**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, 13 July 2015

*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

**(16:00-18:30) (Exercise book)**

*Review and Exercises*## Day 2 - Tuesday, 14 July 2015

*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)

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**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

**(16:00-18:30) (Exercise book)**

*Review and Exercises*## Day 3 - Wednesday, 15 July 2015

*Morning session*

**Estimation I**(8:30-12:30)

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**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

**(16:00-18:30) (Exercise book)**

*Review and Exercises*## Day 4 - Thursday, 16 July 2015

*Morning session*

**Risk Management I**(8:30-12:30)

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**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)

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**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

**(16:00-18:30) (Exercise book) »**

*Review and Exercises***Gala Dinner**(19:00-22:30)

## Day 5 - Friday, 17 July 2015

*Morning session*

**Portfolio Management I**(8:30-12:30)

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**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 )

**(16:00-18:30) (Exercise book)**

*Review and Exercises*## Day 6 - Saturday, 18 July 2015

*Morning session*

**Portfolio Management III**(8:30-12:30)

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**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)

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

**(16:00-18:30) (Exercise book)**

*Review and Exercises*