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Alpha (or residual return) is...
a risk-adjusted measure of the active return on a portfolio:
Ex post IR:
ex ante IR can be only positive
The Residual Frontier:
The manager's information ratio effectively serves as a "budget constraint". She can increase expected residual return only if she accepts a corresponding increase in residual risk:
The aim of active management is to...
maximize the *value added* from residual return
The optimal portfolio:
is the tangency point of the VA curve and the residual frontier
Investors seek to maximize value added, and the decision is independent of the level of risk aversion the manager has displayed. Investors will simply choose a manager with the highest information ratio.
Given his investment opportunity set (which is determined by the ex ante alpha)...
the investment manager will try to invest in the portfolio that has the highest value added
The optimal VA:
This says that no matter how high or low our risk aversion level is, we would choose the investment manager with the highest information ratio. Investors will only differ with respect to how aggressively they implement the manager's strategy.
Check out the level of aggressivenes, moderation in terms of risk
Residual risk (ω*) as a function of IR and risk aversion (λ)