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**Subject 2. Information ratio**

**information ratio**is a risk-reward benchmark that is often used to quantify the performance of an investment, and specifically the effectiveness of a fund manager.

**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 ω

_{P}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:

_{P}= IR x ω

_{P}

#### 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.

1/12^{1/2} = 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

1/4^{1/2} = 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