OR 680: Capstone Project
George Mason University
Department of Systems Engineering & Operations Research
Spring 2010
Executive Summary
The optimal options investment strategy group uses mathematical modeling to find high yield strategies with low risk of catastrophic loss. Most fund managers trade on speculation or intuition based on market data rather than search for optimal strategies using a trading model. A mathematical model provides a spectrum of strategies which produce higher returns, lower risk, or both.
Investors use a very large set of options strategies combining multiple options and positions. To finish the model in the allotted time, the scope is narrowed to a single strategy with limited parameters. The strategy we optimize is the short strangle taking into account these parameters: trade date, put strike price, call strike price, stop-loss, maximum acceptable volatility, and optimal fractional allocation.
The results of the model output show that over short periods of time there are clear optimal solutions, though the same strategy will probably not remain optimal for long periods of time. Analysis of 2004-2006 showed substantially different optimal solutions than 2007-2009, therefore we recommend continuously using recent data to find current optimal investment strategies.
The optimal strategy for 2007-2009 uses call strike +5, put strike -15, stop-loss 20, sold 42 days before expiration, and is fully invested. The return on investment is over 700 times the initial investment over 3 years, or 36 trades. Sensitivity analysis shows that small changes to input parameters can significantly diminish returns but will still result in strategies with above average returns.
We have identified assumptions and limitations in the model which result in overstated returns. Perfect execution of stop-loss is the greatest factor causing inflated model output. There are many areas of future work which can make the model results more realistic and accurate.
Problem Statement
Investment risk and return can be improved through operations research modeling to optimize trading strategies. Currently, top option investors make trades based on their ability to predict the state of the market rather than mathematical modeling. A traditional stock trade is also known as a spot market trade. It requires immediate investment of the current value of a stock. Alternatively, option trading is a higher risk and higher reward investment than traditional stock, as it requires significantly less cash on hand. Investors can leverage their equity multiple times using options in the hopes of attaining higher returns.
There are many tools to analyze stock portfolios, but not many that analyze options trading. Professional investment funds sell investment strategies to customers based on past performance. Picking a winning strategy is difficult, and it becomes even more difficult when considering that all investors may not necessarily have the same risk tolerances. Young investors may be willing to take higher risks for a chance at higher payoffs because they expect to have many more productive years to make up for losses. On the other hand, older investors may not be willing to take higher risks as they need their assets for retirement. Therefore there may be several top strategies depending on an investor’s objectives for return and risk. Mathematical modeling simulates multiple outcomes based on varying constraints providing scientific justification for investment choices in lieu of subjective feelings about the market.
Statement of Need
There is a need for a detailed analysis of option investment strategies to find optimal choices for investors with different goals. Strategies must be robust so that changes in the market do not have a large effect on the payoff or risk of ruin. There is also a need for a computer application that can display equity curves and performance of past options so that investors can test recommended strategies.
Business Case
Investment fund managers control the assets of many clients. To keep customers they must provide satisfactory services. Their goals should be to make decisions in accordance with their customers' financial interests. Our model and tools can aid fund managers to quickly assimilate information about the current options market conditions and act before the market changes. A fund manager can use our model to find the optimal strategy over a specified period of recent history. Once top strategies are found, the fund manager can apply fractional investment to match returns and risk of ruin to customer demand.