Free CFA Level III: Private Markets Formula Sheet (2026)

Every CFA L3 Private Markets formula you need on the test, grouped by topic, rendered with full math notation. 101 formulas across 11 topics, calibrated to the 2026 syllabus. Free forever, no signup required.

101 Formulas
11 Topics
2026 Syllabus
Free Forever

All CFA L3 Private Markets Formulas

Private Investments & Structures 2 items
Distributed to Paid-In (DPI)
DPI=Cumulative DistributionsPaid-In Capital\text{DPI} = \dfrac{\text{Cumulative Distributions}}{\text{Paid-In Capital}} — Distributions = realized cash returned to LPs, Paid-In Capital = capital actually called and funded
Total Value to Paid-In (TVPI)
TVPI=DPI+RVPI=Distributions+NAVPaid-In Capital\text{TVPI} = \text{DPI} + \text{RVPI} = \dfrac{\text{Distributions} + \text{NAV}}{\text{Paid-In Capital}} — Distributions = realized cash, NAV = unrealized value, Paid-In Capital = called and funded
GP & Investor Perspectives 4 items
RVPI (Residual Value to Paid-In)
RVPI=Residual NAVPaid-in capitalRVPI = \frac{\text{Residual NAV}}{\text{Paid-in capital}}
Unrealized portion of TVPI
Declining RVPI over fund life signals realization progress
TVPI = DPI + RVPI
J-curve
Early: negative CFs (calls + fees, no distributions) → negative/low net IRR
Inflection: distributions exceed contributions
Steeper = faster deployment + value creation
Management fee base
Investment period: fees on committed capital.
Post-investment: fees on invested (deployed) capital.
Fee=Rate×Base\text{Fee} = \text{Rate} \times \text{Base} (typically 1.5–2%)
GP catch-up amount (100% catch-up provision)
X=c1−c×PrefX = \dfrac{c}{1-c} \times \text{Pref} — X = GP catch-up, c = carry rate (e.g. 0.20), Pref = LP preferred return distributed
Private Equity 7 items
MOIC (Multiple on Invested Capital)
MOIC=Distributions+Residual NAVInvested capitalMOIC = \frac{\text{Distributions} + \text{Residual NAV}}{\text{Invested capital}}
Also called TVPI. TVPI = DPI + RVPI.
Levered equity return
re=ru+DE(ru−rd)r_e = r_u + \frac{D}{E}(r_u - r_d)
r_u = unlevered asset return, r_d = cost of debt
D/E = debt-to-equity ratio
Leverage amplifies equity returns (and risk)
Waterfall distribution (PE)
Order: Return of capital → Preferred return (hurdle) → GP catch-up → Carry split
American: deal-by-deal. European: whole-fund before carry.
Typical: 20% carry above 8% hurdle.
LBO value creation decomposition
ΔEquity=ΔEBITDA×Mentry+EBITDAexit×ΔM+ΔDebt\Delta \text{Equity} = \Delta \text{EBITDA} \times M_{\text{entry}} + \text{EBITDA}_{\text{exit}} \times \Delta M + \Delta \text{Debt} — M = EV/EBITDA multiple, ΔDebt = debt paid down
Post-money valuation (venture capital method)
Post-money=Exit Value(1+r)n\text{Post-money} = \dfrac{\text{Exit Value}}{(1 + r)^n} — Exit Value = projected exit equity value, r = required IRR, n = years to exit
VC ownership percentage and pre-money valuation
Ownership%=InvestmentPost-money\text{Ownership\%} = \dfrac{\text{Investment}}{\text{Post-money}}; Pre-money=Post-money−Investment\text{Pre-money} = \text{Post-money} - \text{Investment} — Investment = new capital injected
Sponsor IRR in a leveraged buyout
IRR=(Exit EquityEntry Equity)1/n−1\text{IRR} = \left(\dfrac{\text{Exit Equity}}{\text{Entry Equity}}\right)^{1/n} - 1 — Exit Equity = exit EV minus remaining debt, Entry Equity = sponsor equity check, n = hold years
Private Debt 4 items
Loan-to-cost ratio (LTC)
LTC=Loan AmountTotal Project Cost\text{LTC} = \dfrac{\text{Loan Amount}}{\text{Total Project Cost}} — Loan Amount = principal of debt facility; Total Project Cost = acquisition price plus development and soft costs
Interest coverage ratio
Interest Coverage=EBITDAInterest Expense\text{Interest Coverage} = \dfrac{\text{EBITDA}}{\text{Interest Expense}} — EBITDA = earnings before interest, tax, depreciation, amortization; Interest Expense = total cash interest
Total debt to EBITDA leverage ratio
Leverage=Total DebtEBITDA\text{Leverage} = \dfrac{\text{Total Debt}}{\text{EBITDA}} — Total Debt = senior + subordinated principal; typical buyout range 5-7x on quality credits
Fixed charge coverage ratio (FCCR)
FCCR=EBITDA−CapExInterest+Mandatory Principal Amortization\text{FCCR} = \dfrac{\text{EBITDA} - \text{CapEx}}{\text{Interest} + \text{Mandatory Principal Amortization}} — CapEx = capital expenditures; denominator = total debt service
Private Special Situations 1 item
Expected IRR on a distressed debt position
E[IRR]=(E[Recovery]P)1/T−1E[IRR] = \left(\dfrac{E[\text{Recovery}]}{P}\right)^{1/T} - 1 — E[Recovery] = probability-weighted recovery per unit face, P = purchase price, T = expected holding period in years
Private Real Estate 7 items
Loan-to-Value (LTV)
LTV=Loan amountProperty valueLTV = \frac{\text{Loan amount}}{\text{Property value}}
Higher LTV → higher leverage, more risk
Typical real estate: 60–75% LTV
Lenders covenant on LTV and DSCR
Net Operating Income (NOI)
NOI=EGI−Operating expensesNOI = \text{EGI} - \text{Operating expenses}
EGI = Potential gross income − Vacancy & credit losses
Opex excludes debt service, depreciation, income taxes.
Direct capitalization value
V=NOIrcapV = \frac{NOI}{r_{cap}}
Stabilized NOI used (normalized for occupancy, expenses)
Cap rate sourced from comparable sales
Used for income-producing properties
Discounted cash flow value of real estate
V0=∑t=1nCFt(1+r)t+NOIn+1/rexit(1+r)nV_0 = \sum_{t=1}^{n} \dfrac{CF_t}{(1+r)^t} + \dfrac{NOI_{n+1}/r_{exit}}{(1+r)^n} — CF = annual cash flow, r = discount rate, r_exit = exit cap rate, n = hold period
Gordon link between cap rate and discount rate
rcap≈r−gr_{cap} \approx r - g — r_cap = going-in cap rate, r = property discount rate (IRR target), g = expected NOI growth rate
Levered equity cash flow for real estate
CFequity,t=NOIt−Interestt−CapExtCF_{equity,t} = NOI_t - \text{Interest}_t - \text{CapEx}_t — NOI = net operating income, Interest = debt interest expense, CapEx = capital expenditures in period t
Cap-rate sensitivity of property value
%ΔV≈−Δrcaprcap\%\Delta V \approx -\dfrac{\Delta r_{cap}}{r_{cap}} — %ΔV = percent change in value, Δr_cap = change in cap rate (decimal), r_cap = current cap rate
Infrastructure 1 item
Allowed revenue under the regulated asset base approach
Allowed Revenue=RAB×rallowed+Depreciation+Opex \text{Allowed Revenue} = \text{RAB} \times r_{\text{allowed}} + \text{Depreciation} + \text{Opex} — RAB = regulated asset base, r_allowed = allowed return, Opex = operating costs
Topic 1 23 items
Mean-variance optimal portfolio weight
w∗=1λΣ−1(μ−rf1)\mathbf{w}^* = \frac{1}{\lambda} \Sigma^{-1} (\mu - r_f \mathbf{1})
λ\lambda = risk aversion, Σ\Sigma = covariance matrix, μ\mu = expected returns
Corner portfolio blending
wA=E(RP)−E(RB)E(RA)−E(RB)w_A = \frac{E(R_P) - E(R_B)}{E(R_A) - E(R_B)}, wB=1−wAw_B = 1 - w_A
Blend two adjacent corner portfolios A and B to achieve target return E(R_P)
All blends lie on the efficient frontier
Black-Litterman expected return
Equilibrium: Π=δΣwmkt\Pi = \delta \Sigma w_{mkt}
Blended: E(R)=[(τΣ)−1+PTΩ−1P]−1[(τΣ)−1Π+PTΩ−1Q]E(R) = [(\tau\Sigma)^{-1} + P^T \Omega^{-1} P]^{-1}[(\tau\Sigma)^{-1}\Pi + P^T\Omega^{-1}Q]
δ\delta=risk aversion, wmktw_{mkt}=mkt cap weights
Portfolio rebalancing trigger (range-based)
Rebalance when: ∣wi−wi∗∣>Δi|w_i - w_i^*| > \Delta_i
wi∗w_i^* = target weight, Δi\Delta_i = tolerance band
Wider bands → lower costs, less precision
Correlation-adjusted bands: wider for high-correlation assets
Grinold-Kroner expected equity return
E(R)=D/P−ΔS+g+Δ(P/E)E(R) = D/P - \Delta S + g + \Delta(P/E) — D/P = dividend yield, ΔS = net share issuance, g = nominal earnings growth, Δ(P/E) = repricing
Taylor rule policy rate
it=r∗+πt+0.5(πt−π∗)+0.5(yt−y∗)i_t = r^* + \pi_t + 0.5(\pi_t - \pi^*) + 0.5(y_t - y^*) — r* = neutral real rate, π = inflation, π* = inflation target, y - y* = output gap
Covered interest rate parity
F/S=(1+id)/(1+if)F/S = (1 + i_d)/(1 + i_f) — F = forward rate, S = spot rate, i_d = domestic interest rate, i_f = foreign interest rate
Fixed-income expected return building blocks
E(R)=rf+πe+TP+CP+LPE(R) = r_f + \pi^e + TP + CP + LP — r_f = real risk-free rate, π^e = expected inflation, TP = term premium, CP = credit premium, LP = liquidity premium
Expected fixed-income return decomposition
E(RFI)=YTM+Roll-down+ΔPyield−Lcredit−LFXE(R_{FI}) = YTM + \text{Roll-down} + \Delta P_{yield} - L_{credit} - L_{FX} — YTM = yield to maturity, ΔP = price change from curve shift, L = expected losses
GARCH(1,1) variance forecast
σt2=ω+αεt−12+βσt−12\sigma_t^2 = \omega + \alpha \varepsilon_{t-1}^2 + \beta \sigma_{t-1}^2 — ω = long-run vol anchor, α = weight on last squared shock, β = weight on prior variance estimate
Singer-Terhaar blended risk premium
RP=w(σρ⋅SRg)+(1−w)(σ⋅SRg)RP = w(\sigma \rho \cdot SR_g) + (1-w)(\sigma \cdot SR_g) — w = integration weight, σ = asset vol, ρ = correlation with global portfolio, SR_g = global Sharpe ratio
TAA permitted weight range around SAA
wTAA∈[wSAA−b,  wSAA+b]w_{TAA} \in [w_{SAA} - b,\; w_{SAA} + b] — w_SAA = policy weight, b = IPS-defined TAA band (e.g., ±5%)
Net after-cost tactical premium
αnet=αgross−TC−T\alpha_{net} = \alpha_{gross} - TC - T — α_gross = expected gross tactical alpha, TC = transaction costs, T = realized tax cost
Stress liquidity coverage ratio
LCRstress=Accessible liquid assetsstressCash demandsstressLCR_{stress} = \frac{\text{Accessible liquid assets}_{stress}}{\text{Cash demands}_{stress}} — minimum prudent target ≥ 2x for illiquid-heavy portfolios
Endowment spending rate
s=Annual spendingPortfolio values = \frac{\text{Annual spending}}{\text{Portfolio value}} — s = spending rate (e.g., 5% = $40M on $800M)
Number of correlation inputs required for MVO
Nρ=n(n−1)2N_\rho = \frac{n(n-1)}{2} — n = number of asset classes; MVO also needs n expected returns and n standard deviations
Pension funded ratio
FR=ALFR = \frac{A}{L} — A = market value of plan assets, L = present value of liabilities (e.g., PBO)
Dollar duration of a portfolio or liability
DD=MV×DDD = MV \times D — MV = market value (or PV of liabilities), D = modified or effective duration; used to size LDI hedges
Pension surplus
S=A−LS = A - L — A = market value of plan assets, L = present value of liabilities; surplus optimization maximizes return on S
Mean-variance utility function
U=E(Rp)−0.5⋅λ⋅σp2U = E(R_p) - 0.5 \cdot \lambda \cdot \sigma_p^2 — E(R_p) = expected portfolio return, λ = risk aversion coefficient (1-10), σ_p² = portfolio variance
Geometric mean approximation from arithmetic mean and variance
G≈A−0.5σ2G \approx A - 0.5 \sigma^2 — G = geometric (compound) mean return, A = arithmetic mean return, σ² = variance of returns
Total MVO inputs required for n asset classes
N=2n+n(n−1)2N = 2n + \frac{n(n-1)}{2} — N = total inputs, n = asset classes; counts n expected returns, n standard deviations, n(n-1)/2 correlations
Roy's safety-first ratio
SF=E(Rp)−RLσpSF = \dfrac{E(R_p) - R_L}{\sigma_p}, where RLR_L is the minimum acceptable (threshold) return. The optimal portfolio maximizes SF; under normality this minimizes the probability of a return below RLR_L.
Topic 2 26 items
Marginal Contribution to Risk (MCTR)
MCTRi=βi×σpMCTR_i = \beta_i \times \sigma_p
βi=Cov(Ri,Rp)σp2\beta_i = \frac{\text{Cov}(R_i, R_p)}{\sigma_p^2}
Measures risk added by a small increase in asset i's weight
Absolute Contribution to Risk (ACTR)
ACTRi=wi×MCTRi=wi×βi×σpACTR_i = w_i \times MCTR_i = w_i \times \beta_i \times \sigma_p
∑iACTRi=σp\sum_i ACTR_i = \sigma_p (contributions sum to total portfolio risk)
Risk budget = set target ACTRs
Tracking error
TE=σ(Rp−RB)=∑(rp,t−rB,t−αˉ)2T−1TE = \sigma(R_p - R_B) = \sqrt{\frac{\sum(r_{p,t} - r_{B,t} - \bar{\alpha})^2}{T-1}}
Also called active risk or tracking risk
Annualized: TEannual=TEmonthly×12TE_{annual} = TE_{monthly} \times \sqrt{12}
Implementation shortfall (decomposition)
IS=Explicit+Delay+Impact+OpportunityIS = \text{Explicit} + \text{Delay} + \text{Impact} + \text{Opportunity} — explicit = commissions/fees; delay = decision-to-desk drift; impact = price move from trade; opportunity = unfilled-share return.
Square-root market impact model
Impact∝shares/ADV\text{Impact} \propto \sqrt{\text{shares}/\text{ADV}} — shares = order size, ADV = average daily volume; doubling order size raises impact by ~41%, not 100%.
VWAP transaction cost (buy and sell)
VWAP costbuy=Pexec−VWAP\text{VWAP cost}_{\text{buy}} = P_{\text{exec}} - \text{VWAP}; VWAP costsell=VWAP−Pexec\text{VWAP cost}_{\text{sell}} = \text{VWAP} - P_{\text{exec}} — positive = unfavorable; VWAP = period volume-weighted average price.
Effective equity beta from a PE allocation
βeff=weq+wPE×βPE\beta_{eff} = w_{eq} + w_{PE} \times \beta_{PE} — w_eq = public equity weight, w_PE = PE weight, β_PE ≈ 1.3 (PE equity beta)
Effective PE allocation including unfunded commitments
wPEeff=NAV+UCP+UCw_{PE}^{eff} = \dfrac{NAV + UC}{P + UC} — NAV = PE net asset value, UC = unfunded commitments, P = total portfolio value
Liquidity coverage ratio for an alternatives program
LCR=LCF12mLCR = \dfrac{L}{CF_{12m}} — L = liquid assets, CF_{12m} = next-12-month committed cash outflows (capital calls + benefits)
Total PE economic exposure
EPE=NAV+UCE_{PE} = NAV + UC — NAV = net asset value of PE holdings, UC = unfunded capital commitments
Endowment real return target
Rreal=s+cR_{real} = s + c — s = spending rate, c = management cost ratio
Insurer duration-matched immunization
DA×A=DL×LD_A \times A = D_L \times L — D_A = asset duration, A = assets, D_L = liability duration, L = liabilities
Foundation minimum nominal return target
R≥0.05+c+πR \geq 0.05 + c + \pi — 0.05 = 5% IRS minimum distribution floor, c = costs, π = inflation
DV01 (price value of a basis point)
DV01=Dmod×MV×0.0001DV01 = D_{mod} \times MV \times 0.0001 — D_mod = modified duration, MV = market value of the bond/portfolio
Active share of an equity portfolio
AS=12∑i=1N∣wp,i−wb,i∣AS = \tfrac{1}{2} \sum_{i=1}^{N} |w_{p,i} - w_{b,i}| — w_{p,i} = portfolio weight in stock i, w_{b,i} = benchmark weight in stock i, N = combined universe
Required pre-tax nominal return for a private client
r=(S−I)/V+π1−t+fr = \dfrac{(S - I)/V + \pi}{1 - t} + f — S = spending need, I = other income, V = portfolio value, π = inflation, t = tax rate, f = advisory fees
Leveraged portfolio return on equity
rp=ri+VBVE(ri−rB)r_p = r_i + \dfrac{V_B}{V_E}(r_i - r_B) — r_i = asset return, r_B = borrowing cost, V_B = borrowed value, V_E = equity
Human capital as present value of future labor income
HC=∑t=1NE[wt](1+r)tHC = \sum_{t=1}^{N} \dfrac{E[w_t]}{(1+r)^t} — w_t = expected labor income in year t, r = risk-adjusted discount rate, N = remaining working years
Real after-tax return approximation
rreal,at≈rnom−π−t⋅rnomr_{real,at} \approx r_{nom} - \pi - t \cdot r_{nom} — r_nom = nominal return, π = inflation rate, t = tax rate on nominal gain
Modified duration from Macaulay duration
Dmod=DMac1+yD_{mod} = \dfrac{D_{Mac}}{1+y} — D_Mac = Macaulay duration, y = periodic yield to maturity
Taxable-equivalent yield on a municipal bond
TEY=ymuni1−t\text{TEY} = \dfrac{y_{muni}}{1-t} — y_muni = muni pretax yield, t = investor's marginal tax rate
Economic net worth
ENW=FC+PV(HC)−PV(L)−PV(C)ENW = FC + PV(HC) - PV(L) - PV(C); FC = financial capital, PV(HC) = PV of human capital, PV(L) = PV of liabilities, PV(C) = PV of future consumption needs
SWF stabilization sub-fund sizing rule
AUMstab=f×G×nAUM_{stab} = f \times G \times n — f = fiscal dependence on commodity, G = annual government spending, n = years of shortfall coverage
Norway-style SWF fiscal transfer (spending) rule
Tannual=rreal×VfundT_{annual} = r_{real} \times V_{fund} — rrealr_{real} = expected real return (~3%), VfundV_{fund} = fund market value; principal preserved
Commodity SWF energy-sector exposure cap
wenergy≤wbench−Δw_{energy} \leq w_{bench} - \Delta — wbenchw_{bench} = benchmark energy weight, Δ\Delta = transition-risk tilt (e.g., 30%) to offset inflow correlation
SWF maximum single-year withdrawal under charter cap
Wmax=c×AUM‾3yW_{max} = c \times \overline{AUM}_{3y} — c = charter cap (e.g., 5%), AUM‾3y\overline{AUM}_{3y} = 3-year average AUM
Topic 3 12 items
Information ratio
IR=Rˉp−RˉBσ(Rp−RB)=αˉTEIR = \frac{\bar{R}_p - \bar{R}_B}{\sigma(R_p - R_B)} = \frac{\bar{\alpha}}{TE}
αˉ\bar{\alpha} = mean active return, TE = tracking error
Measures active return per unit of active risk
Fundamental Law of Active Management
IR=IC×BRIR = IC \times \sqrt{BR}
IC = information coefficient, BR = investment breadth
Expected active return: E(RA)=IC×BR×σAE(R_A) = IC \times \sqrt{BR} \times \sigma_A (TC assumed = 1)
Sharpe ratio
SRp=Rp−RfσpSR_p = \frac{R_p - R_f}{\sigma_p}
Reward-to-variability ratio using total risk
Sharpe of combined portfolio: SRC2=SRB2+IR2SR_C^2 = SR_B^2 + IR^2
M-squared (M²)
M2=(Rp−Rf)σmσp+RfM^2 = (R_p - R_f) \frac{\sigma_m}{\sigma_p} + R_f
Risk-adjusted return scaled to match market's volatility
M² > R_m → portfolio outperformed on risk-adjusted basis
Brinson allocation effect
Ai=(wp,i−wb,i)(Rb,i−Rb)A_i = (w_{p,i} - w_{b,i})(R_{b,i} - R_b) — w_p = portfolio sector weight, w_b = benchmark sector weight, R_b,i = sector benchmark return, R_b = total benchmark return
Treynor ratio
T=Rp−RfβpT = \frac{R_p - R_f}{\beta_p} — R_p = portfolio return, R_f = risk-free rate, β_p = portfolio beta (systematic risk)
Sortino ratio
Sortino=Rp−MARσd\text{Sortino} = \frac{R_p - MAR}{\sigma_d} — R_p = portfolio return, MAR = minimum acceptable return, σ_d = downside deviation of returns below MAR
Brinson selection effect
Si=wb,i(Rp,i−Rb,i)S_i = w_{b,i}(R_{p,i} - R_{b,i}) — w_b = benchmark sector weight, R_p,i = portfolio sector return, R_b,i = benchmark sector return
Downside capture ratio
DC=Rˉp,downRˉb,down\text{DC} = \dfrac{\bar{R}_{p,\text{down}}}{\bar{R}_{b,\text{down}}} — averaged over periods when benchmark return is negative; <100% means manager dampens losses
Upside capture ratio
UC=Rˉp,upRˉb,up\text{UC} = \dfrac{\bar{R}_{p,\text{up}}}{\bar{R}_{b,\text{up}}} — averaged over periods when benchmark return is positive; >100% means manager amplifies up markets
Up/down capture ratio
Up/Down Capture=Upside CaptureDownside Capture\text{Up/Down Capture} = \dfrac{\text{Upside Capture}}{\text{Downside Capture}} — ratio above 1.0 indicates favorable asymmetry
Symmetric performance-based fee
Fee=Base+s×(Rp−Rb)\text{Fee} = \text{Base} + s \times (R_p - R_b) — Base = base fee, s = sharing rate, R_p = portfolio return, R_b = benchmark return
Topic 4 14 items
Delta of call and put
Call: Δc=N(d1)∈(0,1)\Delta_c = N(d_1) \in (0, 1)
Put: Δp=N(d1)−1∈(−1,0)\Delta_p = N(d_1) - 1 \in (-1, 0)
Put-call: Δc−Δp=1\Delta_c - \Delta_p = 1
Approx change in option price for $1 change in underlying
Protective put payoff
At expiration: Payoff=ST+max⁡(X−ST,0)\text{Payoff} = S_T + \max(X - S_T, 0)
= max⁡(ST,X)\max(S_T, X)
Profit = Payoff − (S_0 + p), where p = put premium
Limits downside while preserving upside
Collar payoff at expiration
Long stock + long put (X_L) + short call (X_H)
Payoff: ST+max⁡(XL−ST,0)−max⁡(ST−XH,0)S_T + \max(X_L - S_T, 0) - \max(S_T - X_H, 0)
= min⁡(max⁡(ST,XL),XH)\min(\max(S_T, X_L), X_H)
Limits gains above X_H, protects below X_L
Covered call payoff at expiration
Long stock + short call (X)
Payoff: ST−max⁡(ST−X,0)=min⁡(ST,X)S_T - \max(S_T - X, 0) = \min(S_T, X)
Profit = Payoff − S_0 + c (c = call premium received)
Caps upside; enhances income in flat/down markets
Number of bond futures to adjust portfolio duration
N=DDT−DDPDDfN = \frac{DD_T - DD_P}{DD_f} — DD_T = target dollar duration, DD_P = current dollar duration, DD_f = dollar duration per futures contract (BPV adjusted by conversion factor)
Variance notional converted from vega notional
Nvar=Nvega2×σstrikeN_{var} = \frac{N_{vega}}{2 \times \sigma_{strike}} — N_vega = vega notional ($ per vol point), σ_strike = strike volatility in whole-number percent
Variance swap payoff at maturity
Payoff=Nvar×(σrealized2−σstrike2)\text{Payoff} = N_{var} \times (\sigma^2_{realized} - \sigma^2_{strike}) — N_var = variance notional, σ_realized = realized volatility (%), σ_strike = strike volatility (%)
Number of equity futures to adjust portfolio beta
N=βT−βPβF×VPf×mN = \frac{\beta_T - \beta_P}{\beta_F} \times \frac{V}{P_f \times m} — β_T = target beta, β_P = current beta, β_F = futures beta, V = portfolio value, P_f = futures price, m = multiplier
Roll yield on a currency forward hedge
Roll yield=F−SS\text{Roll yield} = \dfrac{F - S}{S} — F = forward rate, S = spot rate; approximately equals domestic minus foreign interest rate
Minimum-variance hedge ratio (MVHR)
h∗=ρA,B×σAσBh^* = \rho_{A,B} \times \dfrac{\sigma_A}{\sigma_B} — A = asset hedged, B = hedging instrument, ρ = correlation, σ = volatility
Domestic-currency return on a foreign asset
RDC=(1+RFC)(1+RFX)−1R_{DC} = (1 + R_{FC})(1 + R_{FX}) - 1; R_FC = foreign asset return, R_FX = % change in exchange rate (domestic per foreign); the approximation R_FC + R_FX drops the cross-product, material when either exceeds 5-10%
Maximum loss on short stock plus long call (synthetic long put)
Max Loss=K−S0+C0\text{Max Loss} = K - S_0 + C_0 — K = call strike, S_0 = short entry price, C_0 = call premium paid
Long straddle breakeven prices
BE=K±(C0+P0)BE = K \pm (C_0 + P_0) — K = common strike, C_0 = call premium paid, P_0 = put premium paid
Put-call parity
S+P=C+PV(K)S + P = C + PV(K) — S = stock price, P = put premium, C = call premium, K = strike, PV(K) = present value of strike

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The full question bank with detailed solutions, mixed practice, readiness tracking, lessons (where available), and the formula sheet are all free forever. Fellow ($59/quarter or $149/year per track) unlocks timed mock exams, spaced-repetition flashcards, performance analytics, AI essay grading, and a personalized study plan.
Practice CFA L3 Private Markets questions free →

Formula sheets for other exams

Exam P Exam FM Exam FAM Exam SRM Exam ALTAM Exam ASTAM CFA Level I CFA Level II CFA L3 Portfolio Mgmt CFA L3 Private Wealth CFP CPA AUD

About FreeFellow

FreeFellow is a free exam prep library for actuarial (SOA & CAS), CFA, CFP, CPA, CAIA, GARP FRM, IRS Enrolled Agent, IMA CMA, and FINRA / NASAA securities licensing candidates. The entire question bank, written solutions, and lessons are free for every candidate, with no trial period and no credit card. Lessons include narrated audio, and every constructed-response item has a copy-to-AI prompt builder so candidates can paste their answer into their own ChatGPT or Claude for self-graded feedback; Fellow members get instant AI grading on essays against the official rubric (currently CFA Level III, expanding to other essay-bearing sections).

The 70% you need to pass (question bank, written solutions, lessons, formula sheet, mixed practice, readiness tracking) is free forever, with no trial period and no credit card. Become a Fellow ($59/quarter or $149/year per track) to unlock mock exams, flashcards with spaced repetition, performance analytics, AI essay grading, and a personalized study plan. FreeFellow LLC is a CFA Institute Prep Provider. Our CFA® exam materials are validated by CFA Institute for substantial curriculum coverage and updated annually.