Portfolio Mgmt Q: correlation correct, question, following

joehogue

QUESTION:
Adding a stock to a portfolio will reduce the risk of the portfolio if the correlation coefficient is less than which of the following?
A) 0.00.
B) +1.00.
C) +0.50.
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!
-F

mfleming1983

wannabequant wrote:
Think about the equation for portfolio variance:
Variance of Portfolio = w1^2*variance1 + w2^2*variance2 + 2*w1*w2*correlation(1,2)*stdev1*stdev2
Although the last part of the equation lowers when corr
Maybe what the original question is trying to say is this:  If you are forced to add a stock to your portfolio, having a coefficient of less than 1 will decrease the portfolio’s risk relative to if the correlation was 1. I’d agree with that.

Muddahudda

Short-selling isn’t a constraint. A portfolio can, and often does, contain negative weights. That’s what optimization is all about. You’re right that it’s impossible to reduce the portfolio risk in all situations if you can only go long, but that’s not an assumption. And, even if you couldn’t short, your answer to the original question is still wrong. The ideal answer is the closest possible to 0 (and if you managed to have -1, that would absolutely reduce your risk since there wouldn’t be any), which includes anything between (-1, 1).