TY - JOUR
T1 - Sharpe Ratio analysis in high dimensions
T2 - Residual-based nodewise regression in factor models
AU - Caner, Mehmet
AU - Medeiros, Marcelo
AU - Vasconcelos, Gabriel F.R.
N1 - We are very grateful to the co-editor, Torben Andersen, the Associate Editor and an anonymous referee for very insightful comments and suggestions which led to a much improved version of the manuscript. We thank Vanderbilt Economics Department seminar guests and the participants of the World Congress of the Econometric Society for useful comments. Finally, we are thankful for the comments by Harold Chiang, Maurizio Daniele, Anders Kock, Srini Krishnamurthy, and Michael Wolf. Medeiros acknowledges the partial financial support from CNPq, Brazil and CAPES, Brazil.
We are very grateful to the co-editor, Torben Andersen, the Associate Editor and an anonymous referee for very insightful comments and suggestions which led to a much improved version of the manuscript. We thank Vanderbilt Economics Department seminar guests and the participants of the World Congress of the Econometric Society for useful comments. Finally, we are thankful for the comments by Harold Chiang, Maurizio Daniele, Anders Kock, Srini Krishnamurthy, and Michael Wolf. Medeiros acknowledges the partial financial support from CNPq, Brazil and CAPES, Brazil .
PY - 2022
Y1 - 2022
N2 - We provide a new theory for nodewise regression when the residuals from a fitted factor model are used. We apply our results to the analysis of the consistency of Sharpe Ratio estimators when there are many assets in a portfolio. We allow for an increasing number of assets as well as time observations of the portfolio. Since the nodewise regression is not feasible due to the unknown nature of idiosyncratic errors, we provide a feasible-residual-based nodewise regression to estimate the precision matrix of errors which is consistent even when number of assets, p, exceeds the time span of the portfolio, n. In another new development, we also show that the precision matrix of returns can be estimated consistently, even with an increasing number of factors and p>n. We show that: (1) with p>n, the Sharpe Ratio estimators are consistent in global minimum-variance and mean–variance portfolios; and (2) with p>n, the maximum Sharpe Ratio estimator is consistent when the portfolio weights sum to one; and (3) with p<
AB - We provide a new theory for nodewise regression when the residuals from a fitted factor model are used. We apply our results to the analysis of the consistency of Sharpe Ratio estimators when there are many assets in a portfolio. We allow for an increasing number of assets as well as time observations of the portfolio. Since the nodewise regression is not feasible due to the unknown nature of idiosyncratic errors, we provide a feasible-residual-based nodewise regression to estimate the precision matrix of errors which is consistent even when number of assets, p, exceeds the time span of the portfolio, n. In another new development, we also show that the precision matrix of returns can be estimated consistently, even with an increasing number of factors and p>n. We show that: (1) with p>n, the Sharpe Ratio estimators are consistent in global minimum-variance and mean–variance portfolios; and (2) with p>n, the maximum Sharpe Ratio estimator is consistent when the portfolio weights sum to one; and (3) with p<
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U2 - 10.1016/j.jeconom.2022.03.009
DO - 10.1016/j.jeconom.2022.03.009
M3 - Article
AN - SCOPUS:85130964294
SN - 0304-4076
VL - 235
SP - 393
EP - 417
JO - Journal of Econometrics
JF - Journal of Econometrics
IS - 2
ER -