Beat the Market: The Kelly Criterion and the Capital Asset Pricing Model

Date of Award

Spring 5-2026

Degree Name

Bachelor of Science (BS)

Advisor(s)

Robert Kissell

Abstract

Though probability theory and game theory are commonly discussed and employed in gambling, they can often be employed very successfully in a much bigger game - investing. This paper looks to explore the interplay between probability theory and the financial markets by looking at a specific application. Using Edward O Thorpe's theory surrounding the Kelly Criterion, this paper will find an "ideal bet" on the S&P500 and employ that within the Capital Asset Pricing Model, simulating investment over a period of time. This will yield expected returns of the Kelly Strategy in the actual markets. In comparing these results to those of a standard buy/hold on the S&P500, the success of the Kelly Strategy can be determined. This paper will demonstrate that, through the use of computational tools such as Python and Excel, the Kelly Fraction can be found and employed as a Beta in the Capital Asset Pricing Model. Though this study determines the lack of feasibility that surrounds the use of the Full Kelly fraction in real world investing, another strategy emerges. The use of the Half Kelly provides an investor with a strategy that remains minimally volatile while maintaining a high growth rate. Through the use of the Half Kelly, this paper demonstrates that the Kelly Strategy is in fact a "winning" one when employed and understood correctly.

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