dorsal/arxiv
View SchemaSelf-Consistent Asset Pricing Models
| Authors | Y. Malevergne, D. Sornette |
|---|---|
| Categories | |
| ArXiv ID | physics/0608284 |
| URL | https://arxiv.org/abs/physics/0608284 |
| DOI | 10.1016/j.physa.2007.02.076 |
| Journal | Physica A 382, 149-171 (2007) |
Abstract
We discuss the foundations of factor or regression models in the light of the self-consistency condition that the market portfolio (and more generally the risk factors) is (are) constituted of the assets whose returns it is (they are) supposed to explain. As already reported in several articles, self-consistency implies correlations between the return disturbances. As a consequence, the alpha's and beta's of the factor model are unobservable. Self-consistency leads to renormalized beta's with zero effective alpha's, which are observable with standard OLS regressions. Analytical derivations and numerical simulations show that, for arbitrary choices of the proxy which are different from the true market portfolio, a modified linear regression holds with a non-zero value $\alpha_i$ at the origin between an asset $i$'s return and the proxy's return. Self-consistency also introduces ``orthogonality'' and ``normality'' conditions linking the beta's, alpha's (as well as the residuals) and the weights of the proxy portfolio. Two diagnostics based on these orthogonality and normality conditions are implemented on a basket of 323 assets which have been components of the S&P500 in the period from Jan. 1990 to Feb. 2005. These two diagnostics show interesting departures from dynamical self-consistency starting about 2 years before the end of the Internet bubble. Finally, the factor decomposition with the self-consistency condition derives a risk-factor decomposition in the multi-factor case which is identical to the principal components analysis (PCA), thus providing a direct link between model-driven and data-driven constructions of risk factors.
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"abstract": "We discuss the foundations of factor or regression models in the light of the\nself-consistency condition that the market portfolio (and more generally the\nrisk factors) is (are) constituted of the assets whose returns it is (they are)\nsupposed to explain. As already reported in several articles, self-consistency\nimplies correlations between the return disturbances. As a consequence, the\nalpha\u0027s and beta\u0027s of the factor model are unobservable. Self-consistency leads\nto renormalized beta\u0027s with zero effective alpha\u0027s, which are observable with\nstandard OLS regressions. Analytical derivations and numerical simulations show\nthat, for arbitrary choices of the proxy which are different from the true\nmarket portfolio, a modified linear regression holds with a non-zero value\n$\\alpha_i$ at the origin between an asset $i$\u0027s return and the proxy\u0027s return.\nSelf-consistency also introduces ``orthogonality\u0027\u0027 and ``normality\u0027\u0027 conditions\nlinking the beta\u0027s, alpha\u0027s (as well as the residuals) and the weights of the\nproxy portfolio. Two diagnostics based on these orthogonality and normality\nconditions are implemented on a basket of 323 assets which have been components\nof the S\u0026P500 in the period from Jan. 1990 to Feb. 2005. These two diagnostics\nshow interesting departures from dynamical self-consistency starting about 2\nyears before the end of the Internet bubble. Finally, the factor decomposition\nwith the self-consistency condition derives a risk-factor decomposition in the\nmulti-factor case which is identical to the principal components analysis\n(PCA), thus providing a direct link between model-driven and data-driven\nconstructions of risk factors.",
"arxiv_id": "physics/0608284",
"authors": [
"Y. Malevergne",
"D. Sornette"
],
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"physics.soc-ph",
"physics.data-an",
"q-fin.PR"
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"doi": "10.1016/j.physa.2007.02.076",
"journal_ref": "Physica A 382, 149-171 (2007)",
"title": "Self-Consistent Asset Pricing Models",
"url": "https://arxiv.org/abs/physics/0608284"
},
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