CFA Formula Sheet
Ten formulas, what each one is for, and a worked example.
The CFA curriculum has hundreds of formulas, but a core set turns up across topics and levels. These ten come from Quantitative Methods, Corporate Issuers, Equity, Fixed Income and Portfolio Management, and they matter most at Level I.
CFA Institute doesn't give you a formula sheet in the exam, so you need to know these by heart.
The 10 Formulas
1
Formula
Future value
Expression
FV = PV × (1 + r)ⁿ
Use it for
The base of every time value of money question.
2
Formula
Effective annual rate
Expression
EAR = (1 + Stated rate ÷ m)ᵐ − 1
Use it for
Comparing rates with different compounding frequencies.
3
Formula
Holding-period return
Expression
HPR = (P₁ − P₀ + D₁) ÷ P₀
Use it for
Return over one period, including income.
4
Formula
Two-asset portfolio variance
Expression
σ²_p = w₁²σ₁² + w₂²σ₂² + 2w₁w₂ρσ₁σ₂
Use it for
Portfolio risk and diversification.
5
Formula
CAPM
Expression
E(Rᵢ) = R_f + βᵢ × [E(R_m) − R_f]
Use it for
Required return on equity.
6
Formula
Sharpe ratio
Expression
(R_p − R_f) ÷ σ_p
Use it for
Risk-adjusted performance.
7
Formula
Gordon growth model
Expression
V₀ = D₁ ÷ (r − g)
Use it for
Value of a stock with constant dividend growth.
8
Formula
WACC
Expression
w_d × r_d × (1 − t) + w_p × r_p + w_e × r_e
Use it for
Discount rate for a company's projects.
9
Formula
Price change from duration and convexity
Expression
%ΔP ≈ −ModDur × Δy + ½ × Convexity × (Δy)²
Use it for
Bond price sensitivity to yield changes.
10
Formula
Put-call parity
Expression
S₀ + P₀ = C₀ + X ÷ (1 + R_f)ᵀ
Use it for
Linking European call and put prices.
| # | Formula | Expression | Use it for |
|---|---|---|---|
| 1 | Future value | FV = PV × (1 + r)ⁿ | The base of every time value of money question. |
| 2 | Effective annual rate | EAR = (1 + Stated rate ÷ m)ᵐ − 1 | Comparing rates with different compounding frequencies. |
| 3 | Holding-period return | HPR = (P₁ − P₀ + D₁) ÷ P₀ | Return over one period, including income. |
| 4 | Two-asset portfolio variance | σ²_p = w₁²σ₁² + w₂²σ₂² + 2w₁w₂ρσ₁σ₂ | Portfolio risk and diversification. |
| 5 | CAPM | E(Rᵢ) = R_f + βᵢ × [E(R_m) − R_f] | Required return on equity. |
| 6 | Sharpe ratio | (R_p − R_f) ÷ σ_p | Risk-adjusted performance. |
| 7 | Gordon growth model | V₀ = D₁ ÷ (r − g) | Value of a stock with constant dividend growth. |
| 8 | WACC | w_d × r_d × (1 − t) + w_p × r_p + w_e × r_e | Discount rate for a company's projects. |
| 9 | Price change from duration and convexity | %ΔP ≈ −ModDur × Δy + ½ × Convexity × (Δy)² | Bond price sensitivity to yield changes. |
| 10 | Put-call parity | S₀ + P₀ = C₀ + X ÷ (1 + R_f)ᵀ | Linking European call and put prices. |
What the Symbols Mean
- m
- Number of compounding periods per year.
- w_d, w_p, w_e
- Weights of debt, preferred stock and equity in the capital structure.
- X
- Exercise (strike) price.
The subjects above start from markets fundamentals.
Worked Example: Effective Annual Rate
A deposit pays a 12% stated annual rate, compounded monthly.
- 1
Periodic rate
12% ÷ 12 = 1% a month.
- 2
Compound for a year
(1.01)¹² ≈ 1.1268.
- 3
EAR
1.1268 − 1 = 12.68%, higher than the stated 12%.
Learn Them on Your Calculator
Only the TI BA II Plus and HP 12C are allowed. Practise each time value of money formula on your calculator's TVM keys until you can do it without thinking. That saves minutes in every session.
FAQs
Does the CFA exam provide a formula sheet?expand_more
No. CFA Institute doesn't provide formulas in the exam, so you must memorise the ones you need.
Which calculators can I use?expand_more
Only the Texas Instruments BA II Plus (including the Professional) and the HP 12C (including the Platinum).
Are these formulas only for Level I?expand_more
They're weighted to Level I, but Levels II and III build on every one of them.
Next steps
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