We develop tests for deciding whether a large cross-section of asset prices obey an exact factorstructure at the times of factor jumps. Such jump dependence is implied by standard linearfactor models. Our inference is based on a panel of asset returns with asymptotically increasingcross-sectional dimension and sampling frequency, and essentially no restriction on the relativemagnitude of these two dimensions of the panel. The test is formed from the high-frequencyreturns at the times when the risk factors are detected to have a jump. The test statistic isa cross-sectional average of a measure of discrepancy in the estimated jump factor loadings ofthe assets at consecutive jump times. Under the null hypothesis the discrepancy in the factorloadings is due to a measurement error, which shrinks with the increase of the sampling fre-quency, while under an alternative of a noisy jump factor model this discrepancy contains alsonon-vanishing firm-specific shocks. The limit behavior of the test under the null hypothesis isnon-standard and reflects the strong-dependence in the cross-section of returns as well as theirheteroskedasticity which is left unspecified. We further develop estimators for assessing themagnitude of firm-specific risk in asset prices at the factor jump events. Empirical applicationto S&P 100 stocks provides evidence for exact one-factor structure at times of big market-widejump events.
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