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Risk and Return

Risk and Return - Risk and Return in General Theory and...

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Electronic copy available at: http://ssrn.com/abstract=1420356 1 Risk and Return in General: Theory and Evidence Abstract Empirically, standard, intuitive measures of risk like volatility and beta do not generate a positive correlation with average returns in most asset classes. It is possible that risk, however defined, is not positively related to return as an equilibrium in asset markets. This paper presents a survey of data across 20 different asset classes, and presents a model highlighting the assumptions consistent with no risk premium. The key is that when agents are concerned about relative wealth, risk taking is then deviating from the consensus or market portfolio. In this environment, all risk becomes like idiosyncratic risk in the standard model, avoidable so unpriced. (JEL D01, D81, G11, G12) Eric Falkenstein Minneapolis, MN, USA [email protected] First version: June 2009 This version: January 2010
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Electronic copy available at: http://ssrn.com/abstract=1420356 2 Theoretically, globally concave utility functions are necessary and sufficient for agents to be risk averse. People strictly prefer a certain outcome to an uncertain outcome with the same mean payoff, and so demand payoff premium to be indifferent. To the degree risk is not diversifiable as in ‗market risk‘ , someone must hold it, and because it is disliked those who do hold it must be compensated via a risk premium relative to risk-free securities. Yet it is striking that a first approximation to risk via volatility or beta against the market return generates no positive risk premiums. Consider that assets such as houses have characteristics that require compensation, such as crime, bad schools, or noise, and these factors and their effects are eminently measurable and consistent with intuition (Black 1999; Tita, Petras and Greenbaum 2006). Risk, meanwhile, has devolved into the financial equivalence of dark matter, evident solely by its effects. As asset pricing models have increased in complexity from the simple one- factor CAPM, to ―stochastic discount factor(s) … so general, they place almost no restrictions on financial data‖ (Campbell (2002)). Explai ning asset returns via risk is often more calibration than prediction, as when the risk premiums are functions of atheoretically observed risk factors (see Dai and Singleton 2002; Fama and French 1992). This paper argues a more radical but much simpler solution: There is generally no empirical risk-reward relation, and that the seemingly obvious examples are exceptions to the general rule, explainable as liquidity premiums and measurement error. I present a model that explains the null risk-return result as an equilibrium when people internalize risky decisions by comparing themselves to others, as opposed to the standard approach to risk based on the absolute volatility of their wealth. If utility is a status function, specifically the value of wealth rel ative to one‘s peers, only deviations from the consensus are ‗risky‘ (See Cremers and Petajisto
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