1. Future Value (lump sum): FV = PV(1 + r)^n
2. Present Value (lump sum): PV = FV / (1 + r)^n
3. Effective Annual Rate (discrete compounding): EAR = (1 + r/m)^m − 1
4. Effective Annual Rate (continuous compounding): EAR = e^r − 1
5. Perpetuity (level payments): PV = C / r
6. Growing Perpetuity: PV = C₁ / (r − g), with r > g
7. Ordinary Annuity PV: PV = C × [1 − (1 + r)^{−n}] / r
8. Ordinary Annuity FV: FV = C × [(1 + r)^n − 1] / r
9. Annuity Due: PV or FV of ordinary annuity × (1 + r)
10. Required nominal rate (build-up): i ≈ r_RF + IP + DP + LP + MP

BAII Plus: use N, I/Y, PV, PMT, FV. For annuity due, set 2nd > BGN; for ordinary annuity use END.

1. Holding Period Return: HPR = (P₁ − P₀ + D₁) / P₀
2. Holding Period Yield: HPY = HPR (express as %)
3. Arithmetic Mean Return: R̄ = (ΣRᵢ) / n
4. Geometric Mean Return: R_G = (∏(1 + Rᵢ))^{1/n} − 1
5. Harmonic Mean (e.g. for cost averaging): X_H = n / Σ(1/Xᵢ)
6. Continuously Compounded Return: r = ln(S₁ / S₀)
7. Shortfall Ratio: (E(R_p) − R_target) / σ_p

1. Sample Variance: s² = Σ(xᵢ − x̄)² / (n − 1)
2. Sample Standard Deviation: s = √s²
3. Mean Absolute Deviation: MAD = Σ|xᵢ − x̄| / n
4. Target (Semi) Deviation: s_TD = √[Σmin(0, xᵢ − T)² / (n − 1)]
5. Coefficient of Variation: CV = s / x̄
6. Sample Covariance: s_XY = Σ(xᵢ − x̄)(yᵢ − ȳ) / (n − 1)
7. Sample Correlation: r_XY = s_XY / (s_Xs_Y)
8. Skewness (sample): Skew ≈ [1/n Σ((xᵢ − x̄)³)] / s³
9. Excess Kurtosis (sample): K_excess ≈ [1/n Σ((xᵢ − x̄)⁴)] / s⁴ − 3

1. Location of y-th Percentile: L_y = (n + 1)(y / 100)
2. If L_y is not integer, linearly interpolate between surrounding observations.

1. Odds: Odds(E) = P(E) / (1 − P(E))
2. Addition Rule: P(A or B) = P(A) + P(B) − P(AB)
3. Multiplication Rule: P(AB) = P(A|B)P(B)
4. Conditional Probability: P(A|B) = P(AB) / P(B)
5. Law of Total Probability: P(A) = Σ P(A|Sᵢ)P(Sᵢ)
6. Bayes’ Formula: P(Event|Info) = P(Info|Event)P(Event) / P(Info)
7. Expected Value (discrete): E(X) = Σ p(xᵢ)xᵢ
8. Variance (discrete): Var(X) = Σ p(xᵢ)[xᵢ − E(X)]²
9. Discrete Uniform: p(x) = 1/n for n equally likely outcomes.
10. Continuous Uniform PDF: f(x) = 1/(b − a), a ≤ x ≤ b.
11. Binomial PMF: P(X = x) = C(n, x)pˣ(1 − p)^{n − x}
12. Binomial Mean & Variance: E(X) = np, Var(X) = np(1 − p)
13. Standard Normal z-score: z = (X − μ)/σ
14. Lognormal continuous return: r = ln(S₁/S₀) = ln(1 + R)

1. Standard Error of Mean (σ known): SE = σ / √n
2. Standard Error of Mean (σ unknown): SE = s / √n
3. Confidence Interval: Point estimate ± (reliability factor × SE)
4. General Test Statistic: TS = (Sample statistic − Hypothesized value) / SE

1. Expected Portfolio Return (n assets): E(R_p) = Σ wᵢE(Rᵢ)
2. Portfolio Variance (n assets): σ²_p = ΣΣ wᵢwⱼCov(Rᵢ,Rⱼ)
3. Two-Asset Portfolio Variance: σ²_p = w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ₁₂
4. Correlation from Covariance: ρ₁₂ = Cov(R₁,R₂)/(σ₁σ₂)

1. Regression Line: Y = b₀ + b₁X + ε
2. Slope Estimate: b̂₁ = Cov(X,Y) / Var(X)
3. Intercept Estimate: b̂₀ = ȳ − b̂₁x̄
4. Total / Regression / Error SS: SST = SSR + SSE
5. R² (coefficient of determination): R² = SSR / SST
6. Standard Error of Regression: SEE = √(SSE / (n − 2))

BAII Plus: regression is better done in Excel / calculator with STAT functions; Level I focuses on interpretation and formula usage rather than keystrokes.

1. Own-Price Elasticity: E_D = (%ΔQ_d) / (%ΔP)
2. Income Elasticity: E_I = (%ΔQ_d) / (%ΔIncome)
3. Cross-Price Elasticity: E_XY = (%ΔQ_d,X) / (%ΔP_Y)

1. GDP (expenditure): Y = C + I + G + (X − M)
2. GDP Deflator: Deflator = (Nominal GDP / Real GDP) × 100
3. Savings–Investment–Fiscal–Trade Link: (G − T) = (S − I) − (X − M)

1. Fisher Approximation: Nominal ≈ Real + Inflation
2. Exact Fisher: (1 + nominal) = (1 + real)(1 + inflation)

1. Covered Interest Rate Parity (discrete): F₀ = S₀ × (1 + i_dom)/(1 + i_for)
2. Real Exchange Rate: RER = S × (P_for/P_dom)

1. Gross Margin: Gross Profit / Revenue
2. Operating Margin: Operating Income / Revenue
3. Net Profit Margin: Net Income / Revenue
4. Return on Assets (ROA): ROA = Net Income / Average Total Assets
5. Return on Equity (ROE): ROE = Net Income / Average Shareholders’ Equity

1. Three-Step ROE: ROE = (Net Income / Sales) × (Sales / Assets) × (Assets / Equity)
2. Five-Step ROE: ROE = Tax burden × Interest burden × EBIT margin × Asset turnover × Financial leverage

1. Current Ratio: Current Assets / Current Liabilities
2. Quick Ratio: (Cash + Marketable Securities + Receivables) / Current Liabilities
3. Interest Coverage: EBIT / Interest Expense
4. Debt-to-Equity: Total Debt / Total Equity

1. Free Cash Flow to Firm (FCFF): FCFF = CFO + Interest(1 − t) − FCInv − WCInv
2. Free Cash Flow to Equity (FCFE): FCFE = CFO − FCInv + Net Borrowing

BAII Plus: use CF → NPV/IRR to value discounted cash flows from FCFF / FCFE projections.

1. Net Present Value (NPV): NPV = Σ CF_t / (1 + r)^{t} − CF₀
2. Internal Rate of Return (IRR): discount rate that sets NPV = 0.
3. Payback Period: time for cumulative (undiscounted) cash flows to recover initial investment.

BAII Plus: use CF → NPV, IRR keys.

1. Degree of Operating Leverage (DOL): DOL = %ΔEBIT / %ΔSales
2. Degree of Financial Leverage (DFL): DFL = %ΔEPS / %ΔEBIT
3. Degree of Total Leverage (DTL): DTL = DOL × DFL

1. General DDM: P₀ = Σ D_t / (1 + r)^{t}
2. Gordon Growth (constant g): P₀ = D₁ / (r − g)
3. Justified P₀/E₁: P₀/E₁ = (1 − b)/(r − g)
4. Justified P₀/B₀: P₀/B₀ = (ROE − g)/(r − g)

1. Residual Income (RI): RI_t = Eₜ − r × B_t−1
2. Firm Equity Value (RI model): V₀ = B₀ + Σ RI_t / (1 + r)^t

1. Bond Price with Spot Rates: PV = Σ [PMT / (1 + z_t)^t] + FV/(1 + z_n)^n
2. Flat Price / Full Price: Full Price = Flat Price + Accrued Interest
3. Accrued Interest: AI = (t/T) × PMT (days since last / days in period).
4. Current Yield: Current Yield = Annual Coupon / Flat Price

BAII Plus: use 2nd > BOND for price/yield; set compounding and day count as per question.

1. FRN Price (simplified): Price ≈ Σ[(Ref + QM)FV/m / (1 + (Ref + DM)/m)^t] + FV/(1 + (Ref + DM)/m)^n
2. Discount vs Quoted Margin: if QM > DM, FRN trades above par.

1. Approx. Macaulay/Modified Duration (price-based): Dur ≈ [P₋ − P₊] / [2 × P₀ × Δy]
2. Effective Duration: EffDur = (P₋ − P₊) / [2 × P₀ × ΔCurve]
3. Approximate Convexity: Conv ≈ [P₋ + P₊ − 2P₀] / [P₀ × (Δy)²]
4. Percentage Price Change (duration & convexity): %ΔP ≈ −Dur × Δy + ½ × Conv × (Δy)²
5. Price Value of a Basis Point (PVBP): PVBP ≈ (P_−1bp − P_+1bp) / 2
6. Money Duration: MoneyDur = Dur × Price

1. Duration Gap: Duration Gap = Macaulay Duration − Investment Horizon
2. If positive: price risk > reinvestment risk; if negative: reinvestment risk > price risk.

1. Loss Severity: Loss Severity = 1 − Recovery Rate
2. Expected Loss: E[Loss] = PD × Loss Severity × Exposure
3. Corporate Yield Components: real RF rate + expected inflation + maturity premium + liquidity premium + credit spread.

1. Simple Forward Price (no income/cost): F₀(T) = S₀(1 + r)^T
2. No-Arbitrage Forward (with income & costs, discrete): F₀(T) = [S₀ + PV(Costs) − PV(Income)](1 + r)^T
3. No-Arbitrage Forward (continuous): F₀(T) = S₀ e^{(r + c − q)T}
4. No-Arbitrage Currency Forward (continuous): F₀ = S₀ e^{(r_dom − r_for)T}

1. Value of Long Forward at Time t: V_t = S_t − F₀(1 + r)^{−(T − t)}
2. Value of Currency Forward (long): V_t = S_t − F₀ e^{−(r_dom − r_for)(T − t)}

1. Implied Forward Rate (discrete): IFR_m,n = [(1 + z_n)^n / (1 + z_m)^m]^{1/(n−m)} − 1
2. FRA Settlement (buyer receives): (Reference Rate − FRA Fixed Rate) × Notional × (Days/360 or 365)
3. Price of Interest Rate Futures Contract: Quoted Price = 100 − (100 × MRR)

1. Intrinsic Values at Expiry: Call: max(0, S_T − X), Put: max(0, X − S_T)
2. Lower Bound (European Call on non-dividend stock): c₀ ≥ max(0, S₀ − X/(1 + r)^T)
3. Lower Bound (European Put): p₀ ≥ max(0, X/(1 + r)^T − S₀)

1. Basic Put–Call Parity (European, no income): c₀ + X/(1 + r)^T = p₀ + S₀
2. Put–Call–Forward Parity: c₀ + X/(1 + r)^T = p₀ + F₀(T)/(1 + r)^T

1. Hedge Ratio: h = (C_up − C_down) / (S_up − S_down)
2. Risk-Neutral Probability: π = (1 + r − d)/(u − d)
3. Call Value Today: c₀ = [πC_up + (1 − π)C_down]/(1 + r)

1. Capitalization Rate: Cap Rate = NOI₁ / Value
2. Direct Cap Valuation: Value ≈ NOI₁ / Cap Rate

1. Net IRR: discount rate that sets PV of contributions = PV of distributions to LP.
2. Multiple of Invested Capital (MOIC): MOIC = Σ Distributions / Σ Paid-in Capital

BAII Plus: use CF → IRR for fund IRR; be careful with sign convention on contributions vs distributions.

1. Utility of a Risky Portfolio: U = E(R) − ½ Aσ², where A = risk aversion.

1. Capital Allocation Line (CAL): E(R_C) = R_f + [E(R_P) − R_f] × (σ_C/σ_P)
2. Capital Market Line (CML): E(R_P) = R_f + [(E(R_M) − R_f) / σ_M] × σ_P
3. Security Market Line (SML): E(R_i) = R_f + β_i(E(R_M) − R_f)
4. Beta: β_i = Cov(R_i, R_M)/σ²_M

1. Sharpe Ratio: Sharpe = [E(R_P) − R_f] / σ_P
2. Treynor Ratio: Treynor = [E(R_P) − R_f] / β_P
3. Jensen’s Alpha: α_P = R_P − [R_f + β_P(R_M − R_f)]

1. Money-Weighted Rate of Return (MWR): IRR of the actual cash flows. 0 = Σ CF_t / (1 + r)^{t}
2. Time-Weighted Return (TWR): break horizon into subperiods with external cash flows, compute each subperiod return R_k, then TWR = (∏(1 + R_k) − 1).

BAII Plus: MWR uses CF → IRR. TWR is usually done in Excel; exam focus is conceptual and on simple chained examples.