Integrity Research
New York – today marks a departure from the traditional style of analysis used in our quarterly assessment of research performance. The data used in this analysis is from Investars and the interpretation of the data is Integrity’s.
Today, the question we are asking the data is whether the distribution of sell recommendation portfolios is different from the distribution of the buy recommendation portfolios of the research providers.
We created a histogram (below) which shows the number of research providers (y-axis) that generated each level of return (x-axis) over a one year period. Theoretically, it is more difficult to select sells than it is to select buys. We note that part of the difficulty in selecting sells in the real world relates to the costs of funding these short positions, which means that the timing of shorts is more critical than those of long positions. However, the Investars analysis does not treat sells like short positions, but tracks the portfolio of sells without regard for funding costs.
In the graph above, the buy portfolio of the research providers is much more centrally located (less variance) and has fewer outliers, while the sell portfolio is broadly disbursed, has a large number of outliers and has one fat tail close to the zero return mark. As a result, we must conclude that the buy and sell portfolio distributions are distinct from one another over the time period we have reviewed.
A holyhedron is a polyhedron with each face containing at least one polygon shaped hole. The boundaries of the holes share no point with each other or the boundary of the faces. For example, consider a solid cube with its 6 faces. Next, imagine thrusting a pentagonal rod through 1 face, all the way through the cube to the other side to produce (for example) a pentagonal tunnel, and only 2 of those 11 faces have holes punched in them. Each time we punch a hole, we are creating more faces. The immense challenge to finding a holyhedron is to make the holes such that they eventually punch through more than one face to reduce the number of faces that have no holes.
The holyhedron concept was first introduced by Princeton mathematician John h Conway in the 1990’s, who offered a prize of &10,000 to anyone who could find such an object. He also stipulated that this cash reward would be divided by the number of faces in such an object. In 1997, David W Wilson coined the word holyhedron to indicate a hole filled polyhedron.
Finally, in 1999, American mathematician Jade P. Vinson discovered the world’s first holyhedron specimen with a total of 78,585,627 faces. John Conway has offered a prize of $10000 divided by the number of faces, so this one should be worth approximately $20.3252.
(The Math book, Clifford A. Pickover, PhD Yale)
Domnita and me are a part of Cluj painting club. Last evening we were at the 5 year anniversary. We as capital market researchers don’t make the group as diverse as Dr. S. Istvan. 75 paintings were exhibited. The one above was painted by Istvan. When I saw it, I told him it was a holyhedron. It might look like coincidence but the mathematics we know is a lot about patterns and structures. If there is something mathematical, you will find it in nature. This is why John’s prize money was up for grabs, the moment it was announced. Why is nature mathematical? Because nature is proportional. Nature has all proportions, infinitesimally large and infinitesimally small. Time does not destroy the proportion of nature, even when nature ages, grows and decays. Then why no credit for Time in assisting nature to retain its proportion? Does it not sound intuitive that because Time is proportional, nature mirrors it and mathematics proves it. Time created nature and humans invented mathematics to study and solve the beautiful holyhedron.
