AQIF cheat sheet

Portfolio variance is σ_p² = w'Σw and the Sharpe ratio is (E[r_p] − r_f)/σ_p; both are central to quantitative evaluation of strategies.

Central limit theorem: the sample mean of n independent draws with finite variance is approximately N(μ, σ²/n), so standard error shrinks with 1/√n.

OLS is BLUE under the Gauss–Markov conditions: linearity in parameters, E[ε|X] = 0, homoskedasticity, and no perfect collinearity among regressors.

R² = 1 − SSE/SST; adjusted R² = 1 − [(1 − R²)(n − 1)/(n − k − 1)] penalizes each additional regressor and can fall when a variable adds little.

A p-value is P(statistic at least as extreme | H0 true); it is not the probability that the null hypothesis is true.

Type I error rate equals α (rejecting a true null); Type II equals β (failing to reject a false null); statistical power equals 1 − β.

For an AR(1) process autocorrelation decays geometrically, ρ_k = φ^k, and stationarity requires |φ| < 1.

The augmented Dickey–Fuller test has a unit root under the null; failure to reject implies differencing the series before regression.

The normal distribution has zero skewness and zero excess kurtosis; positive excess kurtosis (fat tails) means normal-based risk measures understate tail losses.

Bond price = Σ C/(1 + y)^t + F/(1 + y)^n; price moves inversely to yield and more so for longer maturities and lower coupons.

ΔP/P ≈ −D_mod × Δy + ½ × convexity × Δy²; convexity is positive for plain vanilla bonds and improves accuracy for large yield moves.

Put–call parity for European options on a non-dividend stock: C − P = S − K e^(−rT); any deviation admits a replicating arbitrage.

Futures fair value F = S e^((r − q)T), where q is dividend or convenience yield; the basis (F − S) converges to zero at expiry.

Black–Scholes assumes lognormal returns, constant volatility, no arbitrage, continuous trading, and frictionless markets with unrestricted short selling.

Option Greeks: delta = ∂V/∂S, gamma = ∂²V/∂S², vega = ∂V/∂σ, theta = ∂V/∂t, rho = ∂V/∂r.

A repo is a sale of securities with a commitment to repurchase at a higher price; the implied repo rate is a collateralised short-term borrowing rate.

Authorized-participant creation and redemption arbitrage holds an ETF's market price close to NAV; persistent premiums or discounts indicate frictions or capacity limits.

A CDS spread compensates the protection buyer for default of the reference entity; widening spreads signal deteriorating credit quality and rising spread duration risk.

Expected squared prediction error decomposes into bias² + variance + irreducible noise; increasing model complexity lowers bias and raises variance.

Lasso (L1) produces sparse coefficients and performs feature selection; ridge (L2) shrinks smoothly without zeroing coefficients; elastic net blends both penalties.

Standard k-fold cross-validation breaks the independence assumption in time series; use purged and embargoed splits so training labels do not overlap test windows.

Tree ensembles are invariant to monotone feature scaling and cannot extrapolate beyond the training range; distance-based and gradient-based models require standardisation.

Bagging (random forest) mainly reduces variance; boosting (gradient boosting) mainly reduces bias, but both overfit readily on low signal-to-noise financial labels.

PCA components are eigenvectors of the covariance matrix ordered by eigenvalue; the ratio of each eigenvalue to the total gives variance explained.

Financial data have low signal-to-noise ratios, so prefer regularised low-complexity models and report the information coefficient or rank IC rather than classification accuracy.

Split data into training, validation, and test sets; tune hyperparameters on validation only and report test performance once without re-tuning.

Portfolio variance is σ_p² = w'Σw; unconstrained maximum-Sharpe weights are proportional to Σ⁻¹(μ − r_f·1).

Two-fund separation: with a risk-free asset, every mean–variance efficient portfolio is a combination of the risk-free asset and the tangency portfolio.

Parametric VaR at confidence level 1 − α: VaR = −(μ_p − z_α σ_p) × V, with z = 1.645 at 95% and 2.326 at 99%.

VaR is not subadditive, so portfolio VaR can exceed the sum of component VaRs; expected shortfall (CVaR) is coherent and subadditive.

Beta β_i = Cov(r_i, r_m)/Var(r_m); a factor model r = α + Bf + ε gives Σ = BΣ_f B' + D.

Risk parity equalises risk contributions RC_i = w_i(Σw)_i/(w'Σw), which generally differs from equal capital weights.

Covariance shrinkage (for example Ledoit–Wolf) and factor-based covariance estimates stabilise optimisation when the number of assets is large relative to the sample length.

Drawdown metrics: maximum drawdown, Calmar ratio = CAGR/|MaxDD|, and Sortino ratio, which replaces σ with downside deviation.

The pipeline runs signal → forecast → risk model → optimiser → execution; each layer adds constraints, turnover, and cost.

Breakeven turnover rule: a signal is viable only if expected alpha exceeds turnover × round-trip transaction cost.

Kelly sizing for continuous returns is f* = μ/σ²; fractional Kelly (half or quarter) reduces drawdowns caused by estimation error in μ and σ.

Volatility targeting sets position size proportional to target volatility divided by realised volatility, stabilising risk but inducing momentum-like exposure.

Common systematic factor families: time-series and cross-sectional momentum, short-term reversal, carry, value, low volatility, and quality.

Market impact scales roughly with the square root of trade size relative to average daily volume, so capacity is finite and alpha decays with AUM.

Execution algorithms include VWAP, TWAP, percentage-of-volume, and implementation shortfall; the choice depends on urgency and available liquidity.

Combine decorrelated signals with weights proportional to IC divided by volatility; equal weighting is a robust low-information baseline.

Biases to remove: look-ahead, survivorship, restatement, and universe selection; use point-in-time data and delisting-inclusive universes.

Costs to model explicitly: commissions, bid–ask spread, slippage, market impact, borrow fees, financing, and taxes.

Multiple testing inflates the maximum observed Sharpe ratio; correct with the Deflated Sharpe Ratio, White's Reality Check, or Bonferroni-type adjustments.

The minimum backtest length grows with the number of configurations tested; short samples combined with many trials produce unreliable results.

Use out-of-sample and walk-forward evaluation; the holdout set must never inform model selection or hyperparameter choice.

Report turnover, capacity, hit rate, drawdown, and performance across sub-periods and market regimes rather than a single headline statistic.

Validation should be independent of the model developer, documented, and reproducible from raw data with versioned code.

Before allocating capital, run paper or shadow trading to verify execution, data latency, and operational controls.

Fiduciary duty requires loyalty, prudence, and care in the client's best interest, with full disclosure of conflicts of interest.

Trading or tipping on material nonpublic information is prohibited; the mosaic theory permits combining public data with non-material nonpublic fragments.

Prohibited market conduct includes spoofing, layering, marking the close, wash trades, front-running, and cherry-picking allocations across accounts.

Best execution weighs price, cost, speed, likelihood of execution, and settlement against the client's stated objectives, not merely the lowest commission.

Fair performance presentation prohibits guaranteeing returns or cherry-picking composites; GIPS requires defined composites and prescribed disclosures.

Model risk governance requires a model inventory, independent validation, documented assumptions, approved ownership, and periodic revalidation.

Recordkeeping and data protection: retain required records per local rules, and under GDPR personal data must be lawful, minimal, and purpose-limited.

Key regulatory frameworks include SEC/FINRA rules, MiFID II, Dodd–Frank, EMIR, Basel III/IV, and IOSCO principles.