Averages: There is Still Something to Learn

The common way to deal with outliers in empirical Economics and Finance is to delete them, either by trimming or winsorizing, or by computing statistics robust to outliers. However, due to their importance, there are situations where the exclusion of these observations is not reasonable and may even be counterproductive. For example, should we exclude the very high stock prices of Amazon and Google from an empirical analysis? Even if the purpose is to compute an average of tech stock prices, does it make economic and financial sense? Maybe not. A solution that would keep the two companies in the data set and yet not penalize the higher observations as much as the median, harmonic and geometric averages, might—were such a solution to be available—constitute an attractive alternative. In this paper we propose and analyze a modified measure, the adjusted median, where the influence of the outlying observations, while not as high as in the arithmetic average would, however, give more weight to the outlying observations than the median, harmonic and geometric averages. Monte Carlo simulations and bootstrapping real financial data confirm how useful the adjusted median could be.