I might be mistaken as I dont know the literature, but when talking to a professor on this topic, I got the impression (and I'm really extending what he said) since the predominate way to estimate asset returns density from options prices is to use black Scholes to get the variance. But the only way to do that, is to assume that the expected return of the distribution is the risk free rate. That means when estimating a density from option prices, the expected return is always the risk free rate. Note this does not exclude other methods for estimating the expected return like CAPM for instance. The problem with using CAPM and other asset pricing models, is that it estimates market expectations of returns from realized returns. This has a couple of problems, 1. with max ent you have two variables to play with, market expected return and the realized return which are calculated independently, with most asset pricing models market expected return is assumed to be expectation[realized return]. 2. related, you cant test if market players are biased and have other behavioral abnormalities as expected return is set to E[realized returns], 3. Most importantly, when calculating market expected returns = E[realized return], you really only have one realization of the future return i.e. you want to calculate the expected return of Ford stock right now for one year in advance, you find 100 different stocks with exactly the same beta and take the expectation of that (obviously simplyfying) to get your expected return. The problem is you arent really taking iid draws for Ford stock, you may be able to control for things with a linear regression, but again that's far from actually getting to simulate Ford stock 100 times from now until one year from now. With max ent, you arent simulating Ford stock 100 times, but using 1000s of peoples choices to buy options and using that to back out the implied expected return from market participants, which is actually even better for calculating what the market expects future returns to be than being able to simulate Ford stock 1000 times, because you dont have to assume market expectations of return = E[return]. Does this makes sense? I'm not great at writing this just in a comment box and as always I could be wrong.