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. 31 formulas across 7 topics, calibrated to the 2026 syllabus. Free forever, no signup required.

31 Formulas
7 Topics
2026 Syllabus
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All CFA L3 Private Markets Formulas

GP & Investor Perspectives 4 items
DPI (Distributed to Paid-In)
DPI=Cumulative distributionsPaid-in capitalDPI = \frac{\text{Cumulative distributions}}{\text{Paid-in capital}}
DPI < 1 → still in J-curve; DPI > 1 → returned capital with profit
Purely realized metric; key for LP liquidity analysis
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%)
Private Equity 4 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.
IRR for private equity
Solve for r in: ∑t=0TCFt(1+r)t=0\sum_{t=0}^{T} \frac{CF_t}{(1+r)^t} = 0
CF_0 = −initial investment (negative), CF_T includes terminal NAV
Gross IRR = fund-level; Net IRR = LP-level (after fees/carry)
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.
Private Real Estate 6 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
Capitalization rate (Cap rate)
rcap=NOIVr_{cap} = \frac{NOI}{V}
NOI = net operating income (stabilized, before debt service)
V = property value
Inverse: V=NOIrcapV = \frac{NOI}{r_{cap}}
Lower cap rate = higher valuation multiple
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
Debt Service Coverage Ratio (DSCR)
DSCR=NOIAnnual debt serviceDSCR = \frac{NOI}{\text{Annual debt service}}
Annual debt service = principal + interest payments
DSCR > 1 → property generates sufficient income to cover debt
Lenders typically require DSCR ≥ 1.2×
NAV per unit (private real estate fund)
NAV=Appraised values+Other assets−LiabilitiesNAV = \text{Appraised values} + \text{Other assets} - \text{Liabilities}
NAV per unit=NAVUnits outstandingNAV\text{ per unit} = \frac{NAV}{\text{Units outstanding}}
Appraisals quarterly; lags public pricing.
Topic 1 4 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
Topic 2 3 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}
Topic 3 5 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)
BHB attribution effects
Allocation: (wp,i−wB,i)(RB,i−RB)(w_{p,i} - w_{B,i})(R_{B,i} - R_B)
Selection: wB,i(Rp,i−RB,i)w_{B,i}(R_{p,i} - R_{B,i})
Interaction: (wp,i−wB,i)(Rp,i−RB,i)(w_{p,i} - w_{B,i})(R_{p,i} - R_{B,i})
Sum of all effects = total active return
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
Topic 4 5 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
Variance swap payoff
Payoff=Nvega×(σrealized2−σstrike2)\text{Payoff} = N_{vega} \times (\sigma_{realized}^2 - \sigma_{strike}^2)
Long variance swap profits when realized variance > strike variance
No delta-hedging needed; pure volatility exposure

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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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