AppliedNumeric answerFree solution

A signal has an information coefficient of 0.050.05 and you make 400400 independent bets a year. What information ratio does the fundamental law predict?

Answer with a number. Fractions, powers and expressions like 23/6 or C(52,5) are read correctly in practice.

Show the answer and worked solution

Answer

11

The fundamental law of active management says IR≈ICBR\mathrm{IR} \approx \mathrm{IC}\sqrt{\mathrm{BR}}, so 0.05×400=0.05×20=10.05 \times \sqrt{400} = 0.05 \times 20 = 1. Read it as skill times opportunity: a very modest per-bet correlation becomes a respectable portfolio once it is applied often enough and independently enough. The word doing the work is independent. Four hundred positions that all load on the same factor are one bet, not four hundred, and the law then overstates the achievable ratio by a factor of twenty.

Worked solution

  1. Formula
    IR=ICBR\mathrm{IR} = \mathrm{IC}\sqrt{\mathrm{BR}}
  2. Substitute
    =0.05×400= 0.05 \times \sqrt{400}
  3. Solve
    =0.05×20= 0.05 \times 20
  4. Answer
    IR=1\mathrm{IR} = 1

Takeaway: IR≈ICBR\mathrm{IR} \approx \mathrm{IC}\sqrt{\mathrm{BR}}.

Answer it in practice – your answer is marked and recorded.

Reported in interviews at

Citadel, Two Sigma, AQR, Point72 and Cubist

More alpha and signal research questions

A signal has an information coefficient of 0.05 and you make 400 independent bets a year. · QuantMax