How Does Removing Zeros Affect Sharpe?

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.