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### Subject 2. Information ratio

The 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.

IR = residual return / residual risk

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:

αP = IR x ωP

#### 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.

Correct Answer: I, II and III

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.

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. 1

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.