# correlation coefficient

Is n’t risk of portfolio will be reduced if correlation coeffficent is less than 0? I did wrong both of the following questions. ------------------------------------------------------- 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) +0.50. B) +0.30. C) 0.00. D) +1.00. Your answer: C was incorrect. The correct answer was D) +1.00. Adding any stock that is not perfectly correlated with the portfolio (+1) will reduce the risk of the portfolio. ------------------------------- There are benefits to diversification as long as: A) there is perfect positive correlation between the assets. B) there must be perfect negative correlation between the assets. C) the correlation coefficient between the assets is 1. D) the correlation coefficient between the assets is less than 1. Your answer: B was incorrect. The correct answer was D) the correlation coefficient between the assets is less than 1. There are benefits to diversification as long as the correlation coefficient between the assets is less than 1.

Key to remembering this is when assets are perfectly positively correlated --> rho=+1 --> portfolio variance is the highest… which means max risk. anything less than 1 – variance is going to be lower, and you’ll get benefit of diversification.

The first question (at least) sounds a bit crappy. If you have two portfolios with A and B in them, the sum of their variances will be less than the variance of the combined (A+B) portfolio, unless correlation=1. The first question though asks whether adding B to a portfolio of A will produce a combined variance less than A’s alone. I think you answer C was correct: var of A+B will only be less than var of A alone if correlation is < 0.

well the way I see it is that D incorporates basically the other 3 answers being more comprehensive

I think you have to assume all stocks have same standard deviations for these 2 to hold true.

Thanks for replies. I selected options for best case scenario, where diversification is best when two of stocks are perfectly negative correlated or when correlation coefficient is less than 0. I guess the question asks for when risk is getting started to reduce. So, the starting point is anything less than +1. Can I assume correlation coefficient to never exceed +1 and never be less than -1? i.e correlation coefficient will be >= -1 & <= +1

well not only assume it that is a given so you should know it looking at the formula you will know that

you are right - chinni - with your assumption. But are you sure you know the meaning of a correlation coefficient? Here some helpful questions, if you are not able to answer them then you should go into quant prep details - How is a correlation coeffient calculated? - Did you ever calculate one? - if not: do it. - What is the range of value? - What is the meaning of positive, what of negative values? - What does it mean if the coeffient has a value of -1? - Is the coefficient about only about linear relationships? - What is difference to Spearmans correlation coefficient? - What scale do you need to calculate the ordinary correlation coeffient? - Did you ever see diagrams, where data with several correlations were shown? @dispotra: Ok I understand what you mean. But can you or anybody else show/proof it? May be the equation VAR(aX1+bX2)=a^2VAR(X1)+b^2VAR(X2)+2abCOV(X1,X2) will help.

I think you should read DarienHacker’s answer again. These questions both suck. If you have a portfolio of \$1M of stock and add another 50,000 worth of stock that is positively correlated to the portfolio it increases the dollar risk for sure. There is some question they are trying to ask about changing the portfolio composition, but they screwed it up.

I trust the wording on the CFA exams will be more precise?

Yep.

JoeyDVivre Wrote: ------------------------------------------------------- > I think you should read DarienHacker’s answer > again. These questions both suck. If you have a > portfolio of \$1M of stock and add another 50,000 > worth of stock that is positively correlated to > the portfolio it increases the dollar risk for > sure. There is some question they are trying to > ask about changing the portfolio composition, but > they screwed it up. Hey Joey, calucalate this pls. and see if the risk reduction even for r>0 can make sense. Var(X)=25 % Var(Y)=25 % correlation=0,5 Calculate the variances for then two portfolios P1=X and P2=0,5X+0,5Y Which variance is bigger?