Portfolio risk, market risk or systematic risk cannot be reduced by increasing the number of securities. Unsystematic risk can be reduced by adding more securities. Can you provide examples of systematic and unsystematic risk? Why do we need to have the covariance less than the variance of the securities? And we know that the variance of the portfolio asymptotically approaches covariance; each additional security will reduce risk. Why?

I get unsystematic and systematic risk. And I understand covariance to the point of moving together in a positive or negative direction. But I don't understand the part from having covariance less than variance and down. Help please.