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Subject 2. Information ratio
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 is the highest ratio of annual residual return to residual risk that a manager can obtain.
- Reasonable level of ex ante IR ranges from 0.5 to 1.0.
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:
- Expected return grows with time.
- Risk grows with the square root of time.
- IR will increase with the square root of time.
The residual frontier: the manager's opportunity set.
- The residual return α versus residual risk ω tradeoffs.
- It describes the opportunities available to the active manager. The active manager can attain any expected residual return and residual risk combination below the frontier line.
- The origin (both α and ω = 0) represents the benchmark portfolio.
- The ex-ante information ratio determines the manager's residual frontier. The higher the IR, the more opportunities the manager has.
The IR defines a "budget constraint" for the active manager:
Practice Question 1
An information ratio of 1.0 usually indicates ______ opportunities.
A. excellent.
B. moderate.
C. few.
A top 10% manager has an IR of 1.0.
Practice Question 2
Which portfolio's information ratio must be exactly zero?
I. benchmark portfolio.
II. risk-free portfolio.
III. cash portfolio.
They all have a zero residual return.
Practice Question 3
The information ratio grows with:
A. higher level of risk.
B. higher level of manager's aggressiveness.
C. longer time horizon.
Practice Question 4
Which line is most likely to be the residual frontier of an active manager?

A. A.
B. B.
C. C.
The residual frontier is a straight line through the origin.
Practice Question 5
Monthly IR is ______ the size of the annual IR.
A. 1/12.
B. 1/3.
C. 0.288.
1/121/2 = 0.288.
Practice Question 6
The residual frontier is per:
A. portfolio.
B. manager.
C. investment strategy.
Every manager has an unique information ratio.
Practice Question 7
Two active managers, A and B, have IRs of 0.7 and 0.8, respectively. Which manager has more opportunities?
A. Manager A.
B. Manager B.
C. cannot determine.
Manager B has a higher IR which indicates more opportunities.
Practice Question 8
Which residual frontier represents the best manager?
A. IR1.
B. IR2.
C. IR3.Correct Answer: C
For a given level of residual risk IR3 has the highest level of residual return.
Practice Question 9
Quarterly information ratio is ______ the size of the annual information ratio.A. 0.25
B. 0.5
C. 1Correct Answer: B
1/41/2 = 0.5.
Practice Question 10
The origin of the residual frontier represents the:A. benchmark portfolio.
B. optimal portfolio.
C. portfolio with λ = 0.Correct Answer: A
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.

Study notes from a previous year's CFA exam:
2. Information ratio