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Previous research has investigated the multivariate normality of stock returns using tests based on the marginal distribution of returns. Due to the contemporaneous correlation across asset returns, these tests are difficult to interpret. We develop a general test procedure that takes account of the correlation across assets and that focuses on both the marginal and joint distributions of returns. We find highly significant evidence that stock returns and market-model residuals are nonnormal. Moreover, this nonnormality appears in both the marginal and joint distributions of asset returns.
Richardson et al. (1993) studied this question.
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