Instructor: Chris Bemis Random Matrix in Finance Understanding and improving Optimal Portfolios...
-
Upload
darren-mccarthy -
Category
Documents
-
view
213 -
download
0
description
Transcript of Instructor: Chris Bemis Random Matrix in Finance Understanding and improving Optimal Portfolios...
Instructor:Chris Bemis
Random Matrix in FinanceUnderstanding and improving Optimal Portfolios
Mantao Wang, Ruixin Yang, Yingjie Ma, Yuxiang Zhou, Wei Shao, Zhengwei Liu
Purpose and Phenomenon of Project
Finding optimal weights
• Covariance matrix• Marchenko-Pustur to fit data• PCA reconstruction
The impact of near-zero eigenvalues in mean-variance optimization
1
2 3
Data300 stocks 546 weeks
Analysisσ, λ, Q
ReconstructionOptimize mean variance
1 Data
• Bouchard’s idea
• Marchenko-Pustur Law
AnalysisEigenvalue Decomposition of Fully Allocated MVO
Data Selection300 stocks Х 546 weeks
Criterion:
•Return history over 10 years of weekly data
•Biggest market capitalization
DataFiltered Variance-Covariance Matrix
Data Selection300 stocks Х 546 weeks
Why some of eigenvalues close to 0?
•Some original return data are extremely small
•Random effect
•Collinearity among 300 stocks
The impact of near-zero eigenvalues in MVO
2 Analysis of Results
• Empirical distribution of eigenvalues
• Marchenko-Pustur Law
• Analysis
Correlation Matrix
Best Fit M-P Distribution
Filter Noisy Data
Goals:To eliminate the random noise in the covariance matrix
Analysis Procedures
Procedure
1
2
3
4
Correlation Matrix
Distribution of Eigenvalues
Best Fit M-P Distribution
Filter Noisy Data
Analysis Procedures
Analysis Ideas
Random & Not Random Marchenko-Pastur Law
Analysis Ideas
Analysis Minimization
Analysis Minimization
Fitting result
Analysis
Analysis of largest λ
•The largest eigenvalue λ=118.3564
Analysis Total variance explained by noise
3 Reconstruction
•Filtered Variance-Covariance Matrix
•An Example of Mean-Variance Optimization
ReconstructionTheory
ReconstructionTheory
AnalysisFiltered Variance-Covariance Matrix
ReconstructionCalculated Filtered Optimal Weight
ReconstructionCalculated Filtered Optimal Weight
Weight from filtered Sample• Less volatility• Lower concentration• No extreme shorting
Weight from Sample• Bigger volatility• Higher concentration• Extreme shorting
ReconstructionComparison the weight
ReconstructionSample Weight and Filtered Weight Comparison
ReconstructionSample Weight and Filtered Weight Comparison
Expected Return from Sample Covariance Matrix is
Expected Return from Sample Covariance Matrix is
ReconstructionCumulative Value of Filtered Portfolio and Sample Portfolio Per Month
ReconstructionCumulative Value of Filtered Portfolio and S&P 500 Per Month
Questions