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### Subject 1. The fundamental law

There are two sources of investment opportunity.

• Strategy's breadth (BR): the number of independent, active decisions available to an active manager per year. It is the number of times per year that an active manager can use his/her skill. It measures diversification.

• Information coefficient (IC): it measures the manager's skill, or the quality of these investment decisions.

In general, improving skill (IC) will lead to more increase in IR compared to increasing BR.

Level of Aggressiveness

The desired level of aggressiveness will increase directly with the:

• Increase in the skill level because it increases the chances of success.
• Increase in square root of the breadth because it facilitates the manager to diversify among the active bets.

Strategies:

• A market timer has good skill: a low BR and high IC.
• A stock selector checks a large number of companies intermittently: a high BR and low IC.
• A specialist examines a small number of companies constantly: a high BR and low IC.

In summary, information ratios, the key to active management, depend on both skill and breadth.

#### Practice Question 1

The measure of a manager's opportunities is:

A. information ratio.
C. information coefficient.

All investors seek managers with the highest information ratios.

#### Practice Question 2

Which one measures the quality of investment decisions?

A. information ratio.
C. information coefficient.

It is the measure of skill - the correlation of each forecast with the actual outcomes.

#### Practice Question 3

The desired level of aggressiveness (ω) will increase with an increase in:

I. BR.
II. IC.
III. λ.

λ is the aversion to residual risk. It is inversely related to the ω.

#### Practice Question 4

A market timer has independent information about market returns each quarter. To have an IR of 0.8, he needs an IC of:

A. 0.20.
B. 0.4.
C. 0.8.

0.8 = IC x 41/2, IC = 0.4. A high level of skill translates into a high information ratio. Note that while market timing strategies can generate very large returns in a particular year, they're heavily dependent on luck. On a risk-adjusted basis, the value added will be small. This will not surprise most institutional managers, who avoid market timing for just this reason.

#### Practice Question 5

What attributes of an investment strategy will determine the information ratio?

II. information coefficient.
III. residual risk.

#### Practice Question 6

An active manager follows 2 companies and revises assessments on each 100 times per year. The manager is a:

A. Market timer.
B. Stock selector.
C. Specialist.

The manager increases its breadth by examining a small number of companies constantly, and does not need a high skill level.

#### Practice Question 7

To double the information ratio, we need to do one of the following:

A. double our skill.
C. double the residual risk.

We need to double our skill, increase our breadth by a factor of 4, or do some combination of the above.

#### Practice Question 8

A stock selector follows 100 companies and revise assessments each quarter. To have an IR of 0.6, he needs an IC of:

A. 0.03.
B. 0.06.
C. 0.006.

0.6 = IC x 4001/2, IC = 0.03.

#### Practice Question 9

A specialist follows 1 company and revise assessments 25 times each quarter. To have an IR of 0.6, he needs an IC of:

A. 0.06.
B. 0.12.
C. 0.0015.

0.6 = IC x 1001/2, IC = 0.06.

#### Practice Question 10

If a manager makes a quarterly forecast of the market, which consists of 10,000 stocks, and the information coefficient for the market forecast is 0.2, the information ratio for the market timing is:

A. 0.2.
B. 0.4.
C. 20.