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Effect across kinds of day
Calm days are of all days and volatile days are . On calm days strategy hits its target of the time and strategy hits it . On volatile days hits and hits . Within each kind of day a coin decides which strategy runs. What is the average effect of running instead of on the hit rate over all days? Give a number of percentage points, negative if is worse.
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Hint
Take the difference within each kind of day, then weight by how common that kind is.
Solution
- On calm days the difference is points.
- On volatile days it is points.
- The weighted effect is .
Answer: