Asymmetric Returns and Semidimensional Risks: Security Valuation with a New Volatility Metric

45 Pages Posted: 6 Nov 2000

See all articles by Cheekiat Low

Cheekiat Low

National University of Singapore (NUS) - Department of Accounting

Date Written: August 2000

Abstract

Most theoretical models in finance measure risk as variance or covariance. However, many financial decision-makers seem to regard risk as the volatility of below-target returns and treat the volatility of above-target returns as a sweetener. Using simple metrics of downside risk and upside potential, constructed from conditional covariances, I test for the empirical content of this asymmetry. I introduce a new composite metric of semidimensional risks which reveals that the nonlinearity in the covariation of stock returns with bearish and bullish conditions of the market is priced in the cross-section of stock returns. In particular, I find that stocks that have concave characteristic regression lines against the market earn higher average returns than stocks that have convex characteristic regression lines. This new metric captures the relevant information in returns asymmetry or nonlinearity better than either coskewness or the square-coefficient from quadratic regression. I also present results that are consistent with a semidimensional risk-based explanation for the twin puzzles of return momentum and reversal. The primitive representation of the security pricing kernel as the negative of covariance between marginal utility of consumption and security returns lends theoretical support for semidimensional risks and provides a unifying perspective for seemingly disparate literature on semivariances, skewness and behavioral finance.

Suggested Citation

Low, Cheekiat, Asymmetric Returns and Semidimensional Risks: Security Valuation with a New Volatility Metric (August 2000). Available at SSRN: https://ssrn.com/abstract=246510 or http://dx.doi.org/10.2139/ssrn.246510

Cheekiat Low (Contact Author)

National University of Singapore (NUS) - Department of Accounting ( email )

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Singapore, 117592
Republic of Singapore
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