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 1An information ratio of 1.0 usually indicates ______ opportunities.
A top 10% manager has an IR of 1.0.
Practice Question 2Which 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 3The information ratio grows with:
A. higher level of risk.
B. higher level of manager's aggressiveness.
C. longer time horizon.
Practice Question 4Which line is most likely to be the residual frontier of an active manager?
The residual frontier is a straight line through the origin.
Practice Question 5Monthly IR is ______ the size of the annual IR.
1/121/2 = 0.288.
Practice Question 6The residual frontier is per:
C. investment strategy.
Every manager has an unique information ratio.
Practice Question 7Two 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 8Which residual frontier represents the best manager?
C. IR3.Correct Answer: C
For a given level of residual risk IR3 has the highest level of residual return.
Practice Question 9Quarterly information ratio is ______ the size of the annual information ratio.
C. 1Correct Answer: B
1/41/2 = 0.5.
Practice Question 10The 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