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Free CFA Level III: Private Wealth Formula Sheet PDF, No Signup (2026)

Private Wealth Management Industry 3 items

Effective blended fee rate on a tiered AUM schedule

f ˉ = \frac{\sum _{i} f _{i} \times A _{i}}{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 \times f

— AUM = assets under management, f = annual fee rate

Total annual client cost of a wrap program

C = AUM \times f_{w} + AUM \times w_{f} \times e ˉ

— f_w = wrap fee, w_f = fund weight, ē = average fund expense ratio

Working With the Wealthy 1 item

Probability of family charter adherence

P_{a d h er e n ce} = P_{c l a r i t y} \times P_{co mmi t m e n t} \times P_{r e v i e w}

— P_clarity = process clarity, P_commitment = leadership commitment, P_review = scheduled review frequency

Wealth Planning 5 items

Human capital present value

H C_{0} = \sum_{t = 1}^{N} \frac{w _{t} \cdot ( 1 - p _{d e a t h, t} )}{( 1 + r ) ^{t}}

w_{t}

=expected earnings, r=discount rate.

Total wealth = financial + human capital.

Tax-deferred account accumulation

F V = (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

F V = (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

— Financial Capital = sellable assets today, Human Capital = PV of future after-tax wages net of consumption.

Goals-based plan funding ratio

Funding Ratio = \frac{P V ( Assets )}{\sum _{i} P V ( 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

r_{A T} = r_{P T} \times (1 - t)

For return with mixed income types:

r_{A T} = r_{C G} (1 - t_{C G}) + r_{I n c} (1 - t_{I n c}) + r_{t a x - f r ee}

r_PT = pre-tax return, t = tax rate

Core capital estimate

C C = \sum_{t = 1}^{T} \frac{E _{t}}{( 1 + r _{A T} ) ^{t}} \times p_{s u r v i v e, 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 = t_{S T} \cdot L - t_{L T} \cdot G_{f}

L=loss harvested,

G_{f}

=future gain at lower basis.

Net positive when

t_{S T} > t_{L T}

or long horizon.

Required minimum distribution for the year

R M D_{t} = \frac{B _{t - 1}}{L E _{a g e}}

— 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

T W R = \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

w_{e q, F C} = \frac{w _{e q, t a r g e t} \cdot W _{t o t a l} - w _{e q, H C} \cdot H C}{F C}

— 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

r_{r e a l} = \frac{1 + r _{n o mina l}}{1 + π} - 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 = G_{M T M} - $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 ($10 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 \times max ($10 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) \times t_{e}

t_e = estate tax rate

Taxable estate = gross estate − debts − marital deduction − charitable deduction

Relative value of gift vs bequest

R V = \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 \times t_{GS T}

Separate exemption; dynasty trusts avoid multi-gen estate tax.

CRT charitable deduction as present value of remainder

D = C \times f_{r e m}

— 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 \cdot s_{n ∣ g}

— C = contribution, g = actual return, n = term, A = annual annuity, s = FV annuity factor

Zeroed-out CLAT annual annuity payment

A = \frac{C}{a _{n ∣ r}}

— C = contribution, n = term in years, r = 7520 rate, a = PV annuity factor

529 plan five-year forward-averaging gift limit

G_{ma x} = 5 \times E_{ann u a l}

— 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^{*} = \frac{1}{λ} Σ^{- 1} (μ - r_{f} 1)

λ

= risk aversion,

Σ

= covariance matrix,

μ

= expected returns

Corner portfolio blending

w_{A} = \frac{E ( R _{P} ) - E ( R _{B} )}{E ( R _{A} ) - E ( R _{B} )}

,

w_{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 = δ Σ w_{mk t}

Blended:

E (R) = [(τ Σ)^{- 1} + P^{T} Ω^{- 1} P]^{- 1} [(τ Σ)^{- 1} Π + P^{T} Ω^{- 1} Q]

δ

=risk aversion,

w_{mk t}

=mkt cap weights

Portfolio rebalancing trigger (range-based)

Rebalance when:

∣ w_{i} - w_{i}^{*} ∣ > Δ_{i}

w_{i}^{*}

= target weight,

Δ_{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 - Δ S + g + Δ (P / E)

— D/P = dividend yield, ΔS = net share issuance, g = nominal earnings growth, Δ(P/E) = repricing

Taylor rule policy rate

i_{t} = r^{*} + π_{t} + 0.5 (π_{t} - π^{*}) + 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 + 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) = r_{f} + π^{e} + T P + C P + L P

— 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 (R_{F I}) = Y T M + Roll-down + Δ P_{y i e l d} - L_{cr e d i t} - L_{F X}

— YTM = yield to maturity, ΔP = price change from curve shift, L = expected losses

GARCH(1,1) variance forecast

σ_{t}^{2} = ω + α ε_{t - 1}^{2} + β σ_{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

R P = w (σ ρ \cdot S R_{g}) + (1 - w) (σ \cdot S R_{g})

— w = integration weight, σ = asset vol, ρ = correlation with global portfolio, SR_g = global Sharpe ratio

TAA permitted weight range around SAA

w_{T AA} \in [w_{S AA} - b, w_{S AA} + b]

— w_SAA = policy weight, b = IPS-defined TAA band (e.g., ±5%)

Net after-cost tactical premium

α_{n e t} = α_{g r oss} - T C - T

— α_gross = expected gross tactical alpha, TC = transaction costs, T = realized tax cost

Stress liquidity coverage ratio

L C R_{s t r ess} = \frac{Accessible liquid assets _{s t r ess}}{Cash demands _{s t r ess}}

— minimum prudent target ≥ 2x for illiquid-heavy portfolios

Endowment spending rate

s = \frac{Annual spending}{Portfolio value}

— s = spending rate (e.g., 5% = $40M on $800M)

Number of correlation inputs required for MVO

N_{ρ} = \frac{n ( n - 1 )}{2}

— n = number of asset classes; MVO also needs n expected returns and n standard deviations

Pension funded ratio

F R = \frac{A}{L}

— A = market value of plan assets, L = present value of liabilities (e.g., PBO)

Dollar duration of a portfolio or liability

D D = M V \times D

— MV = market value (or PV of liabilities), D = modified or effective duration; used to size LDI hedges

Pension surplus

S = 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 (R_{p}) - 0.5 \cdot λ \cdot σ_{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 \approx A - 0.5 σ^{2}

— G = geometric (compound) mean return, A = arithmetic mean return, σ² = variance of returns

Total MVO inputs required for n asset classes

N = 2 n + \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

S F = \frac{E ( R _{p} ) - R _{L}}{σ _{p}}

, where

R_{L}

is the minimum acceptable (threshold) return. The optimal portfolio maximizes SF; under normality this minimizes the probability of a return below

R_{L}

.

Topic 2 26 items

Marginal Contribution to Risk (MCTR)

M C T R_{i} = β_{i} \times σ_{p}

β_{i} = \frac{Cov ( R _{i} , R _{p} )}{σ _{p}^{2}}

Measures risk added by a small increase in asset i's weight

Absolute Contribution to Risk (ACTR)

A C T R_{i} = w_{i} \times M C T R_{i} = w_{i} \times β_{i} \times σ_{p}

\sum_{i} A C T R_{i} = σ_{p}

(contributions sum to total portfolio risk)

Risk budget = set target ACTRs

Tracking error

T E = σ (R_{p} - R_{B}) = \frac{\sum ( r _{p, t} - r _{B, t} - α ˉ ) ^{2}}{T - 1}

Also called active risk or tracking risk

Annualized:

T E_{ann u a l} = T E_{m o n t h l y} \times 12

Implementation shortfall (decomposition)

I S = Explicit + Delay + Impact + Opportunity

— explicit = commissions/fees; delay = decision-to-desk drift; impact = price move from trade; opportunity = unfilled-share return.

Square-root market impact model

Impact \propto shares / ADV

— shares = order size, ADV = average daily volume; doubling order size raises impact by ~41%, not 100%.

VWAP transaction cost (buy and sell)

VWAP cost_{buy} = P_{exec} - VWAP

;

VWAP cost_{sell} = VWAP - P_{exec}

— positive = unfavorable; VWAP = period volume-weighted average price.

Effective equity beta from a PE allocation

β_{e f f} = w_{e q} + w_{P E} \times β_{P E}

— w_eq = public equity weight, w_PE = PE weight, β_PE ≈ 1.3 (PE equity beta)

Effective PE allocation including unfunded commitments

w_{P E}^{e f f} = \frac{N A V + U C}{P + U C}

— NAV = PE net asset value, UC = unfunded commitments, P = total portfolio value

Liquidity coverage ratio for an alternatives program

L C R = \frac{L}{C F _{12 m}}

— L = liquid assets, CF_{12m} = next-12-month committed cash outflows (capital calls + benefits)

Total PE economic exposure

E_{P E} = N A V + U C

— NAV = net asset value of PE holdings, UC = unfunded capital commitments

Endowment real return target

R_{r e a l} = s + c

— s = spending rate, c = management cost ratio

Insurer duration-matched immunization

D_{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 \geq 0.05 + c + π

— 0.05 = 5% IRS minimum distribution floor, c = costs, π = inflation

DV01 (price value of a basis point)

D V 01 = D_{m o d} \times M V \times 0.0001

— D_mod = modified duration, MV = market value of the bond/portfolio

Active share of an equity portfolio

A S = \frac{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 = \frac{( S - I ) / V + π}{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

r_{p} = r_{i} + \frac{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

H C = \sum_{t = 1}^{N} \frac{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

r_{r e a l, a t} \approx r_{n o m} - π - t \cdot r_{n o m}

— r_nom = nominal return, π = inflation rate, t = tax rate on nominal gain

Modified duration from Macaulay duration

D_{m o d} = \frac{D _{M a c}}{1 + y}

— D_Mac = Macaulay duration, y = periodic yield to maturity

Taxable-equivalent yield on a municipal bond

TEY = \frac{y _{m u ni}}{1 - t}

— y_muni = muni pretax yield, t = investor's marginal tax rate

Economic net worth

E N W = F C + P V (H C) - P V (L) - P V (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

A U M_{s t ab} = 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

T_{ann u a l} = r_{r e a l} \times V_{f u n d}

—

r_{r e a l}

= expected real return (~3%),

V_{f u n d}

= fund market value; principal preserved

Commodity SWF energy-sector exposure cap

w_{e n er g y} \leq w_{b e n c h} - Δ

—

w_{b e n c h}

= benchmark energy weight,

Δ

= transition-risk tilt (e.g., 30%) to offset inflow correlation

SWF maximum single-year withdrawal under charter cap

W_{ma x} = c \times A U M_{3 y}

— c = charter cap (e.g., 5%),

A U M_{3 y}

= 3-year average AUM

Topic 3 12 items

Downside deviation (Sortino denominator)

σ_{D} = \frac{1}{n} \sum_{t} min (R_{t} - M A R, 0)^{2}

Standard deviation of returns below the minimum acceptable return only

Penalizes bad volatility; upside dispersion is ignored

Maximum drawdown

M D D = \frac{Trough value - Peak value}{Peak value}

Largest peak-to-trough decline over the evaluation period

Captures the worst realized experience that volatility metrics smooth over

Drawdown duration

Time from the portfolio's peak until it recovers that prior peak

Measures how long the portfolio stayed underwater

Long durations test investor patience and can force liquidation at the bottom

Appraisal ratio

A R = \frac{α}{σ _{ε}}

α

= alpha from a factor regression,

σ_{ε}

= residual (security-specific) risk

Alpha per unit of active bet taken; denominator is residual risk, not tracking error

Brinson allocation effect

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

Fixed-income attribution components

Total active return = duration effect + curve effect + credit (spread) effect + currency effect + residual

Duration = parallel moves, curve = steepening/flattening/butterfly, credit = spread changes, currency = FX

A large residual signals a broken attribution model

Sortino ratio

Sortino = \frac{R _{p} - M A R}{σ _{d}}

— R_p = portfolio return, MAR = minimum acceptable return, σ_d = downside deviation of returns below MAR

Brinson selection effect

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 = \frac{R ˉ _{p, down}}{R ˉ _{b, down}}

— averaged over periods when benchmark return is negative; <100% means manager dampens losses

Upside capture ratio

UC = \frac{R ˉ _{p, up}}{R ˉ _{b, up}}

— averaged over periods when benchmark return is positive; >100% means manager amplifies up markets

Up/down capture ratio

Up/Down Capture = \frac{Upside Capture}{Downside Capture}

— ratio above 1.0 indicates favorable asymmetry

Symmetric performance-based fee

Fee = 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:

Δ_{c} = N (d_{1}) \in (0, 1)

Put:

Δ_{p} = N (d_{1}) - 1 \in (- 1, 0)

Put-call:

Δ_{c} - Δ_{p} = 1

Approx change in option price for $1 change in underlying

Protective put payoff

At expiration:

Payoff = S_{T} + max (X - S_{T}, 0)

=

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:

S_{T} + max (X_{L} - S_{T}, 0) - max (S_{T} - X_{H}, 0)

=

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:

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 = \frac{D D _{T} - D D _{P}}{D D _{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

N_{v a r} = \frac{N _{v e g a}}{2 \times σ _{s t r ik e}}

— N_vega = vega notional ($ per vol point), σ_strike = strike volatility in whole-number percent

Variance swap payoff at maturity

Payoff = N_{v a r} \times (σ_{r e a l i z e d}^{2} - σ_{s t r ik e}^{2})

— N_var = variance notional, σ_realized = realized volatility (%), σ_strike = strike volatility (%)

Number of equity futures to adjust portfolio beta

N = \frac{β _{T} - β _{P}}{β _{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 = \frac{F - S}{S}

— F = forward rate, S = spot rate; approximately equals domestic minus foreign interest rate

Minimum-variance hedge ratio (MVHR)

h^{*} = ρ_{A, B} \times \frac{σ _{A}}{σ _{B}}

— A = asset hedged, B = hedging instrument, ρ = correlation, σ = volatility

Domestic-currency return on a foreign asset

R_{D C} = (1 + R_{F C}) (1 + R_{F X}) - 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 - S_{0} + C_{0}

— K = call strike, S_0 = short entry price, C_0 = call premium paid

Long straddle breakeven prices

B E = 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 + P V (K)

— S = stock price, P = put premium, C = call premium, K = strike, PV(K) = present value of strike

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