Covariance Matrix Estimation

Estimating Covariance Matrices - Litterman, Winkelmann 1998
A wel-conditioned estimator for large-dimensional covariance matrices Ledoit, Wolf 2001
Evnonential weighting and random matrix theory based filtering of financial cOvariance matrices Pafka et al 20O4
Seven sins in portfolio optimization - Schmelzer, Hause 2013
60 vears of portfolio optimization: practical challenges and current trends - Kolm et al 2014
Cleaning Correlation Matrices - Bouchaud, Potters 2016

returns and volatility are two key components in portfolio construction, while return is not path dependent, volatility is
exponential decay: overweighting more recent returns in estimation of volatilities and correlations allows portfolio reacts faster to market behavior
observation periods: to reduce turnover and mitigate issues of observations at different times during the day, there is value in observing overlapping periods on a daily basis
stability of correlations: the key consideration in risk management. several methods include
- eigenvalue clipping (keep larger eigenvalues only)
- matrix shrinkage: integrate prior estimate while increase stability of the covariance matrix

Portfolio Optimization