The utility function for quantifying risk aversion shows up in two different places:

- Reading 21 - Asset Allocation: where U = E® - .005*(Ra)*Variance

where U is Utility from Risk adjusted expected return, E® is expected return, and Ra is the investor’s risk aversion

and

- Reading 27 - Equity Portfolio Mgmt: where U = E® - (Ra)*Variance

Here, U is Utility for active return, E® is the expected active return, and Ra is the active risk aversion

The first equation is for individual investors and the second is for managing a portfolio of managers

My question is why do we discount the individual’s risk aversion (by multplying by .005) and not the active risk aversion for a portfolio of managers? Is the formula for Ra different b/w the two?