Sharpe Ratio analysis in high dimensions: Residual-based nodewise regression in factor models

Mehmet Caner, Marcelo Medeiros, Gabriel F.R. Vasconcelos

Research output: Contribution to journalArticlepeer-review


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<<n, the maximum-out-of-sample Sharpe Ratio estimator is consistent.

Original languageEnglish (US)
Pages (from-to)393-417
Number of pages25
JournalJournal of Econometrics
Issue number2
StateAccepted/In press - 2022
Externally publishedYes

ASJC Scopus subject areas

  • Economics and Econometrics


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