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Title: Portfolio sorting error Authors:  Valentina Corradi - University of Surrey (United Kingdom) [presenting]
Walter Distaso - Imperial College London (United Kingdom)
Abstract: Portfolio sorts are commonly used in finance to unveil the relation between returns and the sorting variable which groups stocks. Sorting can be according to an observable variable, such as size or book to market, or to an unobservable variable, such volatility, (co)-skewness. Sorting according to unobservable variable is infeasible. Hence, we need to replace the sorting variable with an estimated counterpart. In addition to estimation error, due to the fact that sorting is done according to order statistics rather than ``true'' deciles, we need to take into account missclassification. Returns assigned to the bottom decile may instead belong to a higher decile. The objective is to introduce sorting procedures robust to misclassification error. This is accomplished by establishing a rule for eliminating the highest and lowest returns within each deciles. If there is no significant relation between returns and sorting variables, missclassification error does not matter. On the other hand, if there is a significant positive or negative relation then it does matter. Often one wants to test the null that the mean return on top and bottom portfolios is the same, versus the alternative that is smaller (larger). Hence, we want to trim away a sufficient number of observations to affect the outcome of the test under the alternative, but not to affect under the null. In the empirical illustration, we study sorting error for portfolios sorted according to (co)-skewness.