CFA Level 1 Formula Sheet: What to Memorise, What to Recognise, What to Skip

There are several hundred expressions in the CFA Level 1 curriculum. Perhaps sixty are worth committing to memory, and maybe fifteen decide a meaningful number of marks. A formula sheet that lists all of them equally is not a study tool — it is an anxiety generator, and it is why candidates arrive at the exam having memorised the Poisson distribution and forgotten to double the covariance term in portfolio variance.

This sheet is organised by topic and tiered by priority. Each formula sits in one of three tiers:

• Tier 1 — memorise cold. You must be able to produce this from a blank page under time pressure.
• Tier 2 — recognise and apply. Know what it does and when it is called for; you will usually be given enough structure to work with.
• Tier 3 — conceptual only. Understand the idea and the direction of the relationship. Do not spend memorisation effort here.

Quantitative Methods

Tier 1

• Future value: FV = PV(1 + r)ⁿ, and every rearrangement of it
• Effective annual rate: EAR = (1 + periodic rate)^m − 1
• Continuous compounding: EAR = e^r − 1
• Perpetuity: PV = PMT / r  |  growing perpetuity: PV = PMT / (r − g)
• Holding period return: HPR = (P₁ − P₀ + D₁) / P₀
• Coefficient of variation: CV = σ / mean

Tier 2

• Z-score: z = (x − μ) / σ
• Test statistic (mean, known σ): (x̄ − μ₀) / (σ / √n)
• Geometric mean return: the nth root of the product of (1 + R_i), minus 1
• Safety-first ratio: (E(R_p) − R_threshold) / σ_p

Tier 3: Poisson and lognormal distributions, Chebyshev's inequality, Bayes' formula in its algebraic form (understand the logic, work these by table rather than formula).

Trap: the coefficient of variation is a measure where lower is better, and questions are frequently written so that the highest CV looks like the best answer. Time value of money is the foundation for Fixed Income, Equity and Corporate Issuers, so if TVM keystrokes are not automatic on your calculator, fix that before anything else. The Quant breakdown covers what else appears.

Economics

Tier 2

• GDP deflator: (nominal GDP / real GDP) × 100
• Fisher relation: nominal rate ≈ real rate + expected inflation
• Real exchange rate: nominal rate × (foreign price level / domestic price level)
• Forward premium/discount: driven by the interest rate differential — the higher-rate currency trades at a forward discount

Tier 3: the multiplier formulas, elasticity variants, Cobb-Douglas. Understand direction and mechanism; the exam rarely asks for precise computation.

Economics is the topic where formula memorisation pays worst. Marks come from knowing which way a variable moves, not from arithmetic. The Economics guide sets out where the questions actually cluster.

Financial Statement Analysis

Tier 1

• Current ratio: current assets / current liabilities
• Quick ratio: (cash + marketable securities + receivables) / current liabilities
• DuPont (3-part): ROE = net profit margin × asset turnover × financial leverage
• DuPont (5-part): tax burden × interest burden × EBIT margin × asset turnover × leverage

Tier 2

• Inventory turnover: COGS / average inventory
• Days sales outstanding: 365 / receivables turnover
• Days of inventory on hand: 365 / inventory turnover
• Basic and diluted EPS

Trap: memorise the five-part DuPont in order. Questions routinely give you four components and ask you to solve for the fifth, which is trivial if you know the sequence and impossible if you half-remember it. Note also that tax burden and interest burden are ratios below 1, not percentages — candidates lose marks by treating them as rates.

Corporate Issuers

Tier 1

• WACC: (w_d × r_d × (1 − t)) + (w_p × r_p) + (w_e × r_e)
• Cash conversion cycle: DSO + days of inventory − days of payables

Tier 2

• Degree of operating leverage: % change in EBIT / % change in sales
• Degree of financial leverage: % change in net income / % change in EBIT
• Degree of total leverage: DOL × DFL
• Break-even quantity: fixed costs / (price − variable cost per unit)

Trap: the after-tax adjustment in WACC applies to debt only. Applying (1 − t) to the cost of equity is the most common single error in WACC questions, and the resulting number is plausible enough to appear among the answer choices.

Equity Investments

Tier 1

• Gordon growth model: V₀ = D₁ / (r − g)
• Sustainable growth: g = retention ratio × ROE
• Justified leading P/E: (1 − b) / (r − g)
• Justified trailing P/E: ((1 − b)(1 + g)) / (r − g)

Tier 2

• Enterprise value: market cap + total debt − cash and equivalents
• Preferred stock value: D / r
• Two-stage DDM structure (set-up matters more than a memorised formula)

Trap: note the D₁ in the Gordon model. If the question supplies D₀, you must grow it forward one period first. This single omission is responsible for a remarkable share of lost equity marks. The equity valuation guide covers model selection logic.

Fixed Income

Tier 1

• Modified duration: Macaulay duration / (1 + periodic yield)
• Price change approximation: %ΔP ≈ (−ModDur × Δy) + (0.5 × Convexity × Δy²)
• Money duration: annual modified duration × full price of the position

Tier 2

• Forward rate from spot rates: (1 + z₂)² = (1 + z₁)(1 + ₁f₁)
• Price value of a basis point: money duration × 0.0001
• Current yield: annual coupon / price
• Full price: flat price + accrued interest

Trap: the convexity term is always positive for an option-free bond, so it adds to the price change whether yields rise or fall. Candidates who mechanically apply the negative sign to both terms get the direction wrong on falling yields. Practise with rising and falling yields until the sign convention is automatic — the Fixed Income guide works through each of these with numbers.

Derivatives

Tier 1

• Put-call parity: c + X/(1 + r)^T = p + S₀
• Forward price (no income): F₀ = S₀(1 + r)^T

Tier 2

• Value of a long forward at time t: S_t − F₀/(1 + r)^(T−t)
• Option intrinsic values: call max(0, S − X); put max(0, X − S)

Tier 3: the binomial option pricing algebra. Understand the replication logic; the arithmetic is rarely the mark.

Trap: put-call parity is the highest-yield expression in Derivatives because so many questions are solvable by rearranging it rather than by valuing anything. If a question gives you three of the four components, it is a parity question regardless of how it is dressed.

Alternative Investments

Tier 1

• NAVPS: (total assets − total liabilities) / shares or units outstanding
• Management fee: rate × assets under management (or committed capital in private equity — not the same thing)
• Incentive fee: rate × profits, subject to hurdle rate and high-water mark

Trap: fee questions are arithmetic, and the marks are lost on sequencing — specifically whether the incentive fee is computed gross or net of the management fee. The NAVPS and fee guide works through a multi-year example with a high-water mark.

Portfolio Management

Tier 1

• CAPM: E(R_i) = R_f + β_i(E(R_m) − R_f)
• Beta: Cov(R_i, R_m) / Var(R_m) = ρ_i,m × (σ_i / σ_m)
• Two-asset portfolio variance: w₁²σ₁² + w₂²σ₂² + 2w₁w₂Cov(1,2)
• Sharpe ratio: (R_p − R_f) / σ_p

Tier 2

• Treynor ratio: (R_p − R_f) / β_p
• Portfolio beta: the weighted average of component betas
• Covariance from correlation: Cov = ρ × σ₁ × σ₂

Trap: the two-asset variance formula is the one candidates most often reproduce incorrectly under time pressure, almost always by forgetting to double the covariance term. Detailed treatment sits in the CAPM guide and the risk-adjusted return comparison.

What you can safely skip

Nobody writes this section, which is why candidates over-memorise. Deprioritise:

• Every distribution beyond normal, binomial and t — know what they describe, not their density functions
• The algebraic form of Bayes' formula — work these problems with a table
• Macroeconomic multipliers and Cobb-Douglas parameters
• Full binomial option pricing algebra
• Detailed lease and pension computations at Level 1 depth
• Any formula that appears once in the curriculum with no worked example — that is a strong signal about how it will be tested

Deprioritising is not ignoring. Know what each concept does, so a conceptual question is still answerable. What you are declining to do is spend rote memory on things that will not ask for it.

How to actually use a formula sheet

Reading a formula sheet is not studying. Three rules make it useful.

Write it out, do not read it. Once a week, reproduce the Tier 1 list from a blank page. The formulas you cannot produce are the ones you do not know, regardless of how familiar they look when you look at them. Recognition and recall are different capacities, and only one of them is tested.

Attach each formula to a trigger phrase. Knowing modified duration is worth little if you cannot recognise which question calls for it. Against each Tier 1 entry, write the phrase in a question that should trigger it — "for a 50 basis point increase in yield" triggers duration and convexity; "an investor considering adding this fund to a diversified portfolio" triggers Treynor rather than Sharpe.

Prune ruthlessly. By the final month your sheet should be shrinking, not growing. Anything you have reproduced correctly three sittings running comes off, leaving only genuinely fragile items for final-week review. A candidate walking into the exam with a two-page sheet has done this properly. One walking in with fifteen pages has not.