I wrote a proof deriving the distribution of returns for all asset and liability classes. If there were no budget constraint, limitation on liability and liquidity had no cost, then you can prove the distribution of returns follows a Cauchy law. The budget constraint triggers skew that becomes larger and larger the higher the return. The reason is that 100% of the population would accept IBM stock at zero dollars per share, while no one would pay an infinite price. The denominator has to exist because you bought it, but the numerator does not. The probability of a trade declines as the sales price increases and returns can be thought of as the probability of a specific return, given a trade happened, times the probability a trade happened.
Nonetheless, until you get to the upper ends, the Cauchy distribution is a reasonably good fit for returns on securities that are going concerns. Firms that are going to merge or become bankrupt have different distributions. I also empirically tested this and solved the option pricing model as well.
The easiest thing is to go to my author page. https://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=1541471
Start with the article "The Distribution of Returns," it has everything from stocks to bonds to antiques to accounting ratios. Then go to the article on why practitioners should use Bayesian methods, then if you are interested you can look at the empirical test. Finally, that leaves you an option pricing model. It is not THE option pricing model, but a option pricing model. The article discusses realistic extensions. I am preparing two more articles for summer. One extends stochastic calculus to cover macroeconomics and finance as it does not hold under the current assumptions. The second discusses how to build a subjectively optimal portfolio. It takes little work to realize that there cannot exist an objectively optimal portfolio. A person with a mortgage and a child going to college is facing differing constrains than a pension fund.