Monday, June 22, 2009

Samuelson Examplifies my Hypothesis

In an interview with Conor Clarke, Paul Samuelson states
You know that happiness is: 'Having a little more money than your colleagues.'

This preference is for relative status, and it is a zero-sum game. The standard utility function is ignorant of what others have, utility is solely a function of wealth. The increasing, concave utility function is a necessary and sufficient condition for risk aversion, why economists believe that risk must generate a return premium to the risk free asset. Yet in practice no one is indifferent to other's performance, and risk premiums are the exception, not the rule empirically.

Consider the following ideas by the CAPM gurus, whose model is predicated on ignoring what other's do:

“I want a product to be defined relative to a benchmark."
~Bill Sharpe

"Most investors are probably sensitive to the risk of being different from the market, even if overall variability is no higher. Value stocks do not outperform market portfolios regularly or predictably—if they did, they would not be riskier ."
~ Eugene Fama

Given this reality, people define risk relatively.

Consider a choice between two hypothetical worlds, one in which you earn $100,000 a year in perpetuity while others earned $90,000, and another world in which you would earn $110,000 while others earn $200,000. In surveys, almost everyone prefers the world which is in aggregate poorer because they would be relatively richer. Eugene Fama and many others noted that 'small stocks were in a depression' in the 1980s, even though they rose about the same as in the 1970s, its just that in the 1970s they were relative outperformers, in the 1980s, relative underperformers. For someone with sufficient food and shelter, relative wealth is the priority.

The implication of this kind of thinking is that risk becomes a deviation from a consensus, or market portfolio. If you are totally out of the market with your savings, you are taking a risk, because if the market goes on a bull run and you allocated none of your wealth to the market portfolio, you are relatively impoverished. People are not indifferent to this, which is why benchmark asset allocations are so perennially popular: people want to know what their neighbors are doing so they know how to define their risk.

Payoffs to Assets X and Y in States 1 and 2
Total Return
Relative Return
state 1
state 2

As shown in the table above, Y is usually considered riskier, with a 60 point range in payoffs versus a 20 point range for X. Yet on a relative basis, each asset generates identical risk. In State 1, X is a +10 out performer; in State 2, X is a -10 underperformer, and vice versa for asset Y. In relative return space, the higher absolute volatility asset is not riskier; the reader can check this for any example in which the two assets have the same mean absolute payout over the states (i.e., the average for asset X and asset Y is the same) The risk in low volatility assets is its losing ground during good times. If X and Y are the only two assets in the economy, equivalent relative risk can be achieved by taking on an undiversified bet on X or Y, which is identical to taking a position on not-Y and not-X. The positions, from a relative standpoint, are mirror images. Buying the market, in this case allocating half of each, meanwhile, generates zero risk.

The proof of this is rather straightforward, and I outline several models in this SSRN paper here.


RPB said...

fascinating concept

Anonymous said...

examplifies [sic]

there are hypotheses based in biology that would support your hypothesis based in ecomonics