Formula in equity market valuations is E(U) = E®m - (0.5*lambda*variance of market)
Formula in Chapter 25 Equity investments is the same except the last term is not multiplied by 0.5
Is there any logic behind what and why those are different?
Just 2 different conventions!
I think the author of chapter 25 doesn’t work often with Black Scholes model or some kind of mathematical models so he found strange and unnecessary to add the factor 1/2 into the formula.
I remember on the level 1 CFA I struggled to accept the fact that there is no factor 1/2 on the convexity and I felt crazy that I must learn by heart this wrong formula. The author doesn’t know surely what the Taylor’s theorem is.
My conclusion: you should learn the 2 formulas by heart, don’t try to understand the difference between them (because these 2 are exactly the same, just under 2 different conventions).
The difference is between the expected utility from a portfolio and active management.
Expected utility of a portfolio is Rp-.5*lambda*variance(portfolio).
Expected utility of active management = R(active) - lambda*variance(active).
Remember the second only uses active return and active risk not portfolio return.