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**Subject 4. The optimal level of residual risk**

Given the opportunities described by the information ratio, the active manager should choose the portfolio that maximizes value added.

The value added curve is a curve that is tangent to the residual frontier at portfolio P* (i.e. the optimal portfolio).

Mathematically:

As the risk increases, both the expected return and the penalty for risk increase.

The optimal level of residual risk (ω*) which maximizes VA[ω

_{P}] is

The optimal level of residual risk increases if:

- There are more opportunities.
- There is less residual risk aversion.

The implied level of residual risk aversion:

#### Practice Question 1

Which factors determine the manager's optimal level of residual risk?
I. aggressiveness.

II. information ratio.

III. residual risk aversion.

IV. loss in alpha.

#### Practice Question 2

If the information ratio is 1 and residual risk aversion is 0.05, the optimal level of residual risk is:
A. 5%.

B. 10%.

C. 20%.

IR/(2λ) = 1/(2x0.05) = 10.

#### Practice Question 3

__________, the higher the level of aggressiveness.
I. The greater our opportunities

II. The less our opportunities

III. The higher the residual risk aversion

IV. The lower the residual risk aversion

#### Practice Question 4

A risk aversion (λ) of 0.05 usually indicates a ______ residual risk aversion.
A. restrained.

B. moderate.

C. aggressive.

#### Practice Question 5

If the information ratio is 0.75 and residual risk aversion is 0.10, the optimal level of residual risk is:A. 3.75%.

B. 3.33%.

C. 7.50%.Correct Answer: A

IR/(2λ) = 0.75/(2x0.10) = 3.75.

### Study notes from a previous year's CFA exam:

d. calculate the optimal level of residual risk to assume for given levels of manager ability and investor risk aversion;