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The course is fast paced. The prerequisites for the course are
- Linear algebra: matrix/vector notation and manipulations, trace, determinant, eigenvectors, eigenvalues
- Multivariate calculus: derivatives, integrals, Taylor expansions
- Statistics: basic concepts of distributions, probability density function, cumulative distribution function
In order to check if the course suits your background and expectations, it is strongly recommended that you become familiar with Section A.5 (pp 475-480), from Risk and
Asset Allocation which you can find here.
Also, please follow through these examples, complete with solutions, and make sure you feel comfortable with those tools.
No prior MATLAB knowledge is required for attending ARPM'09.
Day 1 - Monday, 17 August 2009
Opening Address (8:30 - 8:40): Dr. Kathleen M. Waldron, President of Baruch College
Morning session (8:40-12:30)
Quest for Invariance
- Invariance and the random walk
- Equities: log-returns
- Fixed-income: changes in yield to maturity
- Derivatives: (log) changes in vol. surface
- Advanced dynamics in discrete time
- Autocorrelation and AR(1) processes
- ARMA processes and Wold's theorem
- Long memory: fractional integration
- Volatility clustering: GARCH
- Advanced dynamics in continuous time
- Random walk: Levy processes
- Autocorrelation: Ornstein-Uhlenbeck
- Long memory: fractional Brownian motion
- Volatility clustering: stochastic volatility
- Volatility clustering: subordination
- Multivariate dynamics
- Copula-marginal factorization
- Multivariate Ornstein-Uhlenbeck process
- Cointegration
- Statistical arbitrage
Afternoon session (14:00-16:00)
Price Modeling
- Projection of invariants to the investment horizon
- Analytical projection: convolution
- Numerical projection by FFT
- Numerical projection by simulations
- Pricing of invariants at the investment horizon
- Analytical: log-distributions
- Numerical: scenario pricing (Monte Carlo/historical)
- Full pricing vs Taylor approximation
- Taylor approximation: theta-delta/vega-gamma
- Taylor approximation: carry-duration-convexity
Afternoon session II (16:00-18:00)
Review
Day 2 - Tuesday, 18 August 2009
Morning session (8:30-12:30)
Factor Modeling
- Dimension reduction
- Generalized r-square
- Explicit factors
- Implicit factors
- Statistical factors
- Explicit factors examples
- Capital Asset Pricing Model
- Arbitrage Pricing Theory
- Fama-French factors
- Statistical factors examples
- Principal component analysis of the swap market
- Level-slope-butterfly interpretation of the components
- Continuum limit: Fourier basis and main frequencies
- Factor modeling pitfalls
- Estimation vs interpretation
- Time-horizon beta
- "Factors on demand"
Afternoon session (14:00-18:00)
Review
Day 3 - Wednesday, 19 August 2009
Morning session (8:30-12:30)
Estimation I
- Estimators
- General definitions
- Evaluation: bias, inefficiency, error
- Stress-testing
- Generalized p-values, generalized t-statistics
- Multivariate non-parametric estimators
- Sample quantile and order statistics.
- Sample mean/covariance and best-fitting ellipsoid
- Sample factor loadings, betas, and OLS
- Multivariate maximum-likelihood estimators
- Normal hypothesis: sample estimators
- Non-normal hypothesis: fat tails and outlier rejection
- Shrinkage estimators
- Stein mean
- Ledoit-Wolf covariance
Afternoon session (14:00-16:00)
Estimation II
- Robust estimators
- 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
- EM algorithm
- ML marginalization
Afternoon session II (16:00-18:00)
Review
Day 4 - Thursday, 20 August 2009
Morning session (8:30-12:30)
Risk Management I
- Investor's objectives
- Total return
- Benchmark allocation
- Net profits
- Portfolio evaluation
- Stochastic dominance
- Satisfaction indices
- Non-dimensional indices
- Sharpe ratio
- Omega
- Sortino ratio
- Kappa
- Expected utility and certainty-equivalent
- Analytical solutions: mean-variance as satisfaction
- Numerical solutions
- Diversification
- Review of common definitions
- Conditional principal portfolios
- Effective number of bets
Afternoon session (14:00-16:00)
Risk Management II
- Quantiles and value at risk (VaR)
- 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
- Expected shortfall (ES) and conditional value at risk (CVaR)
- Contribution to ES from securities and from factors
- Spectral measures of performance
Afternoon session II (16:00-18:00)
Review
Day 5 - Friday, 21 August 2009
Morning session (8:30-12:30)
Portfolio Management I
- Constrained optimization: computationally tractable problems
- Linear and quadratic programming
- Second order and semi-definite cone programming
- Two-step heuristics
- Analytical mean-variance: two-fund theorem
- Numerical mean-variance: quadratic programming
- Mean-CVaR and alternative trade-offs
- Benchmark vs. total-return portfolio management
- Expected outperformance, tracking error, information ratio
- Analytical mean-variance solutions in total-return coordinates
- Analytical mean-variance solutions in relative-return coordinates
- Pitfalls of the mean-variance approach
Afternoon session (14:00-16:00)
Portfolio Management II
- Estimation risk: allocation as a decision
- Opportunity cost as loss of an estimator
- Stress testing
- Simple allocation techniques
- Prior allocation and high efficiency
- Sample-based allocation: unbiasedness and leverage of estimation error
Afternoon session II (16:00-18:00)
Review
Day 6 - Saturday, 22 August 2009
Morning session (8:30-12:30)
Portfolio Management III
- Robust allocation
- Box uncertainty sets
- Elliptical uncertainty sets (second-order cone programming)
- Black-Litterman and enhancements
- Views on market parameters
- Views on the market realizations
- Black-Litterman for derivatives
- Beyond Black-Litterman
- Non-normal markets
- Non-linear views
- Generalized stress-testing
- Ranking allocation
Afternoon session (14:00-16:00)
Portfolio Management IV
- Multivariate Bayesian estimation
- Theoretical background
- Analytical solutions: Normal-Inverse Wishart model
- Numerical solutions: Monte Carlo Markov Chains
- Bayesian allocation
- Predictive return allocation
- Classical-equivalent allocation
Afternoon session II (16:00-18:00)
Review
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