Eric Falkenstein

There are a few areas where we see a risk premium Insurance against accidents Short end of the yield curve On average, no risk premium Negative risk premium to high risk People seem to be gambling, not investing, in practice, with the same expected return to gambling

Say utility is relative Y riskier than X in standard approach Y and X same risk in relative sense Risk is unnecessary: choose ½(X+Y) Like idiosyncratic risk, unnecessary risk unpriced XYavgX-avgY-avg State State Avg10 00

Easterlin Paradox Benchmarking, tracking error as risk Not a new idea Adam Smith, Karl Marx, Thorsten Veblen, Max Weber, all focused on status (didn’t formalize) Pesendorfer (1995) and Rayo and Becker (2006) modeled status orientation formally

Two assets, a risky security and a risk-free security, with returns R E and R f Where (risk free return is certain) There are two identical agents, i and –i, who have wealth in period 0 of k, and spends money, , on the two assets No consumption. In the next period, agent i’s wealth is thus

Utility is relative Max utility subject to budget constraint Substituting for, because the budget constraint holds with equality.

Taking the first order condition, we have Since each agent is identical, in equilibrium each agent holds the same amount So Or Which means, the expected return on risky assets is te risk free rate

Utility is absolute Max utility subject to budget constraint Substituting for, because the budget constraint holds with equality.

Taking the first order condition, we have This is the standard result

Basically, if people are benchmarking against the market,  =1 has no risk Then, Through arbitrage Which means, trivially, that all assets have the same return

Search for alpha like ‘Optimal stopping problem’ Sample various ‘investments’ x j where x j ~N( ,  2 ) Each investment costs c>0 You get T draws (eg, 100) At any stage n, can stop and receive x n in until T Optimal to sample until x n >k(c,n,  2,T), where k is the criterion for stopping

As the cost of sampling goes up, propensity to stop searching increases As the variance of the sampling information increases, the propensity to stop searching decreases As the time left in the draw goes down, the propensity to stop increases

You are willing to pay to take risk because you get value from the extra sampling in many cases (c>0) Sampling more than once, for most parameters, will be the optimal solution for most situations As time goes on, the ability to take such risk decreases because the benefits are not as great High variance increases value for search Forms our intuition

Trying something to see if you have alpha Trying out for football Writing poetry Appearing on American Idol Most fail, miserably. Why it hurts to fail, it reflects on you. Finding your best fit has big payoffs Outside of organized sampling as in school, generally people will tell you, you have no chance

“That the automobile has practically reached the limit of its development” Scientific American 1909 “Heavier-than-air flying machines are impossible” Lord Kelvin 1895 “There is no reason anyone would want a computer in their home” Ken Olson 1977 “We stand on the threshold of rocket mail” US postmaster general Arthur Summerfield 1959 “Nuclear-powered vacuum cleaners will probably be a reality in 10 years” Alex Lewyt President of Lewyt Vacuums, 1955

People overconfident when they search for alpha Good meta-strategy, bad investment strategy Leads to excess demand for super risky assets

AAA-BBB spread, 3mo to 2 yr T-bills No alpha searching here Prescience too hard to prove Everyone needs some amount of safety assets, cash Cash is a ‘medium of exchange’, a property many investments do not have Repos (cash) have T-bills, AAA securities as collateral

Risk Expected Return No Alpha Possible, no hope, no benchmarking Expensive Alpha Searching, Too much hope Alpha Possible, Benchmarking