# Residual-Based Nodewise Regression in Factor Models with Ultra-High Dimensions: Analysis of Mean-Variance Portfolio Efficiency and Estimation of Out-of-Sample and Constrained Maximum Sharpe Ratios

@inproceedings{Caner2020ResidualBasedNR, title={Residual-Based Nodewise Regression in Factor Models with Ultra-High Dimensions: Analysis of Mean-Variance Portfolio Efficiency and Estimation of Out-of-Sample and Constrained Maximum Sharpe Ratios}, author={Mehmet Caner and Marcelo C. Medeiros and Gabriel F. R. Vasconcelos}, year={2020} }

We provide a new theory for nodewise regression when the residuals from a fitted factor model are used to apply our results to the analysis of the maximum Sharpe ratio when the number of assets in a portfolio is larger than its time span. We introduce a new hybrid model where factor models are combined with feasible nodewise regression. Returns are generated from an increasing number of factors plus idiosyncratic components (errors). The precision matrix of the idiosyncratic terms is assumed to… Expand

#### References

SHOWING 1-10 OF 41 REFERENCES

Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy?

- Economics
- 2009

We evaluate the out-of-sample performance of the sample-based mean-variance model, and its extensions designed to reduce estimation error, relative to the naive 1-N portfolio. Of the 14 models we… Expand

Vast Volatility Matrix Estimation Using High-Frequency Data for Portfolio Selection

- Economics, Mathematics
- Journal of the American Statistical Association
- 2012

This article proposes the use of “pairwise-refresh time” and “all-refreset time’ methods based on the concept of ”refreshtime” proposed by Barndorff-Nielsen, Hansen, Lunde, and Shephard for the estimation of vast covariance matrix and compares their merits in the portfolio selection. Expand

The large-sample distribution of the maximum Sharpe ratio with and without short sales

- Mathematics
- 2016

In the Markowitz paradigm the portfolio having maximum Sharpe ratio is optimal. Previously the large sample distribution of this statistic has been calculated when short sales are allowed and sample… Expand

Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps

- Mathematics
- 2002

Mean-variance efficient portfolios constructed using sample moments often involve taking extreme long and short positions. Hence practitioners often impose portfolio weight constraints when… Expand

Approaching Mean-Variance Efficiency for Large Portfolios

- Mathematics
- 2018

To solve the high-dimensional Markowitz optimization problem, a new approach combining sparse regression and estimation of maximum expected return for a given risk level based on random matrix theory… Expand

A Nodewise Regression Approach to Estimating Large Portfolios

- Mathematics
- 2016

Abstract This article investigates the large sample properties of the variance, weights, and risk of high-dimensional portfolios where the inverse of the covariance matrix of excess asset returns is… Expand

New light on the portfolio allocation problem

- Mathematics, Computer Science
- Math. Methods Oper. Res.
- 2003

The problem of the maximum Sharpe ratio achievable from a mean-variance portfolio optimisation procedure is solved explicitly in this paper, and the corresponding optimal portfolio found. Expand

Optimal Portfolio Choice with Parameter Uncertainty

- Economics
- Journal of Financial and Quantitative Analysis
- 2007

Abstract In this paper, we analytically derive the expected loss function associated with using sample means and the covariance matrix of returns to estimate the optimal portfolio. Our analytical… Expand

Nonlinear Shrinkage of the Covariance Matrix for Portfolio Selection: Markowitz Meets Goldilocks

- Economics
- 2017

Markowitz (1952) portfolio selection requires an estimator of the covariance matrix of returns. To address this problem, we promote a nonlinear shrinkage estimator that is more flexible than previous… Expand

Improved estimation of the covariance matrix of stock returns with an application to portfolio selection

- Economics
- 2003

This paper proposes to estimate the covariance matrix of stock returns by an optimally weighted average of two existing estimators: the sample covariance matrix and single-index covariance matrix.… Expand