# Schweser error on correlation?

It says “If 2 assets have perfect negative correlation, the variance of returns for a portfolio that consists of these 2 assets will equal 0”.

Intuitively it makes sense if the weights are 50/50. In that case, portfolio return would always be \$0 and there would be no portfolio variance. Every \$1 earned by one asset would be lost by the other asset.

That statement alone could be correct or incorrect based on the portfolio weights and variances of its 2 components. If it’s 50/50 with equal variance, then it’s correct. If not, it might not be correct.

wow so thats one of the extreme as to how CFAI give us the choice of selection? That statement is the “least likely” correct one among the rest. Schweser Book 4 page 129 Q4. It make sense intuitively but not mathematically.

“Intuitively it makes sense if the weights are 50/50. In that case, portfolio return would always be \$0 and there would be no portfolio variance. Every \$1 earned by one asset would be lost by the other asset.” I dont think so. The correlation between 2 asset doesn’t affect portfolio’s return.

Just to correct some of the points above: 1) Weights dont have to be 50/50 in order to get a 0 variance portfolio. Though, there will be only 1 combination of weights when Variance would be 0 for such a portfolio, but it does not have to be 50/50. It could be ANY combination based on variance of individual assets. 2) Also know that when you get such specific combination, when your portfolio variance (risk) becomes 0, then this Portfolio will always return Risk Free Rate of return (RFR). Otherwise, there will be an arbitrage opportunity. 3) Tungtran wrote: “The correlation between 2 asset doesn’t affect portfolio’s return.” Yes, portfolio’s Expected Return formula does not take into account the correlation between the 2 assets.

Excellent post rus1bus! God knows how many people would have had their PM concepts all wrong if you hadn’t posted here.

Thank you beatthecfa. This was a question in Schweser Mock Exam 1 (AM) asking the rate of return of a portfolio when its risk came out to be 0. And the answer was RFR as mentioned in the question. I was so impressed with the question that I still remember it. L1 takers, please dont expect all concepts to seep in at your first reading. It can be confusing at best and frustrating at worst. But dont let that demotivate you. As you do your revision and start taking more questions on them, they will get set in you for sure.