Mehmet Caner, Marcelo Medeiros, Gabriel Vasconcelos
arXiv 5 Feb 2020 · Finance — Portfolio Management · publishedJournal of Econometrics (2022) · 19 citations (OpenAlex)
arXiv:2002.01800 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Ledoit, O, M. and M. Wolf (2017) Nonlinear shrinkage of the covariance matrix for portfolio selection: Markowitz meets goldilocks | 1.000 | 7 | 3 | 100% |
| 2 | Callot, L., M. Caner, O. Onder, and E. Ulasan (2021) A nodewise regression approach to estimating large portfolios | 1.000 | 5 | 3 | 100% |
| 3 | Ao, M., Y. Li, and X. Zheng (2019) Approaching mean-variance efficiency for large portfolios | 0.946 | 13 | 6 | 85% |
| 4 | Maller, R. and D. Turkington (2002) New light on portfolio allocation problem | 0.874 | 7 | 2 | 100% |
| 5 | Meinshausen, N. and P. Bühlmann (2006) High-dimensional graphs and variable selection with the lasso | 0.874 | 5 | 2 | 100% |
| 6 | Chang, J., Y. Qiu, Q. Yao, and T. Zou (2018) Confidence regions for entries of a large precision matrix | 0.811 | 4 | 2 | 100% |
| 7 | Maller, R., S. Roberts, and R. Tourky (2016) The large sample distribution of the maximum sharpe ratio with and without short sales | 0.811 | 4 | 2 | 100% |
| 8 | Caner, M. and A. Kock (2018) Asymptotically honest confidence regions for high dimensional parameters by the desparsified conservative lasso self | 0.794 | 6 | 3 | 50% |
| 9 | Horn, R. and C. Johnson (2013) Matrix Analysis | 0.714 | 11 | 4 | 36% |
| 10 | Fan, J., Y. Liao, and M. Mincheva (2011) High-dimensional covariance matrix estimation in approximate factor models | 0.669 | 30 | 4 | 30% |
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