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I am looking for examples of approximately risk-neutral firms or people in business.

Is there an industry where risk-neutrality is common for some agents (firms or people)?
Are there perhaps time periods when some agents in some industries turn risk neutral?
Could some investors be argued to be risk neutral?
Is there a literature on risk-neutrality with real-world examples?

I would especially appreciate examples of non-extreme cases if such ones exist.

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Its very hard to give an actual real world example of risk neutral person (firms are just run by people only people can have attitudes to risk) not because they do not exist but because research on micro-level risk neutrality does not publishes name of its participants and all data are anonymized. You also can't say someone is risk neutral just by pointing toward some non-experimental decision they made in real world as in such situation there might be a lot of different effects in play that you cant control for. That being said, there are some studies that try to empirically measure risk attidudes for industries just not really giving particular examples.

For example, Pennings & Philip Garcia (2001) examine the risk attitudes in Dutch farming industry using the certainty equivalence technique. The authors report that in their sample $6\%$ of farmers were shown to be risk neutral, $34\%$ risk averse and $60\%$ risk seeking (see their table 3), but of course they will not provide names of those individuals. So based on this we can conclude that $6\%$ of Dutch farmers out of 373 included in the study were risk neutral.

When it comes to investors, for example Dorn and Huberman (2005) use survey data on self reported attitudes to risk of German investors. The data show that actually most investors are neither too risk averse neither too risk loving. Unfortunately, this does not necessary imply they are exactly risk neutral as they could be just slightly risk averse or risk loving. It is hard to measure what proportion of people are exactly risk neutral outside some experimental framework, but this would seem to suggest some risk-neutral investors probably exist.

I could not find any example of an industry where empirically risk neutral people would dominate. That being said, absence of evidence is not necessary evidence of absence, as it might be due to lack of available data. However, unless there is strong competitive advantage of being risk neutral in some industry I would not expect most people there being risk neutral. The study of Dohmen et al. (2005) conducted on a general population in Germany (they had a nice representative sample of 22,000 individuals) showed that $78\%$ of people are risk averse, $13\%$ risk neutral and $9\%$ to be risk loving. Since the study is quite representative I would expect that it would be generally true for most people. Unless there is some competitive pressure for certain type of individual in the particular industry attitudes of people there should follow the distribution in general population.

Risk attitudes definitely evolve over time (see for example this and this paper), it can even be molded by researchers priming the subjects (see here), but there seem to be no research suggesting that some periods favor risk neutrality as opposed to others. In fact, risk attitudes can be affected by your emotions as well (see Loewenstein et al., 2001) so they are definitely not stable.

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    $\begingroup$ Would the downvoter care to add some constructive criticism in the comments? $\endgroup$ – Richard Hardy Jun 18 at 10:42
  • $\begingroup$ Thank you for your answer! I find it helpful. $\endgroup$ – Richard Hardy Jun 18 at 10:47
  • $\begingroup$ @RichardHardy I am glad you found it helpful - I think that was just another revenge downvote during past month I get consistently(-1) almost every day on one of my posts without any explanation and it seems to be from a single user $\endgroup$ – 1muflon1 Jun 18 at 10:55
  • $\begingroup$ This has happened to me before, though not on a big a small scale and only in a tight interval of time. Consider informing the moderators, perhaps they can help cool the user down (this worked for me on Cross Validated)... $\endgroup$ – Richard Hardy Jun 18 at 10:57
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    $\begingroup$ I am sorry to hear that. At least your reputation score still shows, despite such vandalism, how much the community appreciates your contributions :) $\endgroup$ – Richard Hardy Jun 18 at 11:08

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