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Free CFA Level II Formula Sheet (2026)

Every CFA Level II formula you need on the test, grouped by topic and rendered with full math notation. 114 formulas across 9 topics, calibrated to the 2026 syllabus. Free forever, no signup required.

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All CFA Level II Formulas

Quantitative Methods 14 items
R-squared (coefficient of determination)
R2=RSSSST=1−SSESSTR^2 = \frac{RSS}{SST} = 1 - \frac{SSE}{SST}
RSS = regression sum of squares, SSE = error sum of squares
SST = total sum of squares. Fraction of variation explained.
Adjusted R-squared
Rˉ2=1−n−1n−k−1(1−R2)\bar{R}^2 = 1 - \frac{n-1}{n-k-1}(1 - R^2)
n = observations, k = number of independent variables
Penalizes for adding irrelevant predictors
F-statistic (overall regression)
F=RSS/kSSE/(n−k−1)=MSRMSEF = \frac{RSS/k}{SSE/(n-k-1)} = \frac{MSR}{MSE}
k = predictors, n = observations
Tests H0:allslopecoefficients=0H_0: all slope coefficients = 0
Standard error of regression (SEE)
SEE=SSEn−k−1=MSESEE = \sqrt{\frac{SSE}{n - k - 1}} = \sqrt{MSE}
SSE = sum of squared errors, n = observations, k = independent variables
Measures typical prediction error of the model
AR(1) model one-period forecast
xt=b0+b1xt−1+εtx_t = b_0 + b_1 x_{t-1} + \varepsilon_t, xtx_t = value at time t, b0b_0 = intercept, b1b_1 = lag coefficient (|b1b_1|<1 for stationarity), εtε_t = error
Multiple regression model equation
Y=b0+b1X1+b2X2+⋯+bkXk+eY = b_0 + b_1 X_1 + b_2 X_2 + \dots + b_k X_k + e, Y = dependent variable, b0 = intercept, bj = partial slope on Xj, k = number of independent variables, e = error term
t-statistic for an individual regression coefficient
t=bjsbjt = \frac{b_j}{s_{b_j}}, bj = estimated slope coefficient, sbjs_{bj} = standard error of the coefficient; df = n - k - 1, n = observations, k = independent variables
Partial F-test for a group of regression variables
F=(SSER−SSEU)/qSSEU/(n−kU−1)F = \frac{(SSE_R - SSE_U)/q}{SSE_U/(n - k_U - 1)}, SSERSSE_R = restricted SSE, SSEUSSE_U = unrestricted SSE, q = variables tested, n = observations, kUk_U = unrestricted predictors
Bias-variance decomposition of total prediction error
Total error=bias2+variance+irreducible noise\text{Total error} = \text{bias}^2 + \text{variance} + \text{irreducible noise}, bias = error from oversimplification, variance = error from sensitivity to training data, irreducible noise = inherent randomness
Classification precision and recall
precision=TPTP+FP,recall=TPTP+FN\text{precision} = \frac{TP}{TP + FP}, \quad \text{recall} = \frac{TP}{TP + FN}, TP = true positives, FP = false positives, FN = false negatives
Breusch-Pagan test statistic
BP=n×R2BP = n \times R^2, n = number of observations, R2R^2 = R-squared from regressing squared residuals on the original X variables; compared to chi-squared with k df
Variance inflation factor
VIFj=11−Rj2VIF_j = \dfrac{1}{1 - R_j^2}, Rj2R_j^2 = R-squared from regressing XjX_j on all other independent variables; VIF > 10 = severe multicollinearity
Odds ratio from a logistic coefficient
OR=ebjOR = e^{b_j}, OR = odds ratio (multiplier on odds per unit increase in XjX_j), bjb_j = logistic coefficient on XjX_j; OR>1 increases odds, OR<1 decreases
Logistic regression probability from log-odds
p=11+e−(b0+b1X1+b2X2+… )p = \dfrac{1}{1 + e^{-(b_0 + b_1 X_1 + b_2 X_2 + \dots)}}, p = probability of outcome, b = coefficients, X = predictors, log-odds = b0+b1X1+…b_0 + b_1 X_1 + \dots
Economics 7 items
Covered Interest Rate Parity (CIP)
FS=1+rd1+rf\frac{F}{S} = \frac{1 + r_d}{1 + r_f}
F = forward rate (d/f), S = spot rate (d/f)
rdr_d = domestic rate, rfr_f = foreign rate
No-arbitrage; holds in practice
International Fisher effect
rnom,d−rnom,f≈E(πd)−E(πf)r_{nom,d} - r_{nom,f} \approx E(\pi_d) - E(\pi_f)
Nominal interest rate differentials reflect expected inflation differentials
Combines Fisher effect with PPP
Relative PPP
E(%ΔSd/f)≈πd−πfE(\%\Delta S_{d/f}) \approx \pi_d - \pi_f
Expected % change in spot rate ≈ inflation differential
Holds better over long horizons
Unhedged foreign asset return (in domestic currency)
(1+RDC)=(1+RFC)(1+RFX)(1 + R_{\text{DC}}) = (1 + R_{\text{FC}})(1 + R_{FX}); approx RDC≈RFC+RFXR_{\text{DC}} \approx R_{\text{FC}} + R_{FX}. RFXR_{FX} = foreign-currency appreciation vs. domestic.
Labor productivity growth
gLP=gY−gLg_{LP} = g_Y - g_L, gLPg_{LP} = growth in output per worker, gYg_Y = GDP growth, gLg_L = labor force growth
Uncovered interest rate parity expected spot change
E[%ΔSprice/base]≈rprice−rbaseE[\%\Delta S_{price/base}] \approx r_{price} - r_{base}, E[%ΔS] = expected change in spot (price per base), rpricer_{price} = price-currency rate, rbaser_{base} = base-currency rate
Taylor rule policy rate
i=rn+π+0.5(π−π∗)+0.5(y−y∗)i = r_n + \pi + 0.5(\pi - \pi^*) + 0.5(y - y^*), i = policy rate, rnr_n = neutral real rate, π = inflation, π* = target inflation, y - y* = output gap
Financial Statement Analysis 12 items
Net pension expense components (ASC 715)
NPPC=Service Cost+Interest Cost−Expected Return+Amort PSC±Amort Gain/Loss\text{NPPC} = \text{Service Cost} + \text{Interest Cost} - \text{Expected Return} + \text{Amort PSC} \pm \text{Amort Gain/Loss}. IFRS (IAS 19): net interest on net pension liability replaces expected return.
US GAAP net periodic pension cost
PE=SC+IC−ER±APE = SC + IC - ER \pm A, SC = service cost, IC = interest cost on beginning PBO, ER = expected return on plan assets, A = corridor amortization of actuarial gains/losses
Total periodic pension cost
TPPC=−ΔFS+CTPPC = -\Delta FS + C, ΔFS\Delta FS = change in funded status (plan assets − PBO), C = employer contributions; equals SC + IC − actual return ± actuarial gains/losses
Bank efficiency ratio
Efficiency=Non-interest expenseNII+Non-interest income\text{Efficiency} = \dfrac{\text{Non-interest expense}}{\text{NII} + \text{Non-interest income}}, NII = net interest income; provisions deliberately excluded; lower is better
Full goodwill under the acquisition method
GW=(C+NCIFV)−FVNAGW = (C + NCI_{FV}) - FV_{NA}, GW = goodwill, C = consideration transferred, NCIFVNCI_{FV} = non-controlling interest at fair value, FVNAFV_{NA} = fair value of identifiable net assets
Equity method investment carrying value (CAID)
CV=BegCV+s×NI−Amort−s×Div+s×OCICV = BegCV + s \times NI - Amort - s \times Div + s \times OCI, CV = carrying value, s = ownership share, NI = investee net income, Amort = amortization of excess purchase price, Div = dividends
Pre-CTA translated equity build-up (current rate method)
Epre=Ebeg+NIavg−DivtxnE_{pre} = E_{beg} + NI_{avg} - Div_{txn}, EbegE_{beg} = beginning equity, NIavgNI_{avg} = net income at average rate, DivtxnDiv_{txn} = dividends at transaction rate
Cumulative translation adjustment plug (current rate method)
CTA=Ereq−EpreCTA = E_{req} - E_{pre}, EreqE_{req} = translated net assets (assets − liabilities at current rate), EpreE_{pre} = pre-CTA translated equity
Balance sheet accruals ratio
Accruals ratio=ΔNOAAverage NOA\text{Accruals ratio} = \dfrac{\Delta NOA}{\text{Average } NOA}, NOA = net operating assets = (total assets − cash & investments) − (total liabilities − financial debt); ΔNOA = change in NOA over period
Cash flow accruals ratio
Accruals ratio=NI−CFO−CFIAverage NOA\text{Accruals ratio} = \dfrac{NI - CFO - CFI}{\text{Average } NOA}, NI = net income, CFO = cash flow from operations, CFI = cash flow from investing, NOA = net operating assets
LIFO-to-FIFO equity adjustment
EquityFIFO=EquityLIFO+LR×(1−t)Equity_{FIFO} = Equity_{LIFO} + LR \times (1 - t), LR = LIFO reserve, t = tax rate; inventory rises by full LR and COGS falls by the change in LR
Five-component DuPont decomposition of ROE
ROE=NIEBT×EBTEBIT×EBITRev×RevAssets×AssetsEquityROE = \frac{NI}{EBT} \times \frac{EBT}{EBIT} \times \frac{EBIT}{Rev} \times \frac{Rev}{Assets} \times \frac{Assets}{Equity}, NI = net income, EBT = pretax income, EBIT = operating income, Rev = revenue, Assets = avg total assets, Equity = avg equity
Corporate Issuers 7 items
MM Propositions I & II (with taxes)
Prop I: VL=VU+tDV_L = V_U + tD
debt tax shield adds value.
Prop II: re=r0+(r0−rd)(1−t)DEr_e = r_0 + (r_0 - r_d)(1-t)\frac{D}{E}; WACC declines with leverage. Theoretical optimum: 100% debt.
Pure-play unlevered (asset) beta via Hamada equation
βasset=βequity1+(1−t) (D/E)\beta_{asset} = \dfrac{\beta_{equity}}{1 + (1 - t)\,(D/E)}, β = beta, t = comparable's tax rate, D/E = comparable's debt-to-equity ratio
Weighted average cost of capital (WACC)
WACC=wd rd(1−t)+wp rp+we reWACC = w_d \, r_d(1 - t) + w_p \, r_p + w_e \, r_e, w = target weight, r = component cost, t = tax rate; subscripts d=debt, p=preferred, e=equity
Lintner target payout adjustment model expected dividend
D1=D0+a×(TPR×EPS1−D0)D_1 = D_0 + a \times (\text{TPR} \times \text{EPS}_1 - D_0), D1D_1 = expected dividend, D0D_0 = current dividend, a = adjustment factor, TPR = target payout ratio, EPS1EPS_1 = projected EPS
Post-repurchase earnings per share
EPSnew=EN−C/P\text{EPS}_{new} = \dfrac{E}{N - C/P}, E = total earnings, N = original shares, C = cash spent on repurchase, P = repurchase price per share
LBO multiple of invested capital
MOIC=Exit EquityInitial EquityMOIC = \frac{Exit\ Equity}{Initial\ Equity}, Exit Equity = Exit EV − remaining debt, Initial Equity = sponsor's equity contribution at entry
Acquirer's gain in an acquisition
Gain=PV(Synergies)−PremiumGain = PV(Synergies) - Premium, PV(Synergies) = present value of net after-tax synergies, Premium = offer value above target's pre-announcement market value
Equity Valuation 20 items
FCFF from EBIT
FCFF=EBIT(1−t)+D&A−ΔWC−CapExFCFF = EBIT(1-t) + D\&A - \Delta WC - CapEx
t = tax rate, D&A = depreciation & amortization
ΔWC\Delta WC = change in working capital
FCFE from FCFF
FCFE=FCFF−Int(1−t)+ΔDebtFCFE = FCFF - Int(1-t) + \Delta\text{Debt}
Int = interest expense, t = tax rate, ΔDebt\Delta\text{Debt} = net new borrowing.
Residual income model
V0=B0+∑t=1∞(ROEt−re)Bt−1(1+re)tV_0 = B_0 + \sum_{t=1}^{\infty} \frac{(ROE_t - r_e) B_{t-1}}{(1+r_e)^t}
B0B_0 = book value, ROE = return on equity, rer_e = cost of equity.
Sustainable growth rate
g=ROE×bg = ROE \times b
b = retention ratio = 1 − payout ratio
ROE = net income / equity
Growth rate achievable without changing capital structure or issuing equity
Two-stage DDM
V0=∑t=1nD0(1+gS)t(1+r)t+Vn(1+r)nV_0 = \sum_{t=1}^{n} \frac{D_0(1+g_S)^t}{(1+r)^t} + \frac{V_n}{(1+r)^n}
Vn=Dn+1r−gLV_n = \frac{D_{n+1}}{r - g_L}
gSg_S = high growth (stage 1), gLg_L = long-run growth (stage 2)
FCFE from net income
FCFE=NI+NCC−ΔWC−CapEx+ΔDebtFCFE = NI + NCC - \Delta WC - \text{CapEx} + \Delta\text{Debt}
NI = net income, NCC = non-cash charges (D&A, deferred tax), ΔDebt\Delta\text{Debt} = net new borrowing.
FCFE constant-growth valuation
V0=FCFE1re−gV_0 = \frac{FCFE_1}{r_e - g}. Requires re>gr_e > g; g = sustainable FCFE growth. Gordon-growth analog using FCFE instead of dividends.
Build-up method for cost of equity (private company)
re=rf+ERP+Size premium+Specific-company premium±Industry premiumr_e = r_f + \text{ERP} + \text{Size premium} + \text{Specific-company premium} \pm \text{Industry premium}. Used when CAPM fails for illiquid/private firms.
Sum-of-the-parts enterprise value
VSOTP=∑iVi−(m×OH)V_{SOTP} = \sum_i V_i - (m \times OH), ViV_i = standalone value of segment i, m = overhead capitalization multiple, OH = annual corporate overhead
Expected return as dividend yield plus capital gains yield
E(r)=D1P0+V0−P0P0E(r) = \frac{D_1}{P_0} + \frac{V_0 - P_0}{P_0}, D1D_1 = next dividend, P0P_0 = current price, V0V_0 = intrinsic value
H-model value
V0=D0(1+gL)r−gL+D0⋅H(gS−gL)r−gLV_0 = \dfrac{D_0(1+g_L)}{r-g_L} + \dfrac{D_0 \cdot H (g_S-g_L)}{r-g_L}, D0D_0 = current dividend, gSg_S = initial high growth, gLg_L = long-run growth, H = half the high-growth period, r = required return
Residual income continuing value with persistence factor
CV=ω×RIT1+r−ωCV = \dfrac{\omega \times RI_T}{1 + r - \omega}, ω = persistence factor, RITRI_T = final-year residual income, r = cost of equity
Residual income (spread form)
RI=B×(ROE−r)RI = B \times (ROE - r), B = beginning book value, ROE = return on equity, r = cost of equity
Capitalized cash flow method value
V=CFr−gV = \frac{CF}{r - g}, V = firm value, CF = normalized cash flow, r = required return, g = stable growth rate
FCFF from net income
FCFF=NI+Dep+Int(1−t)−CapEx−ΔWCFCFF = NI + Dep + Int(1-t) - CapEx - \Delta WC, NI = net income, Dep = depreciation, Int = interest expense, t = tax rate, CapEx = capital expenditures, ΔWC = change in working capital
Single-stage FCFF enterprise value
EV=FCFF1WACC−gEV = \frac{FCFF_1}{WACC - g}, EV = enterprise value, FCFF₁ = next-period free cash flow to firm, WACC = weighted average cost of capital, g = stable growth rate
Gordon Growth Model value
V0=D1r−gV_0 = \dfrac{D_1}{r - g}, V0V_0 = intrinsic value, D1=D0(1+g)D_1 = D_0(1+g) = next-period dividend, r = required return on equity, g = constant growth (g < r)
Discount for lack of control from a control premium
DLOC=1−11+CPDLOC = 1 - \frac{1}{1 + CP}, DLOC = discount for lack of control, CP = control premium
Justified price-to-book ratio
PB=ROE−gr−g\frac{P}{B} = \frac{ROE-g}{r-g}, ROE = return on equity, g = growth rate, r = required return on equity
Justified leading price-to-earnings ratio
PE1=1−br−g\frac{P}{E_1} = \frac{1-b}{r-g}, b = retention ratio (1-b = payout), r = required return on equity, g = growth rate
Fixed Income 11 items
Option-Adjusted Spread (OAS)
OAS=Z-spread−Option value (bps)OAS = Z\text{-spread} - \text{Option value (bps)}
Callable: OAS < Z-spread. Putable: OAS > Z-spread.
Effective duration
Deff=P−Δy−P+Δy2P0ΔyD_{\text{eff}} = \frac{P_{-\Delta y} - P_{+\Delta y}}{2 P_0 \Delta y}. Used for bonds with embedded options (callable, putable, MBS).
Portfolio effective duration (market-value weighted)
Deff, port=∑iwiDeff,iD_{\text{eff, port}} = \sum_i w_i D_{\text{eff},i}; wiw_i = market-value weight. Assumes parallel yield-curve shift; use KRDs for non-parallel.
Credit spread decomposition (term structure)
Observed Spread=Expected Loss+Credit Risk Premium+Liquidity Premium\text{Observed Spread} = \text{Expected Loss} + \text{Credit Risk Premium} + \text{Liquidity Premium}. Expected loss = PD × LGD.
Hazard rate from credit spread (reduced-form model)
λ=spread1−R\lambda = \dfrac{\text{spread}}{1 - R}, λ = hazard rate (default intensity), spread = credit spread, R = recovery rate, (1 − R) = loss given default
Value of a callable bond
Vcallable=Voption−free−VcallV_{callable} = V_{option-free} - V_{call}, VoptionV_{option}-free = value of identical option-free bond, VcallV_{call} = value of the embedded call option held by the issuer
Value of a putable bond
Vputable=Voption−free+VputV_{putable} = V_{option-free} + V_{put}, VoptionV_{option}-free = value of identical option-free bond, VputV_{put} = value of the embedded put option held by the bondholder
Rolldown return from riding the yield curve
Rroll=Δy×DR_{roll} = \Delta y \times D, Δy\Delta y = yield change from maturity shortening, D = duration (assumes a stable curve over the holding period)
CDS mark-to-market gain to protection buyer
MTM=(scur−scontract)×D×N\text{MTM} = (s_{cur} - s_{contract}) \times D \times N, scurs_{cur} = current spread, scontracts_{contract} = contracted (entry) spread NOT fixed coupon, D = effective spread duration, N = notional
Backward induction node value in a binomial interest rate tree
Vnode=0.5×(Vup+Vdown)+C1+rnodeV_{node} = \dfrac{0.5 \times (V_{up} + V_{down}) + C}{1 + r_{node}}, V = bond value, C = coupon, r = node rate, 0.5 = risk-neutral probabilities
Lognormal up and down rate relationship in a binomial tree
rup=rdown×e2σr_{up} = r_{down} \times e^{2\sigma}, rupr_{up} = higher node rate, rdownr_{down} = lower node rate, σ = annual std dev of ln of short rate
Derivatives 13 items
Binomial option pricing (one period)
c=πucu+πdcd1+rc = \frac{\pi_u c_u + \pi_d c_d}{1+r}; πu=(1+r)−du−d\pi_u = \frac{(1+r) - d}{u - d}, πd=1−πu\pi_d = 1 - \pi_u (risk-neutral probs). u, d = up/down factors.
Put-call parity
c+X(1+r)T=p+S0c + \frac{X}{(1+r)^T} = p + S_0. Continuous: c+Xe−rT=p+S0c + Xe^{-rT} = p + S_0. Same strike/expiry; European options.
Option gamma
Γ=∂2V∂S2=∂Δ∂S\Gamma = \frac{\partial^2 V}{\partial S^2} = \frac{\partial \Delta}{\partial S}. Highest ATM near expiry; long options are positive gamma, short are negative.
Option vega
ν=∂V∂σ\nu = \frac{\partial V}{\partial \sigma}. Price change per 1-pp vol move. Long call or put = positive vega. Highest ATM with longer expiry.
Delta-gamma-vega option price approximation
ΔC≈δ dS+12γ(dS)2+ν dσ\Delta C \approx \delta \, dS + \tfrac{1}{2} \gamma (dS)^2 + \nu \, d\sigma, δ = delta, γ = gamma, ν = vega, dS = stock move, dσ = vol change
Black-Scholes-Merton call price
C=S N(d1)−Ke−rTN(d2)C = S \, N(d_1) - K e^{-rT} N(d_2), C = call value, S = spot, K = strike, r = risk-free rate, T = time, N = standard normal CDF, d1,d2d_1,d_2 = moneyness terms
Forward rate agreement settlement payment
P=NA×(rf−rFRA)×DCF1+rf×DCFP = \dfrac{NA \times (r_f - r_{FRA}) \times DCF}{1 + r_f \times DCF}, NA = notional, rfr_f = floating reference rate, rFRAr_{FRA} = contract rate, DCF = day-count fraction of reference period
Fixed swap rate from discount factors
s=1−Z(n)∑t=1nZ(t)s = \dfrac{1 - Z(n)}{\sum_{t=1}^{n} Z(t)}, s = periodic fixed swap rate, Z(t) = discount factor for period t, n = number of settlement periods
Option theta (time decay)
Θ=∂V∂t\Theta = \dfrac{\partial V}{\partial t}, the change in an option value per unit of calendar time. Usually negative for long options (value erodes toward expiry); time decay is largest for at-the-money options near expiration.
Payer swaption payoff
Payer=N⋅max⁡(Rmkt−RK,0)⋅A\text{Payer} = N \cdot \max(R_{\text{mkt}} - R_K, 0) \cdot A, N = notional, RmktR_{mkt} = market swap rate, RKR_K = strike rate, A = annuity factor (PV of $1 over swap tenor)
Caplet payoff
Caplet=N⋅max⁡(Rref−Rcap,0)⋅days360\text{Caplet} = N \cdot \max(R_{\text{ref}} - R_{\text{cap}}, 0) \cdot \frac{\text{days}}{360}, N = notional, RrefR_{ref} = reference rate, RcapR_{cap} = cap strike rate, days/360 = day-count fraction
Risk-neutral probability in a binomial tree
p=1+r−du−d p = \frac{1 + r - d}{u - d} , p = risk-neutral (up) probability, r = periodic risk-free rate, u = up factor, d = down factor
Binomial hedge ratio (option delta)
Δ=cu−cdSu−Sd \Delta = \frac{c_u - c_d}{S_u - S_d} , Δ = shares per option, cuc_u/cdc_d = option payoff up/down, SuS_u/SdS_d = stock price up/down
Alternative Investments 14 items
TVPI (Total Value to Paid-In)
TVPI=Distributions+Residual NAVPaid-inTVPI = \frac{\text{Distributions} + \text{Residual NAV}}{\text{Paid-in}} = DPI + RVPI (realized + unrealized multiples).
Direct capitalization (real estate)
V=NOI1Cap RateV = \frac{NOI_1}{\text{Cap Rate}}; NOI1NOI_1 = stabilized first-year NOI (after opex, before debt service/tax). Implicit: cap rate = r − g.
Equity REIT NAV per share
NAV/share=Property value+Other assets−Total liabilitiesShares outstanding\text{NAV/share} = \frac{\text{Property value} + \text{Other assets} - \text{Total liabilities}}{\text{Shares outstanding}}
Property value typically from cap-rate or DCF on stabilized NOI. Price/NAV reveals premium or discount.
Pre-money and post-money valuation
Post-money=Pre-money+New investment\text{Post-money} = \text{Pre-money} + \text{New investment}
Investor share=InvestmentPost-money\text{Investor share} = \frac{\text{Investment}}{\text{Post-money}}
Price per share = pre-money / pre-money shares. PE / VC funding rounds.
Total return on a commodity futures position
Rtotal=Rspot+Rroll+RcollateralR_{total} = R_{spot} + R_{roll} + R_{collateral}, RspotR_{spot} = spot price return, RrollR_{roll} = roll yield, R_collateral = interest earned on posted collateral
Commodity forward price under cost-of-carry
F=S×e(r+c−y)×TF = S \times e^{(r + c - y) \times T}, F = forward price, S = spot price, r = risk-free rate, c = storage cost rate, y = convenience yield, T = time in years
Hard-hurdle incentive fee
Fee=p×(R−h)×AUMFee = p \times (R - h) \times AUM, p = incentive rate, R = gross return, h = hurdle rate, AUM = assets under management (only when R > h)
Unsmoothed variance correction for serially correlated returns
σunsmoothed2=σreported21−ρ2\sigma_{unsmoothed}^2 = \dfrac{\sigma_{reported}^2}{1 - \rho^2}, σ²_reported = reported return variance, ρ = first-order autocorrelation of returns
Funds from operations for a REIT
FFO=NI+DepRE−GsaleFFO = NI + Dep_{RE} - G_{sale}, NI = GAAP net income, DepREDep_{RE} = real estate depreciation/amortization, GsaleG_{sale} = gains on sale of properties
Adjusted funds from operations for a REIT
AFFO=FFO−Capexmaint−SLRAFFO = FFO - Capex_{maint} - SLR, FFO = funds from operations, CapexmaintCapex_{maint} = recurring maintenance capital expenditures, SLR = straight-line rent adjustment
Net operating income for a property
NOI=PGI−V−OpExNOI = PGI - V - OpEx, PGI = potential gross income at full occupancy, V = vacancy and collection losses, OpEx = operating expenses (excludes debt service, capex, income tax)
Cash-on-cash return on a leveraged property
CoC=NOI−DSECoC = \frac{NOI - DS}{E}, NOI = net operating income, DS = annual debt service, E = equity invested
Alpha of an equity long/short fund
α=Rgross−(Enet×Rm)\alpha = R_{gross} - (E_{net} \times R_m), RgrossR_{gross} = fund gross return, EnetE_{net} = net market exposure, RmR_m = market return
Net and gross exposure of a long/short fund
Enet=L−SE_{net} = L - S, Egross=L+SE_{gross} = L + S, LL = long exposure (% of capital), SS = short exposure (% of capital); net = direction, gross = leverage
Portfolio Management 16 items
Treynor ratio
Tp=Rp−RfβpT_p = \frac{R_p - R_f}{\beta_p}
RpR_p = portfolio return, RfR_f = risk-free rate, βp\beta_p = portfolio beta
Excess return per unit of systematic risk
Jensen's alpha
αp=Rp−[Rf+βp(Rm−Rf)]\alpha_p = R_p - [R_f + \beta_p(R_m - R_f)]
Actual return minus CAPM expected return
Positive α\alpha = outperformance after adjusting for systematic risk
Fundamental Law of Active Management
IR=IC×BRIR = IC \times \sqrt{BR}
IC = information coefficient (skill), BR = breadth (independent bets), IR = information ratio.
M-squared (Modigliani-Modigliani)
M2=(Rp−Rf)×σmσp+RfM^2 = (R_p - R_f) \times \frac{\sigma_m}{\sigma_p} + R_f
Levered/delevered portfolio return at market's risk level
Expressed in %, directly comparable across portfolios
Sharpe-information ratio relationship
SRP=SRB2+IR2SR_P = \sqrt{SR_B^2 + IR^2}, SRPSR_P = portfolio Sharpe ratio, SRBSR_B = benchmark Sharpe ratio, IR = information ratio (Pythagorean, never additive)
Optimal level of active risk
σA∗=IRSRB×σB\sigma_A^* = \frac{IR}{SR_B} \times \sigma_B, σAσ_A* = optimal active risk, IR = information ratio, SRBSR_B = benchmark Sharpe ratio, σBσ_B = benchmark standard deviation
Break-even inflation rate
BEI=ynom−yrealBEI = y_{nom} - y_{real}, BEI = market expected average inflation, ynomy_{nom} = nominal government bond yield, yrealy_{real} = inflation-linked bond yield of same maturity
Forward-looking equity risk premium (DDM)
ERP=(DY+g)−rfERP = (DY + g) - r_f, DY = current dividend yield, g = expected nominal earnings growth, rfr_f = risk-free (government bond) rate
Authorized participant creation arbitrage profit
π=(Pmkt−NAV−c)×Q\pi = (P_{mkt} - NAV - c) \times Q, PmktP_{mkt} = ETF market price per share, NAV = net asset value per share, c = transaction cost per share, Q = creation unit size (shares)
Total cost of ETF ownership
TC=(ER×H)+Srt+PDTC = (ER \times H) + S_{rt} + PD, ER = annual expense ratio, H = holding period in years, SrtS_{rt} = round-trip bid-ask spread, PD = premium/discount impact
Arbitrage Pricing Theory expected return
E(Ri)=Rf+∑k=1Kβi,kλkE(R_i) = R_f + \sum_{k=1}^{K} \beta_{i,k} \lambda_k, RfR_f = risk-free rate, β = factor sensitivity, λ = factor risk premium, K = number of factors
Active specific risk from active risk decomposition
σspecific=σtotal2−σfactor2\sigma_{specific} = \sqrt{\sigma_{total}^2 - \sigma_{factor}^2}, σtotalσ_{total} = total active risk (tracking error), σfactorσ_{factor} = active factor risk, σspecificσ_{specific} = active specific risk
Square root of time VaR scaling
VaRT=VaRdaily×TVaR_T = VaR_{daily} \times \sqrt{T}, VaRTVaR_T = VaR over T days, VaRdailyVaR_{daily} = 1-day VaR, T = number of trading days (variance scales linearly, so σ scales with √T)
Parametric (variance-covariance) Value at Risk
VaR=V×z×σVaR = V \times z \times \sigma, V = portfolio value, z = z-score (95% = 1.65, 99% = 2.33), σ = periodic return standard deviation
Annual transaction cost drag from turnover
Drag=T×cDrag = T \times c, T = annual portfolio turnover, c = cost per trade (including market impact, in bps or %)
Bonferroni correction adjusted significance threshold
αadj=αm\alpha_{adj} = \dfrac{\alpha}{m}, αadj\alpha_{adj} = per-test threshold, α\alpha = desired overall significance level, m = number of tests run
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Frequently Asked Questions

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What's covered on the CFA Level II formula sheet?
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Formula sheets for other exams

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