2000 character limit reached
Joint Estimation of Conditional Mean and Covariance for Unbalanced Panels (2410.21858v5)
Published 29 Oct 2024 in stat.ME, cs.LG, q-fin.ST, and stat.ML
Abstract: We develop a nonparametric, kernel-based joint estimator for conditional mean and covariance matrices in large and unbalanced panels. The estimator is supported by rigorous consistency results and finite-sample guarantees, ensuring its reliability for empirical applications. We apply it to an extensive panel of monthly US stock excess returns from 1962 to 2021, using macroeconomic and firm-specific covariates as conditioning variables. The estimator effectively captures time-varying cross-sectional dependencies, demonstrating robust statistical and economic performance. We find that idiosyncratic risk explains, on average, more than 75% of the cross-sectional variance.
- Basak, G. K., R. Jagannathan, and T. Ma (2009): “Jackknife Estimator for Tracking Error Variance of Optimal Portfolios,” Management Science, 55, 990–1002.
- Chamberlain, G. (1983): “Funds, Factors, and Diversification in Arbitrage Pricing Models,” Econometrica, 51, 1305–1323.
- Chamberlain, G. and M. Rothschild (1983): “Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets,” Econometrica, 51, 1281–1304.
- Chen, Y., E. N. Epperly, J. A. Tropp, and R. J. Webber (2023): “Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations,” .
- Cochrane, J. H. (2011): “Presidential Address: Discount Rates,” Journal of Finance, 66, 1047–1108.
- Connor, G., M. Hagmann, and O. Linton (2012): “EFFICIENT SEMIPARAMETRIC ESTIMATION OF THE FAMA-FRENCH MODEL AND EXTENSIONS,” Econometrica, 80, 713–754.
- Dawid, A. P. and P. Sebastiani (1999): “Coherent dispersion criteria for optimal experimental design,” The Annals of Statistics, 27, 65 – 81.
- Drineas, P. and M. W. Mahoney (2005): “On the Nyström Method for Approximating a Gram Matrix for Improved Kernel-Based Learning,” Journal of Machine Learning Research, 6, 2153–2175.
- Engle, R. F., O. Ledoit, and M. Wolf (2019): “Large Dynamic Covariance Matrices,” Journal of Business & Economic Statistics, 37, 363–375.
- Fama, E. F. and K. R. French (1993): “Common risk factors in the returns on stocks and bonds,” Journal of Financial Economics, 33, 3–56.
- ——— (2015): “A five-factor asset pricing model,” Journal of Financial Economics, 116, 1–22.
- ——— (2019): “Comparing Cross-Section and Time-Series Factor Models,” Review of Financial Studies, 33, 1891–1926.
- Fama, E. F. and J. D. MacBeth (1973): “Risk, Return, and Equilibrium: Empirical Tests,” Journal of Political Economy, 81, 607–636.
- Fan, J., Y. Liao, and W. Wang (2016): “PROJECTED PRINCIPAL COMPONENT ANALYSIS IN FACTOR MODELS,” The Annals of Statistics, 44, 219–254.
- Filipović, D. and P. Schneider (2024): “Fundamental properties of linear factor models,” Tech. rep., working paper, EPFL, Universitá della Svizzera Italian, and SFI.
- Fortin, A.-P., P. Gagliardini, and O. Scaillet (2023a): “Eigenvalue Tests for the Number of Latent Factors in Short Panels*,” Journal of Financial Econometrics, nbad024.
- ——— (2023b): “Latent Factor Analysis in Short Panels,” Working paper, University of Geneva, and Universitá delle Svizzera italiana.
- Freyberger, J., A. Neuhierl, and M. Weber (2020): “Dissecting Characteristics Nonparametrically,” Review of Financial Studies, 33, 2326–2377.
- Gu, S., B. Kelly, and D. Xiu (2020a): “Autoencoder asset pricing models,” Journal of Econometrics.
- ——— (2020b): “Empirical Asset Pricing via Machine Learning,” Review of Financial Studies, 33, 2223–2273.
- Kelly, B. T., S. Pruitt, and Y. Su (2019): “Characteristics are covariances: A unified model of risk and return,” Journal of Financial Economics, 134, 501–524.
- Kozak, S. and S. Nagel (2024): “When Do Cross-Sectional Asset Pricing Factors Span the Stochastic Discount Factor?” Working Paper 31275, National Bureau of Economic Research.
- Kozak, S., S. Nagel, and S. Santosh (2020): “Shrinking the cross-section,” Journal of Financial Economics, 135, 271–292.
- Milz, J. (2023): “Sample average approximations of strongly convex stochastic programs in Hilbert spaces,” Optim. Lett., 17, 471–492.
- Reisman, H. (1988): “A General Approach to the Arbitrage Pricing Theory (APT),” Econometrica, 56, 473–476.
- Ross, S. A. (1976): “The arbitrage theory of capital asset pricing,” Journal of Economic Theory, 13, 341–360.
- Sylvester, J. (1851): “XXXVII. On the relation between the minor determinants of linearly equivalent quadratic functions,” The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1, 295–305.
- Welch, I. and A. Goyal (2008): “A Comprehensive Look at The Empirical Performance of Equity Premium Prediction,” Review of Financial Studies, 21, 1455–1508.
- Zaffaroni, P. (2019): “Factor Models for Asset Pricing,” Working paper, Imperial College.
Sponsor
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.