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Free CFA Level 3 formula sheet

Turn a calculation into a portfolio decision. Search common-core and pathway formulas, then practise three written answers.

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12 of 12 selected formulas

Common core

Expected portfolio return

E(Rp) = Σ wi × E(Ri)

Calculator check

(0.60 × 0.08 + 0.40 × 0.03) × 100 = 6 %.

Variables, assumptions & common error

Variables and units: wi: portfolio weights summing to one; E(Ri): expected asset returns for the same horizon.
When it applies: Beginning weights with no intervening rebalance; values are expectations, not promises.
Common error: A weighted-average return does not capture portfolio risk or liability suitability.

Common core

Two-asset portfolio variance

σp² = wA²σA² + wB²σB² + 2wAwBσAσBρAB

Calculator check

0.5^2 × 0.2^2 + 0.5^2 × 0.1^2 + 2 × 0.5 × 0.5 × 0.2 × 0.1 × 0 = 0.0125 squared-return units.

Variables, assumptions & common error

Variables and units: w: asset weights; σ: return standard deviations as decimals; ρ: correlation.
When it applies: A two-asset portfolio; covariance estimates refer to one consistent return period.
Common error: Take the square root to obtain volatility. Variance and standard deviation are not interchangeable.

Common core

Sharpe ratio

Sharpe = (Rp - Rf) / σp

Calculator check

(0.09 - 0.03) / 0.12 = 0.5 ratio units.

Variables, assumptions & common error

Variables and units: Rp: mean portfolio return; Rf: risk-free return; σp: total return volatility over the same frequency.
When it applies: A risk-adjusted historical or expected summary with a strictly positive volatility denominator.
Common error: Total volatility differs from tracking error. Non-normal returns can make this metric incomplete.

Common core

Information ratio

IR = Mean active return / Tracking error

Calculator check

0.02 / 0.04 = 0.5 ratio units.

Variables, assumptions & common error

Variables and units: Active return: portfolio minus benchmark; tracking error: standard deviation of those active returns.
When it applies: Use the same frequency and benchmark for numerator and denominator; tracking error is positive.
Common error: A higher IR is not proof that the benchmark represents the client mandate.

Common core

Brinson-Fachler allocation effect

Allocation_i = (wp,i - wb,i) × (Rb,i - Rb)

Calculator check

(0.40 - 0.30) × (0.10 - 0.06) × 10000 = 40 basis points.

Variables, assumptions & common error

Variables and units: wp/wb: portfolio/benchmark segment weights; Rb,i: benchmark segment return; Rb: total benchmark return.
When it applies: A single-period Brinson-Fachler decomposition with aligned segment classifications.
Common error: Other attribution conventions differ. Do not mix Brinson-Fachler and Brinson-Hood-Beebower terms.

Common core

Equity-futures beta adjustment

N = (βtarget - βcurrent) × Vportfolio / (F × multiplier × βfutures)

Calculator check

(0.80 - 1.10) × 10,000,000 / (200,000 × 1) = -15 contracts.

Variables, assumptions & common error

Variables and units: N: signed contract count; V: portfolio value; F × multiplier: contract notional; βfutures: futures beta.
When it applies: Linear beta exposure, an appropriate futures hedge and no basis-risk adjustment.
Common error: A negative answer means sell contracts. State the rounding policy and residual exposure.

Portfolio Management pathway

Active share

Active share = 0.5 × Σ |wp,i - wb,i|

Calculator check

0.5 × (|0.60 - 0.40| + |0.40 - 0.60|) × 100 = 20 %.

Variables, assumptions & common error

Variables and units: wp/wb: security weights over the union of portfolio and benchmark securities.
When it applies: Fully invested long-only weights here; include zero weights for securities held only on one side.
Common error: Active share measures holdings differences, not realized active return or tracking error.

Private Wealth pathway

Future value with annual return taxation

FV = PV × [1 + r × (1 - t)]^n

Calculator check

100 × (1 + 0.08 × 0.75)^2 = 112.36 currency units at a hypothetical 25% tax rate.

Variables, assumptions & common error

Variables and units: r: annual pre-tax return; t: tax fraction applied annually to all return; n: years.
When it applies: A hypothetical flat annual tax on the entire return; no allowances, deferral or changes in law.
Common error: This teaching model is not any jurisdiction's tax calculation. Deferred gains need a different model.

Private Wealth pathway

Nominal target from a real spending target

1 + rnominal = (1 + rreal) × (1 + inflation)

Calculator check

(1.04 × 1.025 - 1) × 100 = 6.6 %.

Variables, assumptions & common error

Variables and units: rreal: required real return; inflation: expected inflation over the same annual period.
When it applies: An exact purchasing-power identity before tax, costs and uncertainty buffers.
Common error: The client's required return and ability to bear risk can conflict; the equation does not solve that conflict.

Private Markets pathway

Total value to paid-in capital

TVPI = (Distributions + Residual NAV) / Paid-in capital

Calculator check

(40 + 90) / 100 = 1.3 times.

Variables, assumptions & common error

Variables and units: All terms: cumulative currency amounts for the same fund and measurement date.
When it applies: Consistent gross/net-of-fees basis and a positive paid-in-capital denominator.
Common error: Residual NAV is not cash received. TVPI ignores the timing of contributions and distributions.

Private Markets pathway

Distributions to paid-in capital

DPI = Cumulative distributions / Paid-in capital

Calculator check

40 / 100 = 0.4 times.

Variables, assumptions & common error

Variables and units: Distributions: cash or distributed value under the stated convention; paid-in capital: cumulative contributions.
When it applies: Use the same fund, date, currency and fee basis in numerator and denominator.
Common error: DPI leaves out residual holdings. Add RVPI to reconcile to TVPI on a consistent basis.

Private Markets pathway

Residual value to paid-in capital

RVPI = Residual NAV / Paid-in capital

Calculator check

90 / 100 = 0.9 times.

Variables, assumptions & common error

Variables and units: Residual NAV: estimated remaining net asset value; paid-in capital: cumulative contributions.
When it applies: A positive denominator and a consistent valuation/fee basis with DPI and TVPI.
Common error: A valuation uplift raises RVPI without creating a distribution. Check the underlying valuation assumptions.

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Three worked practice exercises

Three original exercises, separate from the level samples. Open explanations freely; written answers are self-reviewed, not graded.

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Question 1 of 3Common core - risk-adjusted returnWritten response
Case facts
A portfolio returns 8%, the risk-free rate is 2% and total volatility is 10%, all annual.
Calculate the Sharpe ratio and distinguish it from an information ratio.
Your response to question 1
Model answer and self-review rubric
Sharpe = (8% - 2%) / 10% = 0.60. An information ratio instead uses benchmark-relative return and tracking error. Common error: calling total volatility tracking error.
Teaching checklist only. No official points or automated grade.
Calculates 0.60.Distinguishes risk-free/total-risk inputs from benchmark/active-risk inputs.
Question 2 of 3Private Wealth pathway - assumptionsWritten response
Case facts
A hypothetical account earns 5% before an annual flat tax of 20% on the entire return. Its opening value is 200 and the horizon is two years.
Calculate terminal wealth under the stated assumptions.
Your response to question 2
Model answer and self-review rubric
After-tax return is 4%; terminal wealth is 200 × 1.04² = 216.32. This stylized model assumes annual taxation of all return and is not a local tax rule. Common error: applying one year of growth to a two-year horizon.
Teaching checklist only. No official points or automated grade.
Calculates 4% after-tax return and 216.32 terminal wealth.States the annual-tax and two-year timing assumptions.
Question 3 of 3Private Markets pathway - fund metricsWritten response
Case facts
A fund has paid-in capital of 50, distributions of 20 and remaining NAV of 45 on a consistent net basis.
Calculate DPI, RVPI and TVPI, then reconcile them.
Your response to question 3
Model answer and self-review rubric
DPI = 0.40; RVPI = 0.90; TVPI = 1.30, all in times. DPI + RVPI = TVPI. Only the distributions have been returned; the NAV remains a valuation estimate. Common error: describing TVPI as an annualized return.
Teaching checklist only. No official points or automated grade.
Calculates 0.40, 0.90 and 1.30 times.Reconciles the measures and distinguishes residual NAV from distributions.

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What to do, at a glance

01Check the model

Match the formula to the requested output.
Read its assumptions before substituting numbers.
Use your official exam-year outline for full coverage.

02Check the inputs

Use decimal rates: 25 bp = 0.0025.
Match rate periods, currencies and cash-flow dates.
Round the final result, not intermediate steps.

03Use the reference

Selected 2026 coverage; not a complete syllabus.
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Quick answers

Does this replace the official curriculum?

No. This is selected independent practice, not a complete syllabus or official exam. Check your exam-year outline.

Are these the official CFA formula sheets?

No. These are independent selected equations with original examples. The linked official outlines establish study scope, not endorsement or verification of these examples.

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Yes. Sign up to create your account and practice in the app. Public exercises remain available without an account; answers from this preview are not transferred.

Sources

Selected 2026 teaching content. Official sources do not endorse or verify these examples.

MiloPrep is an independent study resource, not affiliated with or endorsed by CFA Institute. CFA® and Chartered Financial Analyst® are trademarks owned by CFA Institute.

Find your formula

Expected portfolio return

Two-asset portfolio variance

Sharpe ratio

Information ratio

Brinson-Fachler allocation effect

Equity-futures beta adjustment

Active share

Future value with annual return taxation

Nominal target from a real spending target

Total value to paid-in capital

Distributions to paid-in capital

Residual value to paid-in capital

Three worked practice exercises

Calculate the Sharpe ratio and distinguish it from an information ratio.

Calculate terminal wealth under the stated assumptions.

Calculate DPI, RVPI and TVPI, then reconcile them.

What to do, at a glance

01Check the model

02Check the inputs

03Use the reference

Quick answers

Does this replace the official curriculum?

Are these the official CFA formula sheets?

Can I sign up from this preview?

Sources