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The Problem with Risk Premium: A New Theory by Eric Falkenstein

This article explores the concept of risk premium and challenges the notion that there is a consistent average risk-return relationship in investments. It delves into the idea of relative risk, status orientation, and the utility proof of benchmarking. Additionally, it discusses the impact of overconfidence in searching for alpha and the importance of holding cash as a medium of exchange. Overall, this theory presents a fresh perspective on risk and returns in the investment world.

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The Problem with Risk Premium: A New Theory by Eric Falkenstein

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  1. A New Theory Eric Falkenstein

  2. Problem • 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

  3. Simple Proof of no average risk-return • 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

  4. Why Relative Risk? • 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

  5. Utility Proof • Two assets, a risky security and a risk-free security, with returns RE and Rf • 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

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

  7. Utility Proof • 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

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

  9. Utility Proof Benchmark • Taking the first order condition, we have • This is the standard result

  10. Arbitrage Argument • 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

  11. Adjustment 1: Hope and Alpha • Search for alpha like ‘Optimal stopping problem’ • Sample various ‘investments’ xj where xj~N(m,s2) • Each investment costs c>0 • You get T draws (eg, 100) • At any stage n, can stop and receive xn in until T • Optimal to sample until xn>k(c,n, 2 ,T), where k is the criterion for stopping

  12. Optimal to sample until xn>k(c,n) • 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

  13. Risk taking increases return • 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

  14. What is 'sampling' in practice? • 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

  15. Ignoring the Experts when searching for alpha • “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

  16. So, ignore the odds • People overconfident when they search for alpha • Good meta-strategy , bad investment strategy • Leads to excess demand for super risky assets

  17. Where there is no Alpha, no hope, and Cash is Useful • 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

  18. An Equilibrium Across All Assets No Alpha Possible, no hope, no benchmarking Alpha Possible, Benchmarking Expected Return Expensive Alpha Searching, Too much hope Risk

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