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Quantitative Researcher — Competency Roadmap

Work towards being a quantitative researcher: developing the mathematics, statistics and research judgement needed to find and validate signals in financial data without fooling myself.

This roadmap charts the complete pathway from foundational mathematics to advanced statistical signal extraction, backtesting rigor, and quantitative interview readiness. Given your theory-first learning preference, each phase establishes rigorous probabilistic and econometric intuition before implementing backtests and vectorized pipelines in Python. At 12 hours per week, this represents an intensive multi-year progression that deliberately leaves out speculative trading tricks in favor of empirical scientific method, institutional factor modeling, and structural risk management. Upon completion, you will be capable of formulating falsifiable market hypotheses, designing leak-free vectorized simulation engines, correcting for multiple testing biases, and defending institutional-grade quantitative research papers.

By the end: You will be able to independently formulate, backtest, and statistically validate cross-sectional and time-series alphas using institutional-grade statistical rigor, and present an end-to-end reproducible research paper with production-ready Python code.

Starting levelBeginnerStyleTheory first
12h / week12 phases32 tasks~196h total

This is the map — make this roadmap yours

It shows what this journey generally looks like. Tell Kaidoro your version of the goal and it builds the plan around where you are actually starting, what to do first, the hours you really have, and what you have already finished.

1

Linear Algebra & Multivariable Calculus Foundations

Establishes the essential mathematical language of multi-asset modeling, dimensionality reduction, and portfolio optimization. Can be studied concurrently with foundational programming.

  • Master vector spaces, projections, and matrix factorizations
    ~6hLearn1 resource

    High-dimensional financial data requires linear transformations and dimensionality reduction to isolate systematic market drivers.

    You'll learn

    • Eigendecomposition — factoring a matrix into its constituent eigenvalues and eigenvectors
    • SVD (Singular Value Decomposition) — factorizing any rectangular matrix into orthogonal and singular components
    • Condition Number — measure of how sensitive matrix inversion is to numerical errors

    Develop intuition for linear transformations, eigenvalues, eigenvectors, and singular value decomposition (SVD). These form the backbone of multi-asset covariance matrices and Principal Component Analysis (PCA).

    Done when: you can analytically compute SVD on paper for a 2x2 matrix and describe the geometric meaning of eigenvalues in asset co-movement.

    How to work through it

    1. Review matrix-vector multiplication as linear mapping
    2. Study orthogonal projections and Gram-Schmidt process
    3. Work through spectral theorem and eigendecomposition
    4. Derive Singular Value Decomposition (SVD) and condition numbers
  • Study multivariable optimization and quadratic forms
    ~6hLearn1 resource

    Quantitative finance frames almost every allocation and model estimation problem as a constrained convex optimization.

    You'll learn

    • Hessian Matrix — square matrix of second-order partial derivatives describing local curvature
    • Lagrange Multipliers — method for finding local extrema subject to equality constraints
    • Convex Optimization — minimizing convex functions over convex sets with unique global minima

    Understand unconstrained and constrained optimization using Lagrange multipliers, gradient vectors, and Hessian matrices. This provides the mathematical machinery required for Mean-Variance Optimization and risk parity.

    Done when: you can write the Lagrangian and derive the analytical solution for minimum variance portfolio weights under equality constraints.

    How to work through it

    1. Review partial derivatives, gradients, and directional derivatives
    2. Analyze positive semi-definite quadratic forms and Hessian matrices
    3. Derive Lagrange multipliers for equality constraints
    4. Study Karush-Kuhn-Tucker (KKT) conditions for inequality constraints
  • Implement matrix factorizations and PCA from scratch in pure NumPy
    ~5hBuild

    Building algorithms from scratch exposes numerical instability issues and guarantees deep intuition for computational linear algebra.

    You'll learn

    • Power Iteration — numerical algorithm for computing dominant eigenvalues and eigenvectors
    • Covariance Matrix — square matrix giving pairwise covariances between asset returns

    Translate theoretical matrix algebra into vectorized NumPy code without using scikit-learn. You will build power iteration for eigenvectors, apply SVD, and compress correlated synthetic asset return series.

    Done when: your scratch PCA implementation reproduces NumPy's linalg.eigh outputs up to machine precision on a 100-asset return matrix.

    How to work through it

    1. Write power iteration and deflation for dominant eigenvectors
    2. Build full PCA class returning explained variance ratios and factor loadings
    3. Decompose a 100x100 synthetic asset covariance matrix
    4. Compare numerical stability against numpy.linalg.svd
2

Probability & Mathematical Statistics

Covers probability distributions, statistical estimation, hypothesis testing, and limit theorems that govern financial phenomena where normal distributions fail.

  • Analyze probability spaces, random variables, and heavy-tailed distributions
    ~6hLearn1 resource

    Financial markets generate black swan events far more frequently than Gaussian models predict.

    You'll learn

    • Fat Tails — distributions with higher kurtosis and probability of extreme outcomes than the normal distribution
    • Moment Generating Function — alternative specification of probability distributions used to derive analytical moments
    • Excess Kurtosis — kurtosis relative to Gaussian distribution (3.0), indicating tail risk

    Master continuous and discrete probability distributions, focusing on extreme value theory, Student's t, and Pareto distributions. Financial returns exhibit excess kurtosis (fat tails) that invalidate standard Gaussian assumptions.

    Done when: you can mathematically derive the moment generating function for a Gaussian and compute empirical excess kurtosis on real market data.

    How to work through it

    1. Study probability spaces, conditioning, and Bayes' theorem
    2. Work with expectation, variance, skewness, and kurtosis
    3. Compare Gaussian, Student's t, and Cauchy distribution tail decay
    4. Analyze Law of Large Numbers and Central Limit Theorem breakdown
  • Master point estimation, Maximum Likelihood, and hypothesis testing
    ~6hLearn

    Signal extraction requires estimating parameters accurately while understanding the uncertainty and variance of those estimates.

    You'll learn

    • Maximum Likelihood Estimation (MLE) — finding parameters that maximize the probability of observed sample data
    • Statistical Power — probability of correctly rejecting the null hypothesis when a true signal exists
    • Likelihood Ratio Test — statistical test comparing goodness-of-fit between two nested models

    Learn MLE (Maximum Likelihood Estimation), Method of Moments, confidence intervals, p-values, and statistical power. Emphasize type I (false positive) and type II (false negative) error trade-offs in low signal-to-noise environments.

    Done when: you can write down the log-likelihood function of a Student's t distribution and analytically derive the score vector for a normal distribution.

    How to work through it

    1. Derive analytical MLE for Gaussian and Bernoulli parameters
    2. Formulate likelihood ratio tests, Wald tests, and score tests
    3. Calculate statistical power and minimum detectable effect size
    4. Understand the p-value distribution under the null vs alternative hypothesis
  • Build a heavy-tail distribution fitting and hypothesis testing engine in Python
    ~5hBuild

    Demonstrates practical ability to quantify tail risk and reject naive Gaussian assumptions on empirical data.

    You'll learn

    • Kolmogorov-Smirnov Test — non-parametric test comparing sample empirical cumulative distribution with reference distribution
    • Value at Risk (VaR) — statistical measure quantifying maximum expected loss at a given confidence level

    Construct a Python toolkit using SciPy and NumPy that fits multiple candidate distributions to asset returns via MLE and conducts goodness-of-fit checks using Kolmogorov-Smirnov and Anderson-Darling tests.

    Done when: the script fits Gaussian, Student's t, and Generalized Hyperbolic distributions to empirical S&P 500 return data and outputs statistical rejection metrics.

    How to work through it

    1. Write custom log-likelihood optimizers with scipy.optimize
    2. Implement Kolmogorov-Smirnov test and Q-Q plot generators
    3. Fit 10 years of daily equity returns to Gaussian vs t-distributions
    4. Generate calibrated Value-at-Risk (VaR) estimates from fitted models
3

Python Architecture for Scientific Computing & Market Data

Teaches the high-performance computational stack (NumPy, Polars, Vectorization, Parquet) required to handle millions of tick and bar rows without memory bloat or lookahead bias.

  • Master vectorized data processing and memory-efficient structures
    ~5hLearn1 resource

    Loop overhead in interpreted languages destroys research iteration speed when evaluating tick or minute data across thousands of securities.

    You'll learn

    • SIMD Vectorization — performing a single operation simultaneously across multiple data points in CPU registers
    • Polars LazyFrame — query planner that optimizes transformations before executing memory allocations
    • Apache Arrow — standardized columnar memory format enabling zero-copy data exchange

    Learn memory layouts (C-contiguous vs Fortran), vectorization, memory mapping, and vectorized operations using NumPy and Polars. Replace all Python loops with SIMD-compatible array expressions.

    Done when: you can transform a 10-million-row time series calculation from a multi-second Python loop into a sub-50ms vectorized Polars expression.

    How to work through it

    1. Benchmark Python list vs NumPy array memory overhead and cache locality
    2. Learn Polars expressions, lazy execution, and chunked arrays
    3. Use Apache Arrow and Parquet for zero-copy deserialization
    4. Profile memory consumption and CPU bottlenecks using line_profiler
  • Construct a clean historical market data store with corporate actions adjustment
    ~6hBuild

    Flawed historical data with unadjusted dividends or survivor bias produces phantom signals that collapse in live execution.

    You'll learn

    • Survivorship Bias — skew caused by analyzing only currently surviving entities while ignoring failed/delisted ones
    • Total Return Adjustment — adjusting historical price bars to account for cash distributions and stock splits

    Design an automated data ingestion pipeline that processes raw open-high-low-close-volume (OHLCV) price series, handles splits, cash dividends, and survivor-bias-free universe mapping stored in partitioned Parquet files.

    Done when: the pipeline produces clean, total-return adjusted series for 500 stocks over 10 years, verified against corporate action logs.

    How to work through it

    1. Download unadjusted OHLCV price series and dividend/split tables
    2. Compute backward ratio adjustments for split and dividend events
    3. Implement survivorship tracking to keep delisted securities in history
    4. Save partitioned data by date and ticker into Parquet format
4

Time Series Econometrics & Signal Extraction

Covers stochastic processes, stationarity tests, autoregressive models, cointegration, and frequency-domain filtering for extraction of persistent alpha signals.

  • Study stationarity, unit root tests, and ARIMA-GARCH processes
    ~7hLearn1 resource

    Most quantitative statistical models require stationary input series to ensure estimated parameters remain valid out-of-sample.

    You'll learn

    • Stationarity — property where joint statistical distribution does not change over time shifts
    • GARCH — Generalized Autoregressive Conditional Heteroskedasticity for modeling time-varying volatility clusters
    • Spurious Regression — false appearance of a causal relationship between independent non-stationary variables

    Understand covariance stationarity, ergodicity, random walks, and mean-reverting Ornstein-Uhlenbeck processes. Learn why non-stationary price series generate spurious regressions, and how to model time-varying volatility with GARCH.

    Done when: you can prove analytically why standard OLS t-statistics are invalid when regressors have unit roots (spurious regression).

    How to work through it

    1. Define weak stationarity and autocorrelation function (ACF/PACF)
    2. Derive the Augmented Dickey-Fuller (ADF) and Phillips-Perron tests
    3. Formulate ARMA(p, q) processes and calculate Wold decomposition
    4. Derive ARCH/GARCH models for volatility clustering and conditional heteroskedasticity
  • Study cointegration and pairs trading mechanics
    ~6hLearn

    Cointegration allows statistical arbitrageurs to trade mean-reverting spreads with bounded variance even if individual asset prices drift indefinitely.

    You'll learn

    • Cointegration — property where a linear combination of two non-stationary series forms a stationary series
    • Half-Life of Mean Reversion — expected time required for a mean-reverting process to decay halfway back to equilibrium

    Learn the difference between correlation and cointegration. Master the Engle-Granger two-step method and Johansen vector error correction model (VECM) for discovering stationary linear combinations of non-stationary asset pairs.

    Done when: you can derive the error-correction representation for two cointegrated random walks and test the residuals for mean-reversion speed.

    How to work through it

    1. Differentiate cointegration (long-run equilibrium) from correlation (short-run co-movement)
    2. Implement Engle-Granger two-step residual test for cointegration
    3. Calculate half-life of mean reversion using Ornstein-Uhlenbeck parameter estimation
    4. Formulate Johansen test for multi-asset cointegrating vectors
  • Build a statistical arbitrage cointegration scanner and signal generator
    ~6hBuild

    Demonstrates the bridge between econometric time-series theory and practical quantitative signal production.

    You'll learn

    • Kalman Filter — recursive algorithm that estimates time-varying parameters from noisy measurement streams
    • Z-Score — number of standard deviations a data point lies from the rolling mean

    Construct a Python module that scans an industry universe (e.g., energy equities or crypto pairs), identifies cointegrated pairs while adjusting p-values for multiple comparisons, and generates normalized Z-score spread signals.

    Done when: the scanner identifies statistically valid pairs, logs their half-life, and produces continuous trade signal matrices without lookahead bias.

    How to work through it

    1. Fetch clean price series for 50 related asset tickers
    2. Run pairwise Engle-Granger cointegration tests with dynamic rolling windows
    3. Estimate dynamic hedge ratios via Kalman Filter to avoid static regression bias
    4. Generate standardized Z-score spread series and entry/exit triggers
5

Market Microstructure & Order Book Dynamics

Explores how orders actually execute, bid-ask spread formation, order book imbalance, and high-frequency liquidity dynamics that affect signal execution.

  • Study Limit Order Books (LOB), matching engines, and price discovery
    ~6hLearn1 resource

    Ignoring microstructure dynamics leads to signals that appear profitable on daily bars but lose money immediately upon execution.

    You'll learn

    • Limit Order Book (LOB) — ledger of outstanding limit buy and sell orders organized by price level
    • Order Book Imbalance (OBI) — ratio of bid vs ask volume at best quotes predicting short-term price movement
    • Adverse Selection — risk that your passive order fills only when incoming market participants possess superior information

    Learn the mechanics of continuous double auctions, level 1/2/3 market depth, price-time priority matching, maker-taker fees, and hidden liquidity. Microstructure governs the boundary where theoretical alpha meets execution friction.

    Done when: you can construct a Limit Order Book state from an raw message stream (Add, Cancel, Fill) and compute Level-2 depth imbalance.

    How to work through it

    1. Study limit orders, market orders, cancel messages, and time-in-force
    2. Analyze order book depth profiles, depth imbalance, and book skew
    3. Examine maker-taker fee structures, rebates, and exchange latency
    4. Model queue position dynamics and adverse selection on passive limit orders
  • Study market impact, Kyle's Lambda, and optimal execution algorithms
    ~6hLearn

    Alpha capacity is strictly constrained by transaction costs and market impact; a researcher must know when a strategy's size destroys its edge.

    You'll learn

    • Square-Root Impact Law — empirical rule stating price impact is proportional to square root of traded volume relative to daily volume
    • Implementation Shortfall — difference between decision price and final average execution price including fees and impact
    • Almgren-Chriss Framework — mathematical model determining optimal trade schedule to balance market impact vs risk

    Understand permanent vs temporary market impact, square-root law of market impact, and institutional execution algorithms like TWAP, VWAP, and Almgren-Chriss optimal liquidation models.

    Done when: you can analytically solve the Almgren-Chriss optimization problem to find the optimal execution trajectory balancing market impact against inventory risk.

    How to work through it

    1. Derive Kyle's Lambda (price impact of order flow) and Glosten-Milgrom model
    2. Study the empirical Square-Root Law of market impact
    3. Formulate the Almgren-Chriss framework balancing volatility risk and price impact
    4. Analyze Implementation Shortfall calculation on historical institutional trades
  • Build an LOB reconstruction engine and calculate Order Flow Toxicity (VPIN)
    ~6hBuild

    Provides direct experience manipulating granular microstructure data and building features derived from market plumbing.

    You'll learn

    • VPIN — Volume-Synchronized Probability of Toxicity measuring informed trader presence from order flow asymmetry
    • Micro-Price — fair price estimate adjusting mid-price for volume imbalance at best bid and ask

    Process a tick-by-tick market depth feed in Python to rebuild the order book state and compute Volume-Synchronized Probability of Toxicity (VPIN) and high-frequency micro-price signals.

    Done when: the script processes 1 million raw tick messages, computes rolling VPIN, and demonstrates statistically significant predictive power for imminent volatility spikes.

    How to work through it

    1. Parse raw tick message logs into bid/ask order book price levels
    2. Calculate micro-price weighted by volume at top-of-book levels
    3. Implement trade classification using Lee-Ready tick test
    4. Compute volume-clock bucketed VPIN metrics over time
6

Cross-Sectional Factor Modeling & Machine Learning for Alpha

Covers systematic factor extraction (Fama-French, Barra models), multi-factor cross-sectional regressions, and modern machine learning adapted specifically for low signal-to-noise financial data.

  • Study Fama-French, Barra risk models, and cross-sectional regressions
    ~6hLearn1 resource

    Institutional quantitative research measures alpha exclusively after hedging out known systematic risk factor exposures.

    You'll learn

    • Fama-MacBeth Regression — two-step regression method used to estimate risk premia while accounting for cross-sectional correlation
    • Information Coefficient (IC) — Spearman rank correlation between factor predictions and forward asset returns
    • Idiosyncratic Risk — asset-specific risk remaining after removing systematic factor exposures

    Learn how equity returns decompose into systematic risk factors (Value, Momentum, Quality, Size, Volatility) versus idiosyncratic alpha. Master Fama-MacBeth two-pass regressions to test factor risk premia.

    Done when: you can derive the Fama-MacBeth estimator and explain why standard pooled OLS yields understated standard errors due to cross-sectional correlation.

    How to work through it

    1. Study CAPM, Arbitrage Pricing Theory (APT), and multi-factor expansions
    2. Examine fundamental factor models (Barra) vs statistical factor models (PCA)
    3. Derive Fama-MacBeth two-pass cross-sectional regression methodology
    4. Understand Information Coefficient (IC) and Information Ratio (IR)
  • Learn ML regularization, tree models, and specialized cross-validation for finance
    ~6hLearn1 resource

    Applying standard machine learning workflows without financial cross-validation guarantees massive overfitted results.

    You'll learn

    • Purged Cross-Validation — eliminating training samples whose labels overlap with test evaluation windows
    • Embargoing — dropping training samples immediately following test samples to eliminate autoregressive memory leakage
    • Lasso Regularization — L1 norm penalty that drives irrelevant factor coefficients to exact zero

    Study Ridge, Lasso, ElasticNet, and Gradient Boosted Trees (LightGBM). Learn why standard K-Fold CV fails catastrophically in finance due to serial correlation and leakage, and master Purged & Embargoed Cross-Validation.

    Done when: you can implement Purged K-Fold Cross-Validation with an embargo window and explain why it prevents information leakage across overlapping label periods.

    How to work through it

    1. Analyze L1 (Lasso) vs L2 (Ridge) shrinkage in high-collinearity factor universes
    2. Study Gradient Boosted Decision Trees (LightGBM/XGBoost) for tabular financial data
    3. Analyze how overlapping return labels cause information leakage across train/test splits
    4. Derive Purged Group Time-Series Cross-Validation and Embargo mechanics
  • Build a cross-sectional multi-factor scoring and evaluation pipeline
    ~7hBuild

    Constructs the standard toolset used by quantitative research teams to vet new alpha candidates before portfolio construction.

    You'll learn

    • Winsorization — statistical transformation clipping extreme outliers to specified percentile bounds
    • Sector Neutralization — demeaning factor scores within industry sectors to eliminate uncompensated sector bets
    • Quantile Monotonicity — test verifying that higher factor quantiles produce strictly monotonically increasing returns

    Construct an end-to-end Python pipeline that ingests a universe of 500 stocks, calculates normalized fundamental and technical factors (z-scoring and winsorization), trains a regularized model, and generates ranked fractile returns.

    Done when: the pipeline calculates rolling rank IC, factor decay curves, and quintile spread returns for 5 distinct alpha factors over a 5-year out-of-sample window.

    How to work through it

    1. Generate raw factor values: 12-month momentum, short-term reversal, earnings yield, volatility
    2. Apply cross-sectional winsorization (3 sigma) and sector-neutral z-scoring
    3. Compute rolling Spearman rank Information Coefficient (IC) against 5-day forward returns
    4. Evaluate top-minus-bottom quintile spread Sharpe ratios and monotonic bucket performance
7

Statistical Rigor & Overfitting Prevention

Teaches the mathematical mechanisms that prevent self-deception: multiple hypothesis testing corrections, backtest overfitting probability, and synthetic data generation.

  • Study Multiple Testing Corrections and False Discovery Rates
    ~6hLearn1 resource

    Most published and in-house backtests fail in live trading because researchers treat the best of many tried variants as a single test.

    You'll learn

    • False Discovery Rate (FDR) — expected proportion of false positive discoveries among all rejected hypotheses
    • Deflated Sharpe Ratio (DSR) — Sharpe ratio adjusted downwards for sample length, skewness, kurtosis, and number of trials
    • Family-Wise Error Rate (FWER) — probability of making one or more Type I errors among all hypotheses tested

    Learn the mathematics of data snooping and selection bias. When testing thousands of parameters or signals, standard p-values produce guaranteed false positives. Master Bonferroni, Holm-Bonferroni, and Benjamini-Hochberg False Discovery Rate (FDR).

    Done when: you can analytically prove why testing 100 independent random noise signals at alpha=0.05 yields a ~99.4% probability of finding at least one 'statistically significant' false signal.

    How to work through it

    1. Calculate Family-Wise Error Rate (FWER) under multiple independent tests
    2. Implement Benjamini-Hochberg algorithm for False Discovery Rate control
    3. Analyze Bailey and López de Prado's Deflated Sharpe Ratio (DSR)
    4. Study White's Reality Check and Hansen's Superior Predictive Ability test
  • Build a Combinatorially Symmetric Cross-Validation (CSCV) and PBO Engine
    ~6hBuild

    Gives you a quantitative metric to verify whether a backtest's performance is driven by genuine signal or selection bias.

    You'll learn

    • Probability of Backtest Overfitting (PBO) — probability that a strategy selected as optimal in-sample ranks below median out-of-sample
    • CSCV — cross-validation method generating symmetric combinations of training and testing slices

    Implement Combinatorially Symmetric Cross-Validation (CSCV) to calculate the Probability of Backtest Overfitting (PBO). You will generate synthetic backtest matrix trials and compute the distribution of rank degradation out-of-sample.

    Done when: your code accepts an N-strategy return matrix, runs CSCV permutations, and outputs the exact PBO percentage and stochastic dominance curves.

    How to work through it

    1. Create sub-matrix splitting partitions for time series matrix
    2. Train and rank candidate model configurations across combinatorial training subsets
    3. Evaluate performance ranking deterioration on paired out-of-sample test splits
    4. Compute probability that optimal in-sample strategy performs worse than median out-of-sample
8

Portfolio Construction, Risk Budgeting & Optimization

Covers how to turn raw signal forecasts into optimal position weights while controlling factor risk, transaction cost penalties, and covariance instability.

  • Study Markowitz Mean-Variance, Black-Litterman, and Hierarchical Risk Parity
    ~6hLearn1 resource

    Raw signals are useless without an allocation engine that prevents single-asset concentration and accounts for parameter estimation error.

    You'll learn

    • Ledoit-Wolf Shrinkage — optimal linear combination of sample covariance matrix and structured target to reduce estimation noise
    • Hierarchical Risk Parity (HRP) — portfolio allocation method using hierarchical clustering that does not require matrix inversion
    • Black-Litterman Model — Bayesian framework combining market equilibrium returns with subjective quantitative views

    Learn why unconstrained sample covariance matrices produce extreme, unstable portfolio weights (Markowitz 'error maximization'). Study shrinkage estimators (Ledoit-Wolf), Black-Litterman Bayesian views, and tree-based clustering approaches (Hierarchical Risk Parity).

    Done when: you can mathematically derive the Ledoit-Wolf shrinkage formula and explain how graph-based clustering in HRP avoids matrix inversion.

    How to work through it

    1. Derive analytical Mean-Variance efficient frontier with risk aversion lambda
    2. Analyze condition number explosion and noise in empirical sample covariance matrices
    3. Study Ledoit-Wolf shrinkage towards constant correlation target
    4. Formulate Hierarchical Risk Parity (HRP) using tree clustering of correlation distances
  • Build an institutional portfolio optimizer with transaction cost penalties in CVXPY
    ~6hBuild

    Equips you with production-grade portfolio construction capabilities that mirror how real multi-asset quant funds rebalance daily.

    You'll learn

    • CVXPY — Python library for modeling convex optimization problems with standard solvers (ECOS, OSQP)
    • Turnover Constraint — limit on the total fraction of portfolio value traded in a given rebalance window
    • Factor Neutrality — constraint forcing portfolio exposures to specific risk factors (e.g. market beta, size) to zero

    Construct a convex portfolio optimization engine using CVXPY. Incorporate factor neutrality constraints, maximum position bounds, turnover constraints, and quadratic market impact cost penalties.

    Done when: the optimizer processes 500 asset forecasts, respects sector-neutral and turnover constraints, and outputs trade rebalance vectors that outperform equal-weighted benchmarks net of costs.

    How to work through it

    1. Formulate the objective function in CVXPY with expected alpha, risk penalty, and transaction costs
    2. Add hard constraints: dollar neutrality, maximum weight (2%), beta neutrality, sector limits
    3. Calculate covariance matrix with Ledoit-Wolf shrinkage
    4. Run backtested rebalancing simulation across 3 years of daily factor scores
9

Continuous-Time Stochastic Calculus & Derivative Signals

Covers Ito's Lemma, Brownian motion, Black-Scholes-Merton PDE, and the volatility surface to analyze options-implied signals and volatility arbitrage.

  • Master Brownian Motion, Stochastic Differential Equations, and Ito's Lemma
    ~7hLearn1 resource

    Continuous-time stochastic calculus provides the theoretical mathematical foundation for option pricing, volatility modeling, and continuous risk management.

    You'll learn

    • Ito's Lemma — change of variables formula for stochastic processes with a second-order derivative term
    • Geometric Brownian Motion (GBM) — continuous-time stochastic process where the logarithm of the variable follows Brownian motion
    • Quadratic Variation — sum of squared increments of a process, which is non-zero and equal to time for Brownian motion

    Study Wiener processes, geometric Brownian motion (GBM), and quadratic variation. Derive Ito's Lemma and understand how stochastic calculus differs from standard calculus due to non-zero quadratic variation terms.

    Done when: you can use Ito's Lemma to derive the stochastic differential equation for d(ln S_t) where S_t follows Geometric Brownian Motion.

    How to work through it

    1. Define standard Brownian motion properties and filtration
    2. Prove (dW_t)^2 = dt in mean square limit
    3. Derive 1D and multi-dimensional Ito's Lemma from Taylor expansion
    4. Solve the Ornstein-Uhlenbeck and Geometric Brownian Motion SDEs analytically
  • Study the Volatility Surface, Greeks, and Variance Risk Premium (VRP)
    ~6hLearn

    The options market contains forward-looking probability distributions that provide powerful predictive signals for underlying spot assets.

    You'll learn

    • Variance Risk Premium (VRP) — structural compensation earned by option sellers for providing insurance against volatility spikes
    • Implied Volatility Surface — 3D surface plotting option implied volatility across strike prices and maturities
    • Delta Hedging — trading underlying asset to eliminate directional price risk of an options position

    Derive the Black-Scholes-Merton PDE via delta-hedging arbitrage. Study implied volatility smile/skew, local volatility (Dupire), and the Variance Risk Premium (difference between implied and realized volatility).

    Done when: you can explain the empirical source of the Variance Risk Premium and derive analytical Black-Scholes Greeks (Delta, Gamma, Vega, Theta).

    How to work through it

    1. Derive Black-Scholes PDE using no-arbitrage replicating portfolios
    2. Compute analytical formulas for Delta, Gamma, Vega, and Theta
    3. Study implied volatility smiles and sticky-strike vs sticky-delta regimes
    4. Formulate the Variance Risk Premium (VRP = IV - RV) as a systematic harvesting strategy
  • Build a Volatility Arbitrage & Implied Volatility Surface Extractor
    ~6hBuild

    Demonstrates capability in non-linear financial modeling and derivatives-based quantitative research.

    You'll learn

    • SVI Model — parametric formulation that fits implied volatility smiles while ensuring no-arbitrage conditions
    • Newton-Raphson Method — iterative root-finding algorithm used to solve for implied volatility from market prices

    Construct a Python engine that calibrates implied volatility surfaces from real market option chains using SABR or SVI models, calculates the Variance Risk Premium, and generates volatility trading signals.

    Done when: the script calibrates an arbitrage-free volatility smile to options data and computes historical PnL from an empirical delta-hedged VRP harvesting strategy.

    How to work through it

    1. Ingest historical options chain data across multiple strikes and expiries
    2. Invert Black-Scholes formula using Newton-Raphson to extract implied volatility
    3. Fit SVI (Stochastic Volatility Inspired) parametric model to eliminate butterfly arbitrage
    4. Simulate delta-hedged short variance straddle strategy and analyze drawdown characteristics
10

Institutional-Grade Backtesting System Architecture

Brings together data feeds, signal generation, execution modeling, and portfolio optimization into an event-driven, production-ready research backtest framework.

  • Design a modular, leak-free event-driven backtesting engine in Python
    ~7hBuild1 resource

    Vectorized backtests are prone to subtle lookahead leakage; event-driven simulation enforces true point-in-time execution realism.

    You'll learn

    • Event-Driven Architecture — software design where flow is determined by sequential generation and consumption of events
    • Point-in-Time Data — dataset containing only information that was known and available at that exact historical moment
    • Lookahead Bias — systematic error where information from the future is inadvertently used in past trading decisions

    Architect an event-driven backtester featuring distinct event queues (DataEvent, SignalEvent, OrderEvent, FillEvent). Ensure timestamp synchronization eliminates point-in-time and lookahead leakage.

    Done when: the engine accurately processes streaming historical bar events, manages simulated order book fills with latency lag, and tracks cash balances without lookahead bias.

    How to work through it

    1. Design abstract base classes for DataHandler, Portfolio, ExecutionHandler, and Strategy
    2. Implement event loop managing sequential event progression through time
    3. Add simulated order execution queue introducing configurable 1-bar execution latency
    4. Verify that strategies cannot query data from timestamps t >= current_time
  • Integrate slippage, non-linear market impact, and borrow fees into backtest
    ~5hBuild

    A quantitative researcher must be paranoid about frictional costs; naive zero-cost backtests fool only the researcher.

    You'll learn

    • Hard-to-Borrow (HTB) Fee — annualized financing rate charged to borrow shares required to maintain short positions
    • Gross vs Net Sharpe — performance ratio before vs after subtracting slippage, commissions, impact, and financing

    Upgrade the execution module with Almgren-Chriss square-root price impact models, exchange maker/taker fee tiers, and short-selling borrow costs (hard-to-borrow fees and availability).

    Done when: running a backtest on a small-cap momentum strategy demonstrates how realistic borrow fees and square-root impact convert a naive positive Sharpe into a realistic negative Sharpe.

    How to work through it

    1. Implement square-root market impact function based on trade size relative to average daily volume
    2. Model borrow fee schedules for short positions with utilization-based rates
    3. Add exchange fee schedules with maker rebates vs taker costs
    4. Generate detailed attribution reports comparing gross vs net returns
11

End-to-End Quantitative Research Project & Whitepaper

Synthesizes all skills by conducting an original, institutional-grade quantitative research investigation, writing a formal scientific paper, and open-sourcing the reproducible codebase.

  • Formulate a falsifiable market hypothesis and design experimental study
    ~5hApply

    Top quant funds hire researchers who think like scientists with strong financial intuition, not brute-force data miners.

    You'll learn

    • Falsifiability — capacity for a hypothesis or theory to be proven false through empirical observation
    • Economic Rationale — fundamental structural reason explaining why a persistent alpha premium exists

    Select an uncrowded market anomaly or alternative data signal (e.g. ETF flow pressure, cross-asset lead-lag, supply chain momentum, or funding rate arbitrage). Define exact null and alternative hypotheses before examining data.

    Done when: you produce a 2-page research specification document detailing the economic hypothesis, data requirements, factor construction formulas, and planned falsification tests.

    How to work through it

    1. Formulate an economic mechanism explaining why market participants cannot immediately arbitrage the anomaly
    2. Define explicit mathematical formulas for factor computation
    3. Specify the investment universe, rebalance frequency, and benchmark
    4. Establish out-of-sample holdout datasets and falsification checks
  • Execute the empirical study, backtest, stress testing, and Deflated Sharpe checks
    ~8hBuild

    Generates the empirical results and statistical proof required to back up the research claims.

    You'll learn

    • Stress Testing — evaluating strategy resilience and drawdown severity during historical market crises
    • Tear Sheet — consolidated statistical dashboard displaying risk, return, drawdown, and factor exposures

    Run the complete pipeline: data ingestion, factor scoring, risk neutralization, portfolio optimization, event-driven backtesting, and multiple testing adjustments (DSR, PBO, CSCV).

    Done when: the pipeline executes end-to-end, producing tear sheets containing full return metrics, factor attribution, regime breakdown (bull/bear/high-vol), and Deflated Sharpe Ratio calculation.

    How to work through it

    1. Generate clean factor scores across the full historical universe
    2. Run Purged Cross-Validation and extract out-of-sample predictions
    3. Execute backtester with realistic transaction costs and borrow fees
    4. Run stress tests across historical crisis periods (2008, 2020) and calculate Deflated Sharpe Ratio
  • Author a formal Quantitative Research Whitepaper and clean GitHub repository
    ~8hApply1 resource

    This paper and codebase serve as your primary demonstrable evidence of quantitative research competence for recruitment teams.

    You'll learn

    • Reproducible Research — standards ensuring any third party can replicate published empirical findings from raw code and data
    • LaTeX — document preparation system standard for scientific and mathematical publishing

    Write an institutional-standard research paper in LaTeX. Include abstract, literature review, economic intuition, mathematical methodology, empirical results, cost sensitivity analysis, and failure mode discussion. Package the codebase with clean unit tests.

    Done when: you publish a clean, peer-reviewable LaTeX PDF paper alongside a fully reproducible GitHub repository with documentation and continuous integration tests.

    How to work through it

    1. Draft LaTeX paper following Journal of Financial Data Science formatting
    2. Document mathematical proofs for factor construction and risk model
    3. Include full cost-sensitivity tables and out-of-sample decay analysis
    4. Format repository with pytest unit tests, type annotations, and README reproducibility instructions
12

Quantitative Recruitment Preparation & Technical Interviewing

Prepares for the specific assessment hurdles used by quantitative funds: probability brainteasers, mathematical statistics interviews, coding evaluations, and research presentations.

  • Drill quantitative probability puzzles and mental math conditioning
    ~7hPractice2 resources

    Prop trading shops and hedge funds use rapid probability screening as a strict first-round filter.

    You'll learn

    • Kelly Criterion — formula determining optimal wager fraction to maximize long-run capital growth rate
    • Absorbing Markov Chain — state machine where certain states cannot be left once entered, used in probability puzzles

    Practice conditional probability, Markov chains, random walks, expected values, dice/coin games, and betting sizing (Kelly criterion). These questions test clarity under pressure in initial technical phone screens.

    Done when: you can solve 30 standard quant interview probability puzzles within 5 minutes each with zero mathematical errors.

    How to work through it

    1. Study conditional probability and Bayes rule puzzle variations
    2. Master Markov chain absorbing states and expected step calculations
    3. Practice continuous probability puzzles (stick breaking, geometric distributions)
    4. Drill Kelly Criterion calculation for optimal bet sizing under biased coin flips
  • Conduct timed take-home research project simulations
    ~8hApply

    Take-home data challenges are the primary hurdle between the initial phone screen and an onsite superday offer.

    You'll learn

    • Take-Home Data Challenge — standard hiring assessment where candidates build a signal model from unseen data under tight deadlines

    Simulate take-home data challenges typical of quant research hiring: receiving a raw, anonymized dataset with 48 hours to clean it, discover a predictive signal, backtest it, and submit a 2-page report.

    Done when: you complete a self-timed 48-hour challenge, producing a working Python script, signal validation metrics, and an executive research summary.

    How to work through it

    1. Select an unfamiliar tabular financial dataset (e.g. crypto funding, macro indicators)
    2. Set a strict 48-hour timer to conduct full analysis without assistance
    3. Perform exploratory data analysis, stationarity checks, and feature engineering
    4. Deliver an executive slide deck summarizing methodology, Sharpe, drawdown, and capacity
  • Deliver a 45-minute technical research defense to a peer or mentor
    ~4hApply

    Onsite interviews require defending your research methodology before senior quantitative portfolio managers who actively search for flaws.

    You'll learn

    • Research Defense — rigorous oral interview format where a candidate justifies every empirical and mathematical decision in their work

    Prepare a 15-slide technical presentation based on your Phase 11 research paper. Defend your assumptions, cross-validation choices, transaction cost modeling, and failure modes against aggressive probing.

    Done when: you deliver a live 45-minute presentation followed by a 20-minute Q&A defense without faltering on statistical derivations or data handling specifics.

    How to work through it

    1. Build slide deck: Motivation, Data Hygiene, Alpha Extraction, Risk Neutralization, Net Results
    2. Identify the 5 most vulnerable assumptions in your model (e.g. liquidity, market impact, over-fitting risk)
    3. Rehearse concise verbal explanations of complex mathematical derivations
    4. Record presentation or present to a quantitative practitioner, incorporating all critical feedback

How the plan fits together

12 phases in 6 stages. Anything on the same row can be worked on at the same time, and 2 of them can start straight away.

An arrow points from a phase to the work it unlocks: before starting any phase, every phase with an arrow into it has to be finished first.

STARTSTAGE 2STAGE 3STAGE 4STAGE 5STAGE 61Linear Algebra &Multivariable CalculusFoundations3 tasks · ~17h2Probability & MathematicalStatistics3 tasks · ~17h3Python Architecture forScientific Computing &Market Data2 tasks · ~11h4Time Series Econometrics &Signal Extraction3 tasks · ~19h5Market Microstructure &Order Book Dynamics3 tasks · ~18h6Cross-Sectional FactorModeling & MachineLearning for Alpha3 tasks · ~19h7Statistical Rigor &Overfitting Prevention2 tasks · ~12h8Portfolio Construction,Risk Budgeting &Optimization2 tasks · ~12h9Continuous-Time StochasticCalculus & DerivativeSignals3 tasks · ~19h10Institutional-GradeBacktesting SystemArchitecture2 tasks · ~12h11End-to-End QuantitativeResearch Project &Whitepaper3 tasks · ~21h12Quantitative RecruitmentPreparation & TechnicalInterviewing3 tasks · ~19h
Solid arrow
Must be finished before the phase it points to
Dashed arrow
Same rule, but the prerequisite sits more than one stage back

Resources

16 in this plan's library, beyond the links on individual tasks.

Core Literature & Textbooks

Foundational texts in probability, econometrics, and quantitative portfolio management.

  • A Practical Guide to Quantitative Finance Interviews

    Comprehensive problem set covering brainteasers, stochastic calculus, probability, and algorithmic finance questions used by top quantitative funds.

    CreateSpace · Book · ~$30 · Advanced

  • Advances in Financial Machine Learning

    Presents financial data structures, Triple-Barrier labeling, Purged/Embargoed K-Fold CV, and calculations for Probability of Backtest Overfitting.

    wiley.com · John Wiley & Sons · Book · ~$50–$75

  • Analysis of Financial Time Series

    Definitive guide to financial econometrics, covering stationarity, ARCH/GARCH volatility modeling, and cointegration.

    Wiley · Book · ~$100 · Intermediate

  • Analysis of Financial Time Series, Third Edition

    Covers linear ARMA processes, conditional heteroskedasticity (ARCH/GARCH), unit root testing, cointegration, and multivariate factor models.

    faculty.chicagobooth.edu · John Wiley & Sons · Book · ~$95–$130

  • Introduction to Probability, Second Edition

    Builds an intuitive foundation in conditioning, distributions, Markov chains, and limit theorems without measure-theoretic notation.

    stat110.net · Chapman & Hall/CRC Press · Book · Free online / physical ~$90–$100

  • Market Microstructure in Practice

    Provides mathematical formulation of limit order books, optimal execution, and inventory risk models.

    World Scientific · Book · ~$60 · Advanced

  • MIT 18.06 Linear Algebra (Gilbert Strang)

    Essential foundation for vector spaces, projections, eigenvalues, and SVD used throughout quantitative modeling.

    ocw.mit.edu · MIT OpenCourseWare · MIT OpenCourseWare · Free · Beginner

  • Statistical Inference (2nd Edition)

    The standard rigorous treatment of estimation theory, hypothesis testing, and maximum likelihood essential for statistical modeling.

    Cengage Learning · Book · ~$90 · Intermediate

  • Stochastic Calculus for Finance II: Continuous-Time Models

    Delivers a walkthrough of Brownian motion, Itô's formula, the Black-Scholes-Merton PDE, risk-neutral measures, and term-structure modeling.

    link.springer.com · Springer · Book · ~$65–$90 (or free PDF via SpringerLink institution access)

  • Trading and Exchanges: Market Microstructure for Practitioners

    Details limit order books, bid-ask spread decomposition, market impact, adverse selection, and institutional order types.

    global.oup.com · Oxford University Press · Book · ~$95–$150

Open Source Toolkits & Frameworks

Essential Python libraries for scientific computing, optimization, and backtesting.

  • CVXPY

    Allows formulation and solving of quadratic programs, factor-risk budget constraints, transaction-cost penalized objectives, and long-short portfolio rebalances.

    cvxpy.org · Stanford University / Open-source community · Toolkit / Library · Free (Apache 2.0)

  • NautilusTrader

    Event-driven algorithmic trading engine featuring nanosecond timestamps, order book matching simulation, and parity between backtesting and live execution.

    nautilustrader.io · Nautech Systems Pty Ltd · Framework / Backtesting Engine · Free (LGPL-3.0)

  • Polars

    Provides lazy execution, multithreaded vectorized queries, and out-of-core streaming to process multi-gigabyte tick and bar Parquet datasets.

    pola.rs · Polars open-source project / Polars BV · Toolkit / Library · Free (MIT License)

  • vectorbt

    High-performance vectorized backtesting engine designed for rapid signal testing and parameter optimization across large universes.

    vectorbt.dev · vectorbt Project · Library · Free core library · Intermediate

Data Platforms & Competitions

Platforms providing financial data streams and quantitative research challenges.

  • Numerai

    Supplies standardized, obfuscated global equity datasets to build machine learning models generating market-neutral alpha predictions scored via out-of-sample correlation.

    numer.ai · Numerai LLC · Data Platform & Competition · Free (optional cryptocurrency staking)

  • QuantConnect

    Provides point-in-time multi-asset market data with split/dividend/survivorship adjustments and a cloud research environment for strategy backtesting.

    quantconnect.com · QuantConnect Corporation · Research & Simulation Platform · Free tier available; monthly paid subscriptions for higher compute and live nodes