Thursday, October 26, 2006

"Love of power over men is a base instinct no less petty or universal than greed. "

The CAPM has always been a troubled child. Even though its explanatory power is relativly small it has been a natural part of the basic curriculum at business school for quite a while. However, this working paper from ERIC G. FALKENSTEIN presents an explanation for why it fails to explain reality.

The following excerpt is from mahalanobis:

In the paper, my alter-ego explains this as a consequence of people caring about their relative status, rather than absolute wealth. In such an environment, nondiversifiable risk becomes like diversifiable risk in the traditional CAPM, avoidable, so unpriced. All you have to do is assume people care about relative wealth and using arbitrage or utility theory, risk is not related to returns. A beta=0 asset has the same risk as a beta=2 asset to someone benchmarked against the market. The paper presents a simple model, and goes over the empirical evidence with copious references.

There’s actually been quite a few models using a relative status approach for various parochial problems, so it’s not novel in that aspect, it just takes the approach to the general problem of risk and return. And all the general normative implications for volatility retain, including the desire to hedge, or buy insurance (though not, say, Global Warming insurance). There is one big seemingly counterfactual implication: that the equity risk premium is zero. I address this by noting that the equity risk premium used to be estimated at around 8%, and is now generally estimated around 3.5%, so another 3.5% is not farfetched. Further, that estimate ignores transaction costs, and peso-problems in equity indices, which takes this to zero (is the marginal investor the Vanguard500 investor? A high volume/expense day trader? A 5% front-load paying granny?). It should be noted that the traditional model generates only a 0.35% risk premium for plausible parameters, so this isn't as contrary as it seems (any outside-the-box refinement to the traditional model could well be applicable to this one).

Love of power over men (and the implied greater access to women regardless of aggregate wealth) is a base instinct no less petty or universal than greed. Economists should not shirk the implication because as dismal scientists, we draw the line at greed, not envy. It’s not a normative theory, just a positive one (ie, descriptive, not prescriptive). Not only can a relative status utility function explain the absence of the risk aether’s effects in markets, but it can potentially explain other issues, such as the home bias (people are more concerned about their income relative to their countrymen, not the world), endogenous instability (a world where ‘no risk’ is defined as what everyone else is doing has some arbitrariness), and why aggregate happiness is stagnant in countries 5 times as wealthy as 70 years ago (the rat race is unaffected). Rick Harbaugh has a paper where a similar approach generates the utility function of Prospect theory, which is typically just asserted as a funky preference. So there's much to be gained, and only empirical embarrassment to lose (plus all those canned presentation about CAPM given to students).
The abstract of the original articel :
This paper presents a utility function refinement that explains the empirical irrelevance of risk to returns. The key is that in an environment where people care about relative wealth, risk is a deviation from what everyone else is doing, and therefore becomes like diversifiable risk in the CAPM, avoidable. Using an equilibrium or an arbitrage argument, a relative status oriented utility function creates a zero risk-return correlation via a market model that implies a zero risk premium. This approach is described as being theoretically consistent, intuitive and a better description of the data.

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Remember the costs of information acquisition

When thinking about how to invest your portfolio additional information is not necessarily a good thing as this illustrates:
Seen at Mhalanobis:

A paper by Guiso and Jappelli looked at Information Acquisition and Portfolio Performance. They develop a theoretical model that shows how an overconfident investor is actually made worse off, because they overestimate the precision of their signal. The really interesting part of their paper is a novel set of survey data from an Italian bank that shows people who are confident are generally worse investors than those who are ignorant. Investors experienced a lower Sharpe ratio the more they invest in investment information. It seems people use information to rationalize risk taking that is not commensurate with greater returns; a simple strategy of basic naïve asset allocation dominates the average active investor.

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