Let $\{X_i\}_{i=1}^M$ be i.i.d. positive random variables, and let $$ S_M = \frac1M \sum_{i=1}^M X_i, $$ be the empirical mean of the sample. I am looking for an expression, or an upper bound, for the quantity $$ \Phi = \mathbb{E}\left[\left(\frac1M \sum_{i=1}^M \frac{X_i - S_M}{X_i}\right)^2\right]. $$
This question is similar to what I'm asking, but I think my problem involves the variance of the difference.