Free CFA Level II Formula Sheet (2026)

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

114 Formulas
9 Topics
2026 Syllabus
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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, x_t = value at time t, b_0 = intercept, b_1 = lag coefficient (|b_1|<1 for stationarity), ε_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, s_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)}, SSE_R = restricted SSE, SSE_U = unrestricted SSE, q = variables tested, n = observations, k_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)
r_d = domestic rate, r_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, g_LP = growth in output per worker, g_Y = GDP growth, g_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), r_price = price-currency rate, r_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, r_n = neutral real rate, π = inflation, π* = target inflation, y - y* = output gap
Financial Statement Analysis 13 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
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, NCI_FV = non-controlling interest at fair value, FV_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 10 items
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.
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.
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), D_1 = expected dividend, D_0 = current dividend, a = adjustment factor, TPR = target payout ratio, EPS_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 16 items
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}
B_0 = book value, ROE = return on equity, r_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}
g_S = high growth (stage 1), g_L = long-run growth (stage 2)
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, RI_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}, V_option-free = value of identical option-free bond, V_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}, V_option-free = value of identical option-free bond, V_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, s_cur = current spread, s_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}, r_up = higher node rate, r_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, r_f = floating reference rate, r_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, R_mkt = market swap rate, R_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, R_ref = reference rate, R_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, c_u/c_d = option payoff up/down, S_u/S_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}, R_spot = spot price return, R_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, Dep_RE = real estate depreciation/amortization, G_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, Capex_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}
R_p = portfolio return, R_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}, SR_P = portfolio Sharpe ratio, SR_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, σ_A* = optimal active risk, IR = information ratio, SR_B = benchmark Sharpe ratio, σ_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, P_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, S_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, R_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}, σ_total = total active risk (tracking error), σ_factor = active factor risk, σ_specific = active specific risk
Square root of time VaR scaling
VaRT=VaRdaily×TVaR_T = VaR_{daily} \times \sqrt{T}, VaR_T = VaR over T days, VaR_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

Frequently Asked Questions

Is the CFA Level II formula sheet free?
Yes. The full CFA Level II formula sheet is free, with no signup, no email, and no credit card required. 114 formulas across 9 topics, all rendered with the same KaTeX math notation used in the FreeFellow study app.
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What's covered on the CFA Level II formula sheet?
Every formula is grouped by official syllabus topic, with the formula in math notation plus a one-line note on when to use it (or a watch-out from CAIA, CFA, or other prep-provider commentary). Coverage is calibrated to the 2026 syllabus and refreshed when the corpus changes.
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