In Chapter 54 it’s labeled as Equation (8)

In Chapter 55 it’s labeled as Equation (3)

When do we use one and not the other?

In Chapter 54 it’s labeled as Equation (8)

In Chapter 55 it’s labeled as Equation (3)

When do we use one and not the other?

They are the same basically, but in different contexts. The one in chapter 55 measures value added in terms of IC and Breadth, while the one in chapter 54 measures in terms of IR and aggressiveness-risk aversion.

Also, don’t forget these 2 formulas are not exactly the same, eq(8) is the basic VA, eq(3) is the optimal VA. The latter is more related to equation 12 of chapter 54.