Free CAIA Level I Formula Sheet (2026)

Every CAIA Level I formula you need on the test, grouped by topic, rendered with full math notation. 30 formulas across 5 topics, calibrated to the 2026 syllabus. Free forever, no signup required.

30 Formulas
5 Topics
2026 Syllabus
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All CAIA Level I Formulas

Introduction to Alternative Investments 12 items
TVPI (Total Value to Paid-In)
TVPI=Distributions+Residual NAVPaid-in Capital\text{TVPI} = \dfrac{\text{Distributions} + \text{Residual NAV}}{\text{Paid-in Capital}}
TVPI = DPI + RVPI. >1.0 = fund has created net value (non-time-adjusted).
DPI (Distributions to Paid-In)
DPI=Cumulative DistributionsPaid-in Capital\text{DPI} = \dfrac{\text{Cumulative Distributions}}{\text{Paid-in Capital}}
Realized multiple. DPI > 1.0 = fund returned more than paid-in. Key metric for mature funds.
RVPI (Residual Value to Paid-In)
RVPI=Residual NAVPaid-in Capital\text{RVPI} = \dfrac{\text{Residual NAV}}{\text{Paid-in Capital}}
Unrealized multiple. TVPI = DPI + RVPI. High RVPI = mark-based value subject to valuation uncertainty.
MOIC (Multiple on Invested Capital)
MOIC=Total Value (Realized + Unrealized)Invested Capital\text{MOIC} = \dfrac{\text{Total Value (Realized + Unrealized)}}{\text{Invested Capital}}
MOIC uses INVESTED (deployed) capital; TVPI uses PAID-IN (includes fees). MOIC is cleaner for deal-level performance.
What is the order of distributions in the standard PE waterfall (preferred return + GP catch-up), and what is the GP's net take?
Order: (1) LP return of capital, (2) LP pref return (often 8% IRR hurdle), (3) GP catch-up (100% to GP until 20% of total profit), (4) 80/20 split.
Net effect: GP gets 20% of profit above hurdle.
CAPM / Security Market Line
E[Ri]=Rf+βi(E[Rm]−Rf)E[R_i] = R_f + \beta_i(E[R_m] - R_f)
Expected return as risk-free rate plus beta-scaled equity risk premium. CAIA caveat: VC-style returns rarely reconcile with CAPM, which is why VC GPs use 30-60% target IRRs instead of CAPM-derived hurdles.
Covariance and correlation
Cov(Ri,Rj)=E[(Ri−μi)(Rj−μj)]\text{Cov}(R_i, R_j) = E[(R_i - \mu_i)(R_j - \mu_j)]
ρij=Cov(Ri,Rj)σiσj\rho_{ij} = \dfrac{\text{Cov}(R_i, R_j)}{\sigma_i \sigma_j}
ρ∈[−1,1]\rho \in [-1, 1]. Diversification benefit grows as ρ\rho decreases.
Two-asset portfolio variance
σp2=w12σ12+w22σ22+2w1w2ρ12σ1σ2\sigma_p^2 = w_1^2 \sigma_1^2 + w_2^2 \sigma_2^2 + 2 w_1 w_2 \rho_{12}\sigma_1\sigma_2
Correlation drives the diversification term. Adding low-ρ\rho alts to public assets is the textbook alt-allocation thesis.
Holding period return and multi-period compounding
HPR=P1+D1−P0P0\text{HPR} = \dfrac{P_1 + D_1 - P_0}{P_0}
1+RT=∏t=1T(1+Rt)1 + R_T = \prod_{t=1}^{T}(1 + R_t)
Annualize a T-period total: (1+RT)1/T−1(1 + R_T)^{1/T} - 1. Foundation for TWR (geometric chain of HPRs).
Geometric vs arithmetic mean return
Rg=[∏t=1T(1+Rt)]1/T−1R_g = \left[\prod_{t=1}^{T}(1 + R_t)\right]^{1/T} - 1
Rg≤RaR_g \leq R_a always (equal only with zero variance).
Use geometric for compounded performance, arithmetic for forward-looking expectations. Gap widens with volatility.
Net present value (NPV)
NPV=∑t=0TCFt(1+r)t\text{NPV} = \sum_{t=0}^{T}\dfrac{CF_t}{(1 + r)^t}
Positive NPV at the cost of capital implies value creation. PE GPs decide on target IRR; LPs run NPV at their own discount rate to back into LP-level value.
Effective annual rate (EAR)
EAR=(1+rsm)m−1\text{EAR} = \left(1 + \dfrac{r_s}{m}\right)^m - 1
Continuous compounding: EAR=ers−1\text{EAR} = e^{r_s} - 1. Use to compare quotes across compounding frequencies. PE preferred-return hurdles are usually quoted as IRR (already EAR-equivalent).
Real Assets 2 items
Direct capitalization (real estate)
V=NOICap RateV = \dfrac{NOI}{\text{Cap Rate}}
NOI = Gross rent −- Vacancy −- Opex (excl. debt, tax, depr).
Cap rate =r−g= r - g (implicit constant growth). Lower cap rate ⇒\Rightarrow higher prices/rent growth.
Loan-to-Value (LTV) and Debt Service Coverage Ratio (DSCR)
LTV=LoanProperty Value\text{LTV} = \dfrac{\text{Loan}}{\text{Property Value}}
DSCR=NOIAnnual Debt Service\text{DSCR} = \dfrac{NOI}{\text{Annual Debt Service}}
LTV: leverage (commercial: 60-75%). DSCR: cash-flow cushion (covenants ≥1.25\geq 1.25).
Private Equity 1 item
Money-weighted return (IRR for PE funds)
∑t=0TCFt(1+IRR)t=0\sum_{t=0}^{T}\dfrac{CF_t}{(1 + \text{IRR})^t} = 0
IRR is the rate that zeros NPV. Standard PE fund return; sensitive to LP cash-flow timing (J-curve effect). Pair with KS-PME or Direct Alpha to control for public-market drift.
Hedge Funds 14 items
Sortino ratio
Sortino=Rp−RTσD\text{Sortino} = \dfrac{R_p - R_T}{\sigma_D}
RTR_T = MAR (often 0 or rfr_f). σD\sigma_D = downside deviation.
Preferred over Sharpe for non-normal returns (rewards positive skew).
Calmar ratio
Calmar=Annualized Return∣Max Drawdown∣\text{Calmar} = \dfrac{\text{Annualized Return}}{|\text{Max Drawdown}|}
Common in managed futures/HF. Return per unit of worst-case pain.
Sensitive to drawdown magnitude (not period-by-period vol).
Modified Sharpe ratio (Cornish-Fisher adjusted)
MVaR=μ−zα′σ\text{MVaR} = \mu - z_{\alpha}'\sigma
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. Adjusts for non-normal tails (HF/PE).
Sharpe ratio
Sharpe=Rp−Rfσp\text{Sharpe} = \dfrac{R_p - R_f}{\sigma_p}
Excess return per unit of total volatility. Overstates short-vol and illiquid strategies (assumes normal IID returns); use Sortino / Modified Sharpe for fat-tailed alts.
Treynor ratio
Treynor=Rp−Rfβp\text{Treynor} = \dfrac{R_p - R_f}{\beta_p}
Excess return per unit of SYSTEMATIC risk. Use when the portfolio is well-diversified so idiosyncratic risk is already washed out. Common in fund-of-funds and beta-tilted strategy attribution.
Jensen's alpha
αJ=Rp−[Rf+βp(Rm−Rf)]\alpha_J = R_p - [R_f + \beta_p(R_m - R_f)]
Return after CAPM-implied return. αJ>0\alpha_J > 0 implies manager skill. Sensitive to benchmark choice; alts databases extend to multifactor alpha (e.g., Fama-French) to control for style.
Information ratio
IR=Rp−RbσRp−Rb=Active returnTracking error\text{IR} = \dfrac{R_p - R_b}{\sigma_{R_p - R_b}} = \dfrac{\text{Active return}}{\text{Tracking error}}
Active return per unit of active risk. Targets: 0.5 good, 1.0+ exceptional.
Beta and Dimson beta
βi=Cov(Ri,Rm)Var(Rm)=ρimσiσm\beta_i = \dfrac{\text{Cov}(R_i, R_m)}{\text{Var}(R_m)} = \rho_{im}\dfrac{\sigma_i}{\sigma_m}
Dimson beta sums slope coefficients across multiple lags of RmR_m to correct for stale-pricing autocorrelation in real-asset and HF databases.
Sample standard deviation and annualization
σ=1n−1∑i=1n(Ri−Rˉ)2\sigma = \sqrt{\dfrac{1}{n-1}\sum_{i=1}^{n}(R_i - \bar{R})^2}
σann=σmo12\sigma_{\text{ann}} = \sigma_{\text{mo}}\sqrt{12}
T\sqrt{T} scaling assumes IID; positive autocorrelation requires Lo's adjustment.
Time-weighted return (TWR)
(1+TWR)T=∏t=1T(1+Rt)(1 + \text{TWR})^T = \prod_{t=1}^{T}(1 + R_t)
Link sub-period returns geometrically; removes effect of cash-flow timing. Preferred for HF / open-end manager comparison. IRR remains the right answer for closed-end fund attribution.
Continuously compounded return
rc=ln⁡(P1P0)=ln⁡(1+RHPR)r_c = \ln\left(\dfrac{P_1}{P_0}\right) = \ln(1 + R_{\text{HPR}})
Time-additive across periods (sub-period rcr_c values sum to total). Used in option pricing and quant strategies. rc≤RHPRr_c \leq R_{\text{HPR}} always.
Hedge fund 2-and-20 fee structure
Mgmt fee =m×AUM= m \times \text{AUM} (1.5-2%).
Performance fee =p×max⁡(0,  Profit above hurdle/HWM)= p \times \max(0,\;\text{Profit above hurdle/HWM}) (15-20%).
Net: Rnet=Rgross−m−p⋅max⁡(0,Rgross−h)R_{\text{net}} = R_{\text{gross}} - m - p\cdot\max(0, R_{\text{gross}} - h).
High-water mark (HWM) fee
Performance fee paid only on max⁡(NAVt−HWMt−1,  0)\max(NAV_t - \text{HWM}_{t-1},\; 0). HWM ratchets up after each peak; managers must recoup drawdowns before fees resume. Stops fee double-charging on the same dollar.
Roy's safety-first ratio
SFR=Rp−RTσp\text{SFR} = \dfrac{R_p - R_T}{\sigma_p}
RTR_T = minimum acceptable return. Maximize SFR to minimize P(Rp<RT)P(R_p < R_T) under normal returns. Reduces to Sharpe when RT=RfR_T = R_f; Sortino is the downside-deviation cousin.
Additional Strategies 1 item
Forward exchange rate (covered interest parity)
Ff/d=Sf/d⋅1+rf1+rdF_{f/d} = S_{f/d} \cdot \dfrac{1 + r_f}{1 + r_d}
rfr_f, rdr_d = foreign / domestic rates over the same horizon. Deviation signals capital controls or post-2008 cross-currency basis.

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