Cross-country and intertemporal indexes of risk aversion
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Mark Kritzman* CFA is Managing Partner or Windham Capital Management Boston, a Senior Partner of State Street Associates, and the Research Director of the AIMR Research Foundation. Mr Kritzman holds a BS degree in economics from St John’s University and an MBA with distinction from New York University.
Kenneth Lowry CFA is a Vice President with Global Link, the e-commerce arm of State Street Corporation. Mr Lowry holds a BS in mathematics and computer science from Trinity College (Hartford) and an MBA from the Yale School of Management.
Anne-Sophie Van Royen is Senior Quantitative Strategist for State Street Associates, LLC. She holds a PhD in Mathematical Economics from the Universite´ de Paris-Sorbonne, France. She also holds an MA in Business Studies from the Ecole des Hautes Etudes Commerciales, France. *WCMB, 5 Revere Street, Cambridge, MA 02138, USA Tel: ⫹1 617 576 7360; e-mail: [email protected]
Abstract One of the most common and firmly held views of financial economics is that investors are averse to risk. Although a formal description of risk aversion was proposed by the celebrated mathematician, Daniel Bernoulli, as early as 1738, financial economists are still puzzled about many aspects of risk aversion, including the fact that the realised premium of equities over a risk free asset is too large to accord with ‘normal’ notions of risk aversion. This discrepancy is known as the equity risk premium puzzle. There is also vigorous debate as to the effect of horizon on the willingness of investors to bear risk. To help address these issues and other questions related to risk aversion, a methodology is introduced to infer risk aversion from global portfolio flows and holdings. Specifically, the authors derive a formula for risk aversion based on the assumption that investors maximise expected utility by allocating their portfolio between assets of differing risk. The authors use this formula to approximate the risk aversion of US investors towards specific countries. They demonstrate that risk aversion, as they approximate it, helps to predict bond and stock returns, as well as risk premiums one period forward. Keywords: risk aversion; expected utility; portfolio flows; portfolio holdings; panel regression; risk premium
Introduction One of the most common and firmly held views of financial economics is that investors are averse to risk. In fact, a formal description of risk aversion was proposed by the celebrated
䉷 Henry Stewart Publications 1470-8272 (2002)
mathematician, Daniel Bernoulli, as early as 1738 (1954). Bernoulli described the following game. Two participants, each of whom has 100 ducats, contribute 50 ducats as a stake in a game in which the chance of
Vol. 3, 1, 29-38
Journal of Asset Management
29
Kritzman et al.
Table 1
Expected utility of participating in fair game
Pay-off
Utility of pay-off
50 150 Expected utility
3.91 5.01 4.46
Probability of pay-off (%)
Probability-weighted pay-off
50 50
1.96 2.51
winning is determined by the toss of a coin. Each player, therefore,
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