Risky Choices and Correlated Background Risk

The analysis of a risky project should take into account not only uncertainties about the return from that project ("project risk"), but also uncertainties associated with other ongoing projects and with exogenous factors that can impact final wealth ("background risk"). The presence of background risk can change the optimal course of action with respect to a project, and ignoring such risk might lead to a poor decision. Most work on background risk assumes that project risk and background risk are independent and are additive in their impact on wealth. However, independence is often unrealistic, and background risk operates in a multiplicative manner in many situations. We relax the independence assumption and consider a model with both additive and multiplicative background risk. The optimal decisions in the correlated setting can be very different than those that would appear optimal if the correlation were ignored. The impact of correlation differs in the additive and multiplicative cases, with positive correlation being beneficial in some cases and negative correlation in others. The analytical and numerical results indicate that in analyzing decision-making problems, it is very important to understand the direction and degree of dependence between project risk and background risks.

[1]  Harris Schlesinger,et al.  Multiplicative Background Risk , 2006, Manag. Sci..

[2]  J. Pratt.  RISK AVERSION IN THE SMALL AND IN THE LARGE11This research was supported by the National Science Foundation (grant NSF-G24035). Reproduction in whole or in part is permitted for any purpose of the United States Government. , 1964 .

[3]  Jia He,et al.  The Foreign Exchange Exposure of Japanese Multinational Corporations , 1998 .

[4]  Richard M. Levich,et al.  1998 Survey of Derivatives and Risk Management Practices by U.S. Institutional Investors , 1999 .

[5]  C. Gollier.  The economics of risk and time , 2001 .

[6]  S. Ross.  SOME STRONGER MEASURES OF RISK AVERSION IN THE SMALL AND THE LARGE WITH APPLICATIONS , 1981 .

[7]  D. L. Hanson,et al.  ON THE THEORY OF RISK AVERSION , 1970 .

[8]  John W. Pratt,et al.  Aversion to one risk in the presence of others , 1988 .

[9]  Richard J. Zeckhauser,et al.  Proper risk aversion , 1987 .

[10]  D. V. Gokhale,et al.  Assessment of a Prior Distribution for the Correlation Coefficient in a Bivariate Normal Distribution , 1982 .

[11]  Christian Gollier,et al.  Risk Vulnerability and the temper-ing E ect of Background Risk , 1996 .

[12]  Deborah Lucas,et al.  Portfolio Choice in the Presence of Background Risk , 2000 .

[13]  Miles S. Kimball,et al.  Standard Risk Aversion , 1991 .

[14]  Robert L. Winkler,et al.  Assessing Dependence: Some Experimental Results , 2000 .

[15]  R. Kihlstrom,et al.  RISK AVERSION WITH RANDOM INITIAL WEALTH , 1981 .

[16]  David C. Nachman.  Preservation of "more risk averse" under expectations , 1982 .

[17]  Louis Eeckhoudt,et al.  Risk: Evaluation, Management and Sharing , 1996 .

[18]  David E. Bell.  A contextual uncertainty condition for behavior under risk , 1995 .

[19]  Ronald A. Howard,et al.  Decision analysis: practice and promise , 1988 .

[20]  D. E. Bell.  One-switch utility functions and a measure of risk , 1988 .

[21]  Luc Arrondel,et al.  Portfolio Choice and Background Risk: Theory and Evidence. ∗ , 2003 .

[22]  R. Mehra,et al.  THE EQUITY PREMIUM A Puzzle , 1985 .

[23]  George Allayannis,et al.  Exposure and Markups , 2001 .

[24]  Louis Eeckhoudt,et al.  Are Independent Optimal Risks Substitutes , 2001 .

[25]  R. Nisbett,et al.  The psychometrics of everyday life , 1986, Cognitive Psychology.

[26]  R. Clemen,et al.  Correlations and Copulas for Decision and Risk Analysis , 1999 .

[27]  R. L. Winkler,et al.  Separating probability elicitation from utilities , 1988 .

[28]  Richard J. Zeckhauser,et al.  Another Type of Risk Aversion , 1970 .

[29]  Miles S. Kimball.  Precautionary Saving in the Small and in the Large , 1989 .

[30]  Philippe Jorion,et al.  The Exchange-Rate Exposure of U.S. Multinationals , 1990 .

[31]  Paul R. Milgrom,et al.  A theory of auctions and competitive bidding , 1982 .

[32]  Stephen A. Ross,et al.  Adding Risks: Samuelson's Fallacy of Large Numbers Revisited , 1999, Journal of Financial and Quantitative Analysis.

[33]  P. Samuelson.  Risk and uncertainty: a fallacy of large numbers , 1963 .

[34]  D. E. Bell.  Risk, return, and utility , 1995 .

[35]  R. Bliss,et al.  Option-Implied Risk Aversion Estimates , 2004 .