FOUNDATION OF FINANCE

Foundation of Finance



Foundation of Finance

Part 2 (e) Briefly discuss any limitations of your analysis and how (given more time and information) you might refine your analysis in the future.

Ans2 (e) The Capital Asset Pricing Model (CAPM) developed by the researcher known as Sharpe in 1964 and Lintner in 1965 has been the major factor of the subject of finance, and it has been used in numerous important applications. However, several studies indicate that the cross-section of stock returns cannot be explained by market beta alone as predicted by the CAPM. In particular, the mean-variance CAPM fares poorly in explaining the high risk premiums of portfolios formed by small cap, high book-to-market securities and momentum winners. For example, the researchers known as Harvey and Siddique in 2000 and Dittmar in 2002 studied the three-moment CAPM, which takes into account skewness in addition to mean and variance. The literature on downside risk, in contrast, considers semi variance, rather than variance, as the primary source of risk. These alternative asset pricing models fit stock return data better than the standard mean-variance CAPM, but size, value, and momentum effects remain (Brown & Gibbons, 1985, 381).

A fundamental limitation of the existing asset pricing models is the poor descriptive ability of the utility functions from which they are derived. The literature on decision making under risk points out that models displaying asymmetries in the domains of gains and losses can explain risky choice behavior significantly better than standard utility functions. The researcher known as Piccioni shows that such a utility function can capture the aspects that are crucial to explain how people face risk: (i) preference for security/potential, i.e. downside risk aversion and preference for upside potential; (ii) loss aversion, i.e. the empirical observation that losses loom larger than gains; and (iii) goal achievement, i.e. the importance of satisfying relevant aspiration levels. The three main characteristics of the model allow the A-CAPM to rationalize size, value, and momentum effects. In fact, small cap, high book-to-market securities, and momentum winners deliver higher loadings on the three factors that are priced by the A-CAPM (the risky choice factors). In other words, these securities are riskier according to the A-CAPM; therefore, the model can rationalize their higher risk premiums (Dahlquist & Soderlind, 1999, 383).

The first main feature of the A-CAPM utility function is to display concavity in the domain of losses and mild convexity in the domain of gains. In fact, approximating the utility function with an asymmetric quadratic model, I find a negative parameter for the quadratic term in the negative domain and a slightly positive parameter for the quadratic term in the positive domain. This implies preference for security/potential. Preference for security/potential, in turn, implies preference for positive asymmetry, a factor already included in the three-moment CAPM, which is derived from cubic utility functions. Since stocks are more correlated during market downturns, the market portfolio yields a relatively small reduction in downside risk at the cost of a relatively large reduction in ...