Utility and Portfolio Choice

These preferences contradict each other they imply

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Unformatted text preview: $4,000 20% chance of losing nothing B: $3,000 loss for sure Which do you prefer now, A or B? RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 10/23/2012. © P. KOLM. 18 • For first choice, most respondents select B (a certain gain of $3,000) rather than A (an uncertain outcome with an expected value of $3,200). This choice is consistent with the notion of risk aversion • However, for the second choice most respondents select A over B. They prefer a risky gamble with an expected loss of $3,200 to a certain loss of $3,000. These preferences contradict each other; they imply that investors are risk averse when faced with gains but risk seeking when faced with losses. Classical utility fails to explain this phenomenon. RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 10/23/2012. © P. KOLM. 19 The Kahneman and Tversky utility function RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 10/23/2012. © P. KOLM. 20 References Carol Alexander (2008). Market Risk Analysis: Quantitative Methods in Finance, Wiley Frank J. Fabozzi, Sergio M. Focardi and Petter N. Kolm (2006). Financial Modeling of the Equity Market: From Capm to Cointegration. Hoboken, New Jersey, John Wiley & Sons, Inc. Endnotes 1 Bernoulli, Daniel. 1954. “Exposition of a New Theory on the Measurement of Risk.” Econometrica, (Translation from 1738 version). 2 The latter risk premium is the one more commonly used in economic analysis. It corresponds to a casualty or liability insurance premium. However, in financial problems the compensatory risk premium is more useful. It corresponds to the “extra” return expected on riskier assets. The quantity W − πi is also known as the certainty equivalent of the gamble W + ε , since it is that certain amount which provides the same expected utility. 3 Sufficient conditions for this approximation to be accurate are that u ′′′ and the support of ε are bounded. RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 10/23/2012. © P. KOLM. 21...
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