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In responding to question 8 I did the following: Calculated the IR, which is the ratio active return to active risk. This IR in this case was .75%, which implies that for for each additional unit of active risk you can achieve an additional active return of .75%. This alone indicates that doubling active risk will not double active return. To augment this we can talk about how the IR declines with the IC. That is, as you try to increase alpha you tend to choose securities or increase allocations to sectors you know less about; therefore the information coefficient declines, causing a decline in IR. I don’t understand the logic of the response in the book. Why does the author not bother calculate the current IR and show that even if IR is unchanged, a doubling of risk will not double active return?

If the IR doesn’t change, then doubling active risk does double active return.

Using your example:

1 risk = .75 return.

2 risk = 1.5 return.

Increasing risk has diminishing increases in return because the IR decreases.

who said that the breadth is constant? I don’t see this assumption anywhere…