Singular inverse Wishart distribution and its application to portfolio theory
The inverse of the standard estimate of covariance matrix is frequently used in the portfolio theory to estimate the optimal portfolio weights. For this problem, the distribution of the linear transformation of the inverse is needed. We obtain this distribution in the case when the sample size is sm...
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| Published in: | Journal of multivariate analysis Vol. 143; pp. 314 - 326 |
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| Language: | English |
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| Abstract | The inverse of the standard estimate of covariance matrix is frequently used in the portfolio theory to estimate the optimal portfolio weights. For this problem, the distribution of the linear transformation of the inverse is needed. We obtain this distribution in the case when the sample size is smaller than the dimension, the underlying covariance matrix is singular, and the vectors of returns are independent and normally distributed. For the result, the distribution of the inverse of covariance estimate is needed and it is derived and referred to as the singular inverse Wishart distribution. We use these results to provide an explicit stochastic representation of an estimate of the mean–variance portfolio weights as well as to derive its characteristic function and the moments of higher order. The results are illustrated using actual stock returns and a discussion of practical relevance of the model is presented. |
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| AbstractList | The inverse of the standard estimate of covariance matrix is frequently used in the portfolio theory to estimate the optimal portfolio weights. For this problem, the distribution of the linear transformation of the inverse is needed. We obtain this distribution in the case when the sample size is smaller than the dimension, the underlying covariance matrix is singular, and the vectors of returns are independent and normally distributed. For the result, the distribution of the inverse of covariance estimate is needed and it is derived and referred to as the singular inverse Wishart distribution. We use these results to provide an explicit stochastic representation of an estimate of the mean-variance portfolio weights as well as to derive its characteristic function and the moments of higher order. The results are illustrated using actual stock returns and a discussion of practical relevance of the model is presented. The inverse of the standard estimate of covariance matrix is frequently used in the portfolio theory to estimate the optimal portfolio weights. For this problem, the distribution of the linear transformation of the inverse is needed. We obtain this distribution in the case when the sample size is smaller than the dimension, the underlying covariance matrix is singular, and the vectors of returns are independent and normally distributed. For the result, the distribution of the inverse of covariance estimate is needed and it is derived and referred to as the singular inverse Wishart distribution. We use these results to provide an explicit stochastic representation of an estimate of the mean-variance portfolio weights as well as to derive its characteristic function and the moments of higher order. The results are illustrated using actual stock returns and a discussion of practical relevance of the model is presented. The inverse of the standard estimate of covariance matrix is frequently used in the portfolio theory to estimate the optimal portfolio weights. For this problem, the distribution of the linear transformation of the inverse is needed. We obtain this distribution in the case when the sample size is smaller than the dimension, the underlying covariance matrix is singular, and the vectors of returns are independent and normally distributed. For the result, the distribution of the inverse of covariance estimate is needed and it is derived and referred to as the singular inverse Wishart distribution. We use these results to provide an explicit stochastic representation of an estimate of the mean-variance portfolio weights as well as to derive its characteristic function and the moments of higher order. The results are illustrated using actual stock returns and a discussion of practical relevance of the model is presented. [web URL: http://www.sciencedirect.com/science/article/pii/S0047259X15002353] |
| Author | Bodnar, Taras Podgórski, Krzysztof Mazur, Stepan |
| Author_xml | – sequence: 1 givenname: Taras surname: Bodnar fullname: Bodnar, Taras organization: Department of Mathematics, Stockholm University, Roslagsvägen 101, SE-10691 Stockholm, Sweden – sequence: 2 givenname: Stepan surname: Mazur fullname: Mazur, Stepan organization: Department of Statistics, Lund University, Tycho Brahe 1, SE-22007 Lund, Sweden – sequence: 3 givenname: Krzysztof orcidid: 0000-0003-0043-1532 surname: Podgórski fullname: Podgórski, Krzysztof email: Krzysztof.Podgorski@stat.lu.se organization: Department of Statistics, Lund University, Tycho Brahe 1, SE-22007 Lund, Sweden |
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| Cites_doi | 10.1214/aoms/1177706112 10.1524/stnd.2008.0918 10.1007/s00184-007-0126-7 10.1214/aos/1065705118 10.1007/s00184-013-0432-1 10.1524/strm.2012.1118 10.1016/j.jmva.2008.02.024 10.1198/073500102288618487 10.1016/j.jbankfin.2006.01.002 10.1137/1008107 10.1006/jmva.1997.1689 10.1016/j.jeconom.2005.06.022 10.1016/j.jmva.2013.07.007 10.1016/j.amc.2012.11.049 10.1090/tpms/962 10.14490/jjss.37.53 10.1017/S0022109000004129 10.1016/j.jfineco.2003.05.003 10.1080/13518470802423478 10.1524/strm.2011.1080 10.1214/07-AOS522 10.1214/aoms/1177728789 |
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| Keywords | Mean–variance portfolio 91G10 Moore–Penrose inverse Sample estimate of precision matrix 62H10 Singular Wishart distribution 62H12 |
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| References | Bodnar, Mazur, Okhrin (br000015) 2014; 91 Greville (br000090) 1966; 8 Kan, Zhou (br000100) 2007; 42 Pappas, Kiriakopoulos, Kaimakamis (br000130) 2010; 5 Bodnar, Okhrin (br000020) 2008; 99 Fama (br000080) 1976 Boullion, Odell (br000060) 1971 Giamouridis, Vrontos (br000085) 2007; 31 Srivastava (br000140) 2007; 37 Bodnar, Schmid, Zabolotskyy (br000055) 2013; 76 Muirhead (br000115) 1982 Drton, Massam, Olkin (br000070) 2008; 36 Khatri (br000105) 1959; 30 Engle (br000075) 2002; 20 Bodnar, Schmid, Zabolotskyy (br000050) 2012; 29 Markowitz (br000110) 1952; 7 Gupta, Nagar (br000095) 2000 Bodnar, Schmid (br000045) 2011; 28 Andrews, Askey, Roy (br000005) 2000 Díaz-García, Gutiérrez-Jáimez, Mardia (br000065) 1997; 63 Bodnar, Okhrin (br000025) 2013; 219 Bodnar, Mazur, Okhrin (br000010) 2013; 122 Bodnar, Schmid (br000035) 2008; 26 Bodnar, Schmid (br000030) 2008; 67 Okhrin, Schmid (br000120) 2006; 134 Srivastava (br000135) 2003; 31 Tu, Zhou (br000145) 2004; 72 Bodnar, Schmid (br000040) 2009; 15 Olkin, Roy (br000125) 1954; 25 Bodnar (10.1016/j.jmva.2015.09.021_br000050) 2012; 29 Bodnar (10.1016/j.jmva.2015.09.021_br000035) 2008; 26 Tu (10.1016/j.jmva.2015.09.021_br000145) 2004; 72 Andrews (10.1016/j.jmva.2015.09.021_br000005) 2000 Bodnar (10.1016/j.jmva.2015.09.021_br000045) 2011; 28 Bodnar (10.1016/j.jmva.2015.09.021_br000040) 2009; 15 Fama (10.1016/j.jmva.2015.09.021_br000080) 1976 Engle (10.1016/j.jmva.2015.09.021_br000075) 2002; 20 Srivastava (10.1016/j.jmva.2015.09.021_br000140) 2007; 37 Drton (10.1016/j.jmva.2015.09.021_br000070) 2008; 36 Greville (10.1016/j.jmva.2015.09.021_br000090) 1966; 8 Giamouridis (10.1016/j.jmva.2015.09.021_br000085) 2007; 31 Okhrin (10.1016/j.jmva.2015.09.021_br000120) 2006; 134 Kan (10.1016/j.jmva.2015.09.021_br000100) 2007; 42 Khatri (10.1016/j.jmva.2015.09.021_br000105) 1959; 30 Bodnar (10.1016/j.jmva.2015.09.021_br000020) 2008; 99 Gupta (10.1016/j.jmva.2015.09.021_br000095) 2000 Bodnar (10.1016/j.jmva.2015.09.021_br000030) 2008; 67 Bodnar (10.1016/j.jmva.2015.09.021_br000025) 2013; 219 Markowitz (10.1016/j.jmva.2015.09.021_br000110) 1952; 7 Bodnar (10.1016/j.jmva.2015.09.021_br000055) 2013; 76 Olkin (10.1016/j.jmva.2015.09.021_br000125) 1954; 25 Bodnar (10.1016/j.jmva.2015.09.021_br000015) 2014; 91 Bodnar (10.1016/j.jmva.2015.09.021_br000010) 2013; 122 Muirhead (10.1016/j.jmva.2015.09.021_br000115) 1982 Srivastava (10.1016/j.jmva.2015.09.021_br000135) 2003; 31 Díaz-García (10.1016/j.jmva.2015.09.021_br000065) 1997; 63 Boullion (10.1016/j.jmva.2015.09.021_br000060) 1971 Pappas (10.1016/j.jmva.2015.09.021_br000130) 2010; 5 |
| References_xml | – year: 1976 ident: br000080 article-title: Foundations of Finance contributor: fullname: Fama – volume: 36 start-page: 2261 year: 2008 end-page: 2283 ident: br000070 article-title: Moments of minors of Wishart matrices publication-title: Ann. Statist. contributor: fullname: Olkin – volume: 8 start-page: 518 year: 1966 end-page: 521 ident: br000090 article-title: Note on the generalized inverse of a product matrix publication-title: SIAM Rev. contributor: fullname: Greville – volume: 31 start-page: 199 year: 2007 end-page: 217 ident: br000085 article-title: Hedge fund portfolio construction: A comparison of static and dynamic approaches publication-title: J. Bank. Finance contributor: fullname: Vrontos – volume: 7 start-page: 77 year: 1952 end-page: 91 ident: br000110 article-title: Portfolio selection publication-title: J. Finance contributor: fullname: Markowitz – volume: 25 start-page: 329 year: 1954 end-page: 339 ident: br000125 article-title: On multivariate distribution theory publication-title: Ann. Math. Stat. contributor: fullname: Roy – volume: 30 start-page: 1258 year: 1959 end-page: 1262 ident: br000105 article-title: On the mutual independence of certain statistics publication-title: Ann. Math. Stat. contributor: fullname: Khatri – year: 2000 ident: br000095 article-title: Matrix Variate Distributions contributor: fullname: Nagar – year: 2000 ident: br000005 article-title: Special Functions contributor: fullname: Roy – volume: 31 start-page: 1537 year: 2003 end-page: 1560 ident: br000135 article-title: Singular wishart and multivariate beta distributions publication-title: Ann. Statist. contributor: fullname: Srivastava – volume: 219 start-page: 5440 year: 2013 end-page: 5448 ident: br000025 article-title: Boundaries of the risk aversion coefficient: Should we invest in the global minimum variance portfolio? publication-title: Appl. Math. Comput. contributor: fullname: Okhrin – volume: 72 start-page: 385 year: 2004 end-page: 421 ident: br000145 article-title: Data-generating process uncertainty: what difference does it make in portfolio decisions? publication-title: J. Financial Econ. contributor: fullname: Zhou – volume: 99 start-page: 2389 year: 2008 end-page: 2405 ident: br000020 article-title: Properties of the singular, inverse and generalized inverse partitioned Wishart distributions publication-title: J. Multivariate Anal. contributor: fullname: Okhrin – volume: 29 start-page: 281 year: 2012 end-page: 314 ident: br000050 article-title: Minimum var and minimum cvar optimal portfolios: estimators, confidence regions, and tests publication-title: Stat. Risk Model. contributor: fullname: Zabolotskyy – volume: 134 start-page: 235 year: 2006 end-page: 256 ident: br000120 article-title: Distributional properties of portfolio weights publication-title: J. Econometrics contributor: fullname: Schmid – volume: 37 start-page: 53 year: 2007 end-page: 86 ident: br000140 article-title: Multivariate theory for analyzing high dimensional data publication-title: J. Japan Statist. Soc. contributor: fullname: Srivastava – volume: 63 start-page: 73 year: 1997 end-page: 87 ident: br000065 article-title: Wishart and pseudo-Wishart distributions and some applications to shape theory publication-title: J. Multivariate Anal. contributor: fullname: Mardia – volume: 26 start-page: 179 year: 2008 end-page: 201 ident: br000035 article-title: Estimation of optimal portfolio compositions for gaussian returns publication-title: Statist. Decisions contributor: fullname: Schmid – volume: 67 start-page: 127 year: 2008 end-page: 143 ident: br000030 article-title: A test for the weights of the global minimum variance portfolio in an elliptical model publication-title: Metrika contributor: fullname: Schmid – volume: 42 start-page: 621 year: 2007 end-page: 656 ident: br000100 article-title: Optimal portfolio choice with parameter uncertainty publication-title: J. Financial Quant. Anal. contributor: fullname: Zhou – volume: 122 start-page: 70 year: 2013 end-page: 81 ident: br000010 article-title: On exact and approximate distributions of the product of the Wishart matrix and normal vector publication-title: J. Multivariate Anal. contributor: fullname: Okhrin – volume: 76 start-page: 1105 year: 2013 end-page: 1134 ident: br000055 article-title: Asymptotic behavior of the estimated weights and characteristics of the minimum var and the minimum cvar optimal portfolios for dependent data publication-title: Metrika contributor: fullname: Zabolotskyy – year: 1982 ident: br000115 article-title: Aspects of Multivariate Statistical Theory contributor: fullname: Muirhead – volume: 28 start-page: 319 year: 2011 end-page: 342 ident: br000045 article-title: On the exact distribution of the estimated expected utility portfolio weights: Theory and applications publication-title: Stat. Risk Model. contributor: fullname: Schmid – volume: 15 start-page: 317 year: 2009 end-page: 335 ident: br000040 article-title: Econometrical analysis of the sample efficient frontier publication-title: Eur. J. Finance contributor: fullname: Schmid – volume: 91 start-page: 1 year: 2014 end-page: 15 ident: br000015 article-title: Distribution of the product of singular Wishart Matrix and normal vector publication-title: Theory Probab. Math. Statist. contributor: fullname: Okhrin – volume: 5 start-page: 2305 year: 2010 end-page: 2318 ident: br000130 article-title: Optimal portfolio selection with singular covariance matrix publication-title: Int. Math. Forum contributor: fullname: Kaimakamis – year: 1971 ident: br000060 article-title: Generalized Inverse Matrices contributor: fullname: Odell – volume: 20 start-page: 339 year: 2002 end-page: 350 ident: br000075 article-title: Dynamic conditional correlation: A simple class of multivariate GARCH models publication-title: J. Bus. Econom. Statist. contributor: fullname: Engle – volume: 30 start-page: 1258 year: 1959 ident: 10.1016/j.jmva.2015.09.021_br000105 article-title: On the mutual independence of certain statistics publication-title: Ann. Math. Stat. doi: 10.1214/aoms/1177706112 contributor: fullname: Khatri – volume: 26 start-page: 179 year: 2008 ident: 10.1016/j.jmva.2015.09.021_br000035 article-title: Estimation of optimal portfolio compositions for gaussian returns publication-title: Statist. Decisions doi: 10.1524/stnd.2008.0918 contributor: fullname: Bodnar – volume: 67 start-page: 127 issue: 2 year: 2008 ident: 10.1016/j.jmva.2015.09.021_br000030 article-title: A test for the weights of the global minimum variance portfolio in an elliptical model publication-title: Metrika doi: 10.1007/s00184-007-0126-7 contributor: fullname: Bodnar – volume: 5 start-page: 2305 issue: 47 year: 2010 ident: 10.1016/j.jmva.2015.09.021_br000130 article-title: Optimal portfolio selection with singular covariance matrix publication-title: Int. Math. Forum contributor: fullname: Pappas – volume: 31 start-page: 1537 year: 2003 ident: 10.1016/j.jmva.2015.09.021_br000135 article-title: Singular wishart and multivariate beta distributions publication-title: Ann. Statist. doi: 10.1214/aos/1065705118 contributor: fullname: Srivastava – volume: 76 start-page: 1105 year: 2013 ident: 10.1016/j.jmva.2015.09.021_br000055 article-title: Asymptotic behavior of the estimated weights and characteristics of the minimum var and the minimum cvar optimal portfolios for dependent data publication-title: Metrika doi: 10.1007/s00184-013-0432-1 contributor: fullname: Bodnar – volume: 29 start-page: 281 year: 2012 ident: 10.1016/j.jmva.2015.09.021_br000050 article-title: Minimum var and minimum cvar optimal portfolios: estimators, confidence regions, and tests publication-title: Stat. Risk Model. doi: 10.1524/strm.2012.1118 contributor: fullname: Bodnar – volume: 99 start-page: 2389 year: 2008 ident: 10.1016/j.jmva.2015.09.021_br000020 article-title: Properties of the singular, inverse and generalized inverse partitioned Wishart distributions publication-title: J. Multivariate Anal. doi: 10.1016/j.jmva.2008.02.024 contributor: fullname: Bodnar – year: 1982 ident: 10.1016/j.jmva.2015.09.021_br000115 contributor: fullname: Muirhead – volume: 20 start-page: 339 year: 2002 ident: 10.1016/j.jmva.2015.09.021_br000075 article-title: Dynamic conditional correlation: A simple class of multivariate GARCH models publication-title: J. Bus. Econom. Statist. doi: 10.1198/073500102288618487 contributor: fullname: Engle – volume: 31 start-page: 199 issue: 1 year: 2007 ident: 10.1016/j.jmva.2015.09.021_br000085 article-title: Hedge fund portfolio construction: A comparison of static and dynamic approaches publication-title: J. Bank. Finance doi: 10.1016/j.jbankfin.2006.01.002 contributor: fullname: Giamouridis – volume: 8 start-page: 518 issue: 4 year: 1966 ident: 10.1016/j.jmva.2015.09.021_br000090 article-title: Note on the generalized inverse of a product matrix publication-title: SIAM Rev. doi: 10.1137/1008107 contributor: fullname: Greville – volume: 63 start-page: 73 year: 1997 ident: 10.1016/j.jmva.2015.09.021_br000065 article-title: Wishart and pseudo-Wishart distributions and some applications to shape theory publication-title: J. Multivariate Anal. doi: 10.1006/jmva.1997.1689 contributor: fullname: Díaz-García – volume: 134 start-page: 235 year: 2006 ident: 10.1016/j.jmva.2015.09.021_br000120 article-title: Distributional properties of portfolio weights publication-title: J. Econometrics doi: 10.1016/j.jeconom.2005.06.022 contributor: fullname: Okhrin – volume: 122 start-page: 70 year: 2013 ident: 10.1016/j.jmva.2015.09.021_br000010 article-title: On exact and approximate distributions of the product of the Wishart matrix and normal vector publication-title: J. Multivariate Anal. doi: 10.1016/j.jmva.2013.07.007 contributor: fullname: Bodnar – year: 2000 ident: 10.1016/j.jmva.2015.09.021_br000005 contributor: fullname: Andrews – volume: 219 start-page: 5440 year: 2013 ident: 10.1016/j.jmva.2015.09.021_br000025 article-title: Boundaries of the risk aversion coefficient: Should we invest in the global minimum variance portfolio? publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2012.11.049 contributor: fullname: Bodnar – year: 2000 ident: 10.1016/j.jmva.2015.09.021_br000095 contributor: fullname: Gupta – volume: 91 start-page: 1 year: 2014 ident: 10.1016/j.jmva.2015.09.021_br000015 article-title: Distribution of the product of singular Wishart Matrix and normal vector publication-title: Theory Probab. Math. Statist. doi: 10.1090/tpms/962 contributor: fullname: Bodnar – year: 1971 ident: 10.1016/j.jmva.2015.09.021_br000060 contributor: fullname: Boullion – volume: 37 start-page: 53 issue: 1 year: 2007 ident: 10.1016/j.jmva.2015.09.021_br000140 article-title: Multivariate theory for analyzing high dimensional data publication-title: J. Japan Statist. Soc. doi: 10.14490/jjss.37.53 contributor: fullname: Srivastava – volume: 42 start-page: 621 year: 2007 ident: 10.1016/j.jmva.2015.09.021_br000100 article-title: Optimal portfolio choice with parameter uncertainty publication-title: J. Financial Quant. Anal. doi: 10.1017/S0022109000004129 contributor: fullname: Kan – volume: 72 start-page: 385 year: 2004 ident: 10.1016/j.jmva.2015.09.021_br000145 article-title: Data-generating process uncertainty: what difference does it make in portfolio decisions? publication-title: J. Financial Econ. doi: 10.1016/j.jfineco.2003.05.003 contributor: fullname: Tu – volume: 15 start-page: 317 year: 2009 ident: 10.1016/j.jmva.2015.09.021_br000040 article-title: Econometrical analysis of the sample efficient frontier publication-title: Eur. J. Finance doi: 10.1080/13518470802423478 contributor: fullname: Bodnar – volume: 28 start-page: 319 year: 2011 ident: 10.1016/j.jmva.2015.09.021_br000045 article-title: On the exact distribution of the estimated expected utility portfolio weights: Theory and applications publication-title: Stat. Risk Model. doi: 10.1524/strm.2011.1080 contributor: fullname: Bodnar – year: 1976 ident: 10.1016/j.jmva.2015.09.021_br000080 contributor: fullname: Fama – volume: 7 start-page: 77 year: 1952 ident: 10.1016/j.jmva.2015.09.021_br000110 article-title: Portfolio selection publication-title: J. Finance contributor: fullname: Markowitz – volume: 36 start-page: 2261 year: 2008 ident: 10.1016/j.jmva.2015.09.021_br000070 article-title: Moments of minors of Wishart matrices publication-title: Ann. Statist. doi: 10.1214/07-AOS522 contributor: fullname: Drton – volume: 25 start-page: 329 year: 1954 ident: 10.1016/j.jmva.2015.09.021_br000125 article-title: On multivariate distribution theory publication-title: Ann. Math. Stat. doi: 10.1214/aoms/1177728789 contributor: fullname: Olkin |
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| Snippet | The inverse of the standard estimate of covariance matrix is frequently used in the portfolio theory to estimate the optimal portfolio weights. For this... |
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| SubjectTerms | Inverse problems Matematik matematisk statistik Mathematical Statistics Mathematics Mean-variance portfolio Moore-Penrose inverse Natural Sciences Naturvetenskap Portfolio performance Probability distribution Probability Theory and Statistics Rates of return Sample estimate of precision matrix Sannolikhetsteori och statistik Singular Wishart distribution Stochastic models Studies |
| Title | Singular inverse Wishart distribution and its application to portfolio theory |
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