I am a bit confused about one assumption of the CAPM. My professor said that in the CAPM model all investors share the same utility function and the same degrees of risk aversion. Then as a final consequence all investors will choose a portfolio composed by a portion of the market portfolio and a portion of the risk-free security according to its preferences. (Each investors could have different portions of risk-free security and risky asset)
As far as I am concerned, I agree with the first condition, but I don't understand how is it possible that all investors have same degree of risk aversion. If so, why investors would choose different portion of risk-free security and risky asset?