝐴 𝑁𝑂𝐴 𝑁𝑂𝐴 𝑁𝑂𝐴 ⁄2 𝐶𝐹𝑂 𝐶𝐹𝐼 𝑁𝐼 ⁄2 𝑁𝑂𝐴 𝑁𝑂𝐴 Cash-flow-based accruals = NI – (CFO + CFI) Cash-flow-based accruals ratio NI – (CFO + CFI) 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑁𝑂𝐴 14 𝑇𝑜𝑡𝑎𝑙 𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠 𝑇𝑜𝑡𝑎𝑙 𝐷𝑒𝑏𝑡 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed CORPORATE FINANCE Reading 15: Capital Structure Weighted average cost of capital, 𝑟 𝐷 𝑟 1 𝑉 𝑟 Value of levered firm, 𝑉 𝑉 𝑇 𝐸 𝑟 𝑉 𝑇 𝐷 Cost of equity, 𝑟 𝑟 𝛽 𝑉 1 𝑟 𝑟 𝑟 𝛽 𝛽 𝛽 1 𝑉 𝐸𝐵𝐼𝑇 1 𝑟 𝑇 𝑇 𝐷 𝐸 𝑇 𝐷 𝐸 𝐷 𝐸 𝑟 𝐷 𝑟 𝑇 𝐷 𝑃𝑉 𝐶𝑜𝑠𝑡 𝑜𝑓 𝐹𝑖𝑛𝑎𝑛𝑐𝑖𝑎𝑙 𝐷𝑖𝑠𝑡𝑟𝑒𝑠𝑠 𝐸𝐵𝐼𝑇 𝑟 𝐷 1 𝑟 𝑇 Static Trade-off Theory: 𝑉 𝑟 𝑟 𝑉 Cost of debt (pre-tax) Cost of of an all-equity firm Reading 16: Dividends and Share Repurchases Analysis Target payout adjustment model (Lintner model) 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑇𝑎𝑟𝑔𝑒𝑡 𝑝𝑎𝑦𝑜𝑢𝑡 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝐿𝑎𝑠𝑡 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑟𝑎𝑡𝑖𝑜 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝐴𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛𝑡 𝑓𝑎𝑐𝑡𝑜𝑟 𝐿𝑎𝑠𝑡 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝐴𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛𝑡 𝑓𝑎𝑐𝑡𝑜𝑟 1 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑦𝑒𝑎𝑟𝑠 𝑓𝑜𝑟 𝑎𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛𝑡 𝑡𝑜 𝑡𝑎𝑘𝑒 𝑝𝑙𝑎𝑐𝑒 Constant dividend payout ratio policy 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑝𝑎𝑦𝑜𝑢𝑡 𝑟𝑎𝑡𝑖𝑜 15 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑒𝑎𝑟𝑛𝑖𝑛𝑔𝑠 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Share Repurchase 𝐸𝑃𝑆 𝑎𝑓𝑡𝑒𝑟 𝑏𝑢𝑦𝑏𝑎𝑐𝑘 𝐵𝑉𝑃𝑆 𝑎𝑓𝑡𝑒𝑟 𝑏𝑢𝑦𝑏𝑎𝑐𝑘 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝐴𝑓𝑡𝑒𝑟 𝑡𝑎𝑥 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑓𝑢𝑛𝑑𝑠 𝑆ℎ𝑎𝑟𝑒𝑠 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 𝑎𝑓𝑡𝑒𝑟 𝑏𝑢𝑦𝑏𝑎𝑐𝑘 𝐵𝑜𝑜𝑘 𝑉𝑎𝑙𝑢𝑒 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑠ℎ𝑎𝑟𝑒 𝑏𝑢𝑦𝑏𝑎𝑐𝑘 𝑆ℎ𝑎𝑟𝑒𝑠 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 𝑎𝑓𝑡𝑒𝑟 𝑏𝑢𝑦𝑏𝑎𝑐𝑘 Analysis of Dividend Safety 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑝𝑎𝑦𝑜𝑢𝑡 𝑟𝑎𝑡𝑖𝑜 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑐𝑜𝑣𝑒𝑟𝑎𝑔𝑒 𝑟𝑎𝑡𝑖𝑜 𝐹𝐶𝐹𝐸 𝑐𝑜𝑣𝑒𝑟𝑎𝑔𝑒 𝑟𝑎𝑡𝑖𝑜 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 𝑁𝑒𝑡 𝐼𝑛𝑐𝑜𝑚𝑒 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 𝐹𝐶𝐹𝐸 𝑆ℎ𝑎𝑟𝑒 𝑟𝑒𝑝𝑢𝑟𝑐ℎ𝑎𝑠𝑒𝑠 Reading 18: Mergers and Acquisitions If acquirer pays using shares: 𝐴𝑐𝑞𝑢𝑖𝑟𝑒𝑟 𝑠 𝐶𝑜𝑠𝑡 𝐸𝑥𝑐ℎ𝑎𝑛𝑔𝑒 𝑟𝑎𝑡𝑖𝑜 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 𝑠ℎ𝑎𝑟𝑒𝑠 𝑜𝑓 𝑡𝑎𝑟𝑔𝑒𝑡 𝑐𝑜𝑚𝑝𝑎𝑛𝑦 Comparable Company Analysis 𝑇𝑎𝑘𝑒𝑜𝑣𝑒𝑟 𝑝𝑟𝑒𝑚𝑖𝑢𝑚, 𝑃𝑅𝑀 𝐷𝑃 𝑆𝑃 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑠𝑡𝑜𝑐𝑘 𝑔𝑖𝑣𝑒𝑛 𝑡𝑜 𝑡𝑎𝑟𝑔𝑒𝑡 𝑠ℎ𝑎𝑟𝑒ℎ𝑜𝑙𝑑𝑒𝑟𝑠 𝐷𝑃 𝑆𝑃 𝑆𝑃 Deal price per share of the target company Stock price of the target company Bid Evaluation Target shareholders’ gain = Premium = PT – VT Acquirer’s gain = Synergies – Premium = S – (PT – VT) VA* = VA + VT + S – C where: PT = price paid for the target company VT = pre-merger value of the target company VA* = post-merger value of the combined companies VA = pre-merger value of the acquirer S = synergies created by the business combination C = cash paid to target shareholders 16 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Reading 19: Capital Budgeting Initial Outlay = FCInv + WCInv – Sal0 + T(Sal0 – B0) Annual after-tax operating cash flows, ATOCF 𝐴𝑇𝑂𝐶𝐹 𝑆 𝐶 𝐷𝑒𝑝 1 𝐴𝑇𝑂𝐶𝐹 𝑆 𝐶 1 𝑇 𝑇 𝑇 Terminal year after-tax non-operating cash flow, TNOCF 𝑇𝑁𝑂𝐶𝐹 𝑆𝑎𝑙 𝑊𝐶𝐼𝑛𝑣 𝑇 𝑆𝑎𝑙 𝐷𝑒𝑝 𝐷𝑒𝑝 𝐵 𝐹𝐶𝐼𝑛𝑣 Fixed capital investment (include equipment cost, delivery and installation cost) 𝑊𝐶𝐼𝑛𝑣 Working capital investment Sales proceeds of old equipment (Replacement project) 𝑆𝑎𝑙 Net book value of old equipment 𝐵 𝑇 Marginal tax rate (1 + Nominal rate) = (1 + Real rate)(1 + Inflation rate) Equivalent Annual Annuity (EAA) [PV] = -Project NPV [I/Y] = Project’s discount rate [N] = Project life [FV] = 0 [CPT] [PMT] EAA 𝑃𝑟𝑜𝑗𝑒𝑐𝑡 𝑁𝑃𝑉 𝑤𝑖𝑡ℎ 𝑟𝑒𝑎𝑙 𝑜𝑝𝑡𝑖𝑜𝑛 𝑁𝑃𝑉 𝑛𝑜 𝑟𝑒𝑎𝑙 𝑜𝑝𝑡𝑖𝑜𝑛 17 𝐶𝑜𝑠𝑡 𝑜𝑓 𝑟𝑒𝑎𝑙 𝑜𝑝𝑡𝑖𝑜𝑛 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑟𝑒𝑎𝑙 𝑜𝑝𝑡𝑖𝑜𝑛 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed EQUITY VALUATION Reading 20: 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 Reading 21: Return Concepts 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 𝑉 𝑃 𝑃 V0 = true intrinsic value Equity risk premium, 𝐸𝑅𝑃 𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑒𝑞𝑢𝑖𝑡𝑦 𝑖𝑛𝑑𝑒𝑥 Gordon Growth model: 𝐷 𝑃 𝑔 𝑟 1 ∆𝑃𝐸 1 𝛽 𝐸 𝑅 𝑅 𝐸𝑞𝑢𝑖𝑡𝑦 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 Ibbotson-Chen model: 𝐸𝑞𝑢𝑖𝑡𝑦 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 1 𝑖 1 𝑔 𝑅𝑖𝑠𝑘 𝑓𝑟𝑒𝑒 𝑟𝑎𝑡𝑒 𝑌 𝑖 expected inflation expected real growth in EPS 𝑔 ∆𝑃𝐸 expected changes in the P/E ratio Y = expected yield on the index 𝑅 = expected risk-free rate CAPM: 𝐸 𝑅 where: 𝑅 𝛽 𝐸 𝑅 𝑅 Risk-free rate (tenor matches investment horizon) Beta of security 𝑖 (Systematic risk) 𝑅 Equity risk premium (or Market risk premium) 18 𝑅 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Fama-French Model Required return on stock =𝑅 +𝛽 , 𝑅 , 𝑅 +𝛽 Pastor-Stambaugh Model Required return on stock 𝑅 + 𝛽 =𝑅 +𝛽 , 𝑅 , +𝛽 𝑅 𝑅 𝑅 𝑅 𝑅 𝑅 𝑅 , , 𝑅 𝑅 +𝛽 𝑅 𝑅 + 𝛽 𝑅 , , 𝑅 𝑅 𝑅 1-month T-bill rate (for Fama-French and Pastor-Stambaugh models only) 𝑅 return on value-weighted market index minus risk-free rate 𝑅 small-cap return premium (𝑅 𝑅 ) 𝑅 value return premium (𝑅 𝑅 ) 𝑅 liquidity premium (𝑅 𝑅 Build-up Method: 𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑅𝑒𝑡𝑢𝑟𝑛 𝑅 𝐸𝑞𝑢𝑖𝑡𝑦 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝑆𝑖𝑧𝑒 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑐𝑜𝑚𝑝𝑎𝑛𝑦 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 Bond-Yield-Plus-Risk-Premium Method: Required Return = YTM of company’s long-term debt + Risk premium Blume’s Adjustment for Regression Beta: 2 𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑏𝑒𝑡𝑎 3 Company 1 3 𝑅𝑒𝑔𝑟𝑒𝑠𝑠𝑖𝑜𝑛 𝑏𝑒𝑡𝑎 Equity Beta, 𝜷𝑳 (Levered beta) Debt-to-Equity ratio 𝐷 𝐸 𝐷 𝐸 𝛽 (given) Benchmark public company (X) 𝛽 Nonpublic company (Y) Unlevered beta Asset beta of public company, 𝛽 Levered beta Equity beta of nonpublic company, 𝛽 19 ? 𝛽 𝐷 𝐸 1 𝛽 1 1 𝑡 𝐷 𝐸 1 𝑡 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Country Spread Model 𝐸𝑞𝑢𝑖𝑡𝑦 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝑓𝑜𝑟 𝑒𝑚𝑒𝑟𝑔𝑖𝑛𝑔 𝑚𝑎𝑟𝑘𝑒𝑡 𝐸𝑞𝑢𝑖𝑡𝑦 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝑓𝑜𝑟 𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑 𝑚𝑎𝑟𝑘𝑒𝑡 𝑌𝑇𝑀 𝑜𝑛 𝑒𝑚𝑒𝑟𝑔𝑖𝑛𝑔 𝑚𝑎𝑟𝑘𝑒𝑡 𝑏𝑜𝑛𝑑 𝑖𝑛 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦 𝑜𝑓 𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑 𝑚𝑎𝑟𝑘𝑒𝑡 𝐶𝑜𝑢𝑛𝑡𝑟𝑦 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝐶𝑜𝑢𝑛𝑡𝑟𝑦 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝑌𝑇𝑀 𝑜𝑛 𝑑𝑒𝑣𝑒𝑙𝑜𝑝𝑒𝑑 𝑚𝑎𝑟𝑘𝑒𝑡 𝑔𝑜𝑣𝑒𝑟𝑛𝑚𝑒𝑛𝑡 𝑏𝑜𝑛𝑑 Reading 22: Industry and Company Analysis 𝑁𝑂𝑃𝐿𝐴𝑇 𝐼𝑛𝑣𝑒𝑠𝑡𝑒𝑑 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 Return on invested capital ROIC 𝑁𝑂𝑃𝐿𝐴𝑇 Net operating profit less adjusted taxes 𝐼𝑛𝑣𝑒𝑠𝑡𝑒𝑑 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑎𝑠𝑠𝑒𝑡𝑠 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠 Return on capital employed ROCE 𝐸𝐵𝐼𝑇 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑑 Reading 23: Discounted Dividend Valuation Discounted Dividend Valuation 𝐶𝐹 1 𝑟 𝑉 𝑉 𝐷 1 𝐷 𝑟 1 𝑟 ⋯ 𝐷 1 𝑃 𝑟 1 𝑟 Gordon Growth Model 𝐷 𝐷 1 𝑔 𝑉 𝑟 𝑔 𝑟 𝑔 Fixed-rate perpetual preferred stock 𝐷 𝑉 𝑟 Value of stock = Value of a company + Present value of with zero-growth growth opportunities (PVGO) 𝐸 𝑉 𝑃𝑉𝐺𝑂 𝑟 𝑉 𝐸 𝑃 𝐸 1 𝑟 𝑃𝑉𝐺𝑂 𝐸 20 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed If dividend and earnings growth rate is constant, 𝐷 𝑟 𝑃 𝑔 Two-Stage Dividend Discount Model 𝐷 1 𝑔 1 𝑟 𝑉 𝐷 1 𝑔 1 𝑔 1 𝑟 𝑟 𝑔 The H-Model 𝑉 𝐻 𝐷 1 𝐷𝐻 𝑔 𝑟 𝑔 𝑔 𝑔 half-life in years of the high-growth period Sustainable growth rate, 𝑔 PRAT model 𝑔 𝑏 𝑁𝐼 𝑅𝑂𝐸 𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 𝑁𝐼 𝑁𝐼 𝑆𝑎𝑙𝑒𝑠 𝑆𝑎𝑙𝑒𝑠 𝑇𝐴 𝑇𝐴 𝑇𝐸 Reading 24: Free Cash Flow Valuation Free Cash Flow to the Firm (FCFF) Valuation Approach 𝐹𝐶𝐹𝐹 1 𝑊𝐴𝐶𝐶 𝐹𝑖𝑟𝑚 𝑉𝑎𝑙𝑢𝑒 Equity Value = Firm Value – Market Value of Debt FCFE Valuation Approach 𝐹𝐶𝐹𝐸 1 𝑟 𝐸𝑞𝑢𝑖𝑡𝑦 𝑉𝑎𝑙𝑢𝑒 Single-Stage (Constant Growth) FCFF and FCFE Model FCFF Valuation Approach 𝐹𝑖𝑟𝑚 𝑉𝑎𝑙𝑢𝑒 FCFE Valuation Approach 𝐸𝑞𝑢𝑖𝑡𝑦 𝑉𝑎𝑙𝑢𝑒 𝐹𝐶𝐹𝐹 𝑊𝐴𝐶𝐶 𝑔 𝐹𝐶𝐹𝐸 𝑟 𝑔 21 𝐹𝐶𝐹𝐹 1 𝑔 𝑊𝐴𝐶𝐶 𝑔 𝐹𝐶𝐹𝐸 1 𝑔 𝑟 𝑔 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed 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 = Investment in fixed capital = 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 = CFO – FCInv + Net borrowing where: Net borrowing = Debt issued – Debt repaid 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 If company issues preferred shares: FCFF = CFO + Int(1 – Tax Rate) + Preferred dividends – FCInv Two-Stage Free Cash Flow Models 𝐹𝑖𝑟𝑚 𝑣𝑎𝑙𝑢𝑒 𝐹𝐶𝐹𝐹 𝑊𝐴𝐶𝐶 𝐹𝐶𝐹𝐹 1 𝑊𝐴𝐶𝐶 𝐸𝑞𝑢𝑖𝑡𝑦 𝑣𝑎𝑙𝑢𝑒 𝐹𝐶𝐹𝐸 1 𝑟 22 𝐹𝐶𝐹𝐸 𝑟 𝑔 𝑔 1 𝑊𝐴𝐶𝐶 1 1 1 𝑟 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Value of Firm = Value of operating assets + Value of nonoperating assets Reading 25: 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 investments Trailing P/E Leading P/E P/B Actual 𝑀𝑎𝑟𝑘𝑒𝑡 𝑝𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 𝐸𝑃𝑆 𝑜𝑣𝑒𝑟 𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠 12 𝑚𝑜𝑛𝑡ℎ𝑠 𝑀𝑎𝑟𝑘𝑒𝑡 𝑝𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 𝐹𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝑒𝑑 𝐸𝑃𝑆 𝑜𝑣𝑒𝑟 𝑛𝑒𝑥𝑡 12 𝑚𝑜𝑛𝑡ℎ𝑠 𝑀𝑎𝑟𝑘𝑒𝑡 𝑝𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 𝐵𝑜𝑜𝑘 𝑣𝑎𝑙𝑢𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 𝑀𝑎𝑟𝑘𝑒𝑡 𝑝𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 𝑆𝑎𝑙𝑒𝑠 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 P/S 𝑉 𝑆 Or 𝑉 𝑆 Trailing D/P Leading D/P Earnings yield Justified 𝑏 1 𝑔 𝑟 𝑔 1 𝑏 𝑟 𝑔 𝑅𝑂𝐸 𝑔 𝑟 𝑔 𝐸 1 𝑏 1 𝑔 𝑆 𝑟 𝑔 1 4 𝑀𝑜𝑠𝑡 𝑟𝑒𝑐𝑒𝑛𝑡 𝑞𝑢𝑎𝑟𝑡𝑒𝑟𝑙𝑦 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑀𝑎𝑟𝑘𝑒𝑡 𝑝𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 𝐹𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝑒𝑑 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠 𝑜𝑣𝑒𝑟 𝑛𝑒𝑥𝑡 𝑓𝑜𝑢𝑟 𝑞𝑢𝑎𝑟𝑡𝑒𝑟𝑠 𝑀𝑎𝑟𝑘𝑒𝑡 𝑝𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 𝐸𝑃𝑆 𝑃𝑟𝑖𝑐𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 1 Underlying Earnings = EPS – non recurring gains + non recurring loss Normalized Earnings Method 1: Average EPS Approach Normalized EPS 1 𝑛 𝐸𝑃𝑆 Method 2: Average ROE Approach Normalized EPS 1 𝑛 𝑅𝑂𝐸 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝐵𝑜𝑜𝑘 𝑣𝑎𝑙𝑢𝑒 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 𝑃/𝐸 𝑟𝑎𝑡𝑖𝑜 𝑔 𝑖𝑛 % 𝑃𝐸𝐺 𝑟𝑎𝑡𝑖𝑜 Earnings surprise = Reported EPS – Expected EPS 23 𝐸 𝑆 1 𝑟 𝑟 1 𝑔 𝑔 𝑟 𝑔 𝑏 𝑔 𝑟 𝑔 𝑏 1 𝑔 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed 𝑺𝒄𝒂𝒍𝒆𝒅 𝒆𝒂𝒓𝒏𝒊𝒏𝒈𝒔 𝒔𝒖𝒓𝒑𝒓𝒊𝒔𝒆 𝑅𝑒𝑝𝑜𝑟𝑡𝑒𝑑 𝐸𝑃𝑆 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝐸𝑃𝑆 𝜎 𝐴𝑛𝑎𝑙𝑦𝑠𝑡 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡 𝐸𝑃𝑆 Standardized unexpected earnings (SUE) Portfolio P/E 1 𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 ℎ𝑎𝑟𝑚𝑜𝑛𝑖𝑐 𝑚𝑒𝑎𝑛 𝑤 𝑋 ∑ 𝑤 𝑋 Weight of stock i in portfolio P/E of stock i Reading 26: Residual Income Valuation Economic Value Added (EVA) 𝐸𝐵𝐼𝑇 1 𝐸𝑉𝐴 𝑇 𝑊𝐴𝐶𝐶 𝐼𝑛𝑣𝑒𝑠𝑡𝑒𝑑 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 Market Value Added (MVA) 𝑀𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝐹𝑖𝑟𝑚 𝑀𝑉𝐴 𝐼𝑛𝑣𝑒𝑠𝑡𝑒𝑑 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 Residual Income, RI 𝑅𝐼 Residual Income Model 𝑉 𝐸 𝑟 𝐵 𝑅𝑂𝐸 𝑅𝐼 𝐵 1 𝑟 𝑅𝐼 𝑟 𝐵 𝑅𝐼 1 𝑟 Single-stage residual income valuation model 𝑅𝑂𝐸 𝑟 𝐵 𝑉 𝑟 𝑔 𝐵 1 𝐵 𝑟 ⋯ 𝑅𝐼 𝑟 𝑔 𝑀𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑑𝑒𝑏𝑡 𝑀𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑒𝑞𝑢𝑖𝑡𝑦 𝑅𝑒𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑡𝑜𝑡𝑎𝑙 𝑎𝑠𝑠𝑒𝑡𝑠 𝑇𝑜𝑏𝑖𝑛 𝑠 𝑄 Continuing Residual Income 𝑉 𝐵 𝑅𝐼 1 𝑟 1 𝑅𝐼 𝜔 1 𝑟 0 𝑟 𝜔 1 If RI declines to Long-run level in mature industry, with premium over book value 𝑉 𝑅𝐼 𝐵 1 𝑟 𝑃 1 𝐸 𝐷𝑖𝑣 Clean surplus relationship: 𝐵 𝐵 24 𝐵 𝑟 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Reading 27: Private Company Valuation Capitalized Cash Flow Method (CCM) 𝐹𝑖𝑟𝑚 𝑣𝑎𝑙𝑢𝑒 𝐹𝐶𝐹𝐹 1 𝑔 𝑊𝐴𝐶𝐶 𝑔 𝐸𝑞𝑢𝑖𝑡𝑦 𝑣𝑎𝑙𝑢𝑒 𝐹𝐶𝐹𝐸 1 𝑔 𝑟 𝑔 𝐸𝑞𝑢𝑖𝑡𝑦 𝑣𝑎𝑙𝑢𝑒 → 𝐹𝑖𝑟𝑚 𝑣𝑎𝑙𝑢𝑒 𝑀𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝐷𝑒𝑏𝑡 Excess Earnings Method (EEM) 𝑬𝒙𝒄𝒆𝒔𝒔 𝒆𝒂𝒓𝒏𝒊𝒏𝒈𝒔 𝑁𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 𝑒𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑡𝑜 𝑝𝑟𝑜𝑣𝑖𝑑𝑒 𝑡ℎ𝑒 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝒘𝒐𝒓𝒌𝒊𝒏𝒈 𝒄𝒂𝒑𝒊𝒕𝒂𝑙 𝑎𝑛𝑑 𝒇𝒊𝒙𝒆𝒅 𝒂𝒔𝒔𝒆𝒕𝒔 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑖𝑛𝑡𝑎𝑛𝑔𝑖𝑏𝑙𝑒 𝑎𝑠𝑠𝑒𝑡𝑠 𝐸𝑥𝑐𝑒𝑠𝑠 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑘 𝑔 Value of the firm = Working capital + Fixed assets + Intangible Assets 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) 25 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed FIXED INCOME Reading 28: The Term Structure and Interest Rate Dynamics Forward pricing model 𝐷𝐹 where: 𝐷𝐹 𝐹 𝐷𝐹 𝐹 𝑧 1 , 1 1 𝑧 1 , 1 𝑓, Forward rate model 1 𝑧 𝑓, 1 𝑧 𝑓, Spot rate for period 𝐵 𝐵 𝐴 forward rate that starts in period 𝐴 Calculating spot rate from one-period forward rates 𝑧 Fixed swap rate 𝑠 1 1 ∑ 𝑧 𝐷𝐹 𝐷𝐹 1 1 𝑓, 1 𝑓, … 1 𝑓 ⁄ , 1 𝐷𝑖𝑠𝑐𝑜𝑢𝑛𝑡 𝐹𝑎𝑐𝑡𝑜𝑟 𝑜𝑓 𝐿𝑎𝑠𝑡 𝑃𝑎𝑦𝑚𝑒𝑛𝑡 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 For Parallel shifts in yield curve: %∆𝑃𝑉 𝑀𝑜𝑑𝐷𝑢𝑟 ∆𝑌𝑇𝑀 ∆𝑃𝑉 𝑀𝑜𝑑𝐷𝑢𝑟 ∆𝑌𝑇𝑀 %∆𝑃𝑉 𝐸𝑓𝑓𝐷𝑢𝑟 ∆𝐶𝑢𝑟𝑣𝑒 ∆𝑃𝑉 𝐸𝑓𝑓𝐷𝑢𝑟 ∆𝐶𝑢𝑟𝑣𝑒 Non-parallel shifts (i.e. change in slope or curvature): %∆𝑃𝑉 𝐾𝑒𝑦𝑅𝑎𝑡𝑒𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛 ∆𝐾𝑒𝑦 𝑅𝑎𝑡𝑒 26 𝑃𝑉 𝑃𝑉 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Reading 29: The Arbitrage-Free Valuation Framework Arbitrage-free value of bond: 𝐶 1 𝑆 𝑉 𝑆 𝐶 1 𝑆 𝐹𝑉 𝐶 1 𝑆 ⋯ Spot rate for period n Backward Induction Valuation Methodology 0.5 𝐵𝑜𝑛𝑑 𝑣𝑎𝑙𝑢𝑒 𝑎𝑡 𝑎𝑛𝑦 𝑛𝑜𝑑𝑒 𝑉 𝑉 𝐶 𝑉 0.5 1 𝑖 bond’s value if the higher forward rate is realized one year hence bond’s value if the lower forward rate is realized one year hence coupon payment that is not dependent on interest rates 𝑖 , 𝑖, 𝑒 𝑖 , 𝑖 𝑖 , 𝑒 , 𝑖 , 𝑖 𝑒 𝑖 𝑖 , 𝑒 , 𝑖 , Cox-Ingersoll-Ross (CIR) Model 𝑑𝑟 , 𝑒 𝑖 𝜎 𝑟 𝑑𝑧 𝑟 𝑑𝑡 𝑘 𝜃 𝑖 , Vasicek Model 𝑑𝑟 𝑎 𝑏 𝜎 𝑘 𝜃 𝑟 𝑑𝑡 𝜎𝑑𝑧 Speed of reversion (> 0) Long-run interest rate Interest rate volatility Ho-Lee Model 𝑑𝑟 𝜃 𝑉 𝜃 𝑑𝑡 𝜎𝑑𝑧 Time-dependent drift term Kalotay-Williams-Fabozzi (KWF) Model 𝑑 ln 𝑟 𝜃 𝑑𝑡 27 𝜎𝑑𝑧 , 𝑒 𝐶 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Reading 30: Valuation and Analysis - Bonds with Embedded Options 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 𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 𝑃𝑉 𝑃𝑉 Δ𝐶𝑢𝑟𝑣𝑒 𝑃𝑉 2 𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑐𝑜𝑛𝑣𝑒𝑥𝑖𝑡𝑦 𝑃𝑉 2 𝑃𝑉 Δ𝐶𝑢𝑟𝑣𝑒 𝑃𝑉 𝑃𝑉 Convertible Bonds 𝐶𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑣𝑎𝑙𝑢𝑒 𝑈𝑛𝑑𝑒𝑟𝑙𝑦𝑖𝑛𝑔 𝑠ℎ𝑎𝑟𝑒 𝑝𝑟𝑖𝑐𝑒 𝑴𝒊𝒏𝒊𝒎𝒖𝒎 𝒗𝒂𝒍𝒖𝒆 𝑜𝑓 𝑐𝑜𝑛𝑣𝑒𝑟𝑡𝑖𝑏𝑙𝑒 𝑏𝑜𝑛𝑑 𝑴𝒂𝒙 𝐶𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜 𝐶𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑢𝑛𝑑𝑒𝑟𝑙𝑦𝑖𝑛𝑔 , 𝑆𝑡𝑟𝑎𝑖𝑔ℎ𝑡 𝑏𝑜𝑛𝑑 𝑣𝑎𝑙𝑢𝑒 𝑀𝑎𝑟𝑘𝑒𝑡 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑝𝑟𝑖𝑐𝑒 𝐶𝑜𝑛𝑣𝑒𝑟𝑡𝑖𝑏𝑙𝑒 𝑏𝑜𝑛𝑑 𝑝𝑟𝑖𝑐𝑒 𝐶𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜 𝑀𝑎𝑟𝑘𝑒𝑡 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 𝑀𝑎𝑟𝑘𝑒𝑡 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑝𝑟𝑖𝑐𝑒 𝑀𝑎𝑟𝑘𝑒𝑡 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝑟𝑎𝑡𝑖𝑜 𝑀𝑎𝑟𝑘𝑒𝑡 𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 𝑈𝑛𝑑𝑒𝑟𝑙𝑦𝑖𝑛𝑔 𝑠ℎ𝑎𝑟𝑒 𝑝𝑟𝑖𝑐𝑒 𝑃𝑟𝑒𝑚𝑖𝑢𝑚 𝑜𝑣𝑒𝑟 𝑆𝑡𝑟𝑎𝑖𝑔ℎ𝑡 𝑣𝑎𝑙𝑢𝑒 𝐶𝑜𝑛𝑣𝑒𝑟𝑡𝑖𝑏𝑙𝑒 𝑏𝑜𝑛𝑑 𝑝𝑟𝑖𝑐𝑒 𝑆𝑡𝑟𝑎𝑖𝑔ℎ𝑡 𝑣𝑎𝑙𝑢𝑒 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑐𝑜𝑛𝑣𝑒𝑟𝑡𝑖𝑏𝑙𝑒 𝑏𝑜𝑛𝑑 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡 𝑏𝑜𝑛𝑑 𝑈𝑛𝑑𝑒𝑟𝑙𝑦𝑖𝑛𝑔 𝑠ℎ𝑎𝑟𝑒 𝑝𝑟𝑖𝑐𝑒 1 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑐𝑎𝑙𝑙 𝑜𝑝𝑡𝑖𝑜𝑛 𝑜𝑛 𝑖𝑠𝑠𝑢𝑒𝑟 𝑠 𝑠𝑡𝑜𝑐𝑘 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑖𝑠𝑠𝑢𝑒𝑟 𝑐𝑎𝑙𝑙 𝑜𝑝𝑡𝑖𝑜𝑛 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑖𝑛𝑣𝑒𝑠𝑡𝑜𝑟 𝑝𝑢𝑡 𝑜𝑝𝑡𝑖𝑜𝑛 Reading 31: Credit Analysis Models 𝐺-𝑠𝑝𝑟𝑒𝑎𝑑 𝑌𝑇𝑀 𝑜𝑓 𝐶𝑜𝑟𝑝𝑜𝑟𝑎𝑡𝑒 𝑏𝑜𝑛𝑑 𝑌𝑇𝑀 𝑜𝑓 𝐺𝑜𝑣𝑒𝑟𝑛𝑚𝑒𝑛𝑡 𝑏𝑜𝑛𝑑 𝐿𝑜𝑠𝑠 𝑔𝑖𝑣𝑒𝑛 𝑑𝑒𝑓𝑎𝑢𝑙𝑡 1 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑒𝑥𝑝𝑜𝑠𝑢𝑟𝑒 𝐿𝑜𝑠𝑠 𝑠𝑒𝑣𝑒𝑟𝑖𝑡𝑦 1 𝑅𝑒𝑐𝑜𝑣𝑒𝑟𝑦 𝑟𝑎𝑡𝑒 𝑅𝑒𝑐𝑜𝑣𝑒𝑟𝑦 𝑟𝑎𝑡𝑒 Expected Loss = Probability of Default × Loss Given Default 28 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed 𝐹𝑎𝑖𝑟 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑐𝑟𝑒𝑑𝑖𝑡 𝑟𝑖𝑠𝑘𝑦 𝑏𝑜𝑛𝑑 𝐹𝑎𝑖𝑟 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑏𝑜𝑛𝑑 𝑎𝑠𝑠𝑢𝑚𝑖𝑛𝑔 𝑛𝑜 𝑑𝑒𝑓𝑎𝑢𝑙𝑡 𝑛 𝐸𝐿 1 𝑟𝑓 𝐶𝑉𝐴 𝐶𝑟𝑒𝑑𝑖𝑡 𝑉𝑎𝑙𝑢𝑒 𝐴𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛𝑡 𝑃𝑂𝐷𝑡 𝑡 1 1 𝑟𝑓𝑡 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 Approximation of credit spread 𝑡 𝑅𝑒𝑐𝑜𝑣𝑒𝑟𝑦 𝐸𝐿 1 𝑟𝑓 𝑃𝑉 𝑜𝑓 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑙𝑜𝑠𝑠 𝑓𝑜𝑟 𝑝𝑒𝑟𝑖𝑜𝑑 𝑡 1 𝐶𝑉𝐴 𝐿𝐺𝐷𝑡 𝐸𝐿 Expected loss of bond at time t Probability of default of bond at time t 𝑃𝑂𝐷 Loss given default at time t 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝐸𝑥𝑝𝑜𝑠𝑢𝑟𝑒 𝐿𝐺𝐷 𝑟𝑓 Risk-free rate at time t 𝑛 Bond’s remaining tenor 𝑃𝑂𝐷 𝑉𝑁𝐷 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒 Annual hazard rate × (1 – Recovery rate) Expected percentage price change of a corporate bond 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑐𝑟𝑒𝑑𝑖𝑡 𝑚𝑖𝑔𝑟𝑎𝑡𝑖𝑜𝑛 where %∆𝑃 𝐷𝑢𝑟 %∆𝑃 ∆𝑐𝑟𝑒𝑑𝑖𝑡 𝑠𝑝𝑟𝑒𝑎𝑑 Structural Model 𝐴 In terms of… Equity Debt 𝑆 𝐴 𝐾 𝐷 𝑡, 𝑇 𝑆 Call options 𝐸 𝑇 𝑀𝑎𝑥 𝐴 𝑇 𝐾, 0 𝑀𝑎𝑥 𝐴 𝑇 𝐾, 0 𝐴 𝑇 𝐷 𝑇 Put options 𝐸 𝑇 𝐴 𝑇 𝐾 𝑀𝑎𝑥 𝐾 𝐴 𝑇 , 0 𝐷 𝑇 𝐾 𝑀𝑎𝑥 𝐾 𝐴 𝑇 , 0 𝐸𝑞𝑢𝑖𝑡𝑦 𝑣𝑎𝑙𝑢𝑒 𝑎𝑡 𝑡𝑖𝑚𝑒 𝑡 𝐴𝑠𝑠𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝑎𝑡 𝑡𝑖𝑚𝑒 𝑇 𝐹𝑎𝑐𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑑𝑒𝑏𝑡 Present Value of Expected Loss (PVOEL) = PV of risk-free bond – PV of risky bond 29 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Reading 32: Credit Default Swaps CDS payout amount = Payout ratio × Notional = (1 – Recovery rate) × Notional Upfront payment = PV of protection leg – PV of premium leg 𝑈𝑝𝑓𝑟𝑜𝑛𝑡 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝑃𝑉 𝑜𝑓 𝑃𝑉 𝑜𝑓 𝐶𝑟𝑒𝑑𝑖𝑡 𝑆𝑝𝑟𝑒𝑎𝑑 𝐹𝑖𝑥𝑒𝑑 𝐶𝑜𝑢𝑝𝑜𝑛 𝐶𝑟𝑒𝑑𝑖𝑡 𝐹𝑖𝑥𝑒𝑑 𝐶𝐷𝑆 𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛 𝑆𝑝𝑟𝑒𝑎𝑑 𝐶𝑜𝑢𝑝𝑜𝑛 𝑃𝑟𝑖𝑐𝑒 𝑜𝑓 𝐶𝐷𝑆 100 𝑈𝑝𝑓𝑟𝑜𝑛𝑡 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 % 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝐶𝐷𝑆 𝑝𝑟𝑖𝑐𝑒 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑠𝑝𝑟𝑒𝑎𝑑 𝑖𝑛 𝑏𝑝𝑠 𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛 30 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed DERIVATIVES Reading 33: Pricing and Valuation of Forward Commitments Forward Pricing: 𝐹 𝑆 1 𝑟 𝐹 𝑆 𝐶𝐶 where: 𝐶𝐶 𝐹 𝑆 𝑒 𝐹 𝑆 𝑒 𝐶𝐵 1 𝑟 PV of Carry cost 𝐶𝐵 𝑟 PV of carry benefits continuously compounded risk-free rate Note: CC and CB are continuously compounded rates Forward Valuation (Long Position): 𝑉 0 𝑉 𝐹 𝐹 1 𝑟 𝑉 𝑆 𝑆 𝐹 1 𝑟 𝐹 Forward Rate Agreement (FRA) Payoff at expiration: 𝑳𝒐𝒏𝒈 𝐹𝑅𝐴 𝑝𝑎𝑦𝑜𝑓𝑓 𝑎𝑡 𝒆𝒙𝒑𝒊𝒓𝒂𝒕𝒊𝒐𝒏 𝑜𝑓 𝐹𝑅𝐴 Pricing: 𝐹𝑅𝐴 1 1 𝐿 𝑡 𝐿 𝑡 1 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙 𝐿 𝐹𝑅𝐴 𝑡 1 𝐷 𝑡 1 𝑡 Valuation (prior to FRA expiration): 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐿𝑜𝑛𝑔 𝐹𝑅𝐴 𝑎𝑡 𝑔 𝐷 ℎ 𝑚 𝑇 𝐹𝑅𝐴 𝑡 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙 𝐹𝑅𝐴 1 𝐷 𝑡 Discount rate for m periods at t = h FRA tenor Tenor of the underlying rate (e.g. LIBOR) ℎ 𝑚 Maturity of underlying instrument 31 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Fixed Income Forwards and Futures Pricing: 𝑄𝑢𝑜𝑡𝑒𝑑 𝑓𝑢𝑡𝑢𝑟𝑒𝑠 𝐶𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝐹 𝑓𝑎𝑐𝑡𝑜𝑟 𝑝𝑟𝑖𝑐𝑒 𝐴𝐼 𝐹𝑉𝐶𝐼 𝐴𝐼 𝐹𝑉 𝐵 Valuation for fixed income forward contracts: 𝑃𝑟𝑒𝑠𝑒𝑛𝑡 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑛 𝑓𝑜𝑟𝑤𝑎𝑟𝑑 𝑝𝑟𝑖𝑐𝑒𝑠 𝑉 𝑃𝑉 𝐹 𝐹 Valuation for fixed income futures contracts: Price change since previous day’s settlement 𝑉 𝐵 𝐴𝐼 Quoted bond price 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑐𝑐𝑟𝑢𝑒𝑑 𝑑𝑎𝑦𝑠 𝑠𝑖𝑛𝑐𝑒 𝑙𝑎𝑠𝑡 𝑐𝑜𝑢𝑝𝑜𝑛 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 𝑇𝑜𝑡𝑎𝑙 𝑑𝑎𝑦𝑠 𝑑𝑢𝑟𝑖𝑛𝑔 𝑡ℎ𝑒 𝑐𝑜𝑢𝑝𝑜𝑛 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 𝑝𝑒𝑟𝑖𝑜𝑑 Interest Rate Swaps (IRS) Pricing: 𝐹𝑆 𝑃𝑉 1 ∑ 𝐴𝑛𝑛𝑢𝑎𝑙 𝑐𝑜𝑢𝑝𝑜𝑛 𝐶𝑜𝑢𝑝𝑜𝑛 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑃𝑉 𝑃𝑉 1 1 𝑆𝑝𝑜𝑡 𝑖𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑟𝑎𝑡𝑒 𝐷𝑎𝑦𝑠 𝑡𝑜 𝑀𝑎𝑡𝑢𝑟𝑖𝑡𝑦 360 Valuation: Pay-fixed, receive-floating IRS 𝑉 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙 𝐹𝑆 𝑭𝑺𝟎 𝑃𝑉 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙 𝑭𝑺𝟎 𝐹𝑆 𝑃𝑉 Receive-fixed, pay-floating IRS 𝑉 32 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Currency Swap Pricing for fixed leg of currency swap in currency 𝑎 1 𝑃𝑉 , 𝐹𝑆 ∑ 𝑃𝑉 , Value of a fixed-for-fixed currency swap 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙 𝑉 𝑉 𝑆 𝑉 𝐹𝑆 𝑃𝑉 , 𝑃𝑉 , 𝑉 𝐹𝑆 𝑃𝑉 , 𝑃𝑉 𝑆 Spot exchange rate at time 𝑡 (quoted as 𝑎⁄𝑏) 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙 𝑉 𝑃𝑎𝑟 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦 𝑎 𝑙𝑒𝑔 𝑟𝑒𝑐𝑒𝑖𝑣𝑒 𝑃𝑎𝑟 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦 𝑏 𝑙𝑒𝑔 𝑝𝑎𝑦 , Equity Swap Value of equity swap (receive fixed-rate, pay equity return) 𝑆 𝑉 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙 𝑃𝑉 𝑃𝑎𝑟 𝑉 , 𝐶 𝑆 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦 𝐿𝑒𝑔 Cash flow for equity leg 𝑉 𝑆 𝑆 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙 𝑆 𝑆 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙 𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙 𝑃𝑒𝑟𝑖𝑜𝑑𝑖𝑐 𝑒𝑞𝑢𝑖𝑡𝑦 𝑟𝑒𝑡𝑢𝑟𝑛 𝐶 Value at time 𝑡 of a fixed-rate bond initiated with coupon 𝐶 at Time 0 Current equity index level = Equity index level at last reset date Reading 34: Valuation of Contingent Claims ℎ 𝑐 𝑆 𝑐 𝑆 0 ℎ 𝑝 𝑆 𝑝 𝑆 0 No-arbitrage Approach: 𝑐 ℎ 𝑆 𝑃𝑉 ℎ 𝑆 𝑐 ℎ 𝑆 𝑃𝑉 ℎ 𝑆 𝑐 𝑝 ℎ 𝑆 𝑃𝑉 ℎ 𝑆 𝑝 ℎ 𝑆 𝑃𝑉 ℎ 𝑆 𝑝 33 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Expectations Approach: 1 𝜋 𝑟 𝑢 𝑑 𝑑 One-period binomial model: 𝜋𝑐 𝑐 1 𝜋 𝑐 𝑟 𝜋𝑝 𝑝 Note: For interest rate options, 𝜋 1-period forward rates. 1 1 1 𝜋 𝑝 𝑟 0.5 and discount expected option payoff using the Two-period binomial model: 𝑐 𝑝 𝜋 𝑐 2𝜋 1 𝜋 𝑐 1 𝑟 1 𝜋 𝑐 𝜋 𝑝 2𝜋 1 𝜋 𝑝 1 𝑟 1 𝜋 𝑝 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 Black-Scholes Option Pricing Model 𝑐 𝑝 𝑑 𝑑 ln 𝑆 𝑋 𝑟 1 𝜎 2 𝑆𝑁 𝑑 𝑋𝑒 𝑁 𝑋𝑒 𝑑 𝑇 𝜎√𝑇 𝑑 𝜎√𝑇 34 𝑁 𝑑 𝑆𝑁 𝑑 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed 𝑝 Put-call parity: • • • • 𝑆 𝑐 𝑋𝑒 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) = N(-d2) = Prob(ST < X) BSM model with carry benefits 𝑐 𝑆𝑒 𝑝 𝑁 𝑑 𝑁 𝑋𝑒 𝑆 𝑋 ln 𝑑 𝑑 𝑟 𝑝 𝑁 𝑑 𝑆𝑒 𝑁 𝑑 1 𝜎 2 𝑇 𝛾 𝜎√𝑇 𝑑 𝑑 Put-call parity: 𝑋𝑒 𝑆𝑒 𝑐 𝜎√𝑇 𝑋𝑒 Black Option Valuation Model: European Options on Futures 𝐹 𝑇 𝑁 𝑑 𝑋𝑁 𝑑 𝑐 𝑒 𝑆𝑒 𝑁 𝑑 𝑝 𝑋𝑒 𝑁 𝑑 𝑑 𝑑 ln 𝑑 𝐹 𝑇 1 𝜎 𝑇 2 𝑋 𝜎 √𝑇 𝜎√𝑇 𝑐 Put-call parity: 𝑒 𝐹 𝑇 𝑋 𝑝 Interest Rate Options: 𝑐 𝑝 𝐴𝑃 𝑒 ,𝑡 𝐹𝑅𝐴 0, 𝑡 𝑅 𝑒 𝐴𝑃 𝑒 ln 𝑑 𝑁 𝐹𝑅𝐴 0, 𝑡 𝑋 𝑅 𝑒 𝑑 𝐹𝑅𝐴 0, 𝑡 ,𝑡 1 2𝜎 𝜎 𝑡 𝑑 𝑁 𝑑 𝑑 𝜎 𝑡 35 𝑡 ,𝑡 𝑁 𝑑 𝑁 𝑑 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Payer Swaption 𝑃𝐴𝑌 𝐴𝑃 𝑅 𝑁 𝑑 𝑅 𝑁 𝑑 𝑅 𝑁 𝑑 𝑃𝑉 1 Receiver Swaption 𝐴𝑃 𝑅𝐸𝐶 ln 𝑑 Optimal Number of Hedging Units 𝑒 𝑆𝜎√𝑇 𝑑 1 𝜎 2 𝑇 𝑑 𝜎√𝑇 𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑑𝑒𝑙𝑡𝑎 𝐷𝑒𝑙𝑡𝑎 𝑁 𝐺𝑎𝑚𝑚𝑎 𝑅 𝑅 𝑁 𝜎√𝑇 𝑑 𝐺𝑎𝑚𝑚𝑎 𝑅 𝑛 𝑑 𝑐 𝑐 𝐷𝑒𝑙𝑡𝑎 𝛥𝑆 1 𝐺𝑎𝑚𝑚𝑎 2 𝛥𝑆 𝑝 𝑝 𝐷𝑒𝑙𝑡𝑎 𝛥𝑆 1 𝐺𝑎𝑚𝑚𝑎 2 𝛥𝑆 36 𝑃𝑉 1 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed ALTERNATIVE INVESTMENTS Reading 35: Real Estate Investments Net lease = Gross lease – operating expense Appraisal-based index 𝑁𝑂𝐼 𝑅𝑒𝑡𝑢𝑟𝑛 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝐸𝑛𝑑𝑖𝑛𝑔 𝐸𝑥𝑝𝑒𝑛𝑑𝑖𝑡𝑢𝑟𝑒𝑠 𝑚𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝑚𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 𝐵𝑒𝑔𝑖𝑛𝑛𝑖𝑛𝑔 𝑚𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒 Highest and Best Use Implied land value = Value after construction – Cost to construct building Direct Capitalization Method Value of property at the time of purchase 𝑁𝑂𝐼 𝐶𝑎𝑝 𝑟𝑎𝑡𝑒 Value of property at the time of purchase 𝑅𝑒𝑛𝑡 𝐴𝑙𝑙 𝑟𝑖𝑠𝑘 𝑦𝑖𝑒𝑙𝑑 𝐶𝑎𝑝 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑐𝑜𝑚𝑝𝑎𝑟𝑎𝑏𝑙𝑒 𝐼𝑅𝑅 𝐶𝑎𝑝 𝑟𝑎𝑡𝑒 𝑁𝑂𝐼 𝑆𝑎𝑙𝑒 𝑝𝑟𝑖𝑐𝑒 𝑜𝑓 𝑐𝑜𝑚𝑝𝑎𝑟𝑎𝑏𝑙𝑒 𝐺𝑟𝑜𝑤𝑡ℎ 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑁𝑂𝐼 If property under renovation, Value of property = Value if renovated – Loss in value due to renovation Gross income multiplier 𝑆𝑎𝑙𝑒 𝑝𝑟𝑖𝑐𝑒 𝐺𝑟𝑜𝑠𝑠 𝑖𝑛𝑐𝑜𝑚𝑒 37 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Discounted Cash Flow Method Constant growth rate: 𝑉 𝑁𝑂𝐼 𝑟 𝑔 Appraisal with Terminal Value (or Resale/Reversion Value): 𝑁𝑂𝐼 1 𝑟 𝑉 𝑁𝑂𝐼 𝑇𝑒𝑟𝑚𝑖𝑛𝑎𝑙 𝑐𝑎𝑝 𝑟𝑎𝑡𝑒 𝑉𝑎𝑙𝑢𝑒 𝑁 𝑉𝑎𝑙𝑢𝑒 1 𝑟 𝑁𝑂𝐼 𝑟 𝑔 Investor’s holding period 𝐺𝑜𝑖𝑛𝑔 𝑖𝑛 𝐶𝑎𝑝 𝑅𝑎𝑡𝑒 𝑁𝑂𝐼 𝑉 Private Market Real Estate Debt 𝐿𝑇𝑉 𝑟𝑎𝑡𝑖𝑜 𝐿𝑜𝑎𝑛 𝑃𝑟𝑜𝑝𝑒𝑟𝑡𝑦 𝑣𝑎𝑙𝑢𝑒 𝐷𝑒𝑏𝑡 𝑠𝑒𝑟𝑣𝑖𝑐𝑒 𝑐𝑜𝑣𝑒𝑟𝑎𝑔𝑒 𝑟𝑎𝑡𝑖𝑜, 𝐷𝑆𝐶𝑅 𝐸𝑞𝑢𝑖𝑡𝑦 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑟𝑎𝑡𝑒 𝑁𝑂𝐼 𝐷𝑒𝑏𝑡 𝑠𝑒𝑟𝑣𝑖𝑐𝑒 𝐹𝑖𝑟𝑠𝑡 𝑦𝑒𝑎𝑟 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤 𝐸𝑞𝑢𝑖𝑡𝑦 𝑁𝑂𝐼 𝑀𝑜𝑟𝑔𝑎𝑔𝑒 𝑝𝑎𝑦𝑚𝑒𝑛𝑡 𝑃𝑢𝑟𝑐ℎ𝑎𝑠𝑒 𝑝𝑟𝑖𝑐𝑒 𝐿𝑜𝑎𝑛 𝑎𝑚𝑜𝑢𝑛𝑡 Note: Equity dividend rate also called “cash-on-cash” return. Net Asset Value approach: 𝑁𝐴𝑉 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 where: 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑒𝑠𝑡𝑎𝑡𝑒 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑇𝑜𝑡𝑎𝑙 𝑑𝑒𝑏𝑡 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑒𝑠𝑡𝑎𝑡𝑒 𝑜𝑡ℎ𝑒𝑟 𝑎𝑠𝑠𝑒𝑡𝑠 𝑎𝑛𝑑 𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠ℎ𝑎𝑟𝑒𝑠 𝑜𝑢𝑡𝑠𝑡𝑎𝑛𝑑𝑖𝑛𝑔 𝑁𝑂𝐼 𝐶𝑎𝑝 𝑟𝑎𝑡𝑒 Funds from Operations: 𝐹𝐹𝑂 𝑁𝑒𝑡 𝑖𝑛𝑐𝑜𝑚𝑒 𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝑎𝑛𝑑 𝑎𝑚𝑜𝑟𝑡𝑖𝑧𝑎𝑡𝑖𝑜𝑛 38 𝐺𝑎𝑖𝑛𝑠 𝑜𝑛 𝑠𝑎𝑙𝑒 𝑜𝑓 𝑝𝑟𝑜𝑝𝑒𝑟𝑡𝑦 𝐿𝑜𝑠𝑠 𝑜𝑛 𝑠𝑎𝑙𝑒 𝑜𝑓 𝑝𝑟𝑜𝑝𝑒𝑟𝑡𝑦 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Adjusted Funds from Operations: 𝑁𝑜𝑛 𝑐𝑎𝑠ℎ 𝐴𝐹𝐹𝑂 𝐹𝐹𝑂 𝑟𝑒𝑛𝑡 𝑅𝑒𝑐𝑢𝑟𝑟𝑖𝑛𝑔 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑒𝑥𝑝𝑒𝑛𝑑𝑖𝑡𝑢𝑟𝑒 𝑎𝑛𝑑 𝑙𝑒𝑎𝑠𝑖𝑛𝑔 𝑐𝑜𝑠𝑡𝑠 Reading 36: Private Equity Investments Venture Capital Method Pre-money valuation 𝑷𝒐𝒔𝒕 𝒎𝒐𝒏𝒆𝒚 𝑣𝑎𝑙𝑢𝑎𝑡𝑖𝑜𝑛 New equity injection 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑒𝑞𝑢𝑖𝑡𝑦 𝑎𝑡 𝑒𝑥𝑖𝑡 𝑅𝑂𝐼 𝑁 𝑜𝑙𝑑 𝑠ℎ𝑎𝑟𝑒𝑠 𝑃𝑟𝑖𝑐𝑒 𝑝𝑎𝑖𝑑 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑒𝑞𝑢𝑖𝑡𝑦 𝑎𝑡 𝑒𝑥𝑖𝑡 1 𝐼𝑅𝑅 𝑁𝑒𝑤 𝑒𝑞𝑢𝑖𝑡𝑦 𝑖𝑛𝑗𝑒𝑐𝑡𝑖𝑜𝑛 𝑷𝒐𝒔𝒕 𝒎𝒐𝒏𝒆𝒚 𝑣𝑎𝑙𝑢𝑎𝑡𝑖𝑜𝑛 𝑉𝐶 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑜𝑤𝑛𝑒𝑟𝑠ℎ𝑖𝑝 𝑉𝐶 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑜𝑤𝑛𝑒𝑟𝑠ℎ𝑖𝑝 Post-money valuation 𝑁 𝑛𝑒𝑤 𝑠ℎ𝑎𝑟𝑒𝑠 𝑁 𝑜𝑝𝑡𝑖𝑜𝑛 𝑝𝑜𝑜𝑙 𝑁𝑒𝑤 𝑒𝑞𝑢𝑖𝑡𝑦 𝑖𝑛𝑗𝑒𝑐𝑡𝑖𝑜𝑛 𝑁 𝑛𝑒𝑤 𝑠ℎ𝑎𝑟𝑒𝑠 For two stages of financing (Stage A and Stage B) 𝑆𝑒𝑟𝑖𝑒𝑠 𝐴 𝑖𝑛𝑣𝑒𝑠𝑡𝑜𝑟𝑠 𝑆𝑒𝑟𝑖𝑒𝑠 𝐴 𝑖𝑛𝑣𝑒𝑠𝑡𝑜𝑟𝑠 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑜𝑤𝑛𝑒𝑟𝑠ℎ𝑖𝑝 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑜𝑤𝑛𝑒𝑟𝑠ℎ𝑖𝑝 𝑎𝑓𝑡𝑒𝑟 𝑆𝑒𝑟𝑖𝑒𝑠 𝐵 𝑓𝑖𝑛𝑎𝑛𝑐𝑖𝑛𝑔 𝑎𝑓𝑡𝑒𝑟 𝑆𝑒𝑟𝑖𝑒𝑠 𝐴 𝑓𝑖𝑛𝑎𝑛𝑐𝑖𝑛𝑔 𝑆𝑒𝑟𝑖𝑒𝑠 𝐴 𝑖𝑛𝑣𝑒𝑠𝑡𝑜𝑟𝑠 𝑖𝑚𝑝𝑙𝑖𝑒𝑑 𝑅𝑂𝐼 𝑎𝑓𝑡𝑒𝑟 𝑆𝑒𝑟𝑖𝑒𝑠 𝐵 𝑓𝑖𝑛𝑎𝑛𝑐𝑖𝑛𝑔 𝑁 𝑛𝑒𝑤 𝑠ℎ𝑎𝑟𝑒𝑠 1 𝑆𝑒𝑟𝑖𝑒𝑠 𝐵 𝑖𝑛𝑣𝑒𝑠𝑡𝑜𝑟𝑠 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑜𝑤𝑛𝑒𝑟𝑠ℎ𝑖𝑝 𝑆𝑒𝑟𝑖𝑒𝑠 𝐴 𝑖𝑛𝑣𝑒𝑠𝑡𝑜𝑟𝑠 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑜𝑤𝑛𝑒𝑟𝑠ℎ𝑖𝑝 𝑈𝑝𝑑𝑎𝑡𝑒𝑑 𝐸𝑥𝑖𝑡 𝑉𝑎𝑙𝑢𝑎𝑡𝑖𝑜𝑛 𝑎𝑓𝑡𝑒𝑟 𝑆𝑒𝑟𝑖𝑒𝑠 𝐵 𝑓𝑖𝑛𝑎𝑛𝑐𝑖𝑛𝑔 𝑆𝑒𝑟𝑖𝑒𝑠 𝐴 𝑖𝑛𝑣𝑒𝑠𝑡𝑜𝑟𝑠 𝑒𝑞𝑢𝑖𝑡𝑦 𝑖𝑛𝑗𝑒𝑐𝑡𝑖𝑜𝑛 Return Multiples for Private Equity Funds 𝑃𝑎𝑖𝑑 𝑖𝑛 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑡𝑜 𝑑𝑎𝑡𝑒 𝑃𝑎𝑖𝑑 𝑖𝑛 𝐶𝑎𝑝𝑖𝑡𝑎𝑙, 𝑃𝐼𝐶 𝐶𝑜𝑚𝑚𝑖𝑡𝑡𝑒𝑑 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝐷𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑒𝑑 𝑡𝑜 𝑝𝑎𝑖𝑑 𝑖𝑛, 𝐷𝑃𝐼 𝐶𝑢𝑚𝑢𝑙𝑎𝑡𝑖𝑣𝑒 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛𝑠 𝑝𝑎𝑖𝑑 𝑜𝑢𝑡 𝑡𝑜 𝐿𝑃𝑠 𝐶𝑢𝑚𝑢𝑙𝑎𝑡𝑖𝑣𝑒 𝑖𝑛𝑣𝑒𝑠𝑡𝑒𝑑 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑅𝑒𝑠𝑖𝑑𝑢𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 𝑡𝑜 𝑝𝑎𝑖𝑑 𝑖𝑛, 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐿𝑃 𝑠 𝑠ℎ𝑎𝑟𝑒ℎ𝑜𝑙𝑑𝑖𝑛𝑔 ℎ𝑒𝑙𝑑 𝑤𝑖𝑡ℎ 𝑡ℎ𝑒 𝑃𝐸 𝑓𝑢𝑛𝑑 𝑅𝑉𝑃𝐼 𝐶𝑢𝑚𝑢𝑙𝑎𝑡𝑖𝑣𝑒 𝑖𝑛𝑣𝑒𝑠𝑡𝑒𝑑 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑇𝑜𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 𝑡𝑜 𝑝𝑎𝑖𝑑 𝑖𝑛, 𝑇𝑉𝑃𝐼 𝐷𝑃𝐼 𝑅𝑉𝑃𝐼 39 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed 𝑁𝐴𝑉 𝒃𝒆𝒇𝒐𝒓𝒆 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑁𝐴𝑉 𝒂𝒇𝒕𝒆𝒓 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑁𝐴𝑉 𝒂𝒇𝒕𝒆𝒓 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑁𝐴𝑉 𝒃𝒆𝒇𝒐𝒓𝒆 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝐶𝑎𝑙𝑙𝑒𝑑 𝑑𝑜𝑤𝑛 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝐶𝑎𝑟𝑟𝑖𝑒𝑑 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑂𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑟𝑒𝑠𝑢𝑙𝑡𝑠 𝑀𝑎𝑛𝑎𝑔𝑒𝑚𝑒𝑛𝑡 𝑓𝑒𝑒 𝐷𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛𝑠 Reading 37: Introduction to Commodities and Commodity Derivatives 𝐹𝑢𝑡𝑢𝑟𝑒𝑠 𝑝𝑟𝑖𝑐𝑒 𝑆𝑝𝑜𝑡 𝑝𝑟𝑖𝑐𝑒 𝑜𝑓 𝑝ℎ𝑦𝑠𝑖𝑐𝑎𝑙 𝑐𝑜𝑚𝑚𝑜𝑑𝑖𝑡𝑦 𝐶𝑎𝑙𝑒𝑛𝑑𝑎𝑟 𝑠𝑝𝑟𝑒𝑎𝑑 𝑁𝑒𝑎𝑟 𝑡𝑒𝑟𝑚 𝑓𝑢𝑡𝑢𝑟𝑒𝑠 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 𝑐𝑙𝑜𝑠𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒 𝑆𝑡𝑜𝑟𝑎𝑔𝑒 𝑐𝑜𝑠𝑡𝑠 𝐶𝑜𝑛𝑣𝑒𝑛𝑖𝑒𝑛𝑐𝑒 𝑦𝑖𝑒𝑙𝑑 𝐹𝑎𝑟𝑡ℎ𝑒𝑟 𝑡𝑒𝑟𝑚 𝑓𝑢𝑡𝑢𝑟𝑒𝑠 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 𝑐𝑙𝑜𝑠𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒 𝑃𝑟𝑖𝑐𝑒 𝑟𝑒𝑡𝑢𝑟𝑛 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑝𝑟𝑖𝑐𝑒 𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠 𝑝𝑟𝑖𝑐𝑒 𝑃𝑟𝑒𝑣𝑖𝑜𝑢𝑠 𝑝𝑟𝑖𝑐𝑒 𝑅𝑜𝑙𝑙 𝑟𝑒𝑡𝑢𝑟𝑛 𝑁𝑒𝑎𝑟 𝑡𝑒𝑟𝑚 𝐹𝑎𝑟𝑡ℎ𝑒𝑟 𝑡𝑒𝑟𝑚 𝑓𝑢𝑡𝑢𝑟𝑒𝑠 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 𝑓𝑢𝑡𝑢𝑟𝑒𝑠 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 𝑐𝑙𝑜𝑠𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒 𝑐𝑙𝑜𝑠𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒 𝑁𝑒𝑎𝑟 𝑡𝑒𝑟𝑚 𝑓𝑢𝑡𝑢𝑟𝑒𝑠 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 𝑐𝑙𝑜𝑠𝑖𝑛𝑔 𝑝𝑟𝑖𝑐𝑒 𝑇𝑜𝑡𝑎𝑙 𝑟𝑒𝑡𝑢𝑟𝑛 𝑃𝑟𝑖𝑐𝑒 𝑟𝑒𝑡𝑢𝑟𝑛 𝑅𝑜𝑙𝑙 𝑟𝑒𝑡𝑢𝑟𝑛 𝐶𝑜𝑙𝑙𝑎𝑡𝑒𝑟𝑎𝑙 𝑟𝑒𝑡𝑢𝑟𝑛 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑖𝑛 𝑡ℎ𝑒 𝑓𝑢𝑡𝑢𝑟𝑒𝑠 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡 𝑏𝑒𝑖𝑛𝑔 𝑟𝑜𝑙𝑙𝑒𝑑 𝑅𝑒𝑏𝑎𝑙𝑎𝑛𝑐𝑖𝑛𝑔 𝑟𝑒𝑡𝑢𝑟𝑛 𝑓𝑜𝑟 𝑖𝑛𝑑𝑒𝑥 𝑜𝑛𝑙𝑦 40 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed PORTFOLIO MANAGEMENT Reading 38: 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 % 𝑅𝑜𝑢𝑛𝑑 𝑡𝑟𝑖𝑝 𝑡𝑟𝑎𝑑𝑒 𝑐𝑜𝑠𝑡 % 𝑀𝑎𝑛𝑎𝑔𝑒𝑚𝑒𝑛𝑡 𝑓𝑒𝑒 % 𝑂𝑛𝑒 𝑤𝑎𝑦 𝑐𝑜𝑚𝑚𝑖𝑠𝑠𝑖𝑜𝑛 % 2 𝐵𝑖𝑑 𝑎𝑠𝑘 𝑠𝑝𝑟𝑒𝑎𝑑 % Reading 39: Using Multifactor Models Arbitrage Pricing Theory (APT) 𝐸 𝑅 𝑅 𝜆 𝛽 , ⋯ 𝜆 𝛽 , 𝐸 𝑅 the expected return to portfolio p 𝑅 the risk-free rate the sensitivity of the portfolio to factor j 𝛽, the expected reward for bearing the risk of factor j 𝜆 𝐾 the number of factors Carhart Four-Factor Model 𝑅 𝛽 , 𝑅𝑀𝑅𝐹 𝐸 𝑅 𝛽 , 𝑆𝑀𝐵 𝛽 , 𝐻𝑀𝐿 𝛽 , 𝑊𝑀𝐿 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 𝑅 𝐹 𝑏 𝑎 𝑎 𝑏 𝐹 𝑏 𝐹 ⋯ 𝑏 𝐹 𝜀 the surprise in the factor k the sensitivity of the return on asset i to a surprise in factor k, k = 1, 2, …, Expected return on the portfolio 41 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Fundamental Factor Model Value of attribute 𝑘 for asset 𝑖 Average value of attribute 𝑘 𝑏 𝜎 Values of attribute 𝑘 Return Attribution 𝐴𝑐𝑡𝑖𝑣𝑒 𝑟𝑒𝑡𝑢𝑟𝑛 𝑅 𝑅 𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑠𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 𝑇𝑟𝑎𝑐𝑘𝑖𝑛𝑔 𝑒𝑟𝑟𝑜𝑟, 𝑇𝐸 𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜, 𝑠 𝑅 𝐵𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 𝑠𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 𝑆𝑒𝑐𝑢𝑟𝑖𝑡𝑦 𝑠𝑒𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑅 𝑅 𝑅 𝑅 𝑠 𝑅 𝐼𝑅 𝐹𝑎𝑐𝑡𝑜𝑟 𝑟𝑒𝑡𝑢𝑟𝑛 Active risk squared = Active factor risk + Active specific risk Reading 40: Measuring and Managing Market Risk Parametric VaR (Using Normal Distribution) 𝑉𝑎𝑙𝑢𝑒 𝑎𝑡 𝑅𝑖𝑠𝑘, 𝑉𝑎𝑅 𝐸 𝑅 𝑧 𝜎 𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑉𝑎𝑙𝑢𝑒 Portfolio expected return 𝐸 𝑅 Portfolio standard deviation 𝜎 Two-asset portfolio: 𝑤𝐸 𝑅 𝐸 𝑅 𝑤 𝐸 𝑅 𝜎 𝑤 𝜎 𝑤 𝜎 2𝑤 𝑤 𝜌 , 𝜎 𝜎 Scaling from daily returns to annual returns: 𝑅 250 𝑡𝑟𝑎𝑑𝑖𝑛𝑔 𝑑𝑎𝑦𝑠 Scaling from daily standard deviation to annual standard deviaton: 𝜎 √250 𝐼𝑛𝑐𝑟𝑒𝑚𝑒𝑛𝑡𝑎𝑙 𝑉𝑎𝑅 𝐼𝑉𝑎𝑅 𝑉𝑎𝑅 𝑎𝑓𝑡𝑒𝑟 𝑐ℎ𝑎𝑛𝑔𝑒 Percentage change in bond price: Δ𝑦 ΔB 𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛 1 𝑦 𝐵 𝑉𝑎𝑅 𝑏𝑒𝑓𝑜𝑟𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 1 Δy 𝐶𝑜𝑛𝑣𝑒𝑥𝑖𝑡𝑦 2 1 𝑦 New call price: 𝑐 Δ𝑐 𝑐 Delta Δ𝑆 Gamma Δ𝑆 𝑉𝑒𝑔𝑎 Δ𝜎 New put price: 𝑝 Δ𝑝 𝑝 Delta Δ𝑆 Gamma Δ𝑆 𝑉𝑒𝑔𝑎 Δ𝜎 42 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Reading 42: Economics and Investment Markets One-period real-risk free rate: 𝑙 𝐸 𝑚 1 , 𝐸 𝑚 1 , Inter-temporal rate of substitution , 𝑃𝑟𝑖𝑐𝑒 𝑜𝑓 𝑟𝑖𝑠𝑘𝑦 𝑎𝑠𝑠𝑒𝑡 𝐸𝑃 , 1 𝑙, 𝑐𝑜𝑣 𝑃 ,𝑚 , , where: , risk neutral present value , 𝑐𝑜𝑣 𝑃 𝑠 ,𝑚 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. time to maturity of investment , , Default-free nominal coupon-paying bond: 𝐶𝐹 𝑃 𝑙, 𝜃, 𝜋, 𝜃, 1 𝑙 , 𝜃, 𝜋 , real-risk free rate expected inflation rate uncertainty in future inflation rate 𝜋, Breakeven rate of inflaton Short-dated nominal zero-coupon government bonds (T-bills) 𝐶𝐹 𝑃 1 𝑙, 𝜃, Taylor Rule: 𝑝𝑟 𝐼 𝜋 0.5 𝜋 𝜋∗ 0.5 𝑌 𝑌∗ policy rate at time t 𝑝𝑟 level of real short-term interest rates that balance long-term savings and borrowing in 𝐼 the economy rate of inflation 𝜋 𝜋 ∗ target rate of inflation 𝑌 logarithmic level of actual GDP 𝑌 ∗ logarithmic level of potential real GDP 𝑌 𝑌 ∗ output gap 43 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Corporate bond: 𝐸 𝐶𝐹 𝑃 𝛾, 1 𝑙 𝜃, , 𝜋 𝛾, , Credit premium Equity: 𝐸 𝐶𝐹 𝑃 1 𝑙 , , 𝜋 𝛾, , 𝜅 , 𝐸 𝐶𝐹 𝑃 𝜅 𝜆 𝜃, , 1 𝑙 𝜃, , 𝜋 , 𝜆 , 𝛾, 𝜅 , Equity premium relative to risky bonds 𝛾, 𝜅, Equity risk premium Commercial Real Estate: 𝐸 𝐶𝐹 𝑃 𝜙 , 1 𝑙 , 𝜃, 𝜋 , liquidity risk premium Reading 43: Analysis of Active Portfolio Management Active return, 𝑅 𝐴𝑙𝑝ℎ𝑎, 𝛼 𝑅 𝑉𝑎𝑙𝑢𝑒 𝑎𝑑𝑑𝑒𝑑, 𝑆𝑅 𝜎 𝑅 𝑆𝑅 𝑅 𝑅 𝛽 𝑅 𝑅 ∆𝑤 𝑅 , 𝑤 ,𝑅 , 𝐼𝑅 𝜎 𝑅 𝜎 𝑅 For optimal Sharpe ratio, 𝜎 𝑅 𝐼𝑅 𝜎 𝑅 𝑆𝑅 44 𝜙, Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed 𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡, 𝑇𝐶 𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡, 𝐼𝐶 𝐶𝑜𝑟𝑟 𝐼𝐶 𝐼𝐶 𝑅 𝜇 , 𝜎 𝜎 𝐶𝑜𝑟𝑟 2 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑟𝑖𝑔ℎ𝑡 𝑐𝑎𝑙𝑙 Forecasted active return, 𝜇 𝜇 , ∆𝑤 𝜎 𝜎 1 𝜎 𝑆 where 𝑆 is set of standardized forecasts of expected returns across securities Mean-variance optimal weights: 𝜇𝜎 ∆𝑤 ∗ 𝜎 𝐼𝐶 √𝐵𝑅 Full Fundamental Law: 𝐸 𝑅 𝐼𝑅 𝜎 𝑅 𝑇𝐶 𝐼𝐶 √𝐵𝑅𝜎 𝑇𝐶 𝐼𝐶 √𝐵𝑅 𝑇𝐶 𝐼𝑅∗ 𝜎 𝑅 𝑆𝑅 𝑆𝑅 𝑆𝑅 𝑇𝐶 𝜎 𝜎 𝐼𝑅∗ 𝜎 Performance Measurement 𝑅 𝐸 𝑅 |𝐼𝐶 𝑁𝑜𝑖𝑠𝑒 Proportion of variation in realized performance attributed to realized information 𝑇𝐶 coefficient 𝑤ℎ𝑒𝑟𝑒 𝐼𝐶 realized information coefficient Ex-ante measurement of skill: 𝐼𝐶 𝜎 𝜎 𝐸 𝑅 Independence of Investment Decision: 𝐵𝑅 𝑁 𝑁 1 𝜌 1 45 Noesis Exed CFA Level 2 (2022) Formula Sheet – Noesis Exed Reading 44: Trading Costs and Electronic Markets 𝑀𝑖𝑑𝑞𝑢𝑜𝑡𝑒 𝑝𝑟𝑖𝑐𝑒 𝐵𝑖𝑑 𝑝𝑟𝑖𝑐𝑒 𝐴𝑠𝑘 𝑝𝑟𝑖𝑐𝑒 2 Effective spread transaction cost estimate For buy orders: 𝑇𝑟𝑎𝑑𝑒 𝑠𝑖𝑧𝑒 𝑇𝑟𝑎𝑑𝑒 𝑝𝑟𝑖𝑐𝑒 𝑀𝑖𝑑𝑞𝑢𝑜𝑡𝑒 𝑝𝑟𝑖𝑐𝑒 𝑇𝑟𝑎𝑑𝑒 𝑠𝑖𝑧𝑒 𝑀𝑖𝑑𝑞𝑢𝑜𝑡𝑒 𝑝𝑟𝑖𝑐𝑒 For sell orders: 𝑇𝑟𝑎𝑑𝑒 𝑝𝑟𝑖𝑐𝑒 Note: Midquote price calculated based on bid and ask prices at the time order was entered. 𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑠𝑝𝑟𝑒𝑎𝑑 2 𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑠𝑝𝑟𝑒𝑎𝑑 𝑡𝑟𝑎𝑛𝑠𝑎𝑐𝑡𝑖𝑜𝑛 𝑐𝑜𝑠𝑡 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒 VWAP transaction cost estimate For buy orders: 𝑇𝑟𝑎𝑑𝑒 𝑠𝑖𝑧𝑒 𝑇𝑟𝑎𝑑𝑒 𝑉𝑊𝐴𝑃 𝑉𝑊𝐴𝑃 𝑏𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 𝑇𝑟𝑎𝑑𝑒 𝑠𝑖𝑧𝑒 𝑉𝑊𝐴𝑃 𝑏𝑒𝑛𝑐ℎ𝑚𝑎𝑟𝑘 For sell orders: 46 𝑇𝑟𝑎𝑑𝑒 𝑉𝑊𝐴𝑃

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