FRM Formula Sheet
Ten formulas, what each one is for, and a worked example.
FRM Part I has four books, and each has formulas you must apply quickly. These ten come up most often across Foundations, Quantitative Analysis, Financial Markets and Products, and Valuation and Risk Models.
GARP doesn't give a formula sheet in the exam. A worked hedge-ratio example follows the table.
The 10 Formulas
1
Formula
CAPM
Expression
E(Rᵢ) = R_f + βᵢ × [E(R_m) − R_f]
Use it for
Expected return for systematic risk (Foundations).
2
Formula
Sharpe ratio
Expression
(R_p − R_f) ÷ σ_p
Use it for
Risk-adjusted performance (Foundations).
3
Formula
Portfolio variance
Expression
σ²_p = w₁²σ₁² + w₂²σ₂² + 2w₁w₂ρσ₁σ₂
Use it for
Diversification (Quantitative Analysis).
4
Formula
Forward price (continuous)
Expression
F₀ = S₀ × e^((r − q) × T)
Use it for
Pricing forwards with a yield q (Markets and Products).
5
Formula
Minimum variance hedge ratio
Expression
h* = ρ × σ_S ÷ σ_F
Use it for
Optimal futures hedge per unit of exposure.
6
Formula
Put-call parity
Expression
C + K × e^(−rT) = P + S₀
Use it for
Pricing and arbitrage of European options.
7
Formula
Parametric VaR
Expression
VaR = z × σ × √t × Portfolio value
Use it for
Loss threshold at a confidence level (Valuation and Risk Models).
8
Formula
Expected loss
Expression
EL = PD × LGD × EAD
Use it for
Credit risk.
9
Formula
Duration and convexity
Expression
ΔP ÷ P ≈ −D × Δy + ½ × C × (Δy)²
Use it for
Bond price sensitivity.
10
Formula
Black-Scholes call
Expression
C = S₀N(d₁) − Ke^(−rT)N(d₂)
Use it for
Value of a European call option.
| # | Formula | Expression | Use it for |
|---|---|---|---|
| 1 | CAPM | E(Rᵢ) = R_f + βᵢ × [E(R_m) − R_f] | Expected return for systematic risk (Foundations). |
| 2 | Sharpe ratio | (R_p − R_f) ÷ σ_p | Risk-adjusted performance (Foundations). |
| 3 | Portfolio variance | σ²_p = w₁²σ₁² + w₂²σ₂² + 2w₁w₂ρσ₁σ₂ | Diversification (Quantitative Analysis). |
| 4 | Forward price (continuous) | F₀ = S₀ × e^((r − q) × T) | Pricing forwards with a yield q (Markets and Products). |
| 5 | Minimum variance hedge ratio | h* = ρ × σ_S ÷ σ_F | Optimal futures hedge per unit of exposure. |
| 6 | Put-call parity | C + K × e^(−rT) = P + S₀ | Pricing and arbitrage of European options. |
| 7 | Parametric VaR | VaR = z × σ × √t × Portfolio value | Loss threshold at a confidence level (Valuation and Risk Models). |
| 8 | Expected loss | EL = PD × LGD × EAD | Credit risk. |
| 9 | Duration and convexity | ΔP ÷ P ≈ −D × Δy + ½ × C × (Δy)² | Bond price sensitivity. |
| 10 | Black-Scholes call | C = S₀N(d₁) − Ke^(−rT)N(d₂) | Value of a European call option. |
What the Symbols Mean
- q
- Continuous dividend or income yield on the underlying.
- ρ, σ_S, σ_F
- Correlation between spot and futures changes, and their standard deviations.
- d₁, d₂
- d₁ = [ln(S₀/K) + (r + σ²/2)T] ÷ (σ√T); d₂ = d₁ − σ√T.
Financial markets is the heaviest Part I subject. Start there.
Worked Example: Minimum Variance Hedge Ratio
Spot price changes have a standard deviation of 2%, futures price changes 2.5%, and the correlation is 0.9.
- 1
Apply the formula
h* = 0.9 × 2 ÷ 2.5 = 0.72.
- 2
Read it
Hedge 72% of the exposure with futures, not 100%.
- 3
Number of contracts
Multiply h* by the exposure, then divide by the size of one futures contract.
Continuous or Discrete?
FRM switches between continuous compounding (e^rT) and discrete compounding (1 + r)ᵗ. Read which one the question uses before calculating. The two give noticeably different answers for long maturities.
FAQs
Does GARP give a formula sheet?expand_more
No. You need to memorise the formulas.
Which calculators are allowed?expand_more
GARP allows a short list of models, including the TI BA II Plus and the HP 12C. Check GARP's current list before the exam.
Is Part II formula-heavy too?expand_more
Less so. Part II focuses more on applying concepts, but it builds on these Part I formulas.
Next steps
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