Outside of a sole globally risk averse agent, all other agents in markets are risk seeking agents

What is it about?

The question as to whether all agents in markets inherently are risk averse agents who are willing to entertain some skewness preference is an age old question, a question that, at the very least, is as old as Kraus and Litzenberger (1976). The alternative hypothesis is, markets consist of globally risk averse agents (agents who do not entertain any preference for skewness); risk averse agents who entertain some skewness preference; and risk seeking agents - agents who only are parameterized by skewness preference which exceeds that of non-globally risk averse agents. This study is first to arrive at formal theoretical evidence which provides an answer to the age old question. In stated respect, the formal theory arrives at the important inference, to wit, there does not exist any agent in markets who, simultaneously is parameterized by risk aversion and skewness preference. Every risk averse agent is, as such a globally risk averse agent, that is, an agent who exhibits preference for assets whose risk approximate that of a market portfolio, equivalently preference for assets whose market betas approximate one. Given every market must consist of, at the very least, two risk preference parameters, every other agent in any market is a risk seeking agent. In light of study findings, empirical findings in Kraus and Litzenberger (1976) provide evidence for presence of each of a globally risk averse agent and risk seeking agents in stock markets. The rationale is straightforward, yet hitherto overlooked, namely commencing at a market beta of one, a move to either of left to lower risk assets, or either of the right to higher risk assets results in a deterioration to the ratio of expected returns to the standard deviation of returns (the 'information ratio'). For the sake of argument, suppose otherwise; well then if the information ratio improves consequent on movement to either of the left or right, an asset with a market beta of one does not approximate the most efficient portfolio, clearly arrival at a contradiction. Necessarily, as such relative to market betas that approximate one, information ratios deteriorate, both to the left and to the right of assets whose market betas approximate one. Given a risk averse agent seeks to maximize said ratio - the information ratio (Rothschild and Stiglitz 1970) - a risk averse agent only can seek to invest in assets whose market betas approximate one. Every risk averse agent is, as such a globally risk averse agent. Importantly, study findings establish that the demand for every positive Net Present Value (NPV) asset whose risk falls short of that of an asset whose market beta approaches one ('low risk' assets) is premised on efforts for the exhaustion of investment capital within the populations of globally risk averse and risk seeking agents. The rationale is straightforward, namely since it is rational to take on positive NPV projects, each of globally risk averse and risk seeking agents have incentive to raise capital large enough to invest in the assets that they strictly prefer - 'safest assets' or 'high risk assets' - and in low risk assets. For concreteness, the demand for low risk assets is not from some agent who is less risk averse than the globally risk averse agent - said agent does not exist - rather the demand is from the sole globally risk averse agent and risk seeking agents. Stated finding represents a marked departure from the prior literature, yet is consistent with the demand for diversified portfolios.

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Photo by S O C I A L . C U T on Unsplash

Photo by S O C I A L . C U T on Unsplash

Why is it important?

The conventional wisdom in Economics and Finance is, "it is risk averse agents who make the world go round." This study turns the conventional wisdom on it's head, that is, provides formal theoretical validation for the hypothesis, in Post and Levy (2005), that risk seeking agents drive stock prices. The rationales, which explicitly are mathematical are as follows. Suppose absence of assets whose market betas approximate one in stock markets. But assume presence of assets whose market betas are much greater than one ('high risk' assets), and assets whose market betas are much less than one ('low risk' assets). Necessarily, risk seeking agents exhibit preference for high risk assets. Applying portfolio theory, subsequent to the exhaustion of high risk assets, in presence of wealth that still is in need of positive NPV assets in which to invest, risk seeking agents diversify into low risk assets. Necessarily, the combination of high beta and low beta assets replicates a portfolio whose market beta approximates one, with outcome absent the presence of globally risk averse agents, there exists the feasibility of a 'market portfolio'. Suppose, on the contrary absence of risk seeking agents in markets, but presence of globally risk averse agents. Applying the same sequence of arguments, there is arrival at presence of assets whose market betas approximate one ('safest assets') and presence of low risk assets. Clearly, the combination of market betas that approximate one, and market betas less than one cannot, in aggregate, result in a portfolio with a beta of one. Consider then, that in the absence of risk seeking agents, the most diversified portfolio cannot have a beta of one, as such does not have qualification as a 'market portfolio'. Given, however, that regression models must assume a beta of one for the market portfolio, stated deviation is not decipherable from CAPM-type regressions. The friction that is depicted in the foregoing is well documented, namely the feasibility, to wit, a portfolio that is adopted as the market portfolio does not, simultaneously have parameterization as the 'most efficient portfolio', clearly a contradiction. For a synopsis of the friction and for a list of some related literature, see Levy and Roll (2010). In essence, study findings show that the absence (respectively, presence) of risk seeking agents in markets constitutes a sufficient condition for non-coincidence of the market portfolio with the most efficient portfolio (respectively, coincidence of the market portfolio with the most efficient portfolio). Study findings arrive at mathematical conditions that facilitate the inference as to whether a diversified portfolio really has qualification as a 'market portfolio'. Succinctly, if a diversified portfolio equates to a 'market portfolio', there exist assets whose market betas cannot be differentiated from a realization of 1.00 that dominate each of 'high-expected-return' and 'low-expected-return' assets with respect to information ratios.

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