Adding a stock to a portfolio will reduce the risk of the portfolio if the correlation coefficient is less than which of the following?
Your answer: A was incorrect. The correct answer was B) +1.00.
Adding any stock that is not perfectly correlated with the portfolio (+1) will reduce the risk of the portfolio.
The question’s correct answer doesn’t make sense to me. It places no restrictions on risk or return of the securities. For example, what if I had a portfolio (A) of rtn = 10%, std dev = 5% and a separate security (B) of rtn = 3%, std dev = 50%. Suppose corr(A,B) = 0.99. There is no weight of B that could be added to A that would lower A’s std dev, right? I’m assuming no shorting… maybe they aren’t?
If it were true that adding any non perfectly correlated stock to a portfolio would result in a decrease in std dev, that would mean the Optimal Market Portfolio with individual components approaching infinity would have a std dev approaching zero… right? That’s just silly.
What’s more likely is I’m misunderstanding. Please tell me. Thanks!