Stock returns are not always from the same distribution: Evidence from the Great Recession

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Portfolio allocation strategies, and notably the mean-variance approach, use past returns to assign optimal weights. Even though both past and expected returns should come from the same distribution, a formal test of whether this holds in practice has not been conducted yet. Thus, the study examines if the daily returns of 242 companies with continuous trading in the S&P index come from the same distribution using the Kolmogorov-Smirnov, Cramér-Von Mises, and Wilcoxon rank-sum tests. The tests suggest that generally stock returns do come from the same distribution. However, the hypothesis is rejected during the Great Recession, with the rejection rate increasing as the forecast horizon increased. The rejection rate, using an array of macroeconomic variables, is found to record high levels of persistence. Although macroeconomic variables were not found to be statistically significant determinants of the rejection rate, market distress has a small but significant effect.

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    • Figure 1. Percentage of samples in which distributions were not equal
    • Figure 2. One-hundred (100) observations forecast sample
    • Figure 3. Fifty (50) and two-hundred (200) observation window
    • Figure 4. Percentage of samples in which distributions are not equal using Cramér-von Mises test
    • Figure 5. One-hundred (100) observation forecast sample using Cramér-Von Mises test
    • Figure 6. Fifty (50) and two-hundred (200) observation forecast sample using Cramér-Von Mises test
    • Figure 7. Percentage of samples in which distributions are not equal using Wilcoxon rank-sum test
    • Figure 8. One-hundred (100) observation forecast sample using Wilcoxon rank-sum test
    • Figure 9. Fifty (50) and two-hundred (200) observation forecast sample using Wilcoxon rank-sum test
    • Table 1. Average rejection rate in each period
    • Table 2. Average rejection rate in each period
    • Table 3. Average rejection rate in each period
    • Table 4. Estimation results