scholarly journals Robust and Sparse Estimation of the Inverse Covariance Matrix Using Rank Correlation Measures

2016 ◽  
pp. 35-55
Author(s):  
Christophe Croux ◽  
Viktoria Öllerer
Keyword(s):  
Covariance Matrix ◽  
Rank Correlation ◽  
Sparse Estimation ◽  
Inverse Covariance Matrix ◽  
Correlation Measures

Improving Mean Variance Optimization through Sparse Hedging Restrictions

2015 ◽  
Vol 50 (6) ◽  
pp. 1415-1441 ◽  
Author(s):  
Shingo Goto ◽  
Yan Xu
Keyword(s):  
Covariance Matrix ◽  
Factor Model ◽  
Risk Minimization ◽  
Portfolio Risk ◽  
Finite Samples ◽  
Inverse Covariance Matrix ◽  
Out Of Sample ◽  
Nonnegativity Constraints ◽  
Mean Variance ◽  
Equal Weighting

AbstractIn portfolio risk minimization, the inverse covariance matrix prescribes the hedge trades in which a stock is hedged by all the other stocks in the portfolio. In practice with finite samples, however, multicollinearity makes the hedge trades too unstable and unreliable. By shrinking trade sizes and reducing the number of stocks in each hedge trade, we propose a “sparse” estimator of the inverse covariance matrix. Comparing favorably with other methods (equal weighting, shrunk covariance matrix, industry factor model, nonnegativity constraints), a portfolio formed on the proposed estimator achieves significant out-of-sample risk reduction and improves certainty equivalent returns after transaction costs.

Portfolio Optimization using Rank Correlation

2014 ◽  
pp. 1866-1879
Author(s):  
Chanaka Edirisinghe ◽  
Wenjun Zhou
Keyword(s):  
Portfolio Optimization ◽  
Rank Correlation ◽  
Financial Assets ◽  
Risk Averse ◽  
Out Of Sample ◽  
Return Distributions ◽  
Sample Testing ◽  
Correlation Measures ◽  
Computational Properties ◽  
Critical Challenge

A critical challenge in managing quantitative funds is the computation of volatilities and correlations of the underlying financial assets. We present a study of Kendall's t coefficient, one of the best-known rank-based correlation measures, for computing the portfolio risk. Incorporating within risk-averse portfolio optimization, we show empirically that this correlation measure outperforms that of Pearson's in our out-of-sample testing with real-world financial data. This phenomenon is mainly due to the fat-tailed nature of stock return distributions. We also discuss computational properties of Kendall's t, and describe efficient procedures for incremental and one-time computation of Kendall's rank correlation.

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