Applied prospect theory: assessing the βs of M&A-intensive firms

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Behavioral components of Kahneman and Tversky’s (1979) prospect theory (PT) were applied to derive an adjusted Capital Asset Pricing Model (CAPM) in the estimation of merger and acquisition-intensive firms’ expected returns. The premise was that the CAPM – rooted in expected utility theory – is violated by the behavioral biases identified in prospect theory. Kahneman and Tversky’s prospect theory (1979) has demonstrated that weaknesses abound in the viability of classical utility theory predictions. For mergers and acquisitions, firms appear to be isolated from and immune to human error, yet decisions which involve the undertaking of capital-intensive projects are delegated to senior management. These individuals are prone to cognitive biases and personalized risk appetites that may (and often do) compromize attitudes and behavior when it comes to pricing risky ventures. Having established that beta estimates using linear regression are inferior, the CAPM was implemented utilizing beta estimates obtained from the Kalman filter. The results obtained were assessed for their long-term market price predictive accuracy. The authors test the reliability of the CAPM as a predictor of price, observe the rationality of human behavior in capital markets, and attempt to model premiums to adjust CAPM returns to a level that more appropriately accounts for firm specific risk. The researchers show that market participants behave irrationally when assessing M&A firms’ specific risk. Logistic regression coupled with the development of a risk premium was implemented to correct the original Kalman filter returns and was tested for improvements in predictive power.

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    • Figure 1. Wealth utility for a risk-averse utility maximizer
    • Figure 2. CAPM predicted asset prices vs actual observed price
    • Figure 3. M&A portfolio implied volatility and VIX index
    • Figure 4. Logit curve regression for the probability of loss in revenue
    • Table 1. EUT axioms
    • Table 2. Results of logit curve regression of loss to revenue and IE
    • Table 3. Correlation of adjusted CAPM returns to actual share prices