Idealized Standard Deviation

Abstracts

Brett Hencley, Tracy Reece, Luke Atwell, and Shawn Bradford

QRB/501

October 27, 2014

Gary White

Hencley Abstract

This article looks at investment risk using calculations of standard deviation. Donald (2006) states there are many models used to predict investment risk.  Harry Markowitz won a Nobel Prize for his theory that risk can be mitigated by studying the standard deviations of their returns. Donald argues that this theory works because typically performance stays within the realm of normal distribution.  He also argues that there are risk factors that are not accounted for in the standard deviation theory such as credit risk, gapping risk and other rouge risk such as unforeseen actions by regulatory bodies.   In the end, Donald (2006) recommends using several models in predicting risk and understand that none of them are perfectly accurate.  He recommends be wary of averages and statistics, diversify and challenge the methods used when predicting risk and investment returns.  These recommendations are based on the fact that the standard deviation method may be too simple a formula for predicting risk as it does not take into account outside risk factors.

Atwell Abstract

Measuring Parity: Tying Into the Idealized Standing Deviation aims to quantify parity among sports competitors.  The purpose of the study was to raise issues regarding the customary application of that concept in leagues that do not employ a binomial system for determining rankings, to suggest that the reciprocal of the ISD may be a more intuitive construct if the intent is to represent parity, to provide scholars with a set of ISDs, and to suggest some interesting topics that arise from a quick perusal of the time series (Cain & Haddock, 2006).  The main research question asked in the study is what is the appropriate measure of parity among competitors?  Holding team characteristics constant, shorter series, shorter seasons will more likely result in unbalanced records that will longer ones (Cain & Haddock, 2006).  Recognizing that, Quirk and Fort devised a measure—the idealized standard deviation (ISD)—to enable them to compare records in Major League Baseball across seasons of different lengths and league composition.  Since baseball is accounted on a binomial basis, a win counting as 1 and a loss as 0, they made use of the binomial theorem to develop their parity measure (Cain & Haddock, 2006).  After creating that, Quirk and Fort began comparing parity across the major sports that do not use a binomial system of generating rankings.  The study was most prevalent in English Football where the rankings system is on a win, loss, tie ranking where wins receive 2 points, ties 1, and losses 0.  They found that teams in the Premier League experienced wins 37.705% of the time, losses 37.705% of the time, and draws for the remaining 24.59%.  Based on that, they calculated the standard deviation of the distribution where teams entering a contest had a 25% probability of leaving with a draw (Cain & Haddock, 2006).  Now they had their formula for Standard Deviation= √(.75*N), where N is the number of season games.  They plugged in all of their information, made data tables, and found out that the MLB has generally moved towards greater parity as well as in the English Premier League.