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Han et al. 2021 mention one puzzle in investment is

individual investors are attracted to stocks with high skewness, so-called lottery stocks(...). This behavior is not consistent with standard investor preferences

I am wondering what is standard investor preferences and why that individual investors are attracted by lottery stocks is a puzzle?

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    $\begingroup$ This just as a comment: Standard investor preferences are (more or less) "rational preferences", i.e. preferences that are derived through sensible axioms. Think: Neoclassical utility theory, consumption based asset pricing and the like. Possible explanations for deviations from "non-rational" (as in: not consistent with model group A) stem from research in behavioral economics and psychology. $\endgroup$
    – Kermittfrog
    Nov 2, 2021 at 7:15
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    $\begingroup$ I think the puzzle here is that these stocks have low returns so some people seem to pay too much for them. Preference for positive skewness is not necessarily inconsistent with utility theory. $\endgroup$
    – fes
    Nov 2, 2021 at 8:34

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Standard preferences in classical economics follow certain "consistency rules" such as transitivity etc.pp. These classical preferences such as expected utility capture only the first two moments of a say normal distribution (expected value and volatility/standard deviation). Lottery-like stocks as defined by Alok Kumar ("Who gambles in the stock market") are characterized by a low price, a high volatility and a certain positive skewness. The latter one is the crucial additional feature as, if you believe in the classical utility paradigm, skewness and other higher moments shouldn't matter for asset allocation. However, if you sympathize with behavioral finance and prospect theory in particular, skewness is taken into account by the decision weights. Barberis and Huang have shown in 2007 ("stocks as lotteries") that given an investor with decision weighting functions instead of classical expectations will perceive a certain amount of lottery-like stocks as favourable compared to a portfolio without them. If all investors think this way, they will put a premium on the price (as markets have to be in an equilibrium), which will result in below-average expected returns from that stock. Thats why it's a paradox: people want to pay a higher price as they perceive those unlikely but high returns (=positive skewness) as more likely as physical probabilities suggest, thus driving up the price and lowering the returns..

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    $\begingroup$ Hi, I think you cannot write " classical preferences such as expected utility capture only the first two moments of a distribution". Rational preferences incorporate all moments of a distribution; it is the assumption of normality that will get you to the "simpler" (mu/sigma) models. Do you agree? $\endgroup$
    – Kermittfrog
    Nov 2, 2021 at 7:44
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    $\begingroup$ Good morning, yes, you are right. Without going too much into details i think you can come up with all sorts of higher-moments capturing functions (jstor.org/stable/43611195 and in particular here jstor.org/stable/4494802) but i'm not sure whether this answer would be a bit too much over the top.. :-) $\endgroup$
    – T123
    Nov 2, 2021 at 7:57
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    $\begingroup$ I'd suggest you update the answer correspondingly - I often see people wrongly equating "rational" with mu/sigma; let's counter that :) $\endgroup$
    – Kermittfrog
    Nov 2, 2021 at 9:12
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    $\begingroup$ good point, i edited it, plz. check. Feel free to msg me if needed. $\endgroup$
    – T123
    Nov 2, 2021 at 9:52
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    $\begingroup$ HI Louise, i was referring to this article here: ideas.repec.org/p/nbr/nberwo/12936.html What do you mean by "individual-level bias"? $\endgroup$
    – T123
    Nov 2, 2021 at 10:53

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