ninja1024

I can positively assure you that there are traders out there that have negative Sharpe ratios that last for years. Go figure.

If r = -1 and the expected return is positive then you should always add it. If the expected return is negative it's not clear and depends on the expected returns of the rest of the portfolio and the variances. Realistically an r of -1 means you just have the opposite of your portfolio now, e.g., you own S&P 500 and the new asset is a deep ITM put which wouldn't help your portfolio