CFA Level II: Formula Sheet — All Subjects

▸ Use / trapEach slope = change in Y for a 1-unit change in Xj, holding other X's constant. Reject H0: bj = 0 if p-value < α.

▸ Use / trapTrap: here RSS = Regression sum of squares, NOT residual.

▸ Use / trapAlmost always rises as variables are added, even useless ones — use adjusted R² to compare.

▸ Use / trapR²ₐ ≤ R². Adding a variable with |t| < 1 lowers R²ₐ. Does not test significance.

▸ Use / trapAIC → best for forecasting; BIC → best goodness of fit. BIC penalises more since ln(n) > 2 for n ≥ 8.

▸ Use / trapReject H0 (excluded slopes all = 0) if F > Fc. Always one-tailed.

▸ Use / trapSpecial case of nested F with q = k. One-tailed despite '=' in H0.

▸ Use / trapUse ALL estimated coefficients, even insignificant ones (or re- estimate without them).

▸ Use / trapOne-tailed. Effect: SEs unreliable (usually too small → Type I), F unreliable; coefficients still unbiased. Fix: White robust SEs.

▸ Use / trapPositive serial correlation → SEs too small → Type I. Lagged dependent variable → coefficients inconsistent. Fix: Newey-West SEs.

▸ Use / trapVIF > 5 investigate; > 10 severe. Classic sign: high R², significant F, insignificant t's → SEs too high → Type II.

▸ Use / trapLeverage = extreme X. Outlier = extreme Y. Influential = changes coefficients when removed.

▸ Use / trapOutlier if |t*| > critical t with n − k − 2 df. Page 3 of 59

▸ Use / trapDummy coefficient = difference vs the omitted (reference) class. Using n dummies = perfect multicollinearity. R2 · Time-Series Analysis

▸ Use / trapSlopes change LOG-ODDS, not probability. Use for binary dependent variable (default / no default).

▸ Use / trapLogit analogue of the nested F-test. Pseudo-R² only for comparing models with the same Y. 13 formulas

▸ Use / trapUse when series grows by a constant AMOUNT.

▸ Use / trapUse when series grows at a constant RATE. Trap: forecast is ln(y) — take ex.

▸ Use / trapValid only if covariance stationary: constant finite mean, variance and covariance.

▸ Use / trapMulti-period forecasts are more uncertain than one-period forecasts.

▸ Use / trapAny significant lag → AR model misspecified; add lags. DW is NOT valid for AR models.

▸ Use / trapIf xt above level → forecast falls; below → rises. rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida

▸ Use / trapLowest out-of-sample RMSE = best forecasting model.

▸ Use / trapb1 = 1 (unit root) → b0/0 undefined → not covariance stationary.

▸ Use / trapFail to reject H0 → unit root → first-difference the data.

▸ Use / trapConverts a random walk into a covariance-stationary series (mean-reverting level 0).

▸ Use / trapSignal: significant residual autocorrelation at lag 4 / 12. Still an AR(1) model, not AR(2).

▸ Use / trapARCH → SEs invalid; use generalized least squares. Model can forecast next-period variance. Page 4 of 59

▸ Use / trapReject unit root in residuals → cointegrated → regression valid even if both series nonstationary. R3 · Machine Learning

▸ Use / trapPenalty shrinks/eliminates weak features → parsimonious model; reduces overfitting. R4 · Big Data Projects

▸ Use / trapSensitive to outliers. Use when distribution is unknown.

▸ Use / trapLess sensitive to outliers; assumes normal distribution.

▸ Use / trapHigh precision when Type I is costly; high recall when Type II is costly (e.g., missing a defaulter). COMPARISON TABLES & FRAMEWORKS Regression assumption violations Problem Effect Conditional heteroskedasticity SEs unreliable (too low), F unreliable Serial correlation SEs too low → Type I; inconsistent b if lagge Multicollinearity SEs too high → Type II Model fit metrics — which to use Goal Metric Better if Forecasting AIC Lower Goodness of fit BIC Lower Compare models (different k) Adjusted R² Higher Excluded variables jointly zero? Nested F F > critical Logit nested models LR (χ²) LR > critical Can I regress one time series on another? Y series X series Use regression? Stationary Stationary Yes Stationary Nonstationary No Nonstationary Stationary No Nonstationary Nonstationary Only if cointegrated rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida 1 formulas 6 formulas

▸ Use / trapF1 better than accuracy when classes are unequal (class imbalance).

▸ Use / trapAUC = 0.5 → random guess; closer to 1 → better model.

▸ Use / trapVery high/low-frequency tokens often removed. Mutual information: 0 = token in all classes; → 1 = one class. Detect Correct Residual plot, Breusch-Pagan White robust SEs ed Y DW (1 lag), Breusch-Godfrey Newey-West SEs High R², sig. F, insig. t; VIF Drop variable / new proxy Page 5 of 59 ML algorithms — best suited for Algorithm Type Use LASSO / penalized Supervised Parsimonious models, many regression features SVM Supervised Binary classification (default / no default) KNN Supervised Classification by nearness; choose k CART Supervised Categorical/continuous target, nonlinear Ensemble / random Supervised Reduce overfitting, higher accuracy forest PCA Unsupervised Dimension reduction k-means / hierarchical Unsupervised Clustering Neural nets / deep Either Complex nonlinear, image, text learning Reinforcement learning — Learn by trial and reward ★ Exam signals & key rules — Quantitative Methods 1. p-value < α → reject H0 (coefficient significant). 2. F-tests are always one-tailed. 3. Time-series model choice: plot → trend? → test residuals (DW) → AR → check stationarity (DF) → first-difference → add seasonal lag → test ARCH. 4. Linear trend = constant amount; log-linear = constant rate. rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida 5. Unit root (b1 = 1) → not covariance stationary → first-difference. 6. Overfitting: low bias error, high variance error; fix with complexity reduction or cross-validation. 7. Data split: ~60% training, ~20% validation, ~20% test. Page 6 of 59 01 Economics C FA L E V E L I I 2 0 2 7 · S U B J E C T 0 1 33 formulas 7 tables 12 exam rules R5 · Currency Exchange Rates: Un R5 · Currency Exchange Rates: Understanding Equilibriu

▸ Use / trapDividends received are NOT income; they reduce the investment account. Extra depreciation on fair-value write-ups reduces equity income.

▸ Use / trapGoodwill inside the one-line investment is not amortized. Investment shown as a single noncurrent asset line.

▸ Use / trapRemainder after allocating excess to identifiable assets is goodwill; it is embedded in the investment account.

▸ Use / trapReduce equity income by investor's share of profit on goods not yet sold to third parties; recognize it when the goods are sold.

▸ Use / trapTarget's own pre-existing goodwill is ignored (unidentifiable). Full goodwill gives higher assets and equity → lower ROA and ROE. rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida ysis R8 · Employee Compensation: Post-Employment and Share-Based Evaluating Quality of Financial Reports 13 formulas

▸ Use / trapAlways ≤ full goodwill when parent owns <100%. Difference is mirrored in noncontrolling interest.

▸ Use / trapNCI is reported in equity. Full-goodwill NCI is larger by exactly the goodwill difference.

▸ Use / trapConsolidated NI = parent NI + sub NI − NCI share. Acquisition and equity method report the same NI.

▸ Use / trap100% of sub assets/liabilities included even if <100% owned. Proportionate consolidation includes only % owned share.

▸ Use / trapTest is based on the unit's value decline; loss is based on goodwill's decline. Reversal prohibited. Page 11 of 59

▸ Use / trapSingle-step test.

▸ Use / trapRecognized immediately as a gain in the income statement under both IFRS and US GAAP. R8 · Employee Compensation: Post-Employment and Sh

▸ Use / trapAmortized cost ignores FV changes; FVPL puts unrealized G/L in income; FVOCI puts it in OCI (equity). Interest revenue identical in all three. hare-Based 12 formulas

▸ Use / trapExpense ↓ RE and ↑ share-based compensation reserve → total equity unchanged. No cash flow at grant. Lower volatility assumption → lower expense.

▸ Use / trapExpensed straight-line over vesting period into the share-based compensation reserve.

▸ Use / trapDeduction > cumulative book expense → tax windfall; < → shortfall. IFRS: to equity. US GAAP: through tax expense (volatile ETR).

▸ Use / trapOptions include exercise proceeds, so they create fewer dilutive shares than RSUs with equal unrecognized expense. Net loss → no dilution.

▸ Use / trapNegative = underfunded → net pension liability (IFRS and US GAAP). Underfunded amount is deducted from enterprise value.

▸ Use / trapIFRS implicitly sets expected return on assets = discount rate. Negative IFRS result (underfunded) = net interest expense.

▸ Use / trapReduces US GAAP pension cost in P&L; affects neither PBO nor FV of plan assets. Higher assumed rate → lower reported pension cost.

▸ Use / trapNo amortization if beginning unamortized actuarial loss ≤ corridor. Amortized loss ↑ pension cost; amortized gain ↓ it. IFRS never amortizes.

▸ Use / trapPast service cost goes to OCI and is amortized over remaining service life. Actuarial G/L amortized only beyond corridor. Page 12 of 59

▸ Use / trapPast service cost expensed immediately in P&L. No separate expected-return assumption to manipulate. R9 · Multinational Operations

▸ Use / trapUse it to back out benefits paid. Higher discount rate → lower PBO; higher compensation growth → higher PBO.

▸ Use / trapActual (not expected) return. Employer contributions are the actual cash flow (operating activities). 8 formulas

▸ Use / trapReceivable in FC: FC depreciates → loss. Payable in FC: FC depreciates → gain. Recognized in income statement; placement (operating/non-operating) not specified.

▸ Use / trapCTA is cumulative; the period translation gain/loss = ending CTA − beginning CTA (reported in equity/OCI).

▸ Use / trapReported in the income statement → more volatile net income than current rate method.

▸ Use / trapExposed assets + depreciating FC → loss; exposed liabilities + depreciating FC → gain. Most firms have net monetary liability exposure. R10 · Analysis of Financial Institutions

▸ Use / trapUS GAAP: use temporal method. IFRS: restate for inflation using price index, then translate at current rate.

▸ Use / trapEquity (ex-RE) restated from beginning of period/contribution date; RE is the balance-sheet plug; net purchasing power G/L forces NI to match.

▸ Use / trapHolding net monetary liabilities during inflation → gain (analogous to temporal method with depreciating FC). Recognized in income.

▸ Use / trapReconciliation (statutory → effective) shows foreign-operation effects; changing profit mix across countries changes future ETR. 12 formulas Page 13 of 59

▸ Use / trapRiskier assets → higher RWA → more capital required. Capital ratios use RWA, not total assets. rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida

▸ Use / trapCET1 is the most important tier. Check every tier against its minimum separately.

▸ Use / trapEach compares a discretionary amount (allowance/provision) to an objective one. Falling ratios → under-provisioning, aggressive accounting.

▸ Use / trapBasel III minimum 100%. Measures liquidity under stress (30-day horizon).

▸ Use / trapBasel III minimum 100%. Measures funding stability over one year; retail deposits more stable than corporate.

▸ Use / trapMeasures underwriting/pricing quality. Upward loss-reserve revisions = aggressive earlier profit booking. R11 · Evaluating Quality of Financial Reports

▸ Use / trapMeasures operating efficiency. Note denominator is premium WRITTEN (US GAAP reporting may use premium earned for both ratios).

▸ Use / trapLower = more successful risk estimation.

▸ Use / trapLiquidity measure of dividend cash outflow relative to premium income.

▸ Use / trapCombined ratio > 100% = underwriting loss. Industry ratio high = soft market; low = hard market. CRAD is most comprehensive profitability measure.

▸ Use / trapRecompute excluding unrealized gains to see reliance on fair- value estimates. Used for P&C and L&H.

▸ Use / trapL&H: longer contract period, higher float, higher interest-rate (duration-mismatch) risk than P&C. 13 formulas

▸ Use / trapHigher (less negative) M-score = higher manipulation probability. Cutoff −1.78: M > −1.78 → likely manipulator. Interpret, don't memorize coefficients. rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida

▸ Use / trapLarge increase may indicate revenue inflation (aggressive recognition).

▸ Use / trapGMI > 1 → margin deteriorated → more likely to manipulate. Page 14 of 59

▸ Use / trapAQI > 1 may indicate excessive capitalization of expenses.

▸ Use / trapNot manipulation itself; growth firms face pressure to keep meeting expectations.

▸ Use / trapDEPI > 1 → slower depreciation (longer lives/higher salvage) to boost earnings. DEPI < 1 is NOT consistent with extending lives.

▸ Use / trapRising SG&A % may predispose to manipulation; regression coefficient is negative (unexpected).

▸ Use / trapHigher accruals → higher M-score (coefficient 4.679, largest). R12 · Integration of Financial Statement Analysis Techni

▸ Use / trapCoefficient negative in actual regression results.

▸ Use / trapHigher Z = lower bankruptcy probability; each variable positively related to Z. Limitation: single-period, static, accounting-based.

▸ Use / trapHigher β1 = more persistent (sustainable) earnings = higher quality.

▸ Use / trapAccrual component less persistent than cash component; accrual-heavy (esp. discretionary) earnings mean-revert faster.

▸ Use / trapReceivables growing faster than sales, rising DSO, falling turnover vs peers → poor revenue quality (channel stuffing, bill-and-hold). iques 14 formulas

▸ Use / trapHigher tax/interest burden ratios mean LOWER tax and interest drag. Tax burden = 1 − tax rate.

▸ Use / trapRemoves associate's earnings and investment to show standalone performance. Do NOT adjust leverage unless financing of investment is given. rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida

▸ Use / trapLower ratio = higher earnings quality. Wide fluctuations may signal manipulation.

▸ Use / trapCFF excluded. CFI is negative when investing, so subtracting it adds back. For comparability, US GAAP firms' interest/dividends paid may need moving from CFO to CFF.

▸ Use / trapCompare CGO / operating income: > 1 means operating income confirmed by cash. If IFRS firm puts interest paid in CFF, don't add interest back. Page 15 of 59

▸ Use / trapUsed to confirm earnings quality, ability to fund capex, and debt capacity.

▸ Use / trap> 1 = segment is being grown. Overallocation red flag: ratio > 1 for the lowest-EBIT-margin segment.

▸ Use / trapSegmental cash flow is rarely reported; use the proxy to judge capital allocation on a cash basis.

▸ Use / trapConvert associate earnings at AVERAGE rate, market value at CURRENT (year-end) rate.

▸ Use / trapCompare to index P/E; crude if parent and associate use different accounting standards (US GAAP vs IFRS).

▸ Use / trapDefensive interval falls with higher daily expenditures or lower marketable securities. rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida

▸ Use / trapShorter CCC = better working-capital management (faster collection, faster inventory, slower payment).

▸ Use / trapPure income-statement ratios (margins) are preserved under the current rate method; mixed ratios are not.

▸ Use / trapLeverage ratio alone hides how burdensome liabilities are (debt vs deferred taxes, provisions). Page 16 of 59 COMPARISON TABLES & FRAMEWORKS Intercorporate investments: classification Ownership Influence Accounting treatment < 20% (financial No significant Amortized cost, FVPL, FVOCI assets) influence 20%–50% Significant Equity method (associates) influence > 50% (business Control Acquisition method combination) Joint venture (shared Joint control Equity method (rarely control) proportionate consolidation) Financial assets under IFRS 9 Item Amortized cost Eligible Debt only (business model + cash flow tests) Balance sheet Amortized cost Income statement Interest incl. amortization; realized G/L Equity method vs proportionate consolidation vs acquisition Item Equity Net income Same Equity Same as proportionate Assets, liabilities, revenue Lowest Net profit margin Higher ROE Higher ROA Higher Full vs partial goodwill Item Full goodwill Partial goodwill Allowed US GAAP required; IFRS IFRS only allowed Goodwill Higher Lower NCI basis Subsidiary fair value FV of identifiable net assets Total assets & Higher Lower equity ROA, ROE Lower Higher Goodwill impairment: US GAAP vs IFRS Item US GAAP Test Two steps (reporting unit) Loss Goodwill carrying value − implied goodwill Pension cost components: US GAAP vs IFRS Component US GAAP Current service cost Income statement Past service cost OCI, amortized over service life Interest Beginning PBO × discount rate (P&L) Expected return Assumed rate × plan assets (P&L) Actuarial G/L OCI; amortized beyond 10% corridor Share-based compensation: tax windfall/shortfall Item IFRS US GAAP Windfall (settlement price > grant Directly to Reduces tax expense price) equity Shortfall Directly to Increases tax equity expense ETR volatility Lower Higher rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida FVPL FVOCI Debt and equity Debt and equity Fair value Fair value, G/L in equity Interest, dividends, all G/L Interest, dividends Proportionate Acquisition Same Same Same as equity Higher by NCI In-between Highest In-between Lower Same as equity Lower In-between Lower IFRS One step (cash-generating unit) Carrying amount − recoverable amount IFRS Income statement Income statement immediately Net interest on funded status (P&L) Implicitly = discount rate (in net interest) OCI; never amortized Temporal method vs current rate method Item Temporal Current rate When used Functional = parent's Functional ≠ presentation currency presentation currency Monetary Current rate Current rate assets/liabilities Nonmonetary Historical rates Current rate assets/liabilities Common stock Historical rate Historical rate Revenues, SG&A Average rate Average rate COGS, depreciation, Historical rates Average rate amortization Exposure Net monetary assets Net assets FX gain/loss Income statement Equity (CTA) Page 17 of 59 Gain or loss from exposure Exposure LC appreciating LC depreciating Net assets (current rate) Gain Loss Net liabilities (current rate) Loss Gain Net monetary assets (temporal) Gain Loss Net monetary liabilities (temporal) Loss Gain Hyperinflationary subsidiaries Item US GAAP Definition Cumulative inflation > 100% over 3 years Method Temporal (functional = parent currency) Gain/loss Remeasurement G/L in income Basel III minimums Measure Minimum Horizon / basis CET1 / RWA 4.5% Risk-weighted assets Total Tier 1 / RWA 6% Risk-weighted assets Total capital / RWA 8% Risk-weighted assets LCR 100% 30-day (one-month) stress NSFR 100% One-year funding ★ Exam signals & key rules — Financial Statement Analysis 1. Equity method: dividends reduce the investment account and are never income. 2. Acquisition method shows 100% of subsidiary assets, liabilities, revenues; NCI makes up the unowned share. 3. All three methods (equity, proportionate, acquisition) give the same net income. 4. Option fair value is fixed at grant date; later price moves only affect tax deductions. 5. Firms can lower pension cost by raising the discount rate, cutting 1 compensation growth, shortening life expectancy, or (US GAAP) raising 1 expected return. 1 rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida IFRS Not defined; 100%/3 yrs is one indicator Restate for inflation, then current rate Net purchasing power G/L in income P&C vs L&H insurers Feature P&C L&H Claims Lumpier, less Stable, predictable predictable Contract period Shorter / lower Longer / higher / float Key risk Liquidity Interest rate (duration mismatch) Key ratios Loss, expense, Benefits paid, commissions & combined, CRAD expenses ÷ premiums Accruals ratio: balance sheet vs cash flow approach Item Balance sheet Cash flow statement Accruals NOAEND − NOABEG NI − CFO − CFI Scaled by Average NOA Average NOA Interpretation Lower = higher quality Lower = higher quality Can differ due to Acquisitions, FX, inconsistent items Same 6. Temporal method: functional = parent's currency (integrated subsidiary); current rate: functional = local (self-contained subsidiary). 7. Current rate method preserves pure ratios; mixed ratios (IS numerator, ending BS denominator) rise if FC depreciates. 8. Sales growth from price/volume is more sustainable than growth from currency appreciation. 9. Combined ratio > 100% = underwriting loss; high industry combined ratio = soft pricing market. 10. Beneish M-score above −1.78 flags likely manipulation. 11. Positive net income with negative CFO is a major earnings-quality red flag. 12. Accrual-heavy earnings mean-revert faster, especially discretionary accruals. Page 18 of 59 03 Corporate Issuers 36 formulas C FA L E V E L I I 2 0 2 7 · S U B J E C T 0 3 9 tables 12 exam rules R13 · Analysis of Dividends and S R15 · Cost of Capital: Advanced Topics R16 · Corporate Restructuring R13 · Analysis of Dividends and Share Repurchases

▸ Use / trapAnalyst's alpha opportunity only exists if the valuation error is small; perceived mispricing may be pure model error.

▸ Use / trapUse liquidation value when survival cannot be assumed; orderly liquidation ≥ forced liquidation. R18 · Discounted Dividend Valuation

▸ Use / trapExam signal: an acquirer with synergies → investment value; public stock selection → intrinsic value.

▸ Use / trapQuality-of-earnings red flags (aggressive revenue, reclassified gains, off-BS items) are checked in step 1/2.

▸ Use / trapThree explanations: internal capital inefficiency, endogenous factors (hiding poor performance), research measurement errors. 20 formulas

▸ Use / trapBasic building block; price at end of horizon is itself PV of later dividends.

▸ Use / trapUse calculator CF keys: CF0 = 0, last CF = Dn + Pn.

▸ Use / trapTheoretically sound value = PV of all expected dividends; practical models impose a growth pattern. rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida ons and Processes R18 · Discounted Dividend Valuation rprise Value Multiples R21 · Residual Income Valuation 5 formulas

▸ Use / trapTrap: always discount D1, not D0. Perpetual g above ~5% is suspect (cannot exceed real GDP growth + inflation).

▸ Use / trapGGM with g = 0. Compute Dp = coupon rate × par first.

▸ Use / trapMarket price assumed = intrinsic value. Compare implied g with sustainable g, or implied r with required r. Page 23 of 59

▸ Use / trapGrowth firms: large PVGO; utilities: small. PVGO < 0 when ROE < r. P/E from PVGO = PVGO / E1.

▸ Use / trapExample: Sf60, E1 = 5, r = 10% → PVGO = 10, P/E 12x of which 2x (16.7%) from PVGO.

▸ Use / trapP0 here is fundamental value. P/E rises with payout and g, falls with r.

▸ Use / trapTrailing > leading by factor (1 + g) when earnings grow.

▸ Use / trapExample: 4% + 1.5 × (8% − 4%) = 10%. Trap: if given E(RM), subtract Rf; if given ERP, do not.

▸ Use / trapExample: 0.04 + (0.048 × 0.63) + … = 15.27%. Negative premiums reduce r.

▸ Use / trapTV is at time n; discount it n periods. Use gL, never gS, in the TV. rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida

▸ Use / trapUse for abrupt drop in growth (e.g., patent expiry). Timeline + CF keys is faster: CFn = Dn + Vn.

▸ Use / trapTwo-stage DDM with zero dividends in stage 1. Arena: E5 = 2.75, D5 = 0.55, V4 = 7.86, V0 = 5.00.

▸ Use / trapGrowth declines linearly. First term = value with no high growth. Approximation; more accurate for shorter t or smaller gS − gL.

▸ Use / trapThen discount D1…Dn and Vn. Example: D3 = 0.75(1.12)3; V3 = 26.97; V0 = 23.21.

▸ Use / trapClosed form; two-stage/three-stage implied r requires trial and error (start with the middle answer choice).

▸ Use / trapAssumes constant D/E and no new equity. If actual g > SGR, firm must issue equity unless R, P, A or T rise. Page 24 of 59

▸ Use / trapUse beginning-of-year balance sheet values unless told otherwise. Halo: 0.10 × 0.6 × 1.8 × 1.25 = 13.5%. R19 · Free Cash Flow Valuation

▸ Use / trapMost common trap: wrong rate/cash-flow pairing. WACC on FCFE overstates equity; r on FCFF understates it.

▸ Use / trapAdd back after-tax interest only. Gains on asset sales are removed from NCC (handled in FCInv).

▸ Use / trapWith no sales, FCInv = change in gross PP&E.

▸ Use / trapA decrease in working capital is a cash inflow (added back).

▸ Use / trapCFO already includes NCC and WCInv, so do not subtract WCInv again. rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida 16 formulas

▸ Use / trapNo interest add-back needed: EBIT is pre-interest.

▸ Use / trapTrap: add back only the tax saving on depreciation, not full depreciation.

▸ Use / trapChange in leverage affects FCFE (ST and LT effects partly offset) but not FCFF.

▸ Use / trapAfter-tax interest already deducted in NI and CFO, so no interest adjustment.

▸ Use / trapPreferred treated like debt but dividends not tax deductible; include preferred in WACC. Page 25 of 59

▸ Use / trapDividends, repurchases and share issues are uses of FCF; they do not change FCFF or FCFE.

▸ Use / trapEquity finances (1 − DR) of net capex and WCInv; avoids forecasting net borrowing explicitly.

▸ Use / trapUse target weights if given. Convert D/E to weights: D/E 0.25 → wd = 20%. R20 · Market-Based Valuation: Price and Enterprise Valu

▸ Use / trapSubtract MV of debt (and preferred) for equity. FCFF growth ≠ FCFE growth.

▸ Use / trapFor international/high-inflation cases, use real r and real g consistently.

▸ Use / trapIf stage discount rates differ, discount TV with the compounded stage rates, e.g. 1.203 × 1.153. ue Multiples 22 formulas

▸ Use / trapTrailing not useful if business changed (acquisition); leading not useful if earnings unforecastable.

▸ Use / trapMagnolia: 5.50 − 0.30 + 0.55 = 5.75.

▸ Use / trapAverage ROE method preferred: reflects current firm size. Molodovsky effect: P/E high at cycle trough.

▸ Use / trapRank by E/P when P/E is meaningless; high E/P = cheap. rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida

▸ Use / trapUseful for financials and negative EPS; misleading for asset- light/outsourcing firms.

▸ Use / trapWorks for distressed/start-up firms; ignores cost structure; watch bill-and-hold revenue.

▸ Use / trapEPS + noncash charges ignores WC changes and noncash revenue. EBITDA belongs with EV, not price. Page 26 of 59

▸ Use / trapMostly used for indexes; ignores capital appreciation (dividend displacement of earnings).

▸ Use / trapActual P/E > justified → overvalued. P/E ↑ with g, ↓ with r; inflation pass-through matters.

▸ Use / trapP/B rises with ROE and with ROE − r spread. ROE 14%, r 8%, g 4% → 2.5.

▸ Use / trapMargin raises P/S directly and indirectly through g.

▸ Use / trapP/CF ↑ when r ↓ or g ↑. Justified EV/EBITDA ↑ with FCFF/EBITDA growth, ↓ with WACC.

▸ Use / trapD/P ↑ with r, ↓ with g → high-yield screens reflect a value (not growth) strategy. rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida

▸ Use / trapActual P/E 12 > 9.02 → overpriced. Limits: uncertain predictive power, unstable relationships, multicollinearity.

▸ Use / trapIgnores growth and inflation differences; Yardeni adds growth.

▸ Use / trapP/E falls with interest rates, rises with growth.

▸ Use / trapLower PEG more attractive (similar risk). Drawbacks: P/E–g nonlinear, ignores risk, ignores growth duration.

▸ Use / trapComparables-based TV relies on market data but inherits benchmark mispricing.

▸ Use / trapUse for different leverage, capital-intensive firms, negative EPS. Lower EV/EBITDA → relatively undervalued. Boulevard 647.7/250.7 = 2.6x.

▸ Use / trapUnlike EV, TIC includes cash and ST investments. EV/S suits firms with different capital structures. Page 27 of 59

▸ Use / trapMomentum indicators; a given surprise matters more when historical forecast errors are small. Also relative strength. R21 · Residual Income Valuation

▸ Use / trapIndex/portfolio P/E = weighted harmonic mean (e.g., 8.67). Arithmetic mean most hurt by large outliers; HM weights small values. 14 formulas

▸ Use / trapPositive NI can still mean negative RI (MFS: 80.52m − 98.4m = −17.88m).

▸ Use / trapUse beginning-of-year capital. Adjust: capitalize R&D, cash taxes only, leases as capital, add LIFO reserve.

▸ Use / trapUses end-of-year capital. VBM: EVA = 2,100 − 0.142 × 18,000 = −456; MVA = 24,000 − 21,000 = 3,000.

▸ Use / trapEquity charge uses BEGINNING book value.

▸ Use / trapForecast ending BV. Violated by items bypassing income (CTA, AFS gains, some pension/hedging, IFRS revaluation).

▸ Use / trapValue recognized earlier than DDM/FCFE; less sensitive to terminal value. CF keys: CF0 = B0. rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida

▸ Use / trapEquals GGM value with consistent inputs. Second term = PV of economic profits. ROE = r → V0 = B0.

▸ Use / trapRearrange to back out implied ROE from observed P/B.

▸ Use / trapTellis: P/B 2.5, B0 8, ROE 13%, r 11% → g = 9.67%.

▸ Use / trapRelated concept to P/B.

▸ Use / trapDiscount continuing RI (valued at T − 1) back T − 1 periods.

▸ Use / trapHigher ω: low payout, historically persistent industry RI. Lower ω: high ROE, big nonrecurring items, high accruals.

▸ Use / trapJava Metals: ω = 0 → 6.25; ω = 1 → 8.98; ω = 0.4 → 6.40. Lower ω → lower value. R22 · Private Company Valuation

▸ Use / trapJava: (12.06 − 10.05 + 0.44)/1.10 = 2.23; V0 = 7.50. Market > model → overvalued. 14 formulas

▸ Use / trapArbutus: SG&A −1.5m (comp), +30k (lease), −150k SG&A and −25k dep (vacant building). Synergies only for strategic buyer.

▸ Use / trapFCFF preferred when capital structure will change (WACC less sensitive to leverage). Example FCFF = 2,408,800.

▸ Use / trapRemoves comparable's financial leverage.

▸ Use / trapThen use in CAPM; expanded CAPM adds size and firm-specific premiums.

▸ Use / trap3.6% + 1.3(6%) = 11.4%; expanded 16.4%; build-up 15.6%. Build-up when no public comparables. rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida

▸ Use / trapNot acquirer's WACC, not public-industry weights. Optimal: (0.88 × 16%) + [0.12 × 9% × 0.7] = 14.8%.

▸ Use / trapControl premium 25% → DLOC = 20%.

▸ Use / trapMultiplicative, not additive: 20% and 13% → 30.4% (not 33%).

▸ Use / trapDLOM ↓: impending IPO/sale, larger buyer pool. DLOM ↑: contractual restrictions, ownership concentration.

▸ Use / trapSingle-stage growing perpetuity for small, stable-growth firms with no comparables. Equity = firm value − MV debt.

▸ Use / trapAfter-tax EBIT × (1 − b) proxies for FCFF. Page 29 of 59

▸ Use / trapFor small firms with significant intangibles. Example: 300k + 1,000k + 140k = 1.44m. FCFF may replace normalized earnings. rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida

▸ Use / trapPublic multiples are minority basis: add control premium for controlling interest. Rensselaer: 1.28 × 12.80 = 16.38m.

▸ Use / trapAlready includes control premium. Lafayette: 7.2 × (1 − 0.30) = 5.0; × 18.2m = 91m. Watch contingent and stock consideration. Page 30 of 59 COMPARISON TABLES & FRAMEWORKS Which cash flow measure? Dividends vs FCF vs RI Use when Dividends (DDM) Free cash flow Dividend history Has dividend history None, or unrelated to Link to profitability Policy clear, tied to earnings FCF tracks profitabili Perspective Minority shareholder Controlling sharehold Main weakness Hard for non-payers Negative FCF in heav Life-cycle phase and DDM choice Variable Initial growth Tra Earnings growth Very high Abo Capital investment Significant requirements Dec Profit margin High Abo FCFE Negative Ma ROE vs r ROE > r RO Dividend payout Low or zero Inc Appropriate model Three-stage Two FCFF vs FCFE Item FCFF FCFE Discount rate WACC Required return on equity Gives Firm value (− MV debt = Equity value directly equity) Best when Negative FCFE, high debt, Stable capital changing leverage structure Interest Add back Int × (1 − t) Already deducted Net borrowing Not included Added Change in leverage No effect ST and LT effects partially offset Dividends / No effect No effect repurchases / issues Price multiples: pros and cons Multiple Advantages P/E Earnings drive value; popular; explains returns P/B Usually positive; stable; suits financials, liquidation P/S Always positive; hard to manipulate; less volatile P/CF Harder to manipulate; more stable than P/E D/P Part of total return; dividends less risky EV/EBITDA Different leverage; capital-intensive; EPS negative Fundamental drivers of justified multiples Multiple Rises with Falls with P/E Payout, growth Required return P/B ROE, ROE − r spread, growth Required return P/S Profit margin, growth Required return P/CF Growth Required return EV/EBITDA FCFF/EBITDA growth WACC, risk D/P Required return Growth Private company valuation approaches Approach Methods Income FCF (two-stage), CCM (single-stage), excess earnings Market GPCM, GTM, prior transaction Asset-based Assets − liabilities Private company required return models Model Build CAPM Rf + β × ERP Expanded CAPM CAPM + size + firm-specific Build-up Rf + ERP + industry + size + company-specific rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida Residual income o earnings No dividend history lity Negative FCF foreseeable der (or in-play) Either; needs transparent, high-quality reporting avy-capex years Accrual/accounting manipulation; clean surplus ansition Maturity bove average but falling Stable at long-run level ecreasing Stable at long-run level bove average but falling Stable at long-run level ay be positive, growing Stable at long-run level OE approaching r ROE = r creasing Stable at long-run level wo-stage Gordon growth Effect of financing decisions on free cash flow Decision FCFF FCFE Dividends None None Share repurchase None None Share issue None None Change in leverage None ST & LT effects partially offset Disadvantages Negative EPS; transitory earnings; accounting discretion Ignores intangibles; asset-size and accounting differences Ignores costs/profit; revenue recognition games EPS + NCC ignores WC; FCFE volatile Ignores capital gains; dividend displacement Overstates CFO if WC grows; ignores capex Continuing residual income assumptions Assumption ω PV at T − 1 Persists at current level ω=1 RIT / r Drops to zero ω=0 RIT / (1 + r) Declines as ROE → r 0<ω<1 RIT / (1 + r − ω) Mature long-run level n/a (use P/B) [(PT − BT) + RIT] / (1 + r) Best for High-growth firms (FCF); small stable firms (CCM) Mature firms Early-stage or distressed firms Use when Comparable public betas exist Small, undiversified firm with public comparable No comparable public firms (β = 1) Page 31 of 59 GPCM vs GTM Item GPCM Data Public company trading multiples Control premium Must be added for controlling interest Key issues Transaction type, industry conditions, consideration, reasona ★ Exam signals & key rules — Equity Valuation 1. Always pair FCFF with WACC (firm value) and FCFE/dividends with r (equity value). 2. Discount D1, FCFF1, FCFE1 (next period), never the just-paid amount. 3. Terminal value sits at end of year n (or T − 1 for continuing RI); discount it the right number of periods. 4. Market price > model value → overvalued; actual multiple > justified/benchmark multiple → overvalued. 1 5. Justified trailing P/E = justified leading P/E × (1 + g). 1 6. 'Growth declines linearly' → H-model; 'patent expires / abrupt drop' → two- stage DDM. 1 rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida GTM Acquisition prices of whole companies Already included ableness Transaction type, contingent and type of consideration y 7. 'No dividends, negative FCF, transparent accounting' → residual income model. 8. 'Controlling interest / acquirer / in-play' → FCF; 'minority, stable payout' → DDM. 9. RI equity charge uses beginning book value; EVA uses beginning capital; MVA uses end-of-year capital. 10. DLOC and DLOM combine multiplicatively: 1 − (1 − DLOC)(1 − DLOM). 11. Use target's own WACC and optimal capital structure when valuing a private acquisition. 12. Index/portfolio P/E = weighted harmonic mean of constituent P/Es. Page 32 of 59 05 Fixed Income 68 formulas C FA L E V E L I I 2 0 2 7 · S U B J E C T 0 5 15 tables 12 exam rules R23 · The Term Structure and Int R25 · Valuation and Analysis of Bonds with Embedded Options R26 · Credit An R23 · The Term Structure and Interest Rate Dynamics

▸ Use / trapForward price = spot + net cost of carry. Price makes value of long and short both zero at initiation; it is not a cost to enter.

▸ Use / trapProfit equals actual minus no-arbitrage forward price (e.g., $510 − $507.34 = $2.66). Start with zero cash; buy low, sell high.

▸ Use / trapTrades reverse those of cash-and-carry; e.g., $507.34 − $502 = $5.34.

▸ Use / trap5% annual = ln(1.05) = 4.879% continuous; both give the same FV factor (1.05² = e0.04879×2).

▸ Use / trapIgnore dividends paid after contract maturity. Equities use 365- day basis with periodic compounding.

▸ Use / trapAdjusted spot minus PV of forward price. Short value = −Vt(long). Ignoring dividends overvalues the long by PVD. rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida rward Commitments R29 · Valuation of Contingent Claims 27 formulas

▸ Use / trapPV of the difference between new and locked-in forward price; discount over remaining term T − t. Works for equity and bond forwards.

▸ Use / trapIndexes use 365-day year and continuous compounding (e raised to r × days/365).

▸ Use / trapSame structure as dividend-paying stock; coupons replace dividends. Treasury coupons are semiannual; T = days/365.

▸ Use / trapIf the current forward price FPt is given, use (FPt − FP)/(1 + Rf)(T − t) instead.

▸ Use / trapBuyer pays the full (dirty) price at settlement; quotes are clean.

▸ Use / trapSubtract AIT because the futures price is a clean-price quote at delivery.

▸ Use / trapShort holds the delivery option; long pays futures price × CF at delivery. Use the CTD bond's CF.

▸ Use / trap$1m at 6% for 30 days = $5,000 interest. Unannualized rate = MRR × days/360.

▸ Use / trapPrice of an FRA is a forward interest rate. 1 × 4 FRA: (1.01667/1.00333) − 1 = 1.33% → ×360/90 = 5.32%.

▸ Use / trapInterest savings occur at loan end, so discount back over the loan term at the current market rate. Long gains when rates rise.

▸ Use / trapDiscount over the full remaining period to loan maturity (e.g., 110 days), not just the loan term.

▸ Use / trapFutures value resets to zero at each daily mark-to-market; forwards accumulate value until settlement.

▸ Use / trapConvert annualized MRR to the per-period rate before discounting. Exam often gives Z values directly. rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida

▸ Use / trapFixed rate that makes PV(fixed) = PV(floating), so swap value = 0 at initiation. Fixed payment = SFR(periodic) × NP.

▸ Use / trapPaid by the fixed-rate payer if fixed > floating. Example: fixed $55,000 − floating $37,500 (= 3% × 90/360 × $5m) = $17,500 net.

▸ Use / trapRates up → fixed payer gains. Value to receiver = −value to payer. Curriculum values only on settlement dates for IRS.

▸ Use / trapNotionals are of equal value at inception, exchanged at start and returned at end. Each leg's fixed rate uses its own currency's curve.

▸ Use / trapValue each leg as a bond in its own currency, convert at the current spot rate, then take the difference.

▸ Use / trapValue the fixed side like a bond: PV of coupons plus PV of principal, then × notional.

▸ Use / trapEquity side = notional × (1 + equity return since last payment date). Pricing the fixed rate uses the plain-vanilla SFR formula. Page 41 of 59

▸ Use / trapNo pricing at initiation. Paying stock A (+1.3%), receiving B (−0.8%): (−0.008 − 0.013) × $1m = −$21,000. R29 · Valuation of Contingent Claims

▸ Use / trapTwo-period nodes: S0U², S0UD, S0D² (up-down = down-up).

▸ Use / trapNot actual probabilities; consistent with risk-neutrality. Distinction from actual probabilities is not tested.

▸ Use / trapExpectations approach: option value = PV of risk-neutral expected payoff, discounted at the risk-free rate.

▸ Use / trapWork backward one period at a time; same π at every node for stock trees.

▸ Use / trapProtective put = fiduciary call. Use to back out a put or call price or build synthetics.

▸ Use / trapRearrange parity for any synthetic: synthetic put = long call + long bond − short stock. rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida 25 formulas

▸ Use / trapAmerican call on non-dividend stock = European call. Deep ITM puts may be exercised early (e.g., $10 > $9.44 → value $5.24 vs $4.95).

▸ Use / trapCall overpriced: sell calls, buy h shares per call, borrow. Underpriced: buy calls, short h shares. Put h is negative.

▸ Use / trapCall = leveraged position in h shares; put = long bond plus short h shares (h < 0 for puts).

▸ Use / trapIR calls gain when rates rise; IR puts gain when rates fall. Assume cash settlement at option maturity.

▸ Use / trapRate trees use equal 0.5 risk-neutral probabilities; discount rate differs at each node (not constant). Page 42 of 59

▸ Use / trapEuropean options only. Value = PV of expected payoff in continuous time.

▸ Use / trapCall is a leveraged stock position. If market price > replicating cost: write option, buy replicating portfolio.

▸ Use / trapDividends lower call value and raise put value.

▸ Use / trapReplace S0 with dividend-adjusted price S0e−δT.

▸ Use / trapForeign (base) interest rate plays the role of the dividend yield; strike is discounted at the price-currency rate.

▸ Use / trapBSM with e−Rf × TFT substituted for S0; ignores mark-to-market. Call = long futures (PV × N(d1)) + short bond. rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida

▸ Use / trapForward rate replaces stock price; strike rate replaces exercise price. Options on FRAs use actual/365 (FRAs use 30/360).

▸ Use / trapRight to pay fixed; gains when rates rise. Exercise if market swap rate > X. Value = PV(E(payoff)).

▸ Use / trapRight to receive fixed; gains when rates fall. Long callable bond = option-free bond + short receiver swaption.

▸ Use / trapCall delta rises from 0 to e−δT as S rises; put delta rises from −e−δT to 0. Delta = hedge ratio = slope of pre-expiry curve.

▸ Use / trapLinear approximation; accurate only for small ΔS. Example: 0.58 × $0.75 = $0.435.

▸ Use / trapGamma adds curvature, like convexity for bonds. Long calls and puts have positive gamma; call and put gammas are equal.

▸ Use / trapHigher r shrinks the second term, so call rho > 0; put rho < 0. Rho is a minor sensitivity.

▸ Use / trapLong stock + short calls (or long puts) = delta-neutral. Must rebalance continuously (dynamic hedge); 60,000/0.60 = 100,000 calls. Page 43 of 59 COMPARISON TABLES & FRAMEWORKS Forward/futures pricing and valuation summary Underlying Price (at t = 0) Value to long (at t) No cash flows S0(1 + Rf)T St − FP/(1 + Rf)T−t Stock, discrete (S0 − PVD)(1 + Rf)T (St − PVDt) − FP/(1 + Rf)T−t dividends Equity index c c Continuous-time analogue S0e(Rf − δ )T Coupon bond (S0 − PVC)(1 + Rf)T (St − PVCt) − FP/(1 + Rf)T−t Bond futures [(full)(1 + Rf)T − FVC − Marked to market daily (quoted) AIT]/CF FRA Implied forward rate from PV of interest savings at MRR curve current MRR Any, given FPt — (FPt − FP)/(1 + Rf)T−t Swap pricing and valuation summary Swap Pricing (fixed rate) Interest rate (1 − Zfinal)/ΣZ Currency Each currency's own SFR; notionals at spot Equity (pay fixed) Same SFR formula as IRS Equity for equity No pricing needed Cash-and-carry vs reverse cash-and-carry Condition Trades Forward overpriced Borrow, buy spot, short forward Forward underpriced Short spot, lend proceeds, long forwa Day-count and compounding conventions Contract Year basis Compounding MRR-based (FRAs, swaps, caps, 360 days Simple: r × days/360 floors) Equities, bonds, stock options 365 days Periodic: (1 + r)days/365 Equity indexes 365 days Continuous: er × days/365 Options on FRAs Actual/365 Black model accrual period Direction of BSM option value for an increase in each input Greek Input Calls Delta Asset price (S) Positive, delta > 0 Gamma Delta Gamma > 0 Vega Volatility (σ) Vega > 0 Rho Risk-free rate (r) Rho > 0 Theta Time to expiration (T) Theta < 0 — Exercise price (X) Negatively related Interest rate derivative equivalencies Position Replicated by Long FRA Long IR call + short IR put (strike = FRA rate) Short FRA Short IR call + long IR put (strike = FRA rate) Interest rate cap Series of IR calls (caplets) Interest rate floor Series of IR puts (floorlets) Payer swap Long cap + short floor (same strike) Receiver swap Short cap + long floor (same strike) Payer swap (swaptions) Long payer + short receiver swaption Long callable bond Option-free bond + short receiver swaption rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida Valuation after inception ΣZ × (SFRNew − SFROld) × days/360 × NP (payer) PV each leg as bond; convert at current spot; difference NP × (St/Sreset) − PV(fixed coupons + principal) (Rreceived − Rpaid) × NP Profit at T FPmkt − S0(1 + Rf)T ward S0(1 + Rf)T − FPmkt Puts 0 Negative, delta < 0 Gamma > 0 Vega > 0 Rho < 0 Theta < 0 (deep ITM exception) d Positively related Page 44 of 59 ★ Exam signals & key rules — Derivatives 1. Forward price makes contract value zero at initiation; value changes afterward. 2. Forward overpriced → cash-and-carry; underpriced → reverse cash-and- carry. 1 3. Ignore dividends or coupons paid after the forward contract matures. 1 4. FRA long = long the rate (borrower); gains when rates rise. 5. FRA value: discount savings over the remaining period to loan maturity. 1 6. Fixed-rate swap payer gains when rates rise; receiver gains when rates fall. 7. Currency swap: value each leg in its own currency, convert at current spot. rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida 8. Binomial stock trees use πU = (1 + Rf − D)/(U − D); rate trees use 0.5/0.5. 9. American call on non-dividend stock = European call; deep ITM American puts may be exercised early. 10. N(d2) = risk-neutral probability that a call finishes in the money. 11. Delta-hedged long stock + short calls has negative net gamma (gamma risk on jumps). 12. Market implied volatility below your forecast → options underpriced → buy them. Page 45 of 59 07 Alternative Investments 28 formulas C FA L E V E L I I 2 0 2 7 · S U B J E C T 0 7 7 tables 11 exam rules R30 · Introduction to Commodities R31 · Overview of Types of Real Estate Investment R32 · Investments in Real E R30 · Introduction to Commodities and Commodity Deriv

▸ Use / trapInvestors prefer current consumption (u0 > ut), so mt < 1. Higher expected GDP growth lowers future marginal utility → mt falls, real rates rise.

▸ Use / trapBond price equals the expected inter-temporal rate of substitution; inflation-indexed so inflation is ignored.

▸ Use / trapHigher utility attached to current consumption → lower P0 → higher real rate.

▸ Use / trapRisky assets: covariance negative (high prices when marginal utility low) → lower P0 → positive risk premium. Held to maturity, single period: covariance = 0.

▸ Use / trapFor T-bills, inflation uncertainty is negligible, so no inflation risk premium.

▸ Use / trapθ rises with maturity → explains normally positive term spread (upward-sloping curve). rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida nt Markets R35 · Analysis of Active Portfolio Management ifactor Models R38 · Measuring and Managing Market Risk 12 formulas

▸ Use / trapInflation above target or output above potential → higher policy rate. Rates too low vs. rule = policy error magnifying the cycle.

▸ Use / trapTrap: BEI ≠ expected inflation alone for longer maturities; it also contains θ.

▸ Use / trapSpreads widen in downturns (more defaults, lower recoveries). Spread narrowing helps lower-rated bonds most.

▸ Use / trapEquity is a poor consumption hedge (pro-cyclical) → positive ERP; ERP falls in expansions, rises in recessions.

▸ Use / trapReal estate has bond-like, equity-like and illiquid features; premium close to equity's.

▸ Use / trapSmooths the volatility of unadjusted P/E. Multiples rise with expected growth and fall with any component of required return. Page 50 of 59 R35 · Analysis of Active Portfolio Management

▸ Use / trapEx-post version uses realized returns. Assumes portfolio beta = 1 vs benchmark (otherwise use alpha).

▸ Use / trapActive weights must sum to zero; overweights positive, underweights negative.

▸ Use / trapWeighted average of asset-class returns for each portfolio; difference = active return.

▸ Use / trapTrap: allocation term uses BENCHMARK class returns; selection term uses PORTFOLIO weights.

▸ Use / trapUnaffected by adding cash or leverage (excess return and σ scale together).

▸ Use / trapChanged by adding cash/leverage; unchanged by scaling active weights or blending with the benchmark. Closet indexer: low IR, often negative after fees.

▸ Use / trapLevel of active risk that maximizes portfolio Sharpe ratio; achieve it by mixing active fund and benchmark.

▸ Use / trapHighest IR → highest attainable Sharpe ratio, so choose the manager with the highest IR regardless of risk aversion. rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida 23 formulas

▸ Use / trapUsed to find σP after choosing optimal active risk (e.g., 12% and 6% → 13.4%).

▸ Use / trapThen portfolio excess return = E(RA) + (RB − RF).

▸ Use / trapBlending with benchmark scales active return and active risk proportionally; IR unchanged.

▸ Use / trapUnconstrained portfolio: TC = 1. Constraints (no shorts, risk limits) push TC below 1.

▸ Use / trapConverts a standardized score into an expected active return.

▸ Use / trapSum of active weights times forecast active returns.

▸ Use / trapBreadth example: 10 securities each month → BR = 10 × 12 = 120.

▸ Use / trapTC < 1 → IR < IR* and E(RA) < E(RA)*.

▸ Use / trapConstrained optimal active risk is lower than unconstrained.

▸ Use / trapConstrained Sharpe ratio is below the unconstrained one.

▸ Use / trapTC2 of realized active-return variance is due to realized IC; (1 − TC2) is constraint-induced noise.

▸ Use / trap50% correct → IC = 0. Quarterly calls → BR = 4. R36 · Exchange-Traded Funds: Mechanics and Applicati

▸ Use / trapStd dev of differential return RX − RY, per period of the bet.

▸ Use / trapActive-risk limit: allowable weight deviation = risk limit ÷ annualized strategy active risk (5.20%/17.32% = 30%).

▸ Use / trapCross-sectional or time-series dependence reduces effective breadth below N. tions 6 formulas

▸ Use / trapSpread negatively related to probability of an offsetting secondary-market trade; wider for fixed income, specialized and thinly traded ETFs.

▸ Use / trapPositive = premium (APs create & sell ETF), negative = discount (APs buy & redeem). Sources: timing differences, stale pricing.

▸ Use / trapHolding cost = round-trip trading cost + (years held × annual fee). Short horizon: trading cost dominates; buy-and-hold: fees dominate. rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida

▸ Use / trapTracking error does not show direction (under/outperformance) or when differences occurred; compare annual rolling tracking difference with expense ratio.

▸ Use / trapCompounding with daily reset: +5% then −5% leaves 2× ETF below start. Unsuitable for horizons beyond one month (expectation-related risk).

▸ Use / trapTactical ETFs chosen for low trading cost and liquidity, not low management fee. Page 52 of 59 R37 · Using Multifactor Models

▸ Use / trapAssumptions: unsystematic risk diversifiable, factor model generates returns, no arbitrage. CAPM = special case with one (market) factor.

▸ Use / trapZero cost, zero net factor exposure. Go long high return-per- unit-of-factor, short low (e.g., long D 15%, short C 13% → 2%).

▸ Use / trapThen check a third portfolio: if actual ≠ APT expected return, it is mispriced.

▸ Use / trapOnly SURPRISES move returns. Sign trap: negative sensitivity × negative surprise = positive return (MT: −0.5 × −0.01 = +0.005).

▸ Use / trapFactors are returns (not surprises); intercept has no economic meaning (not expected return).

▸ Use / trapz-score style; computed from data, not regression-estimated (e.g., (15.20 − 11.90)/6.30 = 0.52). R38 · Measuring and Managing Market Risk

▸ Use / trapSecurity selection return is the residual after factor return.

▸ Use / trapExample: −0.60% active = −1.16% factor tilts + 0.56% selection.

▸ Use / trapStandard deviation of active return.

▸ Use / trapComponents add as VARIANCES; active factor risk is the plug. Proportion = component ÷ active risk squared; active risk = √(active risk squared).

▸ Use / trapPure bet on one factor: long (short) that factor portfolio; expect large caps to win → short the SMB factor portfolio.

▸ Use / trapGDP sensitivity 0.8 → 80% short position in GDP factor portfolio. Tracking portfolio = replicates benchmark's factor exposures.

▸ Use / trapMeasures consistency of active return (0.27 = 27 bp of active return per 1% active risk). 15 formulas

▸ Use / trapInput to parametric VaR; VaR is very sensitive to the covariance estimate. rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida 13 formulas

▸ Use / trapVaR = MINIMUM loss with given probability. Example: [0.00036 − 1.65(0.012682)] × (−1) = 0.0206 daily. Page 53 of 59

▸ Use / trapMean scales with T, σ with √T. Annual 5% VaR = [0.09 − 1.65(0.20052)] × (−1) = 0.2409.

▸ Use / trapNo distributional assumption; handles options. Unusually volatile (calm) lookback overstates (understates) VaR.

▸ Use / trapNo lookback period needed. Large sample + same normal distribution and parameters → same result as parametric.

▸ Use / trapEasy with historical or Monte Carlo; mathematically complex with parametric method.

▸ Use / trapChange in VaR from a specific change in allocation to a security.

▸ Use / trap≈ change in VaR for a 1% increase in weight; estimate of a position's contribution to VaR. R39 · Backtesting and Simulation

▸ Use / trap5% monthly relative VaR of 2.5% → 5% of the time underperformance ≥ 2.5%.

▸ Use / trapBeta is the main equity risk sensitivity measure.

▸ Use / trapDuration = first-order; convexity = second-order. Same duration ≠ same risk if yield volatilities differ.

▸ Use / trapDelta first-order; gamma second-order (like convexity); vega = volatility sensitivity.

▸ Use / trapPension funds focus on asset-liability mismatch and surplus volatility.

▸ Use / trapRelative risk measure specific to traditional (long-only) asset managers.

▸ Use / trapUsed by hedge funds with significantly non-normal returns (and CTAs). 6 formulas

▸ Use / trapDownside-risk metric based on actual past losses; used by CTAs and hedge funds. rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida

▸ Use / trapMore comprehensive tail measure than VaR; VaR is sensitive to the assumed distribution shape. Page 54 of 59

▸ Use / trapReported alongside Sharpe ratio and maximum drawdown in backtests.

▸ Use / trapFama–French hedged portfolio approach; drawback: some managers cannot short. COMPARISON TABLES & FRAMEWORKS Risk premium build-up by asset class (R34) Asset Required return / discount rate Short-term default-free bond R+π Long-term default-free bond R+π+θ Credit-risky bond R+π+θ+γ Equity R + π + θ + γ + κ (λ = γ + κ) Commercial real estate R+π+θ+γ+κ+φ Active strategies under the fundamental law (R35) Strategy IC Breadt Security selection Given IC per bet Numbe Market timing 2(% correct) − 1 Calls p Sector rotation 2(% correct) − 1 Bets p Multifactor model types (R37) Feature Macroeconomic Fundamental Factors Surprises in macro variables Returns to firm attributes (P/E, siz Sensitivities Regression slopes Standardized attributes (z-scores Intercept Expected return No economic meaning Weakness — — Factor portfolio vs tracking portfolio (R37) Portfolio Construction Factor portfolio Sensitivity 1 to one factor, 0 to others Tracking portfolio Matches benchmark's set of factor exposures VaR estimation methods (R38) Feature Parametric Histori Inputs Means, variances, covariances Actual Distribution assumption Usually normal None Lookback period Yes Yes Options in portfolio Limited usefulness Handle CVaR Complex Easy (a Risk sensitivity measures by exposure (R38) Exposure First-order Second-order / other Equity Beta — Fixed income Duration Convexity Options Delta Gamma; vega (volatility) rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida

▸ Use / trapMethodology fixed in advance to avoid overfitting; assumes past patterns repeat; may miss extreme downside.

▸ Use / trapUsed in historical scenario analysis (regimes: recession vs expansion, high vs low volatility). Sharpe ratio vs information ratio (R35) Feature Sharpe ratio Information ratio Numerator RP − RF RP − RB (active return) Denominator Total risk σP Active risk σA Adding cash / leverage Unchanged Changes (cash lowers IR) Scaling active weights — Unchanged Blending with benchmark — Unchanged Zero-beta fund, RF benchmark Equals IR Equals SR dth Active risk ber of independent bets/yr Given σA per year (quarterly = 4) Given σA per year (monthly = 12) σC × √BR Statistical ize) Portfolios from factor analysis / principal components es), not estimated Statistically derived — Factors hard to interpret ("mystery") Use Speculate or hedge a single factor Passive replication of benchmark ical simulation Monte Carlo past risk-factor changes Assumed distributions + correlations Any specified No es Handles average tail losses) Easy Page 55 of 59 VaR vs sensitivity vs scenario analysis (R38) Measure Gives VaR Probability of minimum loss Sensitivity Exposure to small change in one factor Scenario / stress Effect of simultaneous large changes Risk measures by organization type (R38) Organization Typical risk measures Banks Duration, FX exposure, leverage, sce Traditional asset managers Relative risk, ex ante tracking error, a Hedge funds Sensitivities, leverage, gross exposur DB pension funds Surplus at risk, asset-liability mismatc P&C insurers Investment-portfolio sensitivities, VaR Life insurers Sensitivities of assets and annuity liab Risk constraints (R38) Constraint What it does Risk budgeting Set total acceptable risk, allocate across units Position limits Cap exposure to security, asset class, country, currency Scenario limits Cap expected loss under a given scenario Stop-loss limits Reduce exposure when losses exceed amount over period Portfolio insurance Hedge with index puts as value falls Backtesting problems and fixes (R39) Problem Cause Survivorship bias Only firms existing today Look-ahead bias Data unavailable at decision date (reporting lag, restateme Data snooping Pick best of many tested models Historical simulation vs Monte Carlo simulation (R39) Feature Historical simulation Monte Carlo simulation Draws Random past returns (with From assumed multivariate replacement = bootstrapping) distribution Time order Ignored N/A Strength Uses actual data, simple Flexible: fat tails, skew, tail dependence Weakness Limited to what happened Complexity; model/estimation error ★ Exam signals & key rules — Portfolio Management 1. Value changes only when expectations change (cash flows, real rates, inflation, or risk premiums). 2. Inverted yield curve signals recession; upward slope as economy exits recession. 3. Credit spreads widen in downturns; narrowing spreads favour lower-rated bonds. 4. Choose the manager with the highest IR; set active risk via σA* = (IR/SRB)σB 1 by blending with the benchmark. 5. 'Constraints', 'long-only', 'cannot short' in a vignette → TC < 1, use full 1 fundamental law. 1 6. 'Correct X% of the time' → IC = 2(X) − 1; quarterly calls → BR = 4, monthly → 12. rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida Lacks Tail size, liquidity, correlation spikes Probability of changes Probability (except historical frequency) enario/stress tests, VaR, economic capital active share, scenario analysis re, stress tests, maximum drawdown tch, hedged vs unhedged exposure R, capital at risk, combined scenarios abilities, mismatch, surplus scenarios Remedy Point-in-time data ents) Point-in-time data or reporting-lag assumption Higher t-stat hurdle (≈3.0); cross-validation 7. Macro model: only surprises (actual − expected) matter; watch sign of sensitivity × surprise. 8. Active risk components add as variances: active risk² = active factor + active specific. 9. VaR is a minimum loss: 5% one-tailed → z = 1.65; scale mean by T and σ by √T. B 10. Need average loss beyond VaR → CVaR; change in VaR from weight change → IVaR / MVaR. 11. Portfolio with options → historical or Monte Carlo VaR, not parametric. 12. Backtest signals: 'stocks that exist today' = survivorship; 'restated/reported later' = look-ahead; 'tested many models' = data snooping. Page 56 of 59 09 Ethics & Professional Stan C FA L E V E L I I 2 0 2 7 · S U B J E C T 0 9 Study & reference sheet 6 tables 12 exam rules COMPARISON TABLES & FRAMEWORKS Code of Ethics — six components (Members and Candidates must:) # Component 1 Act with integrity, competence, diligence, and respect, and in an ethical manner the investment profession, and other participants in the global capital markets 2 Place the integrity of the investment profession and the interests of clients abov 3 Use reasonable care and exercise independent professional judgment when con investment actions, and engaging in other professional activities 4 Practice and encourage others to practice in a professional and ethical manner 5 Promote the integrity and viability of the global capital markets for the ultimate b 6 Maintain and improve their professional competence and strive to maintain and Standards of Professional Conduct I–VII Code Title Core req I Professionalism I(A) Knowledge of the Law Comply I(B) Independence and Objectivity No gifts I(C) Misrepresentation No know I(D) Misconduct No dish I(E) Competence Act with II Integrity of Capital Markets II(A) Material Nonpublic Information Do not a II(B) Market Manipulation No price III Duties to Clients III(A) Loyalty, Prudence, and Care Client in III(B) Fair Dealing Deal fair III(C) Suitability 1(a) inqu III(D) Performance Presentation Fair, acc III(E) Preservation of Confidentiality Keep cli IV Duties to Employers IV(A) Loyalty Act for e IV(B) Additional Compensation Arrangements Compet IV(C) Responsibilities of Supervisors Reasona V Investment Analysis, Recommendations, and Actions V(A) Diligence and Reasonable Basis (1) Dilige V(B) Communication with Clients and Prospective Clients Disclose vs opini V(C) Record Retention Maintain VI Conflicts of Interest VI(A) Avoid or Disclose Conflicts Avoid, o VI(B) Priority of Transactions Client an VI(C) Referral Fees Disclose VII Responsibilities as a CFA Institute Member or CFA Candidate VII(A) Conduct as Participants in CFA Institute Programs Do not c VII(B) Reference to CFA Institute, the CFA Designation, and the CFA Do not m Program rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida ndards er with the public, clients, prospective clients, employers, employees, colleagues in ve their own personal interests onducting investment analysis, making investment recommendations, taking r that will reflect credit on themselves and the profession benefit of society d improve the competence of other investment professionals equirement y with stricter of law or Code; dissociate from violations s/benefits that could compromise independence and objectivity wing misrepresentation; includes guarantees and plagiarism honesty, fraud, deceit or acts reflecting adversely h and maintain competence for professional responsibilities act or cause others to act on MNPI ce distortion or artificial volume to mislead nterests before employer's and own irly and objectively with all clients quire and update; 1(b) suitable vs written IPS; 1(c) total portfolio; 2 follow mandate curate, and complete performance information lient info confidential unless (1) illegal, (2) required by law, (3) client permits employer's benefit; don't divulge confidential info or harm employer ting compensation needs written consent from all parties nable efforts so supervisees comply with laws and Code gence, independence, thoroughness; (2) reasonable and adequate basis se (1) services and costs, (2) process, (3) risks/limitations; (4) key factors; (5) fact ion in records supporting analysis and communications or prominent plain-language full disclosure and employer trades before beneficial-owner trades se compensation received/paid for referrals compromise reputation/integrity of CFA Institute or programs misrepresent or exaggerate membership, designation, candidacy Page 57 of 59 Recommended procedures and key do / don't by standard Standard Do I(A) Track law changes; seek counsel/compliance; document dissociation I(B) Restricted list; pay own commercial travel; token gifts; preapprove IPO b I(C) List firm services; cite sources; keep records of materials used I(D) Firm code of ethics; list of violations/sanctions; check references I(E) Continuing education, designations, seminars, self-study II(A) Seek public dissemination; firewalls; watch, restricted, rumor lists II(B) — III(A) Quarterly itemized statements; best execution; vote proxies; use soft do client III(B) Limit pre-dissemination knowledge; simultaneous dissemination; written allocation; pro rata IPO III(C) Written IPS per client; review periodically; judge in total portfolio III(D) Follow GIPS; composites not single account; include terminated accoun III(E) Share only with authorized co-workers; secure electronic data IV(A) Get employer consent before independent practice IV(B) Immediate written report of proposed outside compensation IV(C) Adequate written compliance; investigate promptly; increase supervisio V(A) Written due-diligence guidance; scenario-test models; review third-part and external advisers V(B) Keep research records; disclose process changes promptly V(C) Retain records (7 years if no other rule) VI(A) Disclose stock ownership, compensation structure, board service VI(B) Limit IPO participation; restrict private placements; blackout periods; pr disclose policies VI(C) Disclose nature and value of referral benefits; quarterly updates to emp VII(A) Follow exam rules and Candidate Pledge VII(B) State facts (e.g., passed exams on first attempt) Additional compensation — disclosure rules (IV(B) professor's note) Situation Requirement One-time client gift for past Disclose to employer (not necessarily performance in writing) Client agreement for future Disclose in writing outperformance pay Side job potentially competing with Written permission required employer Unrelated side job No disclosure required Unsolicited trade requests (III(C)) Impact on total portfolio Action Minimal Discuss why unsuitable; follow firm policy; cli Material Update IPS, or separate client-directed accou Ethics case studies (R42) Case Standard Violation Syyark III(B) Fair Dealing Fills larger clients' orders from ow Syyark III(C) Suitability Blanket 3%; smallest clients used Syyark IV(B) Additional Compensation Mining without informing employe Syyark V(A) Diligence and Reasonable Research not thorough Basis Syyark VI(A) Avoid or Disclose Conflicts Recommends illiquid holding he o Agarway I(A) Knowledge of the Law Soliciting minors; collecting minor Agarway VI(A) Avoid or Disclose Conflicts Club gets preferential intelligence investments rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida Don't Rely on advice known to be illegal; no duty to report to regulators buys Accept gifts that compromise objectivity; issuer-paid research with contingent pay Guarantee returns; plagiarize (recognized statistical services need no citation) Use PCP to settle personal disputes — (CE recommended, not required) Act on MNPI (mosaic theory with nonmaterial info is OK) Trade to create false activity; spread false rumors ollars for Churn accounts; direct brokerage for firm benefit en trade Favour select clients; take hot IPO shares personally Blanket allocations; trade outside mandate nts; disclose Present simulated results as actual; cherry-pick accounts Disclose client info (OK if illegal activity, required by law, or permitted) Solicit clients or take records before leaving Accept competing compensation without written consent on Accept supervision with inadequate procedures (decline in writing) rty research Recommend without reasonable and adequate basis Omit risks/limitations; blur fact and opinion Take former employer's records Hide conflicts or bury them in fine print reclearance; Front-run clients ployer Accept undisclosed referral fees Reveal exam topics, questions, formulas or weightings Imply superior performance; 'partial' designation; use CFA after dues lapse ient acknowledges unt per firm policy; else reconsider relationship Required action wn account Fill all orders pro rata or none from own account d as 'guinea pigs' Assess each client's goals and constraints yer Disclose and obtain written permission first Document research, value drivers, suitable clients owns; late disclosure Disclose to clients and employer up front ors' data Ensure applicant complies with all laws e; competing personal Disclose to all investors Page 58 of 59 ★ Exam signals & key rules — Ethics & Professional Standard 1. Follow the stricter of applicable law and the Code and Standards. 2. On discovering a violation: approach supervisor/compliance, then dissociate; reporting to regulators not required by Standards. 3. Mosaic theory: public info + nonmaterial nonpublic info is permitted; analyst conference calls are not public disclosure. 4. Fair does not mean equal: different service levels OK if disclosed and available to all. 1 5. Client trades → employer trades → personal (beneficial-owner) trades; family accounts that are clients are treated as clients. 1 6. Gifts from clients: disclose; gifts contingent on future performance: written employer consent. 1 rbeiset.com · Mentored by Deepak Goyal — CFA, FRM · Noida ds 7. Supervisor with inadequate compliance procedures: decline supervisory responsibility in writing. 8. Leaving an employer: may prepare, but must not solicit clients or take t records/models before departure. 9. Issuer-paid research: flat fee only, not contingent on conclusions, with disclosure. 10. Significant change in investment process must be disclosed to clients promptly. 11. Records: firm property; 7-year minimum if no other rule; recreate from public sources at a new firm. 12. Never reveal exam topics, questions, formulas or weightings; do not link CFA designation to superior performance. Page 59 of 59