
Answer-first summary for fast verification
Answer: The number of bets per year
## Explanation In Grinold's fundamental law, **breadth (BR)** refers to the **number of independent investment decisions or "bets" per year**. This is the correct interpretation because: - **Breadth measures diversification** in terms of independent opportunities to apply skill - It represents the **frequency of independent forecasting opportunities** - The square root of breadth (√BR) in the formula reflects how diversification improves the information ratio **Why the other options are incorrect:** - **Option B**: The ratio of active return to active risk is actually the **definition of the information ratio (IR) itself**, not breadth - **Option C**: The number of positions in the portfolio doesn't necessarily equal the number of independent bets - some positions may be correlated - **Option D**: The number of securities in an index represents potential investment universe size, not the actual number of independent investment decisions made **Key insight**: Breadth is about the **number of independent opportunities** to apply investment skill, typically measured as bets per year, where each bet represents an independent forecast or decision.
Author: LeetQuiz .
Ultimate access to all questions.
Grinold's fundamental law says that the expected information ratio of an active investment strategy, IR, is given by the information coefficient (IC) multiplied by the square root of the breadth, BR, which is a measure of diversification. In words, as Grinold says, "High information ratios follow from high levels of skill and/or high breadth or diversification." The presumption is that information ratios are the primary measure of value added. In a subsequent development the transfer coefficient, TC, was incorporated as a multiplier such that the extended fundamental law is given by IR = IC x sqrt(BR) x TC. The transfer coefficient, TC, is a measure of efficiency: to what extent do transaction costs and/or other constraints cause the actual portfolio to vary from the optimal portfolio?
Which of the following is the BEST measure of breadth, BR, in the fundamental law?
A
The number of bets per year
B
The ratio of active return to active risk
C
The number of positions (aka, holdings) in the portfolio
D
The number of securities in the relevant global index, e.g., S&P 1500, Russel 3000, or Wilshire 5000
No comments yet.