As the topic title mentions, this one is to Finance gurus, I expect users who would answer my question to have some advanced understanding about the different methods used to price an asset (i.e. stocks).

So as you know guys in valuing the intrinsic value of an asset to a diversified individual investor, one element used in the CAPM model, is the stock's beta and the market's risk premium, which together capture the risk of a certain asset. And risk in finance is described as the standard deviation between actual vs. expected return, or in other words, how much a certain stock's return deviates from its expected return (the more it deviates the more risky an asset is perceived to be).

But isn't this illogical? why would stock A, which deviates more than stock B (both having the same expected return) be priced in such a way as to generate higher returns?

To put you in the same state of mind as me, think of the following:

Suppose that I am about to sell two different tickets, one that entitles its bearer to earn 1$ every time I toss a coin for 10 consecutive tosses no matter the outcome (whether heads or tails), and the other 2$ every time the outcome is heads but nothing for tails. And so I put these two tickets in the open market so that investors can bid on them.

In finance, the latter is a more risky investment and thus current finance theory suggests that the market would price it at a lower price point than the former, being “Risk free”. But if this was the case, then everyone would rush to buy the latter ticket, after all, why would the ticket with a certain payoff be priced more expensively than that of an uncertain one if they both have the same expected return? (especially to a diversified investor)

Notice that both have an expected return of 10$, and so my theory says that eventually, they will be both priced in the market at the same price point (a little less than 10$ per ticket).

This is all to suggest that risk in finance should be measured in a different way, what do you guys think?