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Optimization models for portfolio optimization

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Optimization models for portfolio optimization

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7

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What are the mainstream models for portfolio optimization? We have Markowitz mean-variance model and CVaR-based models (e.g., max return subject to a CVaR constraint). What else is out there in terms of risk measures or formulations?

optimization combinatorial-optimization

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7

$begingroup$

What are the mainstream models for portfolio optimization? We have Markowitz mean-variance model and CVaR-based models (e.g., max return subject to a CVaR constraint). What else is out there in terms of risk measures or formulations?

optimization combinatorial-optimization

share|improve this question

edited 8 hours ago

EhsanK

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asked 8 hours ago

Daniel DuqueDaniel Duque

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New contributor

Daniel Duque is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

$begingroup$

What are the mainstream models for portfolio optimization? We have Markowitz mean-variance model and CVaR-based models (e.g., max return subject to a CVaR constraint). What else is out there in terms of risk measures or formulations?

optimization combinatorial-optimization

share|improve this question

edited 8 hours ago

EhsanK

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asked 8 hours ago

Daniel DuqueDaniel Duque

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New contributor

Daniel Duque is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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share|improve this question

edited 8 hours ago

EhsanK

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asked 8 hours ago

Daniel DuqueDaniel Duque

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Daniel Duque is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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share|improve this question

edited 8 hours ago

EhsanK

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asked 8 hours ago

Daniel DuqueDaniel Duque

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Daniel Duque is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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edited 8 hours ago

EhsanK

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edited 8 hours ago

EhsanK

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asked 8 hours ago

Daniel DuqueDaniel Duque

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Daniel Duque is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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asked 8 hours ago

Daniel DuqueDaniel Duque

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$begingroup$

Here's what is not really mainstream now, but should be. The mean and especially the covariance matrix of returns is not known. Treating estimates of then as though they are known with certainty can lead to very suboptimal results.

Just to start vectoring yourself in the right direction, you can start by looking at

MEAN–VARIANCE PORTFOLIO OPTIMIZATION WHEN MEANS AND COVARIANCES ARE UNKNOWN, TZE LEUNG LAI, HAIPENG XING, and ZEHAO CHEN, Annals of Statistics, 2011, Vol. 5, No. 2A, 798–823.

Improving Portfolios Global Performance with Robust Covariance Matrix Estimation:Application to the Maximum Variety Portfolio, Emmanuelle Jay, Eugenie Terreaux, Jean-Philippe Ovarlez, and Frederic Pascal.

You may also find of interest methods to identify financial risk factors using large data sets.

Identifying Financial Risk Factors with a Low-Rank Sparse Decomposition, Lisa Goldberg and Alex Shkolnik. This decomposes covariance as a sum of a rank-one factor component and a diagonal security specific return component

Here is a semi-classic paper advising you NOT to use the sample covariance matrix for portfolio optimization. "Shrinking" it toward a better conditioned matrix. even though producing a biased estimator of the covariance matrix, can improve the results of portfolio optimization (note that the condition number of the sample covariance matrix is a very biased estimator of the condition number of the true covariance matrix, and is infinite when the number of vector data points is less than the number of variables).

Honey, I Shrunk the Sample Covariance Matrix, Olivier Ledoit and MichaelWolf, The Journal of Portfolio Management Summer 2004, 30 (4) 110-119 (link is to free version of the paper)

share|improve this answer

edited 7 hours ago

answered 7 hours ago

Mark L. StoneMark L. Stone

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1

$begingroup$

Here's what is not really mainstream now, but should be. The mean and especially the covariance matrix of returns is not known. Treating estimates of then as though they are known with certainty can lead to very suboptimal results.

Just to start vectoring yourself in the right direction, you can start by looking at

MEAN–VARIANCE PORTFOLIO OPTIMIZATION WHEN MEANS AND COVARIANCES ARE UNKNOWN, TZE LEUNG LAI, HAIPENG XING, and ZEHAO CHEN, Annals of Statistics, 2011, Vol. 5, No. 2A, 798–823.

Improving Portfolios Global Performance with Robust Covariance Matrix Estimation:Application to the Maximum Variety Portfolio, Emmanuelle Jay, Eugenie Terreaux, Jean-Philippe Ovarlez, and Frederic Pascal.

You may also find of interest methods to identify financial risk factors using large data sets.

Identifying Financial Risk Factors with a Low-Rank Sparse Decomposition, Lisa Goldberg and Alex Shkolnik. This decomposes covariance as a sum of a rank-one factor component and a diagonal security specific return component

Here is a semi-classic paper advising you NOT to use the sample covariance matrix for portfolio optimization. "Shrinking" it toward a better conditioned matrix. even though producing a biased estimator of the covariance matrix, can improve the results of portfolio optimization (note that the condition number of the sample covariance matrix is a very biased estimator of the condition number of the true covariance matrix, and is infinite when the number of vector data points is less than the number of variables).

Honey, I Shrunk the Sample Covariance Matrix, Olivier Ledoit and MichaelWolf, The Journal of Portfolio Management Summer 2004, 30 (4) 110-119 (link is to free version of the paper)

share|improve this answer

edited 7 hours ago

answered 7 hours ago

Mark L. StoneMark L. Stone

2,16455 silver badges2323 bronze badges

$endgroup$

add a comment | 

1

$begingroup$

Here's what is not really mainstream now, but should be. The mean and especially the covariance matrix of returns is not known. Treating estimates of then as though they are known with certainty can lead to very suboptimal results.

Just to start vectoring yourself in the right direction, you can start by looking at

MEAN–VARIANCE PORTFOLIO OPTIMIZATION WHEN MEANS AND COVARIANCES ARE UNKNOWN, TZE LEUNG LAI, HAIPENG XING, and ZEHAO CHEN, Annals of Statistics, 2011, Vol. 5, No. 2A, 798–823.

Improving Portfolios Global Performance with Robust Covariance Matrix Estimation:Application to the Maximum Variety Portfolio, Emmanuelle Jay, Eugenie Terreaux, Jean-Philippe Ovarlez, and Frederic Pascal.

You may also find of interest methods to identify financial risk factors using large data sets.

Identifying Financial Risk Factors with a Low-Rank Sparse Decomposition, Lisa Goldberg and Alex Shkolnik. This decomposes covariance as a sum of a rank-one factor component and a diagonal security specific return component

Here is a semi-classic paper advising you NOT to use the sample covariance matrix for portfolio optimization. "Shrinking" it toward a better conditioned matrix. even though producing a biased estimator of the covariance matrix, can improve the results of portfolio optimization (note that the condition number of the sample covariance matrix is a very biased estimator of the condition number of the true covariance matrix, and is infinite when the number of vector data points is less than the number of variables).

Honey, I Shrunk the Sample Covariance Matrix, Olivier Ledoit and MichaelWolf, The Journal of Portfolio Management Summer 2004, 30 (4) 110-119 (link is to free version of the paper)

share|improve this answer

edited 7 hours ago

answered 7 hours ago

Mark L. StoneMark L. Stone

2,16455 silver badges2323 bronze badges

$endgroup$

add a comment | 

$begingroup$

Here's what is not really mainstream now, but should be. The mean and especially the covariance matrix of returns is not known. Treating estimates of then as though they are known with certainty can lead to very suboptimal results.

Just to start vectoring yourself in the right direction, you can start by looking at

MEAN–VARIANCE PORTFOLIO OPTIMIZATION WHEN MEANS AND COVARIANCES ARE UNKNOWN, TZE LEUNG LAI, HAIPENG XING, and ZEHAO CHEN, Annals of Statistics, 2011, Vol. 5, No. 2A, 798–823.

Improving Portfolios Global Performance with Robust Covariance Matrix Estimation:Application to the Maximum Variety Portfolio, Emmanuelle Jay, Eugenie Terreaux, Jean-Philippe Ovarlez, and Frederic Pascal.

You may also find of interest methods to identify financial risk factors using large data sets.

Identifying Financial Risk Factors with a Low-Rank Sparse Decomposition, Lisa Goldberg and Alex Shkolnik. This decomposes covariance as a sum of a rank-one factor component and a diagonal security specific return component

Here is a semi-classic paper advising you NOT to use the sample covariance matrix for portfolio optimization. "Shrinking" it toward a better conditioned matrix. even though producing a biased estimator of the covariance matrix, can improve the results of portfolio optimization (note that the condition number of the sample covariance matrix is a very biased estimator of the condition number of the true covariance matrix, and is infinite when the number of vector data points is less than the number of variables).

Honey, I Shrunk the Sample Covariance Matrix, Olivier Ledoit and MichaelWolf, The Journal of Portfolio Management Summer 2004, 30 (4) 110-119 (link is to free version of the paper)

share|improve this answer

edited 7 hours ago

answered 7 hours ago

Mark L. StoneMark L. Stone

2,16455 silver badges2323 bronze badges

$endgroup$

share|improve this answer

edited 7 hours ago

answered 7 hours ago

Mark L. StoneMark L. Stone

2,16455 silver badges2323 bronze badges

answered 7 hours ago

Mark L. StoneMark L. Stone

2,16455 silver badges2323 bronze badges

answered 7 hours ago

Mark L. StoneMark L. Stone

2,16455 silver badges2323 bronze badges