In my book Finding Alpha I document 20 different asset classes where the risk premium is either missing or goes the wrong way. But I did not include penny stocks, so it’s a good ‘out of sample’ test of my hypothesis, that he risk premium rises as one goes from super safe to safe, stays flat, then goes the wrong way for lottery ticket investments like sports betting, distressed debt, high volatility stocks, and of course lottery tickets.
Bjorn Eraker and Mark Ready just put out a paper entitled, Do Investors Overpay for Stocks with Lottery-Like Payoffs? An Examination of the Returns on OTC Stocks. They find:
In our nine year sample, approximately $820 Billion traded in the OTC markets. This represents less than a month of typical NYSE volume. Still, the OTC markets are not insignificant: the average stock in our sample lose about 15M dollars from the first observation to the last. In total, stocks in the OTC market lost approximately $180 Billion of market value over our sample period. These numbers themselves are conservative because we did not make any assumption about the value depreciation taking place for stocks that no longer trade.
In case you didn’t know, penny stocks are lousy investments; high risk, negative return. They suggest either the Miller explanation, that differential expectations imply a winner’s curse, or the Barberis and Huang explanation, that people really love positive skew. They leave with the note that they are looking at a model in which investors display risk aversion over losses and risk-loving behaviour over large gains would conceivably explain the results.
That’s the great thing about the ‘risk premium’. It’s not a theory, but rather a framework, so that any anomaly merely rejects an incorrect theory within this framework, and not the framework itself. Nonetheless, it is supposedly the foundation of modern finance, based on Markowitz’s brilliant, and rigorous, insights. It explains everything, because when it doesn’t, you just say people are not risk averse, but rather risk-loving over various parts of the return distribution for specific asset classes. Kahneman and Tversky’s famous prospect theory argued that things like lotteries could be explained by ‘risk-seeking behaviour in losses involving moderate probabilities and of small probability gains’, which of course is different. The Black Swan idea is that people prefer high probability bets with small gains but occasion high losses. The point is clear: the utility function explains residual returns, and places no restrictions on them.
My argument is much less plastic. First, people are benchmarking against their peers and colleagues, and this leads to a zero risk premium as a first order approximation. There is no ‘risk premium’ in financial markets, just as there is no courage premium to the aristocracy. But people also have a strong preference towards lottery tickets, as explained in my post ‘Why are High Risk Stocks so Crappy.’
Benchmarking, or a ‘relative status’ or ‘envy’ utility function, are all the same thing. It explains why risk premiums don’t exist in general. It also explains the Easterlin Paradox, where greater wealth over time has neither reduced the risk free rate, nor increased general happiness. It explains too why people’s asset allocations generally ignore strict mean-variance optimization, because they consider what the ‘standard allocation’ to be risk neutral, because keeping-up-with-the-Joneses is risk neutral. It’s rather straightforward to increase one’s Sharpe ratio (buy low volatility stocks), or one’s covariance with their income (invest in other developed country indices), but this is considered risky, because then you have benchmark risk, which is what investors really hate more than volatility itself.
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