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Improving Mean Variance Optimization through Sparse Hedging Restrictions

Published online by Cambridge University Press:  18 January 2016

Shingo Goto  and
Yan Xu
Shingo Goto*
Affiliation:
shingo.goto@moore.sc.edu, University of South Carolina, Moore School of Business, Columbia, SC 29208
Yan Xu
Affiliation:
yanxuj@hku.hk, University of Hong Kong, Faculty of Business and Economics, Hong Kong.
*
*Corresponding author: shingo.goto@moore.sc.edu
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Abstract

In 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.

Type
Research Articles
Information
Journal of Financial and Quantitative Analysis , Volume 50 , Issue 6 , December 2015 , pp. 1415 - 1441
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2016 

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References

Akaike, H. “A New Look at the Statistical Model Identification.” IEEE Transactions on Automatic Control, 19 (1974), 716–723.Google Scholar
Banerjee, O.; El Ghaoui, L.; and d’Aspremont, A.. “Model Selection through Sparse Maximum Likelihood Estimation for Multivariate Gaussian or Binary Data.” Journal of Machine Learning Research, 9 (2008), 485–516.Google Scholar
Best, M., and Grauer, R.. “On the Sensitivity of Mean-Variance-Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results.” Review of Financial Studies, 4 (1991), 315–342.Google Scholar
Bhojraj, S.; Lee, C.; and Oler, D.. “What’s My Line? A Comparison of Industry Classification Schemes for Capital Market Research.” Journal of Accounting Research, 41 (2003), 745–774.Google Scholar
Black, F., and Litterman, R.. “Global Portfolio Optimization.” Financial Analysts Journal, 48 (1992), 28–43.Google Scholar
Brandt, M. “Portfolio Choice Problems.” In Handbook of Financial Econometrics, Ait-Sahalia, Y. and Hansen, L., eds. Amsterdam: North-Holland (2009).Google Scholar
Chan, L.; Karceski, J.; and Lakonishok, J.. “On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model.” Review of Financial Studies, 12 (1999), 937–974.CrossRefGoogle Scholar
Chan, L.; Lakonishok, J.; and Swaminathan, B.. “Industry Classifications and Return Comovement.” Financial Analysts Journal, 63 (2007), 56–70.Google Scholar
Connor, G. “The Three Types of Factor Models: A Comparison of Their Explanatory Power.” Financial Analysts Journal, 51 (1995), 42–46.Google Scholar
DeMiguel, V.; Garlappi, L.; Nogales, J.; and Uppal, R.. “A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms.” Management Science, 55 (2009), 798–812.Google Scholar
DeMiguel, V.; Garlappi, L.; and Uppal, R.. “Optimal versus Naïve Diversification: How Inefficient Is the 1/N Portfolio Strategy?” Review of Financial Studies, 22 (2009), 1915–1953.Google Scholar
Dempster, A. “Covariance Selection.” Biometrics, 28 (1972), 157–175.Google Scholar
Elton, E., and Gruber, M.. “Estimating the Dependence Structure of Share Prices—Implications for Portfolio Selection.” Journal of Finance, 28 (1973), 1203–1232.Google Scholar
Elton, E.; Gruber, M.; and Urich, T.. “Are Betas Best?” Journal of Finance, 33 (1978), 1375–1384.Google Scholar
Fama, E., and French, K.. “Industry Costs of Equity.” Journal of Financial Economics, 43 (1997), 153–193.Google Scholar
Fan, J.; Fan, Y.; and Lv, J.. “High Dimensional Covariance Matrix Estimation Using a Factor Model.” Journal of Econometrics, 147 (2008), 186–197.Google Scholar
Friedman, J.; Hastie, T.; Höfling, H.; and Tibshirani, R.. “Pathwise Coordinate Optimization.” Annals of Applied Statistics, 2 (2007), 302–332.Google Scholar
Friedman, J.; Hastie, T.; and Tibshirani, R.. “Sparse Inverse Covariance Estimation with the Graphical Lasso.” Biostatistics, 9 (2008), 432–441.Google Scholar
Golub, G., and van Loan, C.. Matrix Computations. Baltimore, MD: Johns Hopkins University Press (1996).Google Scholar
Green, R., and Hollifield, B.. “When Will Mean-Variance Efficient Portfolios Be Well Diversified?” Journal of Finance, 47 (1992), 1785–1809.Google Scholar
Huang, J., and Shi, Z.. “Determinants of Bond Risk Premia.” Working Paper, Penn State University (2011).Google Scholar
Jagannathan, R., and Ma, T.. “Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps.” Journal of Finance, 58 (2003), 1651–1683.Google Scholar
Jobson, J. D., and Korkie, B.. “Performance Hypothesis Testing with the Sharpe and Treynor Measures.” Journal of Finance, 36 (1981a), 889–908.Google Scholar
Jobson, J. D., and Korkie, B.. “Putting Markowitz Theory to Work.” Journal of Portfolio Management, 7 (1981b), 70–74.Google Scholar
Jorion, P. “International Portfolio Diversification with Estimation Risk.” Journal of Business, 58 (1985), 259–278.Google Scholar
Jorion, P. “Bayes-Stein Estimation for Portfolio Analysis.” Journal of Financial and Quantitative Analysis, 21 (1986), 279–292.Google Scholar
Judge, G.; Griffiths, W.; Hill, C.; Lütkepohl, H.; and Lee, T.. The Theory and Practice of Econometrics. Hoboken, NJ: John Wiley & Sons (1980).Google Scholar
Kan, R., and Zhou, G.. “Optimal Portfolio Choice with Parameter Uncertainty.” Journal of Financial and Quantitative Analysis, 42 (2007), 621–656.Google Scholar
Kirby, C., and Ostdiek, B.. “It’s All in the Timing: Simple Active Portfolio Strategies That Outperform Naïve Diversification.” Journal of Financial and Quantitative Analysis, 47 (2012a), 437–467.Google Scholar
Kirby, C., and Ostdiek, B.. “Optimizing the Performance of Sample Mean-Variance Efficient Portfolios.” Working Paper, Rice University (2012b).Google Scholar
Ledoit, O., and Wolf, M.. “Improved Estimation of the Covariance Matrix of Stock Returns with an Application to Portfolio Selection.” Journal of Empirical Finance, 10 (2003), 603–621.Google Scholar
Ledoit, O., and Wolf, M.. “A Well-Conditioned Estimator for Large-Dimensional Covariance Matrices.” Journal of Multivariate Analysis, 88 (2004a), 365–411.Google Scholar
Ledoit, O., and Wolf, M.. “Honey, I Shrunk the Sample Covariance Matrix.” Journal of Portfolio Management, 30 (2004b), 110–119.Google Scholar
Ledoit, O., and Wolf, M.. “Robust Performance Hypothesis Testing with the Sharpe Ratio.” Journal of Empirical Finance, 15 (2008), 850–859.Google Scholar
Markowitz, H. “Portfolio Selection.” Journal of Finance, 7 (1952), 77–91.Google Scholar
Meinshausen, N., and Bühlmann, P.. “High Dimensional Graphs and Variable Selection with the Lasso.” Annals of Statistics, 34 (2006), 1436–1462.Google Scholar
Michaud, R. “The Markowitz Optimization Enigma: Is ‘Optimized’ Optimal?” Financial Analysts Journal, 45 (1989), 31–42.Google Scholar
Plyakha, Y.; Uppal, R..; and Vilkov, G.. “Why Does an Equal-Weighted Portfolio Outperform Value- and Price-Weighted Portfolios?” Working Paper, EDHEC Business School (2012).Google Scholar
Politis, D., and Romano, J.. “The Stationary Bootstrap.” Journal of the American Statistical Association, 89 (1994), 1303–1313.Google Scholar
Politis, D., and White, H.. “Automatic Block-Length Selection for the Dependent Bootstrap.” Econometric Reviews, 23 (2004), 53–70.Google Scholar
Rothman, A.; Bickel, P.; Levina, E.; and Zhu, J.. “Sparse Permutation Invariant Covariance Estimation.” Electronic Journal of Statistics, 2 (2008), 494–515.Google Scholar
Schwarz, G. “Estimating the Dimension of a Model.” Annals of Statistics, 6 (1978), 461–464.Google Scholar
Stevens, G. “On the Inverse of the Covariance Matrix in Portfolio Analysis.” Journal of Finance, 53 (1998), 1821–1827.Google Scholar
Tibshirani, R. “Regression Shrinkage and Selection via the Lasso.” Journal of the Royal Statistical Society, Series B (Methodological), 58 (1996), 267–288.Google Scholar
Tibshirani, R. “The Lasso Problem and Uniqueness.” Electronic Journal of Statistics, 7 (2013), 1456–1490.Google Scholar
Tu, J., and Zhou, G.. “Incorporating Economic Objectives into Bayesian Priors: Portfolio Choice under Parameter Uncertainty.” Journal of Financial and Quantitative Analysis, 45 (2010), 959–986.Google Scholar
Tu, J., and Zhou, G.. “Markowitz Meets Talmud: A Combination of Sophisticated and Naïve Diversification Strategies.” Journal of Financial Economics, 99 (2011), 204–215.Google Scholar
Witten, D., and Tibshirani, R.. “Covariance-Regularized Regression and Classification for High Dimensional Problems.” Journal of the Royal Statistical Society, Series B (Statistical Methodology), 71 (2009), 615–636.Google Scholar
Yuan, M., and Lin, Y.. “Model Selection and Estimation in the Gaussian Graphical Model.” Biometrika, 94 (2007), 19–35.Google Scholar