Morning Session (8:30-12:30)
Multivariate Statistics

Representations of distributions
- analytical (pdf, cdf, quantile, cf)
- Monte Carlo simulations

Copula-marginal factorization
- marginals/grades
- pdf, cdf, simulations of copulas
- special copulas

Dependence/concordance statistics
- Schweizer-Wolff measure
- Kendall tau
- Spearman rho

Summary statistics
- location-dispersion ellipsoid
- principal component factorization
- higher order statistics

Correlation: theory, practice and pitfalls

Multivariate distributions for the markets
- (matrix-variate) normal
- Student t and elliptical
- Log-distributions
- Wishart distribution
- Order statistics
- Mixture distributions

Afternoon Session (14:00-18:00)
Multivariate Estimation

Estimators: definition and evaluation
- loss, bias, inefficiency, error
- generalized hypothesis testing

Non-parametric estimators
- order statistics and VaR estimator
- sample mean/covariance: best-fitting
  ellipsoid
- sample factor loadings: ordinary
  least squares

Multivariate MLE: location, scatter, loadings
- normal hypothesis: sample
  estimators
- non-normal hypothesis: outlier
  rejection

Multivariate shrinkage: location,
scatter, loadings
- Stein mean
- Ledoit-Wolf covariance

Multivariate robust: location, scatter, loadings
- assessing robustness: the influence
  function
- M-robust estimators
- outlier detection and high-breakdown
  ellipsoid

Multivariate Bayesian: location, scatter, loadings
- analytically tractable examples
- numerical techniques

Missing observations and unbalanced panels
- EM algorithm
- ML marginalization

Morning Session (8:30-12:30)
Market Modeling

The quest for invariance: i.i.d. processes
- equities: log-returns
- fixed-income: changes in yield to
  maturity
- derivatives: changes in ATM implied
  volatility

Advanced dynamics
- Levy processes
- ARMA, long-memory processes,
  self-similarity
- GARCH, stochastic volatility,
  subordination
- multivariate generalizations

Projection to horizon: the FFT technique

Pricing
- analytical
- second-order (gamma/convexity)
- full Monte Carlo

Dimension reduction
- Principal component analysis
- Explicit factors

Afternoon Session (14:00-18:00)
Risk Management

Dimension reduction, notable examples
- Capital Asset Pricing Model
- Multi-factors models
- PCA of the swap market

Investor’s objectives
- Total return
- Benchmark allocation
- Net profits

Global portfolio evaluation: stochastic dominance

Summary portfolio evaluation: satisfaction
- non-dimensional indices (Sharpe,
  info ratio)
- expected utility and certainty-
  equivalent
- quantiles and value at risk (VaR)
- coherent measures and exp. shortfall
  (CVaR)
- spectral measures of performance

Volatiliy/VaR/CVaR/Risk decomposition
- elliptical markets: semi-analytical
- generic markets: Monte Carlo
  panel smoothing

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

Mean-variance optimization
- analytical: two-fund theorem
- numerical: quadratic programming
- pitfalls of the mean-variance
  approach

Total return vs. benchmark allocation

Market asymmetries: mean-CVaR optimization

Estimation risk: allocations as decisions
- opportunity cost
- allocation decisions evaluated as
  estimators

Simple allocation techniques
- general equilibrium/benchmark
  implied allocation
- prior allocation
- sample-based allocation

Afternoon Session (14:00-18:00)
Portfolio Management II

Bayesian allocation
- predictive return
- classical-equivalent

Black-Litterman allocation
- views on parameters
- views on market

Beyond Black-Litterman: non-normal markets

Robust allocation (SOCP)
- elliptical uncertainty sets
- box uncertainty sets

Robust/Bayesian allocation

Liquidity issues
- trading costs (fixed, execution,
  opportunity)
- implementation shortfall: temporary
  vs permanent impact
- optimal execution of one-security
  trades
- trading portfolios: the multivariate
  case