In CAPM, we assume people are risk-averse and people get compensated for the systematic risk they suffer. The assumption that most people are risk-averse makes sense, but why are the rational investors also risk-averse? Consider the following example, suppose investment $i$ has an expected return of $10\%$ and beta coefficient $2$ while another safer investment offers $5\%$ but is virtually risk free. By the weak law of large numbers, investment $i$'s average return rate will be close to $10\%$ if many years passes. In fact, if invested for many years, this investment can be seen as an investment with $10\%$ return but less risky because the distribution for the average return rate has less and less varaince as the number of years increases. So a rational investor should understand it and simply choose the investment with the risk premium. The idea is in the long run, yearly varaince on return diminishes.
Any suggestions or criticisms are appreciated.