firat

Check out the 2nd question provided by L3Crucifier in this thread - that’s when you would use Sharpe. Since the portfolio that the stock will be added to is not diversified, then the new stock’s unsystematic risk is actually going to significantly contribute to total risk. As a result, you should look at the relative Sharpes to see if the reward for total risk is worth it.
If the portfolio is diversified, the reward for total risk is irrelevant. All that matters is reward for systematic risk, since the stock’s unsystematic risk will have an insignificant effect on the diversified portfolio.