Investors require a return from investing in stock securities that adequately compensate the investors for the risk level assumed. Therefore, any calculation of expected returns from a stock requires knowledge of the risk of the security. While there is no strong consensus on an ideal risk measure, traditionally risk has been conceptualized as volatility and is measured by the ß of the stock or portfolio. This paper hypothesizes that alternative risk measures such as higher order moments, size, leverage, and price-to-book value add explanatory power to the ß when predicting stock returns. Empirical analysis is conducted using both regression and portfolio methodologies and data collected on over 300 NYSE companies. The results demonstrate a clear lack of statistical significance of alternative risk measures in explaining returns and show that the relationship between returns and ß for the time period 2003 – 2014 is negative. Additional testing is conducted by analyzing the impact of the financial crisis on the results and by changing market indices, neither of which significantly change the results obtained. This paper also builds a theoretical framework that may be used to model stock prices using a martingale process.


Hartman, James

Second Advisor

Sell, John


Business Economics; Mathematics


Portfolio and Security Analysis


alternative risk, risk analysis, CAPM, stock

Publication Date


Degree Granted

Bachelor of Arts

Document Type

Senior Independent Study Thesis Exemplar



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