How Does Removing Zeros Affect Sharpe?

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This question evaluates understanding of the Sharpe ratio and how altering sample composition (removing zero-return observations) influences sample mean and standard deviation and thereby risk-adjusted performance metrics.

How Does Removing Zeros Affect Sharpe?

Company: Squarepoint

Role: Data Scientist

Category: Statistics & Math

Difficulty: hard

Interview Round: Technical Screen

Suppose a return series has `2n` observations. Exactly `n` observations are `0`, and the remaining `n` observations are non-zero returns `x1, x2, ..., xn` with mean `mu` and standard deviation `sigma`. Assume the risk-free rate is `0`, so the Sharpe ratio is defined as: `Sharpe = mean(return) / std(return)` 1. Compare the Sharpe ratio computed on all `2n` observations with the Sharpe ratio computed after removing the `n` zero-return observations. 2. Is the new Sharpe ratio higher or lower? 3. If the answer depends on the sign of the mean return, explain why. 4. Briefly comment on whether the conclusion still holds if the removed `n` observations are not necessarily the zero-return ones.

Quick Answer: This question evaluates understanding of the Sharpe ratio and how altering sample composition (removing zero-return observations) influences sample mean and standard deviation and thereby risk-adjusted performance metrics.

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Squarepoint
Mar 27, 2026, 12:00 AM
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Suppose a return series has 2n observations. Exactly n observations are 0, and the remaining n observations are non-zero returns x1, x2, ..., xn with mean mu and standard deviation sigma. Assume the risk-free rate is 0, so the Sharpe ratio is defined as:

Sharpe = mean(return) / std(return)

  1. Compare the Sharpe ratio computed on all 2n observations with the Sharpe ratio computed after removing the n zero-return observations.
  2. Is the new Sharpe ratio higher or lower?
  3. If the answer depends on the sign of the mean return, explain why.
  4. Briefly comment on whether the conclusion still holds if the removed n observations are not necessarily the zero-return ones.
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