The one with more volatility is more expensive because buyer has to compensate the bearer's risk by paying a risk premium (which you mentioned). More explanation later.
Dude that's exactly what I'm arguing against.
I'm arguing that volatility shouldn't be a factor of risk, nor should it be a reason for asking for more return. I gave the coin tossing as an example, stating that both tickets that entitle you for the earnings of the tosses should be priced the same. And I showed how differences in their prices will make the cheaper more attractive.
Well because it doesn't and it's not true. CAPM is a measure of return not a measure of risk and the formula does not take volatility into factor.
Off-course it does. It is captured by the "beta" in the formula, which basically calculates how volatile an asset is relative to the market. And the market volatility itself has a return that is captured in the market risk premium.
Even though their expected return are the same, their actual return will/should be different. ie 1$ coin toss gets you 10$ in the end but 2$ could give you 20$ or nothing. Since there is a chance to to earn more than the risk free alternative, some people are willing to basically gamble for a higher return and buyers often have to pay a premium for the risk the owner has taken.
Well that's my whole point, I'm arguing that two assets having the same expected return should be priced the same no matter how much their actual return deviates from their expected return.
Look the return rates are set by diversifies investors (mutual funds, hedge funds etc...), off-course if they buy 1 coin paying 2$ or nothing, they might have some risk (although I bet they'd prefer that to buying the risk-free coin), but when you buy 1000 coins, you eliminate the risk (this is what they actually do by buying a big number of stocks).
My arguments lead to the following conclusion: Even if the risk premium was 1% or 2% (as opposed to 5 - 6% nowadays) rational investors would still be better off buying volatile assets and run away from risk-free assets promising a lower return. And with time this is what I think will actually happen. Risk premium will go down and investors will still invest in risky assets.
CAPM is one of the more simpler models for simple estimates. Different asset classes have different and more complex models already exists and are used.
I know but that's irrelevant to my discussion as risk in finance is always calculated in the same way (volatility).
My argument is that volatility is not how risk should be calculated.