Here at Tradier Inc. we believe that being as well prepared as possible is important. To that end we will be introducing a guest blog series. Kicking us off is a series of posts from Craig Hilsenrath of Option Workbench from “Enhancing Option Portfolio Returns Using Probability and Statistics” Craig has built some outstanding technical tools for analyzing options data and in this series of posts will explain the importance of statistics in that kind of analysis.

**Enhancing Option Portfolio Returns Using Probability and Statistics**

*Overview*

With nearly four thousand optionable U.S. equities and ETFs and over 400,000 individual option contracts available on a daily basis, retail option traders need a way to determine the optimal way to allocate their investment capital. By employing some well known statistical techniques to calculate the expected profit and return for a set of option positions an option strategist can rank possible trades. These techniques can be used across diverse positions, assets and asset classes to compare positions and determine the optimal utilization of investment capital.

**Introduction**

One of the advantages of investing with options is that mathematical models can be used to compute a theoretical value for the options. The theoretical value can then be compared to market prices to determine whether trading opportunities exist. Using some of the statistical techniques that underly option pricing one can also construct measurements of option performance. One such measure is expected return. Expected return is a statistical measure of a position’s estimated return on investment.

In this paper we will first examine the calculation of expected value. The expected value is used in many diverse industries and situations including manufacturing, medical research, gaming and finance; it is also the basis for the computation of expected return. The first section examines how expected value is calculated in general and provides examples of how casinos use expected value to make their profits.

As opposed to casino games where the probabilities are known and constant, those associated with an option position’s expected profit are based on a trader’s assumptions about future market conditions. The second section shows how to calculate the expected profit for an option position with an emphasis on how to compute the probabilities.

Simply using expected profit to compare positions is not sufficient to make an informed decision. A position with a high expected profit may entail a large amount of risk. Therefore, a position with a lower expected profit and lower risk may be more desirable.

The final section examines how expected return is calculated and used to compare positions.

**To Be Continued.....**

Stay tuned for the next installment from Craig Hilsenrath of Option Workbench, “Expected Value”.