The Ex Post IR
The ex post (looking backward) information ratio is a measure of achievement. It can be used to evaluate active manager's performance.
It can be negative.
The Ex Ante IR
The ex ante (looking forward) information ratio is a measure of opportunity.
IR for portfolio P:
where ωP is the portfolio's residual risk.
Our personal IR is the maximum IR an investor can attain over all possible portfolios:
The IR is independent of the manager's level of aggressiveness. It depends on the time horizon:
The residual frontier: the manager's opportunity set.
The IR defines a "budget constraint" for the active manager:
A top 10% manager has an IR of 1.0.
I. benchmark portfolio.
II. risk-free portfolio.
III. cash portfolio.
They all have a zero residual return.
A. higher level of risk.
B. higher level of manager's aggressiveness.
C. longer time horizon.
The residual frontier is a straight line through the origin.
1/121/2 = 0.288.
C. investment strategy.
Every manager has an unique information ratio.
A. Manager A.
B. Manager B.
C. cannot determine.
Manager B has a higher IR which indicates more opportunities.
For a given level of residual risk IR3 has the highest level of residual return.
1/41/2 = 0.5.
A. benchmark portfolio.
At the origin both α and ω are zero. The benchmark portfolio, by definition, has no residual return. The riskless portfolio also resides at the origin.