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### A realized approach to estimate conditional alphas

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Corradi, Valentina, Distaso, Walter and Fernandes, Marcelo
(2011)
*A realized approach to estimate conditional alphas.*
In: 2011 Australasian Meeting of the Econometric Society, Adelaide, 4-7 July 2011
(Unpublished)

**Full text not available from this repository.**

Official URL: http://editorialexpress.com/conference/ESAM2011/pr...

## Abstract

This paper proposes a two-step procedure to back out the realized alpha of a given stock from high-frequency returns. The first step estimates the realized factor loadings of the stock, whereas we retrieve the conditional alpha by estimating the conditional expectation of the stock return in excess over the realized risk premia. In particular, consider the following factor model for returns: ri;t = fii;t+PKk=1 fii;k;tFk;t+fii;t, where Ft = (F1;t; : : : ; FK;t) denote a vector of observable factors at the high frequency. For instance, Ft would include the S&P 500 index and its powers within the context of the CAPM with higher-order moments, whereas one could employ exchange-traded funds (ETFs) based on size and book-to-market considerations to proxy for the Fama-French three-factor model. To estimate the realized factor loadings, we must first orthogonalize the factors Ft by taking linear combinations of the intraday returns on the risk factors, namely, F m;t = BtFm;t with Fk;m;t ? F;m;t for

all 1 k K as well as for every instant m within day t (or week, whatever). Note that the rotation matrix Bt is known even if it changes every day and hence it is possible to recover the original (daily) factor loadings i;k;t from the daily loadings of the orthogonal factors ;k;t. We estimate the latter using the standard realized beta approach, yielding a realized loading for each orthogonal factor given by (M) i;k;t and so a realized risk premium of PK k=1 (M) i;k;t Fk;t = PK k=1 M) i;k;t Fk;t. By subtracting the realized risk premia from the individual stock return, we find the realized counterpart of ei;t = i;t+i;t, that is to say, e(M) i;t ri;t PK k=1 M) i;k;t Fk;t. Identification of the conditional alpha results from the fact that the conditional expectation of i;t is zero, whereas i;t is measurable in the information set. It thus follows that i;t E(ei;tjZt), where Zt is the vector of state variables. The second step of the procedure then amounts to estimating (M) i;t = E(e(M) i;t jZt) using kernel methods. Note that there is an extensive list of state variables to include in Zt if we pay attention to the conditional alpha-beta literature. This means that we should think about employing dimension-reduction techniques by imposing either an additive or a single-index dependence structure.

Item Type: | Conference Item (Paper) |
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Subjects: | H Social Sciences > HG Finance |

Divisions: | Faculty of Social Sciences > Economics |

Official Date: | 5 July 2011 |

Status: | Not Peer Reviewed |

Publication Status: | Unpublished |

Description: | All presentations by Corradi alone. |

Version or Related Resource: | Corradi, Valentina, et al. (2011). A realized approach to estimate conditional alphas. In: Invited Speaker : Economics External Seminars, University of Birmingham. Birmignham, 12 Oct 2011. |

Conference Paper Type: | Paper |

Title of Event: | 2011 Australasian Meeting of the Econometric Society |

Type of Event: | Conference |

Location of Event: | Adelaide |

Date(s) of Event: | 4-7 July 2011 |

Related URLs: | |

URI: | http://wrap.warwick.ac.uk/id/eprint/45838 |

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