# Corona Plots

Dr. John Elder developed Corona Plots in the late 1990s to visualize the effect of selecting stocks for an investment portfolio according to all possible linear weightings of two features of a stock. The name derives from its resemblance to the sun’s corona (outer atmosphere) that can be seen during a solar eclipse. This plot became the inspiration for our company logo. (Corona Plots have only the “crown” shape in common with the Coronavirus, but if you are seeking analysis on that pandemic, we have several insightful blogs).

A Corona Plot illustrates the return of a portfolio’s top-scoring stocks (say top 10%) when the score comes from the relative weighting of the features given by the angle along the circle.  The baseline, or return of all the stocks, is represented by the black unit circle. Portfolio returns greater than the baseline appear outside the circle (and are more red), and lesser ones are plotted inside (and are more blue). For instance, the 45-degree point along the circle represents the result of choosing a decile of stocks according to a score which is an equal average between the two features.  Likewise, the negative-45-degree angle point reveals how well a portfolio does when stocks are chosen by maximizing an equal mixture of positive-X and negative-Y components.

Note that it is possible for both sides of a Corona plot to be positive (or negative); that is, for both a strategy and its exact opposite to both beat the baseline (or lose to it).  Below, on the righthand chart for example, results at 80 and -100 degrees are both losing compared to the baseline.  This counter-intuitive result can happen when less than half of the population is to be selected, since the hidden stocks in the center of the distribution, that don’t end up in either tail, could have unusual returns.

Corona plots can be made 3-dimensional.  Tubular versions show how coronas shift over time, and spherical versions reveal the impact of a third input feature (but must be examined interactively).  Still, 2-dimensional Coronas are the most used.  Below, are two such Coronas plotting return (on the left) and υ/σ (on the right) for a portfolio 20% the size of the baseline population.