Generalized Little's Law and an Asset Picking System to Model an Investment Portfolio: A Working Prototype

Abstract

We are not aware of any meaningful application of Little's Law in the finance field. Our ambitious goal is to create an Asset Picking System (APS) structure that, combined with Little's Law (LL), Generalized Little's Law (GLL) and its corollaries, generates the GLL-APS model, a financial engineering tool bridging operations research and finance. In the process we extend Little's Law in certain ways and make its vocabulary specific to our application. Consider a financial adviser working with a customer to select and maintain a portfolio of investments over a time period. Individual investments are bought or sold and enter or leave the portfolio, which is thought of as a queue. The total value of the portfolio at a point in time is the sum of the values of each investment in the system. When an investment is sold, it departs, and its selling price becomes cash. Cash may be kept in a money market fund, waiting for re-investment, or accumulated in a savings account to be used for personal consumption. Little's Law (LL) in its basic form simply counts the number of investments and so deals with their rate of arrival, the average number in the system, and the average time an investment stays in the system. However, there is an advanced version of LL that we call Generalized Little's Law (GLL), in which each investment can be weighted, for example, by its dollar amount. Then we can calculate the average dollars of investments in the portfolio over a time interval and the average time that an investment remains in the portfolio with the duration of each investment weighted by its dollar size, as well as knowing the average arrival rate of investments. Our process uses decision rules to create the APS structure. which, through a four step process, selects assets and their numbers of shares to build a portfolio. Any change is accepted or rejected by the adviser and, ultimately, by the customer. Various environmental events, notably, recurrent global recessions, can negatively impact certain classes of investments and make them less appealing as choices for the customer. All clients are more concerned about the market opportunities and hold more reasonable expectations than before such crises. We take that into consideration. We concentrate on customizing and maintaining an investment portfolio for the person who owns it. The GLL-APS model does this. Currently it is a working prototype because it is operational but is evaluated by computer simulation with only one of the three customer profiles we have collected so far. Our investments test bed consists of a set of 14 asset classes, each with 10 blue chip securities. Later we intend to expand the number of customers and assets and plan an orderly rollout of our model in multiple phases.