ARPM Bootcamp - Program

One-week, Heavily Quantitative, Omni-Comprehensive Buy-side Training

    Overview of the Bootcamp's logistic, pricing, audience, charity, etc, see here

    The Advanced Risk and Portfolio Management Bootcamp provides in-depth understanding of buy-side modeling from the foundations to the most advanced statistical and optimization techniques, in 6 intensive days of theory and MATLAB live examples and exercises:

  • Market modeling: random walk, ARMA, GARCH, Levy, long memory, stochastic volatility
  • Multivariate statistics: non-parametric, non-normal MLE, shrinkage, robust, Bayesian estimation; copula/marginal factorization; location-dispersion ellipsoid
  • Factor modeling: theory and pitfalls of time-series and cross-sectional factor models, CAPM, APT, principal components analysis, random matrix theory
  • Pricing: full evaluation, Greeks, stress-matrix interpolation; analytical, Monte Carlo, historical
  • Risk analysis: diversification, stochastic dominance, expected utility, Sharpe ratio, Omega, Kappa, Sortino, value at risk, expected shortfall, coherent and spectral measures
  • Portfolio construction: robust/SOCP optimization, shrinkage/Bayesian allocations, Black-Litterman and beyond; transaction costs, liquidity, market impact; statistical arbitrage; convex/concave dynamic strategies, CPPI, delta-replication


  • Day 1 - Monday, 11 August 2014

    Morning session: Intro/Quest for Invariance (8:30-12:30)

    • »P vs Q: the worlds of quantitative finance (Publication)
    • »The "Prayer": modular steps of ARPM (Publication)
      - P1: Quest for Invariance
      - P2: Estimation
      - P3: Projection
      - P4: Pricing
      - P5: Aggregation
      - P6: Attribution
      - P7: Evaluation
      - P8: Optimization
      - P9: Execution
      - P10: Ex-Post Analysis
    • »Invariance and the random walk (Textbook)
      - Equities: log-returns3
      - Fixed-income: changes in yield to maturity
      - Derivatives: (log) changes in vol. surface
    • »Advanced dynamics in discrete time (Publication)
      - Autocorrelation and AR(1) processes
      - ARMA processes and Wold's theorem
      - Long memory: fractional integration
      - Volatility clustering: GARCH

    Afternoon session: Quest for Invariance/Projection/Pricing (13:30-16:00)

    • »Advanced dynamics in continuous time (Publication)
      - Random walk: Levy processes
      - Autocorrelation: Ornstein-Uhlenbeck
      - Long memory: fractional Brownian motion
      - Volatility clustering: stochastic volatility
      - Volatility clustering: subordination
    • »Projection to the investment horizon (Textbook; Publication; Publication)
      - Analytical projection: convolution
      - Numerical projection by FFT
      - Numerical projection by simulations
    • »Pricing of invariants at the investment horizon (Textbook)
      - Full analytical: log-distributions
      - Full numerical: scenario pricing (Monte Carlo/historical)
      - Taylor approximation: theta-delta/vega-gamma; carry-duration-convexity
      - Stress-matrix approximation

    Review and Exercises (16:00-18:30) (Exercise book)

    Day 2 - Tuesday, 12 August 2014

    Morning session Quest for Invariance II (8:30-12:30)

    • »Multivariate statistics (Textbook)
      - Distribution taxonomy
      - Representations: pdf, cdf, cf, quantiles, scenario/probabilities
      - Spectral theorem / covariance visualization
    • »Copulas (Publication; Publication)
      - Copulas in theory
      - Copulas in practice: Copula-Marginal Algorithm
      - Panic copulas with Fully Flexible Probabilities
    • »Multivariate dynamics (Publication)
      - Multivariate Ornstein-Uhlenbeck process
      - Cointegration
      - Statistical arbitrage
    • »Linear factor models (Textbook; Publication)
      - Systematic-idiosyncratic vs dominant-residua LFM's
      - Distributional r-square
      - Time-series, cross-sectional, statistical/PCA LFM's
      - Factor analysis

    Afternoon session I Factor Models (13:30-16:00)

    • »The five applications of LFM's
      - Multivariate estimation
      - Asset pricing theory
      - Search for alpha
      - Portfolio optimization
      - Risk attribution/hedging
    • »LFM's case studies (Textbook; Publication)
      - Swap market: PCA and Fourier basis
      - Stock market: fundamental, macro, random matrix theory
    • »Factor modeling pitfalls (Publication; Publication)
      - Returns vs. invariants vs. P&L
      - The idiosyncratic myth
      - CAPM vs. APT vs. LFM's
      - Time-horizon beta

    Review and Exercises (16:00-18:30) (Exercise book)


    Day 3 - Wednesday, 13 August 2014

    Morning session Estimation I (8:30-12:30)

    • »Estimators (Textbook)
      - General definitions
      - Evaluation: bias, inefficiency, error
      - Stress-testing
      - Generalized p-values, generalized t-statistics
    • »Multivariate non-parametric estimators (Textbook )
      - Sample quantile and order statistics.
      - Sample mean/covariance and best-fitting ellipsoid
      - Sample factor loadings, betas, and OLS
    • »Multivariate maximum-likelihood estimators (textbook)
      - Normal hypothesis: sample estimators
      - Non-normal hypothesis: fat tails and outlier rejection
    • »Shrinkage estimators (Textbook)
      - Stein mean
      - Ledoit-Wolf covariance

    Afternoon session Estimation II (13:30-16:00)

    • »Robust estimators (Textbook )
      - Assessing robustness: the influence function
      - Huber's "M" robust estimators: location, scatter and betas
      - Outlier detection and high-breakdown estimators
      - Minimum-volume ellipsoid and minimum-covariance determinant
    • »Missing data (Textbook )
      - EM algorithm
      - ML marginalization

    Review and Exercises (16:00-18:30) (Exercise book)

    Day 4 - Thursday, 14 August 2014

    Morning session Risk Management I (8:30-12:30)

    • »Portfolio aggregation (Publication)
      - P&L vs. returns
      - Holdings vs. weights
    • »Investor's objectives (Textbook)
      - Total return
      - Benchmark allocation
      - Net profits
    • »Portfolio attribution (Publication)
      - Bottom up approach
      - Factors on Demand
      - Portfolio-specific factor models
      - Non-Greek few-out-of-many hedging
    • »Portfolio evaluation (Textbook; Textbook)
      - Stochastic dominance
      - Satisfaction indices
    • »Non-dimensional indices
      - Sharpe ratio, Omega, Sortino ratio, Kappa
    • »Diversification (Publication)
      - Review of common definitions
      - Conditional principal portfolios
      - Effective number of bets

    Afternoon session Risk Management II (13:30-16:00)

    • »Expected utility and certainty-equivalent (Textbook)
      - Analytical solutions: mean-variance as satisfaction
      - Numerical solutions
    • »Quantiles and value at risk (VaR) (Textbook)
      - Semi-analytical solutions in elliptical markets
      - Cornish-Fisher approximation
      - Extreme value theory (EVT)
      - Numerical solutions
      - Contribution to VaR from securities and from factors
    • »Coherent measures of performance (Textbook)
      - Expected shortfall (ES) and conditional value at risk (CVaR)
      - Contribution to ES from securities and from factors
      - Spectral measures of performance
    • »Stress Testing for estimation risk (Publication; Publication; Publication)
      - Basic stress testing
      - Panic copulas with Copula-Marginal Algorithm
      - Fully Flexible Probabilities (time/state/entropy pooling conditioning)
      - Fully Flexible Bayesian networks

    Review and Exercises (16:00-18:30) (Exercise book)

    »Gala Dinner (19:00-22:30)

    Day 5 - Friday, 15 August 2014

    Morning session Portfolio Management I (8:30-12:30)

    • »Constrained optimization: computationally tractable problems (Textbook)
      - Linear and quadratic programming
      - Second order and semi-definite cone programming
    • »Two-step heuristics (Textbook)
      - Affine equivariance of expectation and covariance
      - Analytical mean-variance: two-fund theorem
      - Numerical mean-variance: quadratic programming
      - Mean-CVaR and alternative trade-offs
    • »Benchmark vs. total-return portfolio management (Textbook)
      - Expected outperformance, tracking error, information ratio
      - Frontier in total-return coordinates
      - Frontier in relative-return coordinates
    • »Pitfalls of the mean-variance approach (Textbook; Publication)

    Afternoon session Portfolio Management II (13:30-16:00)

    • »Estimation risk: allocation as a decision (Textbook )
      - Opportunity cost as loss of an estimator
      - Stress testing
    • »Simple allocation techniques (Textbook)
      - Prior allocation: efficiency
      - Sample-based allocation: unbiasedness
    • »Robust allocation (textbook )
      - Box uncertainty sets
      - Elliptical uncertainty sets (second-order cone programming)
    • »Re-sampled allocation (Textbook )

    Review and Exercises (16:00-18:30) (Exercise book)

    Day 6 - Saturday, 16 August 2014

    Morning session Portfolio Management III (8:30-12:30)

    • »Multivariate Bayesian estimation (Textbook )
      - Theoretical background
      - Analytical solutions: Normal-Inverse Wishart model
      - Numerical solutions: Monte Carlo Markov Chains
    • »Bayesian allocation (Textbook )
      - Predictive return allocation
      - Classical-equivalent allocation
    • »Tactical portfolio construction (Textbook ; Publication; Publication)
      - Rosenberg-Grinold
      - Black-Litterman
      - Black-Litterman for derivatives
    • »Beyond Black-Litterman (Publication)
      - Entropy Pooling and Fully Flexible Views
      - Non-normal markets
      - Non-linear views
      - Generalized stress-testing
      - Ranking allocation

    Afternoon session Portfolio Management IV (13:30-16:00)

    • »Dynamic allocation strategies (Publication)
      - Convex/concave strategies
      - CPPI
      - Delta-replication
      - Drawdown control
    • »Liquidity (Publication)
      - Transaction costs
      - Market impact
      - Best execution

    Review and Exercises (16:00-18:30) (Exercise book)