Free CAIA Level II Formula Sheet (2026)

Every CAIA Level II formula you need on the test, grouped by topic, rendered with full math notation. 25 formulas across 7 topics, calibrated to the 2026 syllabus. Free forever, no signup required.

25 Formulas
7 Topics
2026 Syllabus
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All CAIA Level II Formulas

Institutional Asset Owners 2 items
Risk parity portfolio weights
Inverse-vol approx: wi∝1/σi∑j1/σjw_i \propto \dfrac{1/\sigma_i}{\sum_j 1/\sigma_j}. Equal RISK per asset (not equal capital). Full form uses MRC: MRCi=wi(Σw)i/σp\text{MRC}_i = w_i (\Sigma w)_i / \sigma_p. Typically levered 2-3x.
Kelly criterion (optimal fraction to bet)
Binary: f∗=p(b+1)−1bf^* = \dfrac{p(b+1) - 1}{b}. Continuous: f∗=μ−rfσ2f^* = \dfrac{\mu - r_f}{\sigma^2}. Maximizes log-wealth; often run at f∗/2f^*/2 or f∗/4f^*/4 for drawdown control.
Asset Allocation 2 items
Surplus and surplus return (asset-liability framework)
St=At−LtS_t = A_t - L_t
RS=RA⋅A−RL⋅LA−LR_S = \dfrac{R_A \cdot A - R_L \cdot L}{A - L}
Surplus = assets minus liabilities; surplus risk = vol of RSR_S. Pension and insurer programs optimize on surplus Sharpe, not pure-asset Sharpe.
Brinson active-return decomposition (allocation + selection)
Active return = Allocation + Selection + Interaction.
Allocation: ∑i(wp,i−wb,i)Rb,i\sum_i (w_{p,i} - w_{b,i}) R_{b,i}
Selection: ∑iwb,i(Rp,i−Rb,i)\sum_i w_{b,i}(R_{p,i} - R_{b,i})
Isolates sector tilts vs security picks.
Risk and Risk Management 8 items
Kaplan-Schoar PME (KS-PME)
KS-PME=∑tDt/Mt∑tCt/Mt\text{KS-PME} = \dfrac{\sum_t D_t / M_t}{\sum_t C_t / M_t}. DtD_t = distributions, CtC_t = contributions, MtM_t = public index. >1.0 means PE beat benchmark; <1.0 means underperformed.
Tracking error
TE=σ(Rp−Rb)=Var(Rp−Rb)\text{TE} = \sigma(R_p - R_b) = \sqrt{\text{Var}(R_p - R_b)}
Stdev of active return. Sets the active-risk budget for benchmark-relative managers. Information ratio = active return / TE.
Parametric VaR (normal)
VaRα=−(μ+σ⋅zα)\text{VaR}_{\alpha} = -(\mu + \sigma \cdot z_{\alpha})
z0.95=−1.645z_{0.95} = -1.645, z0.99=−2.326z_{0.99} = -2.326. Reported as positive loss. Underestimates HF / PE tails; use Modified VaR or CVaR for fat tails.
Maximum drawdown (MDD)
MDD=min⁡t≤TVt−max⁡s≤tVsmax⁡s≤tVs\text{MDD} = \min_{t \leq T}\dfrac{V_t - \max_{s \leq t} V_s}{\max_{s \leq t} V_s}
Largest peak-to-trough decline in NAV. Feeds Calmar / Sterling ratios; recovery time matters as much as magnitude for path-dependent strategies.
Direct Alpha (PE benchmarking)
Discount flows by public index ItI_t: C~t=Ct/It\tilde{C}_t = C_t/I_t, D~t=Dt/It\tilde{D}_t = D_t/I_t.
Direct Alpha = IRR({−C~t→D~t})\text{IRR}(\{-\tilde{C}_t \to \tilde{D}_t\}).
Annualized excess vs public market; cleaner than KS-PME across periods.
Modified VaR (Cornish-Fisher)
MVaRα=−(μ+σ⋅zα′)\text{MVaR}_{\alpha} = -(\mu + \sigma \cdot z_{\alpha}')
zα′=zα+(zα2−1)S6+(zα3−3zα)K24z_{\alpha}' = z_{\alpha} + (z_{\alpha}^2 - 1)\dfrac{S}{6} + (z_{\alpha}^3 - 3z_{\alpha})\dfrac{K}{24}
SS=skew, KK=excess kurtosis. Corrects normal VaR for HF / PE fat tails.
Risk contribution and marginal contribution to risk
MRCi=wi(Σw)iσp\text{MRC}_i = \dfrac{w_i (\Sigma w)_i}{\sigma_p}
Risk Contributioni=wi⋅MRCi\text{Risk Contribution}_i = w_i \cdot \text{MRC}_i
Decomposes portfolio vol additively: σp=∑iRisk Contribi\sigma_p = \sum_i \text{Risk Contrib}_i. Risk parity sets all risk contributions equal.
Expected loss (credit risk)
EL=PD×LGD×EAD\text{EL} = \text{PD} \times \text{LGD} \times \text{EAD}
PD = probability of default. LGD = loss given default = 1 −- recovery. EAD = exposure at default. Basel pillar 1; private-credit underwriting.
Methods and Models 7 items
Merger arbitrage annualized return
Rarb=Poffer−PcurrentPcurrent×365Days to closeR_{\text{arb}} = \dfrac{P_{\text{offer}} - P_{\text{current}}}{P_{\text{current}}} \times \dfrac{365}{\text{Days to close}}. Conditional on close; multiply by P(completion) for risk-adjusted.
Convertible arbitrage delta hedge
Hedge ratio = convertible delta ×\times conversion ratio. Short Δ\Delta shares per bond; rebalance as delta moves (gamma). P/L from gamma, carry, spread tightening, rising IV.
Hedge fund fund-of-funds effective fee
Fees compound: FoF 1-and-10 on top of HF 2-and-20 ⇒\Rightarrow ~3% mgmt + ~28% of gross alpha. Creates a hurdle the FoF must beat net-of-fees; drove post-2008 FoF decline.
Fama-French 3-factor model
E[Ri]−Rf=βM(Rm−Rf)+βS⋅SMB+βV⋅HMLE[R_i] - R_f = \beta_M (R_m - R_f) + \beta_S \cdot \text{SMB} + \beta_V \cdot \text{HML}
Market + Size (small minus big) + Value (high minus low B/M). Captures equity risk premia missed by CAPM; used for HF style attribution.
Lo's autocorrelation-adjusted Sharpe
Sharpeadj=Sharpenaive1+2∑k=1q−1(1−k/q)ρk\text{Sharpe}_{\text{adj}} = \dfrac{\text{Sharpe}_{\text{naive}}}{\sqrt{1 + 2\sum_{k=1}^{q-1}(1 - k/q)\rho_k}}
ρk\rho_k = lag-kk autocorrelation. Naive Sharpe overstates HF returns 30%+ under positive serial correlation.
Geltner unsmoothing (appraisal-based returns)
Rt∗=Rt−ρRt−11−ρR_t^* = \dfrac{R_t - \rho R_{t-1}}{1 - \rho}
ρ\rho = lag-1 autocorrelation of reported returns. Recovers "true" market vol from smoothed real-estate / PE marks; raises σ\sigma, lowers Sharpe, raises β\beta to public benchmarks.
Modified Internal Rate of Return (MIRR)
MIRR=(FV(+CF at rr)∣PV(-CF at rf)∣)1/T−1\text{MIRR} = \left(\dfrac{FV(\text{+CF at } r_r)}{|PV(\text{-CF at } r_f)|}\right)^{1/T} - 1
Reinvests positives at rrr_r, discounts negatives at rfr_f. Avoids multiple-IRR issues from non-conventional flows.
Accessing Alternative Investments 2 items
Commodity futures total return decomposition
Rfutures=Rspot+Rroll+RcollateralR_{\text{futures}} = R_{\text{spot}} + R_{\text{roll}} + R_{\text{collateral}}; Rroll=Fnear−FnextFnearR_{\text{roll}} = \dfrac{F_{\text{near}} - F_{\text{next}}}{F_{\text{near}}}. Positive in backwardation, negative in contango.
Trend-following signal (simple moving average crossover)
Long when MAshort>MAlongMA_{\text{short}} > MA_{\text{long}}; short when reversed. Position size = Target volσt×Signal\dfrac{\text{Target vol}}{\sigma_t} \times \text{Signal}. Vol targeting keeps portfolio vol constant.
Due Diligence and Selecting Managers 1 item
Information ratio and Fundamental Law
IR=αω=Active returnTracking error\text{IR} = \dfrac{\alpha}{\omega} = \dfrac{\text{Active return}}{\text{Tracking error}}
Fundamental Law: IR≈ICBreadth\text{IR} \approx \text{IC}\sqrt{\text{Breadth}}. IC = skill correlation, breadth = independent bets per year.
Volatility and Complex Strategies 3 items
Conditional Value-at-Risk (CVaR / Expected Shortfall)
CVaRα=E[L∣L≥VaRα]\text{CVaR}_{\alpha} = E[L \mid L \geq \text{VaR}_{\alpha}]; for normal returns: μ+σ⋅ϕ(zα)1−α\mu + \sigma \cdot \dfrac{\phi(z_{\alpha})}{1-\alpha}. Coherent (sub-additive); used in Basel III.
Omega ratio
Ω(r)=∫r∞(1−F(x)) dx∫−∞rF(x) dx\Omega(r) = \dfrac{\int_r^\infty (1 - F(x))\,dx}{\int_{-\infty}^r F(x)\,dx}. Prob-weighted gains above threshold rr over losses below. Captures all moments; preferred for skewed/fat-tailed returns.
Long-short market-neutral PnL
Rport=wLRL−wSRS−cborrowwS−cfinwLR_{\text{port}} = w_L R_L - w_S R_S - c_{\text{borrow}} w_S - c_{\text{fin}} w_L
Dollar-neutral: wL=wSw_L = w_S. Beta-neutral: βLwL=βSwS\beta_L w_L = \beta_S w_S. Alpha is cross-sectional; PnL hinges on borrow cost.

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What's covered on the CAIA Level II formula sheet?
Every formula is grouped by official syllabus topic, with the formula in math notation plus a one-line note on when to use it (or a watch-out from CAIA, CFA, or other prep-provider commentary). Coverage is calibrated to the 2026 syllabus and refreshed when the corpus changes.
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