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

Every CFA L3 Private Wealth 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
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All CFA L3 Private Wealth Formulas

Private Wealth Management Industry 3 items
Effective blended fee rate on a tiered AUM schedule
fˉ=∑ifi×AiAUM\bar{f} = \frac{\sum_i f_i \times A_i}{\text{AUM}} — f_i = marginal rate in tier i, A_i = assets in tier i, AUM = total assets
Annual advisory revenue from an AUM fee
Revenue=AUM×f\text{Revenue} = \text{AUM} \times f — AUM = assets under management, f = annual fee rate
Total annual client cost of a wrap program
C=AUM×fw+AUM×wf×eˉC = \text{AUM} \times f_w + \text{AUM} \times w_f \times \bar{e} — f_w = wrap fee, w_f = fund weight, ē = average fund expense ratio
Working With the Wealthy 1 item
Probability of family charter adherence
Padherence=Pclarity×Pcommitment×PreviewP_{adherence} = P_{clarity} \times P_{commitment} \times P_{review} — P_clarity = process clarity, P_commitment = leadership commitment, P_review = scheduled review frequency
Wealth Planning 5 items
Human capital present value
HC0=∑t=1Nwt⋅(1−pdeath,t)(1+r)tHC_0 = \sum_{t=1}^{N} \frac{w_t \cdot (1 - p_{death,t})}{(1 + r)^t}
wtw_t=expected earnings, r=discount rate.
Total wealth = financial + human capital.
Tax-deferred account accumulation
FV=(1+r)n(1−Tn)FV = (1+r)^n (1 - T_n)
T_n = tax rate at withdrawal
Contributions pre-tax; all withdrawals taxed as ordinary income
Favorable when future tax rate < current rate
Tax-exempt account accumulation
FV=(1+r)nFV = (1+r)^n
After-tax contributions; all growth and withdrawals tax-free
Favorable when future tax rate > current rate
Roth IRA / Roth 401(k) structure
Total wealth (holistic balance sheet)
Total Wealth=Financial Capital+Human Capital\text{Total Wealth} = \text{Financial Capital} + \text{Human Capital} — Financial Capital = sellable assets today, Human Capital = PV of future after-tax wages net of consumption.
Goals-based plan funding ratio
Funding Ratio=PV(Assets)∑iPV(Goali)\text{Funding Ratio} = \frac{PV(\text{Assets})}{\sum_i PV(\text{Goal}_i)} — PV(Assets) = present value of all financial capital, PV(Goal_i) = present value of liability for goal i; >1 means over-funded.
Investment Planning 6 items
After-tax return
rAT=rPT×(1−t)r_{AT} = r_{PT} \times (1 - t)
For return with mixed income types:
rAT=rCG(1−tCG)+rInc(1−tInc)+rtax−freer_{AT} = r_{CG}(1-t_{CG}) + r_{Inc}(1-t_{Inc}) + r_{tax-free}
r_PT = pre-tax return, t = tax rate
Core capital estimate
CC=∑t=1TEt(1+rAT)t×psurvive,tCC = \sum_{t=1}^{T} \frac{E_t}{(1+r_{AT})^t} \times p_{survive,t}
E_t = expenses in year t, r_AT = after-tax return
p_survive,t = probability of surviving to year t
Core capital must be preserved; surplus is investable
Tax-loss harvesting benefit
Benefit=tST⋅L−tLT⋅Gf\text{Benefit} = t_{ST} \cdot L - t_{LT} \cdot G_f
L=loss harvested, GfG_f=future gain at lower basis.
Net positive when tST>tLTt_{ST} > t_{LT} or long horizon.
Required minimum distribution for the year
RMDt=Bt−1LEageRMD_t = \dfrac{B_{t-1}}{LE_{age}} — B_{t-1} = prior year-end account balance, LE_age = IRS Uniform Lifetime Table factor for account holder's age
Time-weighted return over n sub-periods
TWR=∏i=1n(1+ri)−1TWR = \prod_{i=1}^{n}(1 + r_i) - 1 — r_i = return in sub-period i, n = number of sub-periods linked geometrically
Required equity weight on the financial portfolio given human capital
weq,FC=weq,target⋅Wtotal−weq,HC⋅HCFCw_{eq,FC} = \dfrac{w_{eq,target} \cdot W_{total} - w_{eq,HC} \cdot HC}{FC} — w = equity weight, W_total = HC + FC, HC = human capital, FC = financial capital
Preserving the Wealth 1 item
Real return from nominal return and inflation
rreal=1+rnominal1+π−1r_{real} = \frac{1 + r_{nominal}}{1 + \pi} - 1 — r_nominal = nominal return, π = inflation rate, r_real = inflation-adjusted return
Advising the Wealthy 3 items
Section 877A exit tax taxable base
Base=GMTM−$821,000\text{Base} = G_{MTM} - \$821{,}000 — G_MTM = mark-to-market gain on all assets day before expatriation, $821,000 = 2026 indexed exclusion for covered expatriates
QSBS Section 1202 gain exclusion ceiling
Exclusion cap=max⁡($10M, 10×B)\text{Exclusion cap} = \max(\$10\text{M},\ 10 \times B) — B = original cost basis of C-corp QSBS held >5 years, issuer met $50M gross-asset test at issuance
Stacked QSBS exclusion across non-grantor trusts
Total=N×max⁡($10M, 10×B)\text{Total} = N \times \max(\$10\text{M},\ 10 \times B) — N = number of separate qualifying holders (donor plus non-grantor trusts), B = per-holder basis
Transferring the Wealth 7 items
Estate tax (simple)
Tax=(Estate value−Exemption)×te\text{Tax} = (\text{Estate value} - \text{Exemption}) \times t_e
t_e = estate tax rate
Taxable estate = gross estate − debts − marital deduction − charitable deduction
Relative value of gift vs bequest
RV=(1+rg)n(1−Te)(1+re)n(1−Tg)+Tg−TeRV = \frac{(1+r_g)^n(1-T_e)}{(1+r_e)^n(1-T_g) + T_g - T_e}
r_g = after-tax return if gifted, r_e = after-tax return if bequested
T_e = estate/bequest tax rate, T_g = gift tax rate
RV > 1 → gifting preferred
Generation-Skipping Transfer (GST) tax
Applies to transfers skipping a generation (grandparent → grandchild).
GST tax=Transfer amount×tGST\text{GST tax} = \text{Transfer amount} \times t_{GST}
Separate exemption; dynasty trusts avoid multi-gen estate tax.
CRT charitable deduction as present value of remainder
D=C×fremD = C \times f_{rem} — C = contribution FMV, f_rem = IRS remainder factor at the 7520 rate over the trust term or life expectancy
CLAT family remainder when assets outperform the 7520 rate
R=C(1+g)n−A⋅sn‾∣gR = C(1+g)^n - A \cdot s_{\overline{n}|g} — C = contribution, g = actual return, n = term, A = annual annuity, s = FV annuity factor
Zeroed-out CLAT annual annuity payment
A=Can‾∣rA = \dfrac{C}{a_{\overline{n}|r}} — C = contribution, n = term in years, r = 7520 rate, a = PV annuity factor
529 plan five-year forward-averaging gift limit
Gmax=5×EannualG_{max} = 5 \times E_{annual} — E_annual = per-donee annual exclusion ($19,000 in 2026), yielding $95,000 single or $190,000 couple
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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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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FreeFellow LLC is a CFA Institute Prep Provider. CFA Institute does not endorse, promote, review, or warrant the accuracy or quality of the products or services offered by FreeFellow LLC.
What else is free at FreeFellow for CFA L3 Private Wealth candidates?
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 Wealth 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 Markets 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.